CFA Ebook Questions (Section 1) Quantative Methods

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Intercept -Coefficients = 5.767264 -Standard Error =0.445229 -t-Stat. =12.95348 Shift -Coefficients = −−5.13912 -Standard Error = −0.629649 -t-Stat. =−8.16188 . Testing whether there is a change in the money supply growth after the shift in policy, using a 0.05 level of significance, we conclude that there is: A.sufficient evidence that the money supply growth changed. B.not enough evidence that the money supply growth is different from zero. C.not enough evidence to indicate that the money supply growth changed.

A. sufficient evidence that the money supply growth changed. A is correct. The null hypothesis of no difference in the annual growth rate is rejected at the 0.05 level: The calculated test statistic of −8.16188 is outside the bounds of ±2.048.

"Fintech" is best described as: A. technology-driven innovation in the financial service industry. B. the collection of large quantities of financial data from a variety of sources in multiple formats. C. the use of technical models to describe patterns in financial markets and make trading decisions.

A. technology-driven innovation in the financial service industry. Correct. In its broadest sense, the term "fintech" generally refers to technology-driven innovation occurring in the financial service industry.

An analyst discards the lowest 2.5% and the highest 2.5% of values in a sample, and computes the mean of the remaining 95% of values. The resulting mean is best described as a: A. trimmed mean. B. harmonic mean. C. winsorized mean.

A. trimmed mean. Correct because the trimmed mean is computed by excluding a stated small percentage of the lowest and highest values and then computing an arithmetic mean of the remaining values. For example, a 5% trimmed mean discards the lowest 2.5% and the highest 2.5% of values and computes the mean of the remaining 95% of values.

Given a large random sample, which of the following types of data are least appropriately analyzed with nonparametric tests? A. Signed data (e.g., number of positives and negatives) B. Ranked data (e.g., 1st, 3rd) C. Numerical values (e.g., 28.43, 79.11)

C. Numerical values (e.g., 28.43, 79.11) Correct. Nonparametric tests are primarily concerned with ranks, signs, or groups, and they are used when numerical parameters are not known or do not meet assumptions about distributions. Even if the underlying distribution is unknown, parametric tests can be used on numerical data if the sample is large. Hypothesis Testing • compare and contrast parametric and nonparametric tests, and describe situations where each is the more appropriate type of test

An investor has three options for receiving payments from an investment: Option 1: a single payment of $136,000 today; Option 2: 30 annual payments of $12,000, beginning one year from today; Option 3: 20 annual payments of $13,000, beginning today. If the annual discount rate is 8%, the option with the highest present value is: A. Option 1. B. Option 2. C. Option 3.

C. Option 3. Correct because Option 3 (annuity due with 20 payments of $13,000 each) has the highest present value of the annuities and the $136,000 lump sum. Calculator solution for Option 2: End mode; N = 30; I/Y = 8; PMT = -12,000; compute PV = 135,093. Calculator solution for Option 3: Begin mode; N = 20; I/Y = 8; PMT = -13,000; compute PV = 137,847.

If a stock's continuously compounded return is normally distributed, the future stock price is most likely: A. normally distributed. B. uniformly distributed. C. lognormally distributed.

C. lognormally distributed. Correct because the relationship between normal and lognormal distributions is if a stock's continuously compounded return is normally distributed, then future stock price is necessarily lognormally distributed. Quantitative Methods explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices when using continuously compounded asset returns

In evaluating portfolio performance, the return measure most affected by an addition of funds to the portfolio just before a market downturn is the: A. time-weighted return. B. arithmetic mean return. C. money-weighted return.

C. money-weighted return. Correct because, if funds are added to a portfolio, the money-weighted rate of return puts a greater weight on the time period after the funds were added. (As a corollary, if funds are taken out of a portfolio, the money-weighted rate of return puts a greater weight on the time period before the funds were removed.) So, if a client gives an investment manager more funds to invest at an unfavorable time, the manager's money-weighted rate of return will tend to be depressed.

Once an investor chooses a particular course of action, the value forgone from alternative actions is best described as a(n): A. sunk cost. B. required return. C. opportunity cost.

C. opportunity cost. Correct. An opportunity cost is the value that investors forgo by choosing a particular course of action. Rates and Returns • interpret interest rates as required rates of return, discount rates, or opportunity costs and explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk

The probability of correctly rejecting a false null hypothesis is best described as one minus the: A. test statistic's p-value. B. probability of a Type I error. C. probability of a Type II error.

C. probability of a Type II error. Correct because the power of a test is the probability of Correct ly rejecting the null-that is, the probability of rejecting the null when it is false. Failing to reject the null hypothesis when it is false is a Type II error. So the power of the test is equal to one minus the probability of Type II error. Quantitative Methods explain hypothesis testing and its components, including statistical significance, Type I and Type II errors, and the power of a test.

The time preference of individuals for current instead of future real consumption is captured by the: A. liquidity premium. B. maturity premium. C. real risk-free interest rate.

C. real risk-free interest rate. Correct because the real risk-free rate reflects the time preferences of individuals for current versus future real consumption. interpret interest rates as required rates of return, discount rates, or opportunity costs and explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk

Which of the following best describes when a transformation of the data may be needed to enable the use of a simple linear regression model? When the: A. dependent variable is non-normally distributed B. pairs of the dependent and independent variables are uncorrelated with one another C. relationship between the independent variable and the dependent variable is non-linear

C. relationship between the independent variable and the dependent variable is non-linear Correct because if the relationship between the independent variable and the dependent variable is not linear, we can often transform one or both of these variables to convert this relation to a linear form, which then allows the use of simple linear regression.

A nonparametric test is most appropriate when: A. comparing differences between means. B. data are given in ranks. C. data meet distributional assumptions.

B. data are given in ranks. Correct. A nonparametric test is used under three circumstances: 1) when the data do not meet distributional assumptions, 2) when the data are given in ranks, and 3) when the hypothesis does not concern a parameter.

The level of significance of a hypothesis test is best used to: A.calculate the test statistic. B.define the test's rejection points. C.specify the probability of a Type II error.

B. define the test's rejection points. B is correct. The level of significance is used to establish the rejection points of the hypothesis test. A is correct because the significance level is not used to calculate the test statistic; rather, it is used to determine the critical value. C is incorrect because the significance level specifies the probability of making a Type I error.

A parametric test is most likely preferred to a non-parametric test when: A. the data are given in ratio or ordinal scale. B. defined sets of assumptions are given. C. the population is heavily skewed.

B. defined sets of assumptions are given. Correct. A parametric test is more appropriate than a non-parametric one when an analyst is concerned with parameters whose validity depends on a definite set of assumptions—for example, assumptions about the distribution of the population producing the sample

A pooled estimator is used when testing a hypothesis concerning the: A.equality of the variances of two normally distributed populations. B.difference between the means of two approximately normally distributed populations with unknown but assumed equal variances. C.difference between the means of two at least approximately normally distributed populations with unknown and assumed unequal variances.

B. difference between the means of two approximately normally distributed populations with unknown but assumed equal variances. B is correct. The assumption that the variances are equal allows for the combining of both samples to obtain a pooled estimate of the common variance.

The sampling error is best described as the: A. sample standard deviation divided by the square root of the sample size. B. difference between the observed value of a statistic and the quantity it is intended to estimate. C. sum of squared deviations from the mean divided by the sample size minus one.

B. difference between the observed value of a statistic and the quantity it is intended to estimate. Correct. The sampling error is the difference between the observed value of a statistic and the quantity it is intended to estimate.

An analyst runs a simple linear regression to test whether the variation in the demand for corn explains the variation in the supply of wheat. In this model, the supply of wheat is a(n): A. indicator variable. B. explained variable. C. independent variable.

B. explained variable. Correct because variation in the demand for corn is being used to explain the variation in the supply of wheat. Therefore the variation in the supply of wheat is the dependent variable, or explained variable. We refer to the variable whose variation is being explained as the dependent variable, or the explained variable; it is typically denoted by Y.

. A Type II error is best described as: A.rejecting a true null hypothesis. B.failing to reject a false null hypothesis. C.failing to reject a false alternative hypothesis.

B. failing to reject a false null hypothesis. B is correct. A Type II error occurs when a false null hypothesis is not rejected.

In contrast to normal distributions, lognormal distributions: A. are skewed to the left. B. have random variables that cannot be negative. C. are more suitable for describing asset returns than asset prices.

B. have random variables that cannot be negative. Correct. By definition, lognormal random variables cannot have negative values.

The central limit theorem: A. requires that the population be approximately normally distributed. B. implies that the sample mean is a consistent estimator of the population mean. C. states that the product of independent random variables is normally distributed.

B. implies that the sample mean is a consistent estimator of the population mean. Correct because the central limit theorem states that the variance of the distribution of the sample mean is σ2/n. The positive square root of variance is standard deviation. The standard deviation of a sample statistic is known as the standard error of the statistic. The sample mean, in addition to being an efficient estimator, is also a consistent estimator of the population mean: As sample size n goes to infinity, its standard error, σ/√n, goes to 0 and its sampling distribution becomes concentrated right over the value of population mean, µ.

An analyst creating a dataset composed largely of product reviews would most likely classify the data sources as generated by: A.sensors. B. individuals. C. business processes.

B. individuals. Correct. Product reviews would most likely come from individual sources.

The lognormal distribution: A. is unbounded. B. is asymmetrical. C. has the same mean as that of its associated normal distribution.

B. is asymmetrical. Correct because the two most noteworthy observations about the lognormal distribution are that it is bounded below by 0 and it is skewed to the right (it has a long right tail), i.e. it is asymmetrical.

A population has a non-normal distribution with mean µ and variance σ2. The sampling distribution of the sample mean computed from samples of large size from that population will have: A.the same distribution as the population distribution. B.its mean approximately equal to the population mean. C.its variance approximately equal to the population variance.

B. its mean approximately equal to the population mean. B is correct. Given a population described by any probability distribution (normal or non-normal) with finite variance, the central limit theorem states that the sampling distribution of the sample mean will be approximately normal, with the mean approximately equal to the population mean, when the sample size is large.

The simple linear regression model in which only the independent variable is in logarithmic form is best described as the: A. log-lin model. B. lin-log model. C. log-log model.

B. lin-log model. Correct because the lin-log model is similar to the log-lin model, but only the independent variable is in logarithmic form.

Which of the following statements is most accurate? The money-weighted return: A. ignores cash withdrawals and additional cash investments. B. measures what the investor actually earned on the funds invested. C. should be used to compare the performance of different investment managers.

B. measures what the investor actually earned on the funds invested. Correct because the money-weighted return is an accurate measure of what the investor actually earned on the money invested.

An analyst considers the population of all existing stocks and selects those where the company name starts with the letter P. This sampling procedure is most likely an example of: A. systematic sampling. B. non-probability sampling. C. two-stage cluster sampling.

B. non-probability sampling. Correct because the sampling procedure does not give every member of the population an equal chance of being selected. It is based on the analyst's convenience. Non-probability sampling depends on factors other than probability considerations, such as a sampler's judgment or the convenience to access data.

For a given expected return and standard deviation, investors are most likely to be attracted to return distributions that are: A. negatively skewed. B. positively skewed. C. normal.

B. positively skewed. Correct. For a given expected return and standard deviation, investors are most likely to be attracted by a positive skew because the mean return lies above the median. Relative to the mean return, positive skew amounts to limited, though frequent, downside returns compared with somewhat unlimited, but less frequent, upside returns.

The probability of correctly rejecting a null hypothesis is best defined as the: A. p-value. B. power of the test. C. level of significance.

B. power of the test. Correct because the power of a test is the probability of Correct ly rejecting the null—that is, the probability of rejecting the null when it is false.

Mylandia Corporation pays an annual dividend to its shareholders, and its most recent payment was CAD2.40. Analysts following Mylandia expect the company's dividend to grow at a constant rate of 3 percent per year in perpetuity. Mylandia shareholders require a return of 8 percent per year. The expected share price of Mylandia is closest to: A.CAD48.00. B.CAD49.44. C.CAD51.84.

B.CAD49.44. B is correct. Mylandia's next expected dividend is CAD2.472 (=2.40×1.03), and using Equation 14, 𝑃𝑉𝑡=2.40(1+0.03)0.08−0.03=2.4720.05=49.44PVt=2.401+0.030.08−0.03=2.4720.05=49.44.

All else being equal, which of the following would most likely lead to a wider prediction interval for the dependent variable when re-estimating a linear regression model? An increase in the: A. sample size B. level of significance C. standard error of the estimate

C. standard error of the estimate Correct because the prediction interval is equal to the predicted value of the dependent variable plus/minus the critical t-value times the standard error of the forecast. The better the fit of the regression model, the smaller the standard error of the estimate (se) and, therefore, the smaller standard error of the forecast. When the standard error of the estimate increases, the standard error of the forecast will increase, which will lead to a wider prediction interval if holding other things constant.

Sampling error is the difference between the observed value of a: A. random variable and the respective statistic. B. random variable and its hypothesized value. C. statistic and the quantity it is intended to estimate.

C. statistic and the quantity it is intended to estimate. Correct because sampling error is the difference between the observed value of a statistic and the quantity it is intended to estimate.

Grouping all publicly traded US firms by sector and then randomly selecting subsamples of firms from each sector according to the sector's proportion in the total population is an example of: A. cluster sampling. B. simple random sampling. C. stratified random sampling.

C. stratified random sampling. Correct because, in stratified random sampling, the population is divided into subpopulations (strata) based on one or more classification criteria. Simple random samples are then drawn from each stratum in sizes proportional to the relative size of each stratum in the population. Quantitative Methods compare and contrast simple random, stratified random, cluster, convenience, and judgmental sampling and their implications for sampling error in an investment problem

Based on Exhibit 2, the number of degrees of freedom for the t-test of the slope coefficient in this regression is: A.48. B.49. C.50. A. 48 A is correct. The degrees of freedom are the number of observations minus the number of parameters estimated, which equals 2 in this case (the intercept and the slope coefficient). The number of degrees of freedom is 50 − 2 = 48.

(Look at ebook question) Anh Liu is an analyst researching whether a company's debt burden affects investors' decision to short the company's stock. She calculates the short interest ratio (the ratio of short interest to average daily share volume, expressed in days) for 50 companies as of the end of the year and compares this ratio with the companies' debt ratio (the ratio of total liabilities to total assets, expressed in decimal form). Liu provides a number of statistics in Exhibit 1. She also estimates a simple regression to investigate the effect of the debt ratio on a company's short interest ratio. The results of this simple regression, including the analysis of variance (ANOVA), are shown in Exhibit 2. In addition to estimating a regression equation, Liu graphs the 50 observations using a scatter plot, with the short interest ratio on the vertical axis and the debt ratio on the horizontal axis.

Which of the following should Liu conclude from the results shown in Exhibit 2? A.The average short interest ratio is 5.4975. B.The estimated slope coefficient is different from zero at the 0.05 level of significance. C.The debt ratio explains 30.54 percent of the variation in the short interest ratio. B.The estimated slope coefficient is different from zero at the 0.05 level of significance. B is correct. The t-statistic is −2.2219, which is outside the bounds created by the critical t-values of ±2.011 for a two-tailed test with a 5 percent significance level. The value of 2.011 is the critical t-value for the 5 percent level of significance (2.5 percent in one tail) for 48 degrees of freedom. A is incorrect because the mean of the short interest ratio is 192.3 ÷ 50 = 3.846. C is incorrect because the debt ratio explains 9.33 percent of the variation of the short interest ratio.

Based on Exhibit 1 and Exhibit 2, if Liu were to graph the 50 observations, the scatter plot summarizing this relation would be best described as: A.horizontal. B.upward sloping. C.downward sloping. C.downward sloping. C is correct. The slope coefficient (shown in Exhibit 2) is negative.

(Look at ebook) Anh Liu is an analyst researching whether a company's debt burden affects investors' decision to short the company's stock. She calculates the short interest ratio (the ratio of short interest to average daily share volume, expressed in days) for 50 companies as of the end of the year and compares this ratio with the companies' debt ratio (the ratio of total liabilities to total assets, expressed in decimal form). Liu provides a number of statistics in Exhibit 1. She also estimates a simple regression to investigate the effect of the debt ratio on a company's short interest ratio. The results of this simple regression, including the analysis of variance (ANOVA), are shown in Exhibit 2. In addition to estimating a regression equation, Liu graphs the 50 observations using a scatter plot, with the short interest ratio on the vertical axis and the debt ratio on the horizontal axis.

Based on Exhibit 1 and Exhibit 2, the correlation between the debt ratio and the short interest ratio is closest to: A.−0.3054. B.0.0933. C.0.3054. A.−0.3054. A is correct. In simple regression, the R2 is the square of the pairwise correlation. Because the slope coefficient is negative, the correlation is the negative of the square root of 0.0933, or −0.3055.

The dependent variable in Liu's regression analysis is the: A.intercept. B.debt ratio. C.short interest ratio. C.short interest ratio. C is correct. Liu explains the variation of the short interest ratio using the variation of the debt ratio.

Which of the interpretations best describes Liu's findings? A.Interpretation 1 B.Interpretation 2 C.Interpretation 3 C.Interpretation 3 C is correct. Conclusions cannot be drawn regarding causation; they can be drawn only about association; therefore, Interpretations 1 and 2 are incorrect.

Based on Exhibit 1, Olabudo should calculate a prediction interval for the actual US CPI closest to: A.2.7506 to 2.7544. B.2.7521 to 2.7529. C.2.7981 to 2.8019. A.2.7506 to 2.7544.

(Look at ebook) Doug Abitbol is a portfolio manager for Polyi Investments, a hedge fund that trades in the United States. Abitbol manages the hedge fund with the help of Robert Olabudo, a junior portfolio manager. Abitbol looks at economists' inflation forecasts and would like to examine the relationship between the US Consumer Price Index (US CPI) consensus forecast and the actual US CPI using regression analysis. Olabudo estimates regression coefficients to test whether the consensus forecast is unbiased. If the consensus forecasts are unbiased, the intercept should be 0.0 and the slope will be equal to 1.0. Regression results are presented in Exhibit 1. Additionally, Olabudo calculates the 95 percent prediction interval of the actual CPI using a US CPI consensus forecast of 2.8. (Look at graph)

Based on Exhibit 2 and Vasileva's prediction of the crude oil return for Month 37, the estimate of Amtex share return for Month 37 is closest to: A.−0.0024. B.0.0071. C.0.0119.

(Look at ebook) Elena Vasileva recently joined EnergyInvest as a junior portfolio analyst. Vasileva's supervisor asks her to evaluate a potential investment opportunity in Amtex, a multinational oil and gas corporation based in the United States. Vasileva's supervisor suggests using regression analysis to examine the relation between Amtex shares and returns on crude oil. Vasileva notes the following assumptions of regression analysis: Assumption 1. The error term is uncorrelated across observations. Assumption 2. The variance of the error term is the same for all observations. Assumption 3. The dependent variable is normally distributed. Vasileva runs a regression of Amtex share returns on crude oil returns using the monthly data she collected. Selected data used in the regression are presented in Exhibit 1, and selected regression output is presented in Exhibit 2. She uses a 1 percent level of significance in all her tests

Which of Vasileva's assumptions regarding regression analysis is incorrect? A.Assumption 1 B.Assumption 2 C.Assumption 3

At a 0.01 level of significance, Jones should conclude that: A.the mean net profit margin is 0.5987 percent. B.the variation of the fixed asset turnover explains the variation of the natural log of the net profit margin. C.a change in the fixed asset turnover from three to four times is likely to result in a change in the net profit margin of 0.5987 percent. B is correct. The p-value corresponding to the slope is less than 0.01, so we reject the null hypothesis of a zero slope, concluding that the fixed asset turnover explains the natural log of the net profit margin.

(Look at ebook) Espey Jones is examining the relation between the net profit margin (NPM) of companies, in percent, and their fixed asset turnover (FATO). He collected a sample of 35 companies for the most recent fiscal year and fit several different functional forms, settling on the following model: ln(NPM𝑖)=𝑏0+𝑏1FATO𝑖.ln(NPMi)=b0+b1FATOi. The results of this estimation are provided in Exhibit 1.

The coefficient of determination is closest to: A.0.0211. B.0.9789. C.0.9894.

Based on Batten's regression model, the coefficient of determination indicates that: A.Stellar's returns explain 2.11 percent of the variability in CPIENG. B.Stellar's returns explain 14.52 percent of the variability in CPIENG. C.changes in CPIENG explain 2.11 percent of the variability in Stellar's returns. C is correct. R2 is the coefficient of determination. In this case, it shows that 2.11% of the variability in Stellar's returns is explained by changes in CPIENG.

(Look at ebook) Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the world's largest companies, Stellar is in the business of refining and marketing oil. As part of his analysis, Golub wants to evaluate the sensitivity of the stock's returns to various economic factors. For example, a client recently asked Golub whether the price of Stellar Energy Corp. stock has tended to rise following increases in retail energy prices. Golub believes the association between the two variables is negative, but he does not know the strength of the association. Golub directs his assistant, Jill Batten, to study the relationships between (1) Stellar monthly common stock returns and the previous month's percentage change in the US Consumer Price Index for Energy (CPIENG) and (2) Stellar monthly common stock returns and the previous month's percentage change in the US Producer Price Index for Crude Energy Materials (PPICEM). Golub wants Batten to run both a correlation and a linear regression analysis. In response, Batten compiles the summary statistics shown in Exhibit 1 for 248 months. All the data are in decimal form, where 0.01 indicates a 1 percent return. Batten also runs a regression analysis using Stellar monthly returns as the dependent variable and the monthly change in CPIENG as the independent variable. Exhibit 2 displays the results of this regression model.

Based on the regression, if the CPIENG decreases by 1.0 percent, the expected return on Stellar common stock during the next period is closest to: A.0.0073 (0.73 percent). B.0.0138 (1.38 percent). C.0.0203 (2.03 percent). C.0.0203 (2.03 percent). C is correct. From the regression equation, Expected return = 0.0138 + (−0.6486 × −0.01) = 0.0138 + 0.006486 = 0.0203, or 2.03 percent.

For the analysis run by Batten, which of the following is an incorrect conclusion from the regression output? A.The estimated intercept from Batten's regression is statistically different from zero at the 0.05 level of significance. B.In the month after the CPIENG declines, Stellar's common stock is expected to exhibit a positive return. C.Viewed in combination, the slope and intercept coefficients from Batten's regression are not statistically different from zero at the 0.05 level of significance. C.Viewed in combination, the slope and intercept coefficients from Batten's regression are not statistically different from zero at the 0.05 level of significance. C is the correct response because it is a false statement. The slope and intercept are both statistically different from zero at the 0.05 level of significance.

Which of the following best describes Batten's regression? A.Time-series regression B.Cross-sectional regression C.Time-series and cross-sectional regression (Opposite look at answer) A. Time-Series regression.

Based on Exhibit 1, the sample covariance is closest to: A.−9.2430. B.−0.1886. C.8.4123. B.−0.1886. B is correct. The sample covariance is calculated as follows: ∑𝑛𝑖=1(𝑋𝑖−𝑋⎯⎯⎯)(𝑌𝑖−𝑌⎯⎯⎯)𝑛−1=−9.2430÷49=−0.1886∑i=1nXi−X¯Yi−Y¯n−1=−9.2430÷49=−0.1886.

(Look at ebook)z Anh Liu is an analyst researching whether a company's debt burden affects investors' decision to short the company's stock. She calculates the short interest ratio (the ratio of short interest to average daily share volume, expressed in days) for 50 companies as of the end of the year and compares this ratio with the companies' debt ratio (the ratio of total liabilities to total assets, expressed in decimal form). Liu provides a number of statistics in Exhibit 1. She also estimates a simple regression to investigate the effect of the debt ratio on a company's short interest ratio. The results of this simple regression, including the analysis of variance (ANOVA), are shown in Exhibit 2. In addition to estimating a regression equation, Liu graphs the 50 observations using a scatter plot, with the short interest ratio on the vertical axis and the debt ratio on the horizontal axis.

For Batten's regression model, 0.0710 is the standard deviation of: A.the dependent variable. B.the residuals from the regression. C.the predicted dependent variable from the regression. B. the residuals from the regression B is correct. The standard error of the estimate is the standard deviation of the regression residuals.

(Look ay ebook) Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the world's largest companies, Stellar is in the business of refining and marketing oil. As part of his analysis, Golub wants to evaluate the sensitivity of the stock's returns to various economic factors. For example, a client recently asked Golub whether the price of Stellar Energy Corp. stock has tended to rise following increases in retail energy prices. Golub believes the association between the two variables is negative, but he does not know the strength of the association. Golub directs his assistant, Jill Batten, to study the relationships between (1) Stellar monthly common stock returns and the previous month's percentage change in the US Consumer Price Index for Energy (CPIENG) and (2) Stellar monthly common stock returns and the previous month's percentage change in the US Producer Price Index for Crude Energy Materials (PPICEM). Golub wants Batten to run both a correlation and a linear regression analysis. In response, Batten compiles the summary statistics shown in Exhibit 1 for 248 months. All the data are in decimal form, where 0.01 indicates a 1 percent return. Batten also runs a regression analysis using Stellar monthly returns as the dependent variable and the monthly change in CPIENG as the independent variable. Exhibit 2 displays the results of this regression model. Exhibit 1: Descriptive Statistics Stellar Common Stock Monthly ReturnLagged Monthly

A portfolio manager would like to calculate the compound rate of return on an investment. Which of the following mean returns will he most likely use? A. Geometric B. Harmonic C. Arithmetic

A. Geometric Correct. The geometric mean return represents the growth rate or compound rate of return on an investment.

A small-cap growth fund's monthly returns for the past 36 months have been consistently outperforming its benchmark. An analyst is determining whether the standard deviation of monthly returns is greater than 6%. Which of the following best describes the hypothesis to be tested? A. H0: σ2 ≤ 0.36% B. Ha: σ2 > 6% C. H0: σ2 ≥ 0.36%

A. H0: σ2 ≤ 0.36% Correct because this is a one-tailed hypothesis testing with a "greater than" alternative hypothesis. A squared standard deviation is being used to obtain a test of variance. The hypotheses are H0: σ2 ≤ 0.36% versus Ha: σ2 > 0.36%.

An investment requires 10 equal annual payments, starting today, and will pay out a lump sum of $500,000 15 years from today. If the interest rate is 4% per year compounded annually, the required annual payment is closest to: A. $32,913. B. $34,230. C. $40,044.

A. $32,913. (Look at study guide) Correct because the present value of the future lump sum payment is PV = FVN(1 + r)-N = $500,000(1 + 0.04)-15 = $277,632.25. The 10 annual payments form an annuity due (since the payments start today) whose present value equals the present value of an ordinary annuity with 9 annual payments plus the first payment, i.e. PV = A + A[1 - 1/(1 + r)N]/r = A(1 + [1 - 1/(1 + 0.04)9]/0.04) = 8.4353(A). Setting the PV of the cash outflows (the annuity) equal to the PV of the cash inflows (the return in 15 years), we can solve for the annual payment amount; A = $277,632.25/8.4353 ≈ $32,913. Calculator solution: BGN; N = 10; I/Y = 4; PV = 277,632.25; solve for PMT = 32,913.

A pension fund needs to pay a lump sum $10,000,000 to its participants in 15 years. If the fund is expected to earn 5% per year compounded semi-annually, the amount needed today to meet its liability in 15 years is closest to: A. $4,767,427. B. $4,810,171. C. $4,892,771.

A. $4,767,427. (Look at ebook) Correct because using the equation PV = FVN (1 + rs/m)-Nm where m = number of compounding periods per year rs = quoted annual interest rateN = number of years we compute PV = $10,000,000 × (1 + 0.05/2)-15×2 = $4,767,426.85 ≈ $4,767,427. In applying the equation, we use the periodic rate (in this case, the semi-annual rate) and the appropriate number of periods with semi-annual compounding. Alternative solution using a financial calculator in END mode: N = 30; I/Y = 0.025; PMT = 0; FV = 10,000,000; CPT PV = $4,767,426.852 ≈ $4,767,427

An investor purchased a stock for $450 and then sold the stock immediately after receiving a dividend of $2. If the holding period return is a loss of 10.2%, the investor sold the stock at a price closest to: A. $402. B $404. C. $406.

A. $402. Correct because a holding period return is the return earned from holding an asset for a single specified period of time. ... This return can be generalized and shown as a mathematical expression in which P is the price and I is the income: R = [(P1 - P0) + I1]/P0. The subscript indicates the time of the price or income, (t = 0), is the beginning of the period and (t = 1) is the end of the period. Hence, P1 = R × P0 + P0 - I1 = -10.2% × $450 + $450 − $2 = $402.1 ≈ $402.

An analyst tabulates the ranks of four paired observations of random variables X and Y as follows: *Observation 1 -Rank of X = 1 --Rank of Y = 2 *Observation 2 -Rank of X = 2 --Rank of Y = 3 *Observation 3 -Rank of X = 3 --Rank of Y = 4 *Observation 4 -Rank of X = 4 --Rank of Y = 1 The Spearman rank correlation coefficient between X and Y is closest to: A. -0.2. B. 0.8. C. 1.0.

A. -0.2. (Look at ebook) Correct because with n as the sample size, the Spearman rank correlation is given by: rs = 1 - (6 ∑di2)/(n(n2 - 1))" = 1 - 6(12)/(4(42 - 1)) = 1 - 6/5 = -1/5 = -0.2, where the sum of squared differences in ranks ∑di2 = (2 - 1)2 + (3 - 2)2 + (4 - 3)2 + (1 - 4)2 = 1 + 1 + 1 + 9 = 12.

A portfolio provides the following returns over a five-year period. Year12345Return10%-25%8%5%7% The average compound rate of return of the portfolio across the five-year period is closest to: A. 0.02%. B. 1.00%. C. −9.31%.

A. 0.02%. (Look at study ebook) Correct. The geometric mean return is the correct approach to calculate portfolio average returns across a period of time:𝑅𝐺=[∏𝑡=1𝑇(1+𝑅𝑡)]1/𝑇−1RG=[∏t=1T(1+Rt)]1/T−1 where RG = the geometric mean return T = 5 and is the length of the period t = the index of time (i.e., t = 1 for Year 1, t = 2 for Year 2, ...) Rt = the return during period t In this problem, the geometric mean return is: RG = [(1 + 0.10) × (1 − 0.25) × (1 + 0.08) × (1 + 0.05) × (1 + 0.07)]1/5 − 1 = (1.10 × 0.75 × 1.08 × 1.05 × 1.07)1/5 − 1 = 0.02%.

An analyst assumes that a company's future EPS will be either $2.00, $2.20, or $2.40. If each scenario is equally likely, the variance [in $2] of the company's future EPS is closest to: A. 0.03. B. 0.16. C. 0.20.

A. 0.03. Correct because the variance of a random variable is the expected value (the probability-weighted average) of squared deviations from the random variable's expected value: σ2(X) = E[X - E(X)]2. Since each scenario is equally likely (probability = 1/3), E(X) = (2.0 + 2.2 + 2.4)/3 = 2.2, so σ2(X) = [(2.0 - 2.2)2 + (2.2 - 2.2)2 + (2.4 - 2.2)2]/3 = [0.04 + 0.04]/3 = 0.08/3 = 0.0267 ≈ 0.03 [in $2].

The null hypothesis for the F-distributed test statistic in a simple linear regression model tests whether the: A. slope is equal to zero. B. intercept is equal to zero. C. slope is not equal to zero.

A. slope is equal to zero. Correct because in regression analysis, we can use an F-distributed test statistic to test whether the slopes in a regression are equal to zero, with the slopes designated as bi, against the alternative hypothesis that at least one slope is not equal to zero for simple linear regression, these hypotheses simplify to H0: b1 = 0. Ha: b1 ≠ 0.

An analyst collects the following data related to paired observations for Sample A and Sample B. Assume that both samples are dependent and are drawn from normally distributed populations and that the population variances are not known. *Paired Observation = 1 -Sample A Value = 25 ~Sample B Value = 18 *Paired Observation = 2 -Sample A Value = 12 ~Sample B Value = 9 *Paired Observation = 3 -Sample A Value = -5 ~Sample B Value = -8 *Paired Observation = 4 -Sample A Value = 6 ~Sample B Value = 3 *Paired Observation = 5 -Sample A Value = -8 ~Sample B Value = 1 The t-statistic to test the hypothesis that the mean difference is equal to zero is closest to: A. 0.52. B. 0.27. C.0.23.

A. 0.52. (Look at study guide) Correct. First, the mean difference is calculated: 𝑑⎯⎯=1𝑛∑𝑖=1𝑛𝑑𝑖d¯=1n∑i=1ndi Then, the sample variance and the standard error of the mean difference are calculated: 𝑠2𝑑=∑𝑖=1𝑛(𝑑𝑖−𝑑⎯⎯)2𝑛−1sd2=∑i=1n(di−d¯)2n−1 𝑠𝑑⎯⎯=𝑠𝑑/𝑛⎯⎯√sd¯=sd/n Then, the t-statistic is calculated: 𝑡=𝑑⎯⎯−𝜇𝑑0𝑠𝑑⎯⎯⎯t=d¯−μd0sd¯ In this case, the mean difference is 1.4. The sample variance is 36.8. The standard error of the mean difference is 2.712932. The t-statistic is 0.51605 ~ 0.52. Paired ObservationSample A ValueSample B ValueDifferencesDifferences Minus the Mean Difference, Then Squared125187(7 − 1.4)2 = 31.3621293(3 − 1.4)2 = 2.563−5−83(3 − 1.4)2 = 2.564633(3 − 1.4)2 = 2.565−81−9(−9 − 1.4)2 = 108.16Sum = 7Sum of squared differences = 147.2 7/5 = mean difference (𝑑⎯⎯)(d¯) of 1.4 Sample Variance (𝑠2𝑑)(sd2): 147.2/4 = 36.8 Standard Error (𝑠𝑑⎯⎯)(sd¯): (36.8/5)0.5 = 2.712932 t-statistic: (1.4 − 0)/2.712932 = 0.51605 ~ 0.52

An investor gathers the following information about a stock: *Stock price at t=0 , $20 *Dividend paid at t = 1 , $3 *Stock price at t = 1, $12 *Dividend paid at t = 2, $1 *Stock price at t = 2, $20 The investor purchased one unit of the stock at t = 0 and sold it at t = 2. If the dividends were not reinvested, the money-weighted rate of return is closest to: A. 10% B. 15%. C. 20%.

A. 10% (Look at ebook) Correct because the money-weighted return and its calculation are similar to the internal rate of return and the yield to maturity. Just like the internal rate of return, amounts invested are cash outflows from the investor's perspective and amounts returned or withdrawn by the investor, or the money that remains at the end of an investment cycle, is a cash inflow for the investor. For the stock investment this is: $20 = $3/(1 + r) + ($20 + $1)/(1 + r)2, yielding r = 10.24% ≈ 10%. Calculator solution: CF0 = -20; CF1 = 3; CF2 = 21; IRR CPT = 10.24.

A company estimates its revenue will be 50% higher than today in four years' time. The compound annual growth rate is closest to: A. 10.7%. B. 11.8%. C. 12.5%.

A. 10.7%. Correct because a growth rate (g) is calculated as g = (FVN/PV)1/N - 1, where FV is the future value, PV is the present value and N is the number of periods. Here, g = (1.5/1)1/4 - 1 = 0.10668 ≈ 10.7%.

Question The following table shows the volatility of a series of funds that belong to the same peer group, ranked in ascending order: Fund 1 *Volatility= 9.81 Fund 2 *Volatility= 10.12 Fund 3 *Volatility= 10.84 Fund 4 *Volatility= 11.33 Fund 5 *Volatility= 12.25 Fund 6 *Volatility= 13.39 Fund 7 *Volatility= Fund 8 *Volatility= 13.42 Fund 9 *Volatility= 14.47 Fund 10 *Volatility= 14.85 Fund 11 *Volatility= 15.00 Fund 12 *Volatility= 17.36 Fund 13 *Volatility= 17.89 The approximate value of the first quintile is closest to: A. 10.70% B. 11.09%. C. 10.84%.

A. 10.70% (Look at study ebook) Correct. The position of the first quintile is found with the following formula: Ly = (n + 1) × (y/100),where y = the percentage point at which the distribution is divided. In this case, y = 20, which corresponds to the 20th percentile (first quintile) n = the number of observations (funds) in the peer group. In this case, n = 13 L20 = the location of the 20th percentile (first quintile) L20 = (13 + 1) × (20/100) = 2.80. Therefore, the location of the first quintile is between the volatility of Fund 2 and Fund 3 (because they are ranked in ascending order). Linear interpolation is used to find the approximate value of the first quintile: P20 ≈ X2 + (2.80 − 2) × (X3 − X2) where X2 = the volatility of Fund 2 X3 = the volatility of Fund 3 P20 = the approximate value of the first quintile P20 ≈ 10.12% + (2.80 − 2) × (10.84% − 10.12%) = 10.70%

A USD25 million equity portfolio is financed 20 percent with debt at a cost of 6 percent annual cost. If that equity portfolio generates a 10 percent annual total investment return, then the leveraged return is: A.11.0 percent. B.11.2 percent. C.13.2 percent

A. 11.0 percent A is correct. 𝑅𝐿=𝑅𝑝+𝑉𝐵𝑉𝐸(𝑅𝑝−𝑟𝐷)RL=Rp+VBVERp−rD=10% +𝑈𝑆𝐷5𝑚𝑖𝑙𝑙𝑖𝑜𝑛𝑈𝑆𝐷20𝑚𝑖𝑙𝑙𝑖𝑜𝑛(10%−6%)=10% +USD5millionUSD20million10%−6%=10% +0.25×4% =11.0%=10% +0.25×4% =11.0%.

Grupo Ignacia issued 10-year corporate bonds four years ago. The bonds pay an annualized coupon of 10.7 percent on a semiannual basis, and the current price of the bonds is MXN97.50 per MXN100 of par value. The YTM of the bonds is closest to: A.11.28 percent. B.11.50 percent. C.11.71 percent.

A. 11.28 percent. Question Q. Grupo Ignacia issued 10-year corporate bonds four years ago. The bonds pay an annualized coupon of 10.7 percent on a semiannual basis, and the current price of the bonds is MXN97.50 per MXN100 of par value. The YTM of the bonds is closest to: A.11.28 percent. B.11.50 percent. C.11.71 percent. Solution A is correct. The YTM is calculated by solving for the RATE spreadsheet function with the following inputs: number of periods of 12 (=6 × 2), coupon payments of 5.35 (=10.7/2), PV of −97.50, and FV of 100. The resulting solution for RATE of 5.64 percent is in semiannual terms, so multiply by 2 to calculate annualized YTM of 11.28 percent. B is incorrect, as 11.50 percent is the result if number of periods used is eight, instead of 12. C is incorrect, as 11.71 percent is the result if the number of periods used is 6, instead of 12.

The figure below shows the histogram for the distribution of weekly returns on an index. (Look at ebook) The median of the returns on the index, if compared to the mean, will most likely be: A. smaller. B. equal. C. greater.

A. smaller. Correct. The histogram clearly shows that the return distribution of the index is positively skewed (skewed to the right) and is unimodal (it has one most frequently occurring value). For a positively skewed unimodal distribution, the median is always less than the mean.

The joint probability of returns for securities A and B are as follows: Joint Probability Function of Security A and Security B Returns (Entries Are Joint Probabilities) *Return on Security A =25%, --Return on Security B = 30% = 0.60 --Return on Security B = 20% =0 *Return on Security A = 20% --Return on Security B = 30% = 0 --Return on Security B = 20% = 0.40 The covariance of the returns between Securities A and B is closest to: A. 12. B. 14. C. 13.

A. 12. (Look at ebook) Correct. First calculate the expected returns on securities A and B with the formula: 𝐸(𝑋)=∑𝑖=1𝑛𝑃(𝑋𝑖)𝑋𝑖E(X)=∑i=1nP(Xi)Xi Expected return on security A = 0.6 × 25% + 0.4 × 20% = 15% + 8% = 23% Expected return on security B = 0.6 × 30% + 0.4 × 20% = 18% + 8% = 26% Then calculate the covariance of returns between securities A and B with the formula: Cov(RA,RB) = ∑𝑖∑𝑗𝑃(𝑅𝐴,𝑖,𝑅𝐵,𝑗)(𝑅𝐴,𝑖−𝐸𝑅𝐴)(𝑅𝐵,𝑗−𝐸𝑅𝐵)∑i∑jP(RA,i,RB,j)(RA,i−ERA)(RB,j−ERB) where RA and RB = the returns on securities A and B, respectively P = the joint probability ERA and ERB = the expected returns of securities A and B, respectively i and j = the line and column of the joint probability function table above Cov(𝑅𝐴,𝑅𝐵)=0.6[(25−23)(30−26)]+0.4[(20−23)(20−26)]=0.6[2×4]+0.4[(−3)(−6)]=0.6×8+0.4×18=4.8+7.2=12

#18 The following 10 observations are a sample drawn from an approximately normal population: Observation: 1 Value = -3 Observation: 2 Value = -11 Observation: 3 Value = 3 Observation: 4 Value = - ...18 Observation: 5 Value = 18 Observation: 6 Value = 20 Observation: 7 Value = -6 Observation: 8 Value = 9 Observation: 9 Value = 2 Observation: 10 Value = -16 The sample standard deviation is closest to: A. 13.18. B. 11.92. C. 12.50.

A. 13.18. (Look at ebook) Correct. The sample mean is: 𝑋⎯⎯⎯=∑𝑖=1𝑛𝑋𝑖𝑛X¯=∑i=1nXin = (−3 − 11 + 3 − 18 + 18 + 20 − 6 + 9 + 2 − 16)/10 = −2.00/10 = −0.20 The sample variance is: 𝑠2=∑𝑖=1𝑛(𝑋𝑖−𝑋⎯⎯⎯⎯)2(𝑛−1)s2=∑i=1n(Xi−X¯)2(n−1) The sample standard deviation is the (positive) square root of the sample variance. ValueDifference vs. Mean[Value − (−0.20)]Difference Squared−3−2.87.84−11−10.8116.6433.210.24−18−17.8316.841818.2331.242020.2408.04−6−5.833.6499.284.6422.24.84−16−15.8249.64Sum of squared differences1563.6Divided by n − 1173.7333333Square root13.18079411

A discrete random variable X has the following probability distribution: Probability = 0.20 *Outcome = 35 Probability = 0.30 *Outcome = 50 Probability = 0.50 *Outcome = 80 The standard deviation of X is closest to: A. 18.73. B. 20.00. C. 22.91.

A. 18.73. (Look at ebook study guide) Correct because the expected value E(X) = Σi=1nP(Xi)Xi = (0.20 × 35) + (0.30 × 50) + (0.50 × 80) = 62. The variance σ2(X) = E{[X - E(X)]2} = Σi=1nP(Xi)[X - E(X)]2 = 0.20 × (35 - 62)2 + 0.30 × (50 - 62)2 + 0.50 × (80 - 62)2 = 351. Standard deviation is the positive square root of variance: σ = 3511/2 ≈ 18.73.

If the price of a stock goes from $15.00 to $16.20 in one year, the continuously compounded rate of return is closest to: A. 7.70%. B. 8.33%. C. 8.00%.

A. 7.70%. (Look at ebook) Correct. The continuously compounded rate of return is calculated with the following formula: r0,T = ln(ST/S0) where r0,T = r0,1 = and is the continuously compounded rate of return from time 0 to time T (1 year) S0 = 15.00 and is the price of the stock at time 0 ST = 16.20 and is the price of the stock at time T (1 year) The continuously compounded rate of return is: r0,1 = ln(16.20/15.00) = 7.70%. Alternatively, the end of period price, 16.20 can be found from 15.00 × e0.077×1.

An investor purchases 100 shares of stock at $40 per share. The investor holds the shares for exactly one year and then sells all of them at $41.50 per share. On the date of sale, the investor receives dividends totaling $200. The holding period return (HPR) on the investment is closest to: A. 8.75%. B. 3.75%. C. 8.43%

A. 8.75%. (Look at ebook) Correct. HPR = (P1 − P0 + D1)/P0. In this problem: (41.50 − 40 + 2)/40 = 8.75%.

An analyst draws samples from an original sample to estimate the standard error of a population mean. Which of the following best describes this sampling procedure? A. Bootstrap method B. Cluster sampling method C. Convenience sampling method

A. Bootstrap method Correct because in bootstrap, we repeatedly draw samples from the original sample, and each resample is of the same size as the original sample. Note that each item drawn is replaced for the next draw (i.e., the identical element is put back into the group so that it can be drawn more than once). Assuming we are looking to find the standard error of sample mean, we take many resamples and then compute the mean of each resample.

Which of the following is required to compute the standard error of a sample mean using the bootstrap resampling method? A. The mean of each resample B. The mean of the original sample C. The standard deviation of the original sample

A. The mean of each resample Correct because the equation to estimate the standard error of the sample mean effectively computes the sample standard deviation of the different means generated across all resamples. Hence the mean of each resample is required. However, neither the mean, nor the standard deviation, of the original sample are required.

Which of the following statements is most accurate with respect to the widespread adoption of algorithmic trading in financial markets? A. The need for low-latency networks has grown. B. Markets have become less fragmented in terms of trading venues. C. Average trade size has increased as algorithmic trading is used to execute large institutional orders.

A. The need for low-latency networks has grown. Correct because algorithmic trading requires access to low-latency networks, and with the wide-spread adoption of algorithmic trading, the need for low-latency networks has grown. Low-latency systems—systems that operate on networks that communicate high volumes of data with minimal delay (latency)—are essential for automated trading applications that make decisions based on real-time prices and market events. In contrast, high-latency systems do not require access to real-time data and calculations. High-frequency trading is a form of algorithmic trading that makes use of vast quantities of granular financial data (tick data, for example) to automatically place trades when certain conditions are met. Trades are executed on ultra-high-speed, low-latency networks in fractions of a second.

An analyst performs a hypothesis test concerning the difference between the mean returns of two portfolios, assuming normally distributed populations with unknown but equal variances. If the analyst decides to change the hypothesized difference in mean returns from 0% to 1%, which of the following will change? A. The value of the test statistic B. The degrees of freedom used in the test C. The pooled estimate of the common population variance

A. The value of the test statistic (Look at ebook) Correct because when the unknown population variances are equal, a t-test based on independent random samples is given by t = (X1 - X2 - μ1 + μ2)/(sp2/n1 + sp2/n2)½ where sp2 is a pooled estimator of the common variance. Hence, a change in hypothesized difference μ1 - μ2 will change the value of the test statistic.

If a client controls the timing of cash flows into and out of a portfolio, which of the following is most appropriate when evaluating the performance of the portfolio manager? A. Time-weighted rate of return B. Arithmetic mean rate of return C. Money-weighted rate of return

A. Time-weighted rate of return Correct because the time-weighted rate of return is the preferred performance measure as it neutralizes the effect of cash withdrawals or additions to the portfolio, which are generally outside of the control of the portfolio manager.

Which of the following is an underlying assumption of the simple linear regression model? The regression residuals: A. are normally distributed. B. have high correlations across observations. C. have different variances across observations.

A. are normally distributed. Correct because one of the four key assumptions we need to make to be able to draw valid conclusions from a simple linear regression mode is that regression residuals are normally distributed.

For a continuous positively skewed unimodal distribution: A. both the mode and the median are less than the mean. B. both the mode and the median are greater than the mean. C. the mode is less than the mean and the median is greater than the mean.

A. both the mode and the median are less than the mean. Correct because for a continuous positively skewed unimodal distribution, the mode is less than the median, which is less than the mean.

In which of the following cases is cluster sampling most likely used? When: A. conducting a market survey B. auditing financial statements C. creating a bond portfolio to mirror the performance of a specified index

A. conducting a market survey Correct because, in cluster sampling, the population is divided into clusters, each of which is essentially a mini-representation of the entire populations. Then certain clusters are chosen as a whole using simple random sampling. Cluster sampling is commonly used for market surveys, and the most popular version identifies clusters based on geographic parameters.

If the covariance between two positively correlated random variables remains the same but the variance of both variables increases, the correlation between the two variables: A. decreases. B. stays the same. C. increases.

A. decreases. Correct because the correlation between two random variables, Ri and Rj, is defined as ρ(Ri,Rj) = Cov(Ri,Rj)/[σ(Ri)σ(Rj)], where Cov denotes the covariance and σ the standard deviation. Since the standard deviation of each asset occurs in the denominator of the correlation formula, it is clear that, all else being equal, an increase in the variance (hence standard deviation) of either variable will decrease the correlation.

Roy's safety-first criterion: A. evaluates only downside risk. B. uses semideviation as a risk measure. C. assumes asset prices are normally distributed.

A. evaluates only downside risk. Correct because mean-variance analysis generally considers risk symmetrically in the sense that standard deviation captures variability both above and below the mean. An alternative approach evaluates only downside risk. We discuss one such approach, safety-first rules, as it provides an excellent illustration of the application of normal distribution theory to practical investment problems. Safety-first rules focus on shortfall risk, the risk that portfolio value will fall below some minimum acceptable level over some time horizon. Roy's safety-first criterion states that the optimal portfolio minimizes the probability that portfolio return, RP, falls below the threshold level, RL.

The conditional expected value of a random variable is best described as the: A. expected value of a random variable given an event or scenario. B. probability-weighted average of the possible outcomes of the random variable. C. weighted average of the probabilities of an event given all possible scenarios.

A. expected value of a random variable given an event or scenario Correct. The conditional expected value of a random variable is the expected value of a random variable given an event or scenario.

The liquidity premium can best be described as compensation to investors for the: A. risk of loss relative to an investment's fair value if the investment needs to be converted to cash quickly. B. increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended. C. possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount.

A. risk of loss relative to an investment's fair value if the investment needs to be converted to cash quickly. Correct. The liquidity premium compensates investors for the risk of loss relative to an investment's fair value if the investment needs to be converted to cash quickly.

Question A return distribution with negative skew and a mean of zero most likely has: A. frequent small gains and a few extreme losses. B. frequent small losses and a few extreme gains. C. frequent extreme losses and a few small gains

A. frequent small gains and a few extreme losses. Correct because a return distribution with negative skew has frequent small gains and a few extreme losses.

*Introduction to Big Data Techniques (7 of 7) A characteristic of Big Data is that: A.it involves formats with diverse structures. B.one of its traditional sources is business processes. C.real-time communication of it is uncommon due to vast content.

A. it involves formats with diverse structures. A is correct. Big Data is collected from many different sources and is in a variety of formats, including structured data (e.g., SQL tables), semistructured data (e.g., HTML code), and unstructured data (e.g., video messages).

Equity return distributions are best described as being: A. leptokurtic. B. platykurtic. C. mesokurtic.

A. leptokurtic. Correct. Most equity return distributions are best described as being leptokurtic (i.e., more peaked than normal).

A portfolio has a mean return of 1.0% and a standard deviation of returns of 2.7%. If the specified minimum target return is 1.0%, the sample target semideviation is: A. less than 2.7%. B. equal to 2.7%. C. greater than 2.7%.

A. less than 2.7%. Correct because the target downside deviation = [Σ(Xi - B)2/(n - 1)]0.5, where Xi are the periodic returns below the target return, B is the target return, and n is the total number of periods. Since the sample has a standard deviation of 2.7%, it will have values below and above its mean of 1.0%. Since the target downside deviation ignores the deviations above the mean, it will be less than the standard deviation.

An analyst gathers the following sample returns for a security: *Return = -2% , -1% , 1%, 2% The mean absolute deviation of the sample returns is: A. less than the sample standard deviation. B. equal to the sample standard deviation. C. greater than the sample standard deviation.

A. less than the sample standard deviation. (Look at study guide) Correct because the mean absolute deviation of 1.5% is less than the sample standard deviation of 1.83%. The mean absolute deviation, MAD, is calculated as:, where the sample mean,. As the sample mean is:, the calculation of MAD is:= 1.5000%, while the sample standard deviation ofnobservations,, is, here:= 1.8257%.

For a set of return observations, the coefficient of variation is best described as a measure of: A. risk per unit of mean return. B. mean excess return earned per unit of risk. C. average absolute deviation around the mean return.

A. risk per unit of mean return. Correct because when the observations are returns, the coefficient of variation measures the amount of risk (standard deviation) per unit of mean return.

Consider the investment in the following table: *Start of Year 1 = One share purchased at $100 *End of Year 1 = $5.00 dividend/share paid and one additional share purchased at $125 *End of Year 2 = $5.00 dividend/share paid and both shares are sold for $140 per share Assuming dividends are not reinvested, compared with the time-weighted return, the money-weighted return is: A. lower. B. the same. C. higher.

A. lower. (Look at ebook) The following table represents cash flows of the investment: YearContributionStart-of-Year Value after ContributionEnd-of-Year DividendEnd-of-Year Value after Dividend11 × $1001 × $100 = $1001 × $5 = $5$125 + 5 = $13021 × $1252 × $125 = $2502 × $5 = $10(2 × 140) + 10 = $290 The time-weighted rate of return (TWR) on this investment is found by taking the geometric mean of the two holding period returns (HPRs): TWR = [(1 + HPRYear 1) × (1 + HPRYear 2)]1/2 − 1 where HPRYear 1 = ($125 − $100 + $5)/$100 = 30.0% HPRYear 2 = ($280 − $250 + $10)/$250 = 16.0% TWR = [(1 + 0.30) × (1 + 0.16)]1/2 − 1 = 22.80% The money-weighted rate of return (MWR) is the internal rate of return (IRR) of the cash flows associated with the investment: 0=−100+(−125+5)(1+𝑟1)+(280+10)(1+𝑟2)0=−100+(−125+5)(1+r1)+(280+10)(1+r2), where r = MWR. Using the cash flow (CF) function of a financial calculator: CF0 = −100, CF1 = (−125 + 5), CF2 = (280 + 10), and solving for IRR: MWR or IRR = 20.55%. The difference between the TWR and MWR of this investment = 22.80% − 20.55% = 2.25%, or 225 bps, with MWR being lower than TWR.

A tree diagram is most likely used when dealing with investment problems that involve outcomes that are: A. mutually exclusive. B. independent at each node. C. unconditional at each node.

A. mutually exclusive. Correct. The following figure depicts an example of a tree diagram: (Look at Ebook) A tree diagram is a diagram with branches emanating from nodes representing either mutually exclusive outcomes or mutually exclusive decisions. Mutually exclusive outcomes are dependent (the occurrence of one outcome does affect the probability of occurrence of the other outcome). In addition, outcomes at each node are conditional (the probability of an outcome is conditioned on another outcome).

A graphical depiction of a continuous distribution shows the left tail to be longer than the right tail. The distribution is best described as having: A. negative skewness. B. leptokurtosis. C. positive skewness.

A. negative skewness. Correct. A negatively skewed distribution appears as if the left tail has been pulled away from the mean. The average magnitude of negative deviations from the mean is larger than the average magnitude of positive deviations.

The correlation between two variables measures: A. only their linear relationship. B. only their non-linear relationship. C. both their linear and non-linear relationships.

A. only their linear relationship. Correct because the correlation coefficient is a measure of the linear association between two variables; it would not be approp riate to use the correlation coefficient to measure the non-linear relationship between variables.

A descriptive measure of a population characteristic is best described as a: A. parameter. B. sample statistic. C. frequency distribution.

A. parameter. Correct because any descriptive measure of a population characteristic is called a parameter.

Which of the following is most likely to be an explanation of the power of a test? The power of a test is the probability of: A. rejecting the null when it is false. B. not accepting the alternative when it is false. C. a Type I error.

A. rejecting the null when it is false. Correct. The power of a test is the probability of correctly rejecting the null—that is, the probability of rejecting the null when it is false.

An analyst observes the following EPS for four companies: -£0.50, £0.50, £2.50, and £5.50. The 50th percentile of the EPS values is closest to: A. £1.50. B. £2.00. C. £2.50.

A. £1.50. Correct because the 50th percentile is the median, which is the average of the two middle items; (£0.50 + £2.50)/2 = £1.50. In an odd-numbered sample of n items, the median occupies the (n + 1)/2 position. In an even-numbered sample, we define the median as the mean of the values of items occupying the n/2 and (n + 2)/2 positions (the two middle items). Calculating the median may also be more complex; to do so, we need to order the observations from smallest to largest, determine whether the sample size is even or odd and, on that basis, apply one of two calculations. Alternatively, the 50th percentile when Ly is not a whole number or integer, Ly lies between the two closest integer numbers (one above and one below), and we use linear interpolation between those two places to determine Py. That is, Ly = (n + 1)(y/100) = (4 + 1)(50/100) = 2.5. Hence, 2 is the closest integer below the calculated location and 3 is the closest integer above the calculated location. Using linear interpolation, P50 = £0.50 + (£2.50 - £0.50) × (2.5 - 2) = £1.50.

An investor invests a fixed amount of money into a fund each year for three years as follows: *Year = 1 -Price per Share = €14.00 *Year = 2 -Price per Share = €12.00 *Year = 1 -Price per Share = €17.00 The investor's average cost per share is closest to: A. €14.05. B. €14.33. C. €14.63.

A. €14.05. (Look at study guide) Correct because the harmonic mean is used to determine the average price paid per share when using cost averaging; The weighted mean formula could also be used, where the weights would be the proportion of the total number of shares purchased. However, in order to use this method a fixed investment amount would need to be created.

A consumer purchases an automobile using a loan. The amount borrowed is €30,000, and the terms of the loan call for the loan to be repaid over five years using equal monthly payments with an annual nominal interest rate of 8% and monthly compounding. The monthly payment is closest to: A. €608.29. B. €626.14. C. €700.00.

A. €608.29. (Look at ebook) Correct. Using a financial calculator: N = 60, I/Y = 8/12, PV = 30000, FV = 0, and compute PMT. Note, 5 years = 60 months. The nominal rate of 8% must be divided by 12 to find the monthly periodic rate of 0.6666667%. Alternatively, using the present value of an annuity formula, solve: PV = 𝐴[1−1[1+(𝑟𝑠/𝑚)]𝑚𝑁𝑟𝑠/𝑚]A[1−1[1+(rs/m)]mNrs/m] 30,000 = 𝐴[1−1(1+0.08/12)12×50.08/12]A[1−1(1+0.08/12)12×50.08/12] 30,000 = A × 49.318433 A = 30,000/49.318433 = 608.291829

The quarterly returns on a portfolio are as follows: Quarter 1 Return =20% Quarter 2 Return = -20% Quarter 3 Return =10% Quarter 4 Return = -10% The time-weighted rate of return of the portfolio is closest to: A. −5.0%. B. −1.3%. C. 0.0%.

A. −5.0%. Correct. The time-weighted rate of return of this portfolio = (1 + r1)(1 + r2)(1 + r3)(1 + r4) − 1,where r1 = holding period return (HPR) for the first quarter, second quarter, and so on: = (1 + 0.20)(1 − 0.20)(1 + 0.10)(1 − 0.10) − 1 = −4.96% (or ~ −5.0%).

The price of a stock at t = 0 is USD208.25 and at t = 1 is USD186.75. The continuously compounded rate of return, r1,T for the stock from t = 0 to t = 1 is closest to: A.-10.90 percent. B.-10.32 percent. C.11.51 percent.

A.-10.90 percent. (Look at ebook) The continuously compounded return from t = 0 to t = 1 is r0,1 = ln(S1/S0) = ln(186.75/208.25) = -0.10897 = -10.90%.

Kenneth McCoin, CFA, is a challenging interviewer. Last year, he handed each job applicant a sheet of paper with the information in Exhibit 1, and he then asked several questions about regression analysis. Some of McCoin's questions, along with a sample of the answers he received to each, are given below. McCoin told the applicants that the independent variable is the ratio of net income to sales for restaurants with a market cap of more than $100 million and the dependent variable is the ratio of cash flow from operations to sales for those restaurants. Which of the choices provided is the best answer to each of McCoin's questions? (Look at ebook) . The coefficient of determination is closest to: A.0.7436. B.0.8261. C.0.8623.

A.0.7436. A is correct. The coefficient of determination is the same as R2, which is 0.7436 in the table.

An analyst has estimated a model that regresses a company's return on equity (ROE) against its growth opportunities (GO), defined as the company's three-year compounded annual growth rate in sales, over 20 years, and produces the following estimated simple linear regression: ROEi = 4 + 1.8 GOi + εi. Both variables are stated in percentages, so a GO observation of 5 percent is included as 5. Question Q. The change in ROE for a change in GO from 5 percent to 6 percent is closest to: A.1.8 percent. B.4.0 percent. C.5.8 percent

A.1.8 percent. A is correct. The slope coefficient of 1.8 is the expected change in the dependent variable (ROE) for a one-unit change in the independent variable (GO).

Consider the following annual return for Fund Y over the past five years: *Exhibit 1: Five-Year Annual Returns *Year 1: -Return (%) = 19.5 *Year 2 -Return (%) = -1.9 *Year 3 -Return (%) = 197 *Year 4 -Return (%) = 35.0 ------------------------- *Year 5 -Return (%) = 5.7 The geometric mean return for Fund Y is closest to: A.14.9 percent. B.15.6 percent. C.19.5 percent.

A.14.9 percent. (Look at ebook) is correct. The geometric mean return for Fund Y is calculated as follows: 𝑅⎯⎯⎯𝐺R¯G= [(1 + 0.195) × (1 − 0.019) × (1 + 0.197) × (1 + 0.350) × (1 + 0.057)](1/5)− 1= 14.9%.

*Simulation Methods (6 of 6) The weekly closing prices of Mordice Corporation shares are as follows: *Mordice Corporation Shares Date: August 1 *Closing Price (euros) = 112 Date: August 8 *Closing Price (euros) = 160 Date: August 15 *Closing Price (euros) = 120 The continuously compounded return of Mordice Corporation shares for the period August 1 to August 15 is closest to: A.6.90 percent. B.7.14 percent. C.8.95 percent.

A.6.90 percent. A is correct. The continuously compounded return of an asset over a period is equal to the natural log of the asset's price change during the period. In this case, ln(120/112) = 6.90%. Note that the continuously compounded return from period 0 to period T is the sum of the incremental one-period continuously compounded returns, which in this case are weekly returns. Specifically: Week 1 return: ln(160/112) = 35.67%.Week 2 return: ln(120/160) = -28.77%.Continuously compounded return = 35.67% + -28.77% = 6.90%.

In the step "stating a decision rule" in testing a hypothesis, which of the following elements must be specified? A.Critical value B.Power of a test C.Value of a test statistic

A.Critical value A is correct. The critical value in a decision rule is the rejection point for the test. It is the point with which the test statistic is compared to determine whether to reject the null hypothesis, which is part of the fourth step in hypothesis testing. B is incorrect because the power of a test refers to the probability of rejecting the null hypothesis when it is false. C is incorrect because the value of the test statistic is specified in the 'Identify the appropriate test statistic and its probability distribution" step.A.Critical value

Grey Pebble Real Estate seeks a fully amortizing fixed-rate five-year mortgage loan to finance 75 percent of the purchase price of a residential building that costs NZD5 million. The annual mortgage rate is 4.8 percent. The monthly payment for this mortgage would be closest to: A.NZD70,424. B.NZD93,899. C.NZD71,781.

A.NZD70,424. A is correct. The present value of the mortgage is NZD3.75 million (=0.75×5,000,000), the periodic discount rate is 0.004 (=0.048/12), and the number of periods is 60 (=5×12). Using Equation 8, 𝐴=$70,424=0.4%(NZD3,750,000)1−(1+0.4%)−60A=$70,424=0.4%NZD3,750,0001−1+0.4%−60. Alternatively, the spreadsheet PMT function may be used with the inputs stated earlier. B is incorrect. NZD93,899 is the result if NZD5 million is incorrectly used as the present value term. C is incorrect. NZD71,781 is the result if the calculation is made using 4.8 percent as the rate and 5 as the number of periods, then the answer is divided by 12.

. Which of the following best describes a Type I error? A.Rejecting a true null hypothesis B.Rejecting a false null hypothesis C.Failing to reject a false null hypothesis

A.Rejecting a true null hypothesis A is correct. The definition of a Type I error is when a true null hypothesis is rejected.

Q. A stock currently trades at USD25. In one year, it will either increase in value to USD35 or decrease to USD15. An investor sells a call option on the stock, granting the buyer the right, but not the obligation, to buy the stock at USD25 in one year. At the same time, the investor buys 0.5 units of the stock. Which of the following statements about the value of the investor's portfolio at the end of one year is correct? A.The portfolio has a value of USD7.50 in both scenarios. B.The portfolio has a value of USD25 in both scenarios. C.The portfolio has a value of USD17.50 if the stock goes up and USD7.50 if the stock goes down.

A.The portfolio has a value of USD7.50 in both scenarios. A is correct. Regardless of whether the stock increases or decreases in price, the investor's portfolio has a value of USD7.50 as follows: If stock price goes to USD35, value = 0.5×35 - 10 = 7.50.If stock price goes to USD15, value = 0.5×15 - 0 = 7.50. If the stock price rises to USD35, the sold call option at USD25 has a value to the buyer of USD10, offsetting the rise in the stock price.

In which of the following situations would a nonparametric test of a hypothesis most likely be used? A.The sample data are ranked according to magnitude. B.The sample data come from a normally distributed population. C.The test validity depends on many assumptions about the nature of the population.

A.The sample data are ranked according to magnitude. A is correct. A nonparametric test is used when the data are given in ranks.

Which of the following statements is correct regarding the chi-square test of independence? A.The test has a one-sided rejection region. B.The null hypothesis is that the two groups are dependent. C.If there are two categories, each with three levels or groups, there are six degrees of freedom.

A.The test has a one-sided rejection region. A is correct. The test statistic includes squared differences between the observed and expected values, so the test involves only one side, the right side. B is incorrect because the null hypothesis is that the groups are independent, and C is incorrect because with three levels of groups for the two categorical variables, there are four degrees of freedom.

*Estimation and Inference (13 of 13) Which one of the following statements is true about non-probability sampling? A.There is significant risk that the sample is not representative of the population. B.Every member of the population has an equal chance of being selected for the sample. C.Using judgment guarantees that population subdivisions of interest are represented in the sample.

A.There is significant risk that the sample is not representative of the population. A is correct. Because non-probability sampling is dependent on factors other than probability considerations, such as a sampler's judgment or the convenience to access data, there is a significant risk that non-probability sampling might generate a non-representative sample.

The current exchange rate between the euro and US dollar is USD/EUR1.025. Risk-free interest rates for one year are 0.75 percent for the euro and 3.25 percent for the US dollar. The one-year USD/EUR forward rate that best prevents arbitrage opportunities is: A.USD/EUR1.051. B.USD/EUR1.025. C.USD/EUR0.975.

A.USD/EUR1.051. A is correct. To avoid arbitrage opportunities in exchanging euros and US dollars, investors must be able to lock in a one-year forward exchange rate of USD/EUR1.051 today. The solution methodology is shown below. In one year, a single unit of euro invested risk-free is worth EUR1.0075 (=e0.0075). In one year, a single unit of euro converted to US dollars and then invested risk-free is worth USD1.0589 (=1.025*e0.0325). To convert USD1.0589 into EUR1.0075 requires a forward exchange rate of USD/EUR1.051 (=1.0589/1.0075).

The probability distribution for a company's sales is: Probability Sales (USD, millions) *0.05 70 *0.70 40 *0.25 25 The standard deviation of sales is closest to which of the following? A.USD9.81 million. B.USD12.20 million. C.USD32.40 million.

A.USD9.81 million. (Look at ebook0 A is correct. The analyst must first calculate expected sales as 0.05 × USD70 + 0.70 × USD40 + 0.25 × USD25 = USD3.50 million + USD28.00 million + USD6.25 million = USD37.75 million. After calculating expected sales, we can calculate the variance of sales: σ2 (Sales) = P(USD70)[USD70 - E(Sales)]2 + P(USD40)[USD40 - E(Sales)]2 + P(USD25)[USD25 - E(Sales)]2= 0.05(USD70 - 37.75)2 + 0.70(USD40 - 37.75)2 + 0.25(USD25 - 37.75)2= USD52.00 million + USD3.54 million + USD40.64 million = USD96.18 million. The standard deviation of sales is thus σ = (USD96.18)1/2 = USD9.81 million.

. A chi-square test is most appropriate for tests concerning: A.a single variance. B.differences between two population means with variances assumed to be equal. C.differences between two population means with variances not assumed to be equal.

A.a single variance. A is correct. A chi-square test is used for tests concerning the variance of a single normally distributed population.

An analyst is examining the annual growth of the money supply for a country over the past 30 years. This country experienced a central bank policy shift 15 years ago, which altered the approach to the management of the money supply. The analyst estimated a model using the annual growth rate in the money supply regressed on the variable (SHIFT) that takes on a value of 0 before the policy shift and 1 after. She estimated the values in Exhibit 1: Intercept -Coefficients = 5.767264 -Standard Error =0.445229 -t-Stat. =12.95348 Shift -Coefficients = −−5.13912 -Standard Error = −0.629649 -t-Stat. =−8.16188 Critical t-values, level of significance of 0.05: eOne-sided, left side: −1.701 fOne-sided, right side: +1.701 gTwo-sided: ±2.048 The variable SHIFT is best described as: A.an indicator variable. B.a dependent variable. C.a continuous variable.

A.an indicator variable. A is correct. SHIFT is an indicator or dummy variable because it takes on only the values 0 and 1.

An analyst is examining the annual growth of the money supply for a country over the past 30 years. This country experienced a central bank policy shift 15 years ago, which altered the approach to the management of the money supply. The analyst estimated a model using the annual growth rate in the money supply regressed on the variable (SHIFT) that takes on a value of 0 before the policy shift and 1 after. She estimated the values in Exhibit 1: Intercept -Coefficients = 5.767264 -Standard Error =0.445229 -t-Stat. =12.95348 Shift -Coefficients = −−5.13912 -Standard Error = −0.629649 -t-Stat. =−8.16188 Critical t-values, level of significance of 0.05: eOne-sided, left side: −1.701 fOne-sided, right side: +1.701 gTwo-sided: ±2.048 The interpretation of the intercept is the mean of the annual growth rate of the money supply: A.before the shift in policy. B.over the entire period. C.after the shift in policy.

A.before the shift in policy. A is correct. In a simple regression with a single indicator variable, the intercept is the mean of the dependent variable when the indicator variable takes on a value of zero, which is before the shift in policy in this case.

A nonparametric test is most appropriate when the: A.data consist of ranked values. B.validity of the test depends on many assumptions. C.sample sizes are large but are drawn from a population that may be non-normal.

A.data consist of ranked values. A is correct. When the samples consist of ranked values, parametric tests are not appropriate. In such cases, nonparametric tests are most appropriate.

At the beginning of Year 1, a fund has USD10 million under management; it earns a return of 14 percent for the year. The fund attracts another net USD100 million at the start of Year 2 and earns a return of 8 percent for that year. The money-weighted rate of return of the fund is most likely to be: A.less than the time-weighted rate of return. B.the same as the time-weighted rate of return. C.greater than the time-weighted rate of return.

A.less than the time-weighted rate of return. (Look at ebook) Computation of the money-weighted return, r, requires finding the discount rate that sums the present value of cash flows to zero. Because most of the investment came during Year 2, the money-weighted return will be biased toward the performance of Year 2 when the return was lower. The cash flows are as follows: CF0= −10CF1= −100CF2= +120.31 The terminal value is determined by summing the investment returns for each period [(10 × 1.14 × 1.08) + (100 × 1.08)]. CF0(1+IRR)0+CF1(1+IRR)1+CF2(1+IRR)2−101+−100(1+IRR)1+120.31(1+IRR)2=0CF01+IRR0+CF11+IRR1+CF21+IRR2−101+−1001+IRR1+120.311+IRR2=0. This results in a value of IRR = 8.53 percent. The time-weighted return of the fund is calculated as follows: 𝑅TWRTW=(1.14)(1.08)⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2−11.141.082−1= 10.96%.

The value of a test statistic is best described as the basis for deciding whether to: A.reject the null hypothesis. B.accept the null hypothesis. C.reject the alternative hypothesis.

A.reject the null hypothesis. A is correct. In hypothesis testing, a test statistic is a quantity whose value is the basis for deciding whether to reject the null hypothesis.

Using the following sample results drawn as 25 paired observations from their underlying distributions, test whether the mean returns of the two portfolios differ from each other at the 1% level of statistical significance. Assume the underlying distributions of returns for each portfolio are normal and that their population variances are not known. (Look at ebook) t-statistic for 24 degrees of freedom and at the 1% level of statistical significance = 2.807 Null hypothesis (H0): Mean difference of returns = 0 Based on the paired comparisons test of the two portfolios, the most appropriate conclusion is that H0 should be: A.rejected because the computed test statistic exceeds 2.807. B.accepted because the computed test statistic exceeds 2.807. C.accepted because the computed test statistic is less than 2.807.

A.rejected because the computed test statistic exceeds 2.807. Correct because the test statistic is: 𝑑⎯⎯−𝜇𝑑0𝑠𝑑/𝑛√d¯−μd0sd/n where 𝑑⎯⎯d¯ = the mean difference μd0 = the hypothesized difference in the means sd = the sample standard deviation of differences n = the sample size In this case, the test statistic equals: (4.25−0)(6.25/25√)(4.25−0)(6.25/25) = 3.40. Because 3.40 2.807, the null hypothesis that the mean difference is zero is rejected.

Compared with bootstrap resampling, jackknife resampling: A.is done with replacement. B.usually requires that the number of repetitions is equal to the sample size. C.produces dissimilar results for every run because resamples are randomly drawn.

B.usually requires that the number of repetitions is equal to the sample size. B is correct. For a sample of size n, jackknife resampling usually requires n repetitions. In contrast, with bootstrap resampling, we are left to determine how many repetitions are appropriate.

Analysts performing bootstrap: A.seek to create statistical inferences of population parameters from a single sample. B.repeatedly draw samples of the same size, with replacement, from the original population. C.must specify probability distributions for key risk factors that drive the underlying random variables.

A.seek to create statistical inferences of population parameters from a single sample. A is correct. Bootstrapping through random sampling generates the observed variable from a random sampling with unknown population parameters. The analyst does not know the true population distribution, but through sampling can infer the population parameters from the randomly generated sample. B is incorrect because, when performing bootstrap, the analyst repeatedly draws samples from the original sample and not population, where each individual resample has the same size as the original sample and each item drawn is replaced for the next draw. C is incorrect because, when performing bootstrap, analysts simply use the observed empirical distribution of the underlying variables. In a Monte Carlo simulation, in contrast, the analyst would specify probability distributions for key risk factors that drive the underlying variables.

*Parametric & Non-Parametric Tests of Independence (2 of 2) Jill is analyze how returns on stock of Stellar Energy Corp. related w/ previous month's % change in the US Consumer Price Index for Energy . Based on 248 observations, she computed sample correlation between the Stellar &CPIENG variables to be −0.1452. She wants to determine if the sample correlation is different from 0. The critical value for the test statistic at 0.05 level of significance is approximately 1.96. Jill should conclude statistical relationship between Stellar & CPIENG is: A.significant, because the calculated test statistic is outside the bounds of the critical values for the test statistic. B.significant, because the calculated test statistic has a lower absolute value than the critical value for the test statistic. C.insignificant, because the calculated test statistic is outside the bounds of the critical values for the test statistic.

A.significant, because the calculated test statistic is outside the bounds of the critical values for the test statistic. A is correct. The calculated test statistic is 𝑡=𝑟𝑛−2⎯⎯⎯⎯⎯⎯⎯⎯⎯√1−𝑟2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√=−0.1452248−2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√1−(−0.1452)2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√=−2.30177.t=rn−21−r2=−0.1452248−21−(−0.1452)2=−2.30177. Because the value of t = −2.30177 is outside the bounds of ±1.96, we reject the null hypothesis of no correlation and conclude that evidence is sufficient to indicate that the correlation is different from zero.A.significant, because the calculated test statistic is outside the bounds of the critical values for the test statistic.

Based on Exhibit 2, the short interest ratio expected for MQD Corporation is closest to: A.3.8339. B.5.4975. C.6.2462. A.3.8339. A is correct. The predicted value of the short interest ratio = 5.4975 + (−4.1589 × 0.40) = 5.4975 − 1.6636 = 3.8339.

Anh Liu is an analyst researching whether a company's debt burden affects investors' decision to short the company's stock. She calculates the short interest ratio (the ratio of short interest to average daily share volume, expressed in days) for 50 companies as of the end of the year and compares this ratio with the companies' debt ratio (the ratio of total liabilities to total assets, expressed in decimal form). Liu provides a number of statistics in Exhibit 1. She also estimates a simple regression to investigate the effect of the debt ratio on a company's short interest ratio. The results of this simple regression, including the analysis of variance (ANOVA), are shown in Exhibit 2. In addition to estimating a regression equation, Liu graphs the 50 observations using a scatter plot, with the short interest ratio on the vertical axis and the debt ratio on the horizontal axis.

Based on Liu's regression results in Exhibit 2, the F-statistic for testing whether the slope coefficient is equal to zero is closest to: A.−2.2219. B.3.5036. C.4.9367. C.4.9367. C is correct. The calculation is 𝐹=Mean square regressionMean square error=38.44047.7867=4.9367

A test of independence is based on the data in a contingency table with 5 rows and 4 columns. Using a nonparametric test statistic that is chi-square distributed, the number of degrees of freedom is: A. 7. B. 12. C. 20.

B. 12. Correct because for a contingency table we can perform a test of independence using a nonparametric test statistic that is chi-square distributed this test statistic has (r - 1)(c - 1) degrees of freedom, where r is the number of rows and c is the number of columns. Here, r = 5 and c = 4, so degrees of freedom = (5 - 1)(4 - 1) = 4 × 3 = 12.

An investor needs to make the following payments to cover college tuition fees, starting 10 years from today: *Annual fee (payable at the beginning of each year) = $50,000 *Number of years of fee payments = 4 If the investor's annual discount rate is 3%, the minimum investment amount required today to fund all four years of college tuition is closest to: A. $138,294. B. $142,442. C. $146,716.

B. $142,442. (Look at ebook) Correct because the present value (PV) of the annuity due 10 years from today equals PV10 = $50,000 + $50,000 × [1 - 1/(1.03)3]/0.03 = $50,000 + $50,000 × 2.828611 = $191,431. The PV of the annuity today equals PV0 = $191,431/(1.03)10 = $142,442.Calculator solution: BEGIN mode; N = 4; I/Y = 3%; PMT = 50,000; solve for PV = 191,431. Discounted back 10 years: N = 10; I/Y = 3%; FV = 191,431; solve for PV = 142,442.Alternatively, the annuity can be treated as an ordinary annuity, with a PV 9 years from today of PV9 = $50,000 × [1 - 1/(1.03)4]/0.03 = $50,000 × 3.717098 = $185,855. The PV of the annuity today equals PV0 = $185,855/(1.03)9 = $142,442.Calculator solution: END mode; N = 4; I/Y = 3%; PMT = 50,000; solve for PV = 185,855. Discounted back 9 years: N = 9; I/Y = 3%; FV = 185,855; solve for PV = 142,442.

An investment pays $1,000 annually for five years, with the first payment occurring three years from today. If the discount rate is 6% compounded annually, the present value of the investment today is closest to: A. $3,537. B. $3,749. C. $4,212.

B. $3,749. (Look at the Quantitative Methods) Correct because by drawing a time line, the investment is recognized as a delayed annuity with the first payment starting at t = 3. The first step is to compute the present value of an ordinary annuity at t = 2 because the first annuity payment is then one period away, as PV2 = A[1 - 1/(1 + r)N] / r = $1,000 × [1 - 1/(1 + 0.06)5/0.06 = $4,212.36. Using the present value formula for a lump sum to bring the single cash flow from t = 2 to t = 0, PV0 = FVN(1 + r)-N = $4,212.36 (1 + 0.06)-2 = $3,748.99 ~ $3,749. Calculator solution: (1) END mode; N = 5; I = 6%; PMT = −1,000; FV = 0; solve for PV = 4,212.36. (2) END mode; N = 2; I = 6%; PMT = 0; FV = 4,212.36; solve for PV = 3,748.99 ~ 3,749. A second method to compute the present value of the investment is to recognize it as an annuity due with first payment at t = 3, and then discount back three periods using the present value formula for a lump sum. PV3 ;= {A[1 - 1/(1 + r)N] / r}(1 + r) = $1,000 × {[1 - 1/(1 + 0.06)5]/0.06} × (1 + 0.06) = $4,465.11. Using the present value formula for a lump sum to bring the single cash flow from t = 3 to t = 0, PV0 = FVN(1 + r)-N = $4,465.11 (1 + 0.06)-3 = $3,748.99 ~ $3,749. Calculator solution: (1) BGN mode; N = 5; I = 6%; PMT = −1,000; FV = 0; solve for PV = 4,465.11. (2) END mode; N = 3; I = 6%; PMT = 0; FV = 4,465.11; solve for PV = 3,748.99 ~ 3,749. Another method to compute the Correct answer is to calculate the present value of a series of equal cash flows, with the first cash flow in the third year. Using a calculator with CF0=0, CF1=0, CF2=0, CF3=1000, CF4=1000, CF5=1000, CF6=1000, CF7=1000; I=6%; solve for NPV= 3,748.99 ~ 3,749.

An annuity makes seven annual payments of $10,000 each, with the first payment occurring five years from today. If the discount rate is 6% per year, the value of the annuity today is closest to: A. $41,715. B. $44,218. C. $55,824

B. $44,218. (Look at ebook) Correct because the present value in Year 4 of an ordinary annuity with 7 payments of $10,000 at a 6% discount rate is calculated as follows: PV = A[1 - 1/(1 + r)N]/r PV4 = $10,000 × [1 - 1/(1 + 0.06)7]/0.06 PV4 = $55,823.81 Then, using a time line, the PV of the annuity in today's dollars is PV0 = FV4(1 + r)-N PV0 = $55,823.81 × (1 + 0.06)-4 PV0 = $44,217.69 ≈ $44,218. Calculator solution: (1) END mode; N = 7; I = 6; PMT = -10,000; FV = 0; solve for PV = 55,823.81. (2) END mode; N = 4; I = 6; PMT = 0; FV = ->55,823.81; solve for PV = 44,217.69.

A consultant starts a project today that will last for three years. Her compensation package includes the following: *Year = 1 -End of Year Payment = $100,000 *Year = 2 -End of Year Payment = $150,000 *Year = 3 -End of Year Payment = $200,000 If she expects to invest these amounts at an annual interest rate of 3%, compounded annually until her retirement 10 years from now, the value at the end of 10 years is closest to: A. $618,994. B. $566,466. C. $460,590.

B. $566,466. (Look at ebook) Correct. First calculate the present value of the three cash flows with the following formula: PV = FV𝑁(1+𝑟)𝑁FVN(1+r)N We obtain: PVCash flow 1 = ($100,000/1.03) = $97,087 (rounded) PVCash flow 2 = [$150,000/(1.03)2] = $141,389 (rounded) PVCash flow 3 = [$200,000/(1.03)3] = $183,028 (rounded) Then, sum the three present values: $97,087 + $141,389 + $183,028 = $421,504 Calculate the FV of $421,504 ten years from now with the formula: FVN = PV × (1 + r)N FV10 = PV × (1 + r)10 FV10 = $421,504 × (1.03)10 = $566,466 (rounded) The future value 10 years from now is $566,466. Alternatively, calculate directly the FV of each of the cash flows to the end of 10 years: FV10 = $100,000 × (1.03)9 + $150,000 × (1.03)8 + $200,000 × (1.03)7 = $130,477 + $190,016 + $245,975 = $566,468 (rounded).

An analyst performs a simple linear regression of a stock's monthly return on the monthly return of a market index (both in %) and gathers the following information: *Estimated slope = 1.0 *Estimated intercept = 1.2% *Standard error of the forecast = 1.4% *Critical t-values at a 5% significance level±2.032 The 95% prediction interval for the stock's monthly return, given that the forecasted monthly return on the index is 3.5%, is closest to: A. 0.7% to 6.3%. B. 1.9% to 7.5%. C. 3.3% to 6.1%.

B. 1.9% to 7.5%. Correct because a forecasted value of the dependent variable, Yf, is determined using the estimated intercept and slope, as well as the expected or forecasted independent variable, Xf: Yf = b0 + b1Xf," where b0 and b1 are the estimated intercept and slope coefficients, respectively. Hence, Yf = 1.2% + 1.0 × 3.5% = 4.7%. Next, the prediction interval is Yf ± tcritical for α/2sf," where sf denotes the standard error of the forecast. Hence, the prediction interval is given by: 4.7% ± 1.4% × 2.032 ≈ (1.9%, 7.5%).

An analyst gathers the following information about a portfolio's returns: Year 1 -Return = 6% Year 2 -Return = 7% Year 3 -Return = 3% Year 4 -Return = 2% Year 5 -Return = 4% If the target return is 5%, the target downside deviation is closest to: A. 1.7%. B. 1.9%. C. 2.2%.

B. 1.9%. (Look at ebook study guide _ Correct because the formula for target downside deviation is [Σ(Xi - B)2/(n - 1)]0.5, where Xi is the return for the period, B is the target return and n is the total number of sample observations. Moreover, the summation is taken over only those observations (Xi) that are less than or equal to the target B. YearReturn (%)Deviations from the targetSquared deviations1600270033-2442-3954-11 Since the sum of squared deviations is 14, the target downside deviation = [14/(5 - 1)]0.5, resulting in 1.87% ≈ 1.9%.

If a unimodal return distribution is negatively skewed, which of the following most likely has the highest value? A. Mean B. Mode C. Median

B. Mode Correct because for the continuous negatively skewed unimodal distribution, the mean is less than the median, which is less than the mode. Therefore, the mode has the highest value.

An investor summarizes end-of-year cash outlays and proceeds from a two-year investment in a company's shares below: *Year 0 -Outlays = $100 to purchase the first share ~ - Proceeds = ---- *Year 1 -Outlays = $110 to purchase the second share ~ - Proceeds = $10 dividend received from first share (not reinvested) *Year 2 -Outlays = ----- ~ - Proceeds = $230 received from selling two shares at $115 per share The annualized time-weighted rate of return of the investment over the two-year period is closest to: A. 9.7%. B. 12.0%. C. 12.3%.

B. 12.0%. Correct because the time-weighted rate of return measures the compound rate of growth of $1 initially invested in the portfolio over a stated measurement period.... We find this time-weighted return by taking the geometric mean of the two holding period returns. A holding period return is the return earned from holding an asset for a single specified period of time. ... This return can be generalized and shown as a mathematical expression in which P is the price and I is the income: R = [(P1 - P0) + I1]/P0. The subscript indicates the time of the price or income, (t = 0), is the beginning of the period and (t = 1) is the end of the period. Thus, the holding period return between time 0 and 1 is HPR1 = [(110 - 100) + 10]/100 = 0.2 = 20%, and the holding period return between time 1 and 2 is HPR2 = [(230 - 220) + 0]/220 = 0.04545 ≈ 4.5%, where 220 = 110 × 2 is the price (value) of the two shares held by the investor at time 1. The time-weighted rate of return is then [(1 + HPR1) × (1 + HPR2)]0.5 - 1 = [(1 + 0.2) × (1 + 0.04545)]0.5 - 1 = 0.12006 ≈ 12.0%.

An investor wants to maximize the possibility of earning at least 5% on her investments each year. *Portfolio=1 *Expected Return=--- *Standard Deviation of Returns=--- *Safety-First Ratio= 0.35 *Portfolio=2 *Expected Return=---- *Standard Deviation of Returns=--- *Safety-First Ratio= 0.64 *Portfolio=3 *Expected Return=22% *Standard Deviation of Returns=40% *Safety-First Ratio= ?? Using Roy's safety-first criterion, the most appropriate choice for the investor is portfolio: A. 3. B. 2. C.1.

B. 2. Correct. The portfolio with the highest safety-first ratio (SFRatio) is preferred. The SFRatio is calculated by subtracting the threshold return (RL) from the expected return [E(RP)] and dividing by the standard deviation (σP). SFRatio = [E(RP) − RL]/σP. For the choices given: -Roy's Safety First Criterion *Portfolio 1 --0.35 *Portfolio 2 --0.64 *Portfolio 3 --0.425=[(22-5)/40]

An equally weighted portfolio consists of two securities, each with a standard deviation of 3%. If the two securities' returns are uncorrelated, the portfolio's standard deviation is closest to: A. 0.0%. B. 2.1%. C. 3.0%

B. 2.1%. (Look at ebook) Correct because the portfolio standard deviation is 2.1%;or 2.12%, using the formulawhere the Cov(R1,R2) =, which is equal to zero because the funds are uncorrelated;

*Portfolio Mathematics (6 of 6) Q. An analyst produces the following joint probability function for a foreign index (FI) and a domestic index (DI). (Look at chart ebook) RDI = 30% RDI = 25% RDI = 15% RFI = 25% 0.25 RFI = 15% 0.50 RFI = 10% 0.25 The covariance of returns on the foreign index and the returns on the domestic index is closest to: A.26.39. B.26.56. C.28.12.

B. 26.56. (Look at ebook) B is correct. The covariance is 26.56, calculated as follows. First, expected returns are E(RFI) = (0.25 × 25) + (0.50 × 15) + (0.25 × 10)= 6.25 + 7.50 + 2.50 = 16.25 andE(RDI) = (0.25 × 30) + (0.50 × 25) + (0.25 × 15)= 7.50 + 12.50 + 3.75 = 23.75. Covariance is Cov(RFI,RDI) =∑𝑖∑𝑗𝑃(𝑅𝐹𝐼,𝑖,𝑅𝐷𝐼,𝑗)(𝑅𝐹𝐼,𝑖−𝐸𝑅𝐹𝐼)(𝑅𝐷𝐼,𝑗−𝐸𝑅𝐷𝐼)∑i∑jPRFI,i,RDI,jRFI,i−ERFIRDI,j−ERDI= 0.25[(25 - 16.25)(30 - 23.75)] + 0.50[(15 - 16.25)(25 - 23.75)] + 0.25[(10 - 16.25)(15 - 23.75)]= 13.67 + (-0.78) + 13.67 = 26.56B.26.56.

An analyst examines 30 paired monthly returns for two stock indexes. To determine if the mean difference of the returns is zero, the number of degrees of freedom of the t-test is: A. 28 . B. 29. C. 58.

B. 29. Correct because the t-statistic for a paired comparisons test has n - 1 degrees of freedom, where n is the number of pairs of observations. When n = 30, the number of degrees of freedom is 30 - 1 = 29.

A sample of 25 observations has a mean of 8 and a standard deviation of 15. The standard error of the sample mean is closest to: A. 1.60. B. 3.00. C. 3.06.

B. 3.00. (Look at ebook) Correct. The standard error of the sample mean, when the sample standard deviation is known, is: 𝑠𝑋⎯⎯⎯⎯=𝑠/𝑛⎯⎯√sX¯=s/n In this case, 𝑠𝑋⎯⎯⎯⎯=15/25⎯⎯⎯⎯√=3.00sX¯=15/25=3.00.

An analyst estimates the following information from a simple linear regression: *Sum of squares error = 280 *Sum of squares regression = 25 *Number of paired observations = 30 The standard error of the estimate is closest to: A. 2.5. B. 3.2. C. 10.0.

B. 3.2. Correct because it is the standard error of the estimate calculated as the square root of the mean square error; (10)0.5 = 3.2. The mean square error (MSE) is calculated as SSE / (n - 2); 280 / (30 - 2) = 10.0, where SSE is the sum of squares error.

The following sample of 10 items is selected from a population. The population variance is unknown. 10 , 20 , -8 , 2 , -9 , 5 , 0 , -8 , 3 , 21 The standard error of the sample mean is closest to: A. 3.60. B. 3.43. C. 10.84.

B. 3.43. (Look at ebook) Correct. When the population variance is unknown, the standard error of the sample mean is calculated as 𝑠𝑋⎯⎯⎯⎯=𝑠/𝑛⎯⎯√sX¯=s/n, where s is the sample standard deviation and n is the size of the sample. The sample standard deviation is 𝑠=[∑𝑖=1𝑛(𝑋𝑖−𝑋⎯⎯⎯)2/(𝑛−1)]0.5s=[∑i=1n(Xi−X¯)2/(n−1)]0.5. In this problem, 𝑋⎯⎯⎯X¯ = (10 + 20 − 8 + 2 − 9 + 5 + 0 − 8 + 3 + 21)/10 = 3.6. Deviation from MeanSquared Deviation(10 - 3.6) = 6.46.4²=40.96(20 - 3.6) = 16.416.4² = 268.96(-8 - 3.6) = -11.6-11.6² = 134.56(2 - 3.6) = -1.6-1.6² = 2.56(-9 - 3.6) = -12.6-12.6² = 158.76(5 - 3.6) = 1.41.4² = 1.96(0 - 3.6) = -3.6-3.6² = 12.96(-8 - 3.6) = -11.6-11.6² = 134.56(3 - 3.6) = -0.6-0.6² = 0.36(21 - 3.6) = 17.417.4² = 302.76Total1058.4Variance1058.4/9 = 117.6Standard Deviation(s):117.6⎯⎯⎯⎯⎯⎯⎯⎯⎯√117.6 = 10.844 The standard error of the sample mean is therefore 10.844/100.5 = 3.429 ~ 3.43.

An investor is considering two term deposits with the following characteristics: *Compounding frequency -Term Deposit 1 = Quarterly -Term Deposit 2 = Continuous *Stated annual rate -Term Deposit 1 = 4% -Term Deposit 2 = ? The stated annual rate for Term Deposit 2 that should make the investor indifferent between the two term deposits is closest to: A. 3.92%. B. 3.98%. C. 4.06%.

B. 3.98%. (Look at study guide) Correct because the investor will be indifferent if the EAR for both term deposits is the same. Therefore, we need to find the stated annual rate with continuous compounding that corresponds to the EAR of the quarterly compounded term deposit. Calculations: EAR of Term Deposit 1 = (1 + 0.04/4)4 - 1 = 0.040604. Hence, EAR of Term Deposit 2 = 0.040604 = er - 1, leading to a stated annual rate for Term Deposit 2 of r = ln(1.040604) = 0.039801 = 3.98%.

During the past 36 months, the standard deviation of a portfolio's monthly returns has been 4.9%. To test a claim that this portfolio's investment strategy results in a standard deviation of monthly returns that is less than 5.0%, the value of the test statistic is closest to: A. 34.30. B. 33.61. C. 34.57.

B. 33.61. (Look at ebook) Correct. The most appropriate test is chi-square, with 36 − 1 = 35 degrees of freedom. The calculated test statistic is: 𝜒2=(𝑛−1)𝑠2𝜎20=(36−1)(0.049)2(0.05)2=33.61χ2=(n−1)s2σ02=(36−1)(0.049)2(0.05)2=33.61 where χ2 = is the chi-square test statistic n = is the sample size s2 = is the sample variance 𝜎20σ02 = the hypothesized value of the variance σ2

Assume the following: The real risk-free rate of return is 3%. The expected inflation premium is 5%. The market-determined interest rate of a security is 12%. The sum of the default risk premium, liquidity premium, and maturity premium for the security is closest to: A. 10%. B. 4%. C. 8%.

B. 4%. Correct. The market-determined interest rate is equal to the real risk-free rate of return plus an inflation premium plus risk premiums for default risk, liquidity, and maturity. In this case, 12 = 3 + 5 + X. Solving for X: X = 4.

An individual wants to be able to spend €80,000 per year for an anticipated 25 years in retirement. To fund this retirement account, he will make annual deposits of €6,608 at the end of each of his working years. He can earn 6% compounded annually on all investments. The minimum number of deposits that are needed to reach his retirement goal is closest to: A. 28. B. 40. C. 51.

B. 40. (Look at ebook) The following figure represents the timeline for the problem: Using a financial calculator, the funds needed at retirement (R on the timeline) are calculated: N = 25; I/Y = 6%; PMT = €80,000; Future value (FV) = €0; Mode = End. The calculated present value (PV) is €1,022,668.PV=𝐴[1−1(1+𝑟)𝑁𝑟]=80,000[1−1(1.06)250.06]=1,022,688PV=A[1−1(1+r)Nr]=80,000[1−1(1.06)250.06]=1,022,688 Then, €1,022,668 is used as the FV (at R on the timeline) for the accumulation phase annuity as per: I/Y = 6%; PV = €0; PMT = −€6,608; FV = €1,022,668; Mode = End. The computed N is 40. Alternatively, 40 could be calculated with the formula: FV=𝐴[(1+𝑟)𝑁−1𝑟]FV=A[(1+r)N−1r] and solving for N, 1,022,668=6,608[(1+0.06)𝑁−10.06]

An analyst gathers the following returns for seven funds: 12% 7% 5% 4% 8% 3% 3% The second quartile return is: A. 4%. B. 5%. C. 6%.

B. 5%. (Look at study guide) Correct because the formula for the position of a percentile in an array with n entries sorted in ascending order is Ly = ( n + 1) × y/100, where y is the percentage point at which we are dividing the distribution and Ly is the location ( L) of the percentile ( Py) in the array sorted in ascending order. With seven entries, the location of the second quartile, or 50th percentile, is: Ly = (7 + 1) × 50/100 = 4. When placing the funds' returns in ascending order (3%; 3%; 4%; 5%; 7%; 8%; 12%), the return of the 4th fund is 5%.Alternatively, candidates might realize that the second quartile or 50th percentile is the median. The median is the value of the middle item of a set of items that has been sorted into ascending or descending order. In an odd-numbered sample of n items, the median occupies the ( n + 1)/2 position. Hence, the median return is 5%.

In a parametric test of the correlation between two variables with a sample size of 51 and sample correlation of 0.6, the t-statistic is closest to: A. 0.07. B. 5.25. C. 6.64.

B. 5.25. Correct because for a Parametric Test of a Correlation if the two variables are normally distributed, we can test to determine whether the null hypothesis (H0: ρ = 0) should be rejected using the sample correlation, r. The formula for the t-test is r√(n - 2) / √(1 - r2)" = (0.6)√(51 - 2) / √(1 - 0.36) = (0.6)(7)/0.8 = 5.25.

The annualized return for an investor who has achieved a return of 5% over a six-week period is closest to: A. 43.33%. B. 52.63%. C. 54.24%.

B. 52.63%. Correct. Annualized return is calculated as (1 + 5%)52/6 - 1 = 52.63.

The return measure that best allows one to compare asset returns earned over different length time periods is the: A. holding period return. B. annualized return. C. net portfolio return.

B. annualized return. Correct. The annualized return is an average return measure that can be calculated using return data for a period that is shorter (or longer) than one year. In many cases, it is most convenient to annualize all available returns in order to compare returns when the time periods during which a return is earned or computed vary. It reflects the return that would be earned over a one-year period, assuming that money can be reinvested repeatedly while earning a similar return.

If the relationship between the dependent variable and independent variable is linear, the regression residuals when plotted against the independent value should appear to: A. be linear. B. be random. C. follow a pattern.

B. be random. Correct because when we look at the residuals of a model, what we would like to see is that the residuals are random. The residuals should not exhibit a pattern when plotted against the independent variable.

Question An analyst has established the following prior probabilities regarding a company's next quarter's earnings per share (EPS) exceeding, equaling, or being below the consensus estimate. *EPS exceed consensus- Prior Probabilities 25% *EPS equal consensus - Prior Probabilities 55% *EPS are less than consensus - Prior Probabilities 20% Probabilities the Company Cuts Dividends, Conditional on EPS Exceeding/Equaling/Falling below Consensus *P(Cut div | EPS exceed) -5% *P(Cut div | EPS equal) - 10% *P(Cut div | EPS below) - 85% The analyst thus determines that the unconditional probability for a cut in the dividend, P(Cut div), is equal to 23.75%. Using Bayes' formula, the updated (posterior) probability that the company's EPS are below the consensus is closest to: A. 85%. B. 72%. C. 20%.

B. 72%. (Look at ebook) Correct. Bayes' Formula: Updated probability of event given the new information =Probability of the new information given eventUnconditional probability of the new information×Prior probability of event=Probability of the new information given eventUnconditional probability of the new information×Prior probability of event where Updated probability of event given the new information: P(EPS below | Cut div); Probability of the new information given event: P(Cut div | EPS below) = 85%; Unconditional probably of the new information: P(Cut div) = 23.75%; Prior probability of event: P(EPS below) = 20%. Therefore, the probability of EPS falling below the consensus is updated as: P(EPS below | Cut div) = [P(Cut div | EPS below)/P(Cut div)] × P(EPS below) = (0.85/0.2375) × 0.20 = 0.71579 ~ 72%

An investor purchases one share of stock for $85. Exactly one year later, the company pays a dividend of $2.00 per share. This is followed by two more annual dividends of $2.25 and $2.75 in successive years. Upon receiving the third dividend, the investor sells the share for $100. The money-weighted rate of return on this investment is closest to: A. 7.97%. B. 8.15%. C. 8.63%.

B. 8.15%. (Look at study ebook) Correct. The money-weighted rate of return is the internal rate of return (IRR) of the cash flows associated with the investment. The following figure represents the timeline for the problem: Using the cash flow (CF) function of a financial calculator: CF0 = −85, CF1 = 2, CF2 = 2.25, CF3 = 102.75; and solving for IRR: IRR = 8.15%.

An analyst calculates the following statistics for a sample with 100 observations: *First quartile -Value = 11 *Second quartile -Value = 62 *Third quartile -Value = 93 *Fourth quartile -Value = 359 The interquartile range of the sample is equal to: A. 31. B. 82. C. 348.

B. 82. Correct because the interquartile range (IQR) is the difference between the third quartile and the first quartile, or IQR = Q3 − Q1 " = 93 - 11 = 82. Quartiles divide the distribution into quarters.

An asset earns 13.1% over a 16-month period. The asset's annualized compound rate of return is closest to: A. 9.3%. B. 9.7%. C. 9.8%.

B. 9.7%. Correct because a general equation to annualize returns is given, where c is the number of periods in a year. For a quarter, c = 4 and for a month, c = 12: rannual = (1 + rperiod)c - 1. That is, for 16 months, c = 12/16 = 0.75 and the annualized return is (1 + 0.13100)0.75 - 1 = 1.09672 - 1 = 0.09672 ≈ 9.7%.

For a given dataset with different non-negative observations, which of the following will have the largest value? A. Harmonic mean B. Arithmetic mean C. Geometric mean

B. Arithmetic mean Correct because the arithmetic mean of a given dataset with different observations is higher than the harmonic and geometric means. Unless all the observations in a dataset have the same value, the harmonic mean is less than the geometric mean, which, in turn, is less than the arithmetic mean.

Which of the following test statistics is most appropriate for a hypothesis test concerning the mean difference between two normally distributed populations? A. t-statistic B. F-statistic C. Chi-square statistic

B. F-statistic Correct because for a Test of Mean Differences (Normally Distributed Populations, Unknown Population Variances), when we have data consisting of paired observations from samples generated by normally distributed populations with unknown variances, a t-test is based on t = (d − μd0)/sd, with n − 1 degrees of freedom, where n is the number of paired observations, d is the sample mean difference, and sd is the standard error of d.A. t-statistic

For a positively skewed unimodal distribution, which of the following measures is most accurately described as the largest? A. Median B. Mean C. Mode

B. Mean Correct. For a positively skewed unimodal distribution, the mode is less than the median, which is less than the mean.

An investor currently has a portfolio valued at $700,000. The investor's objective is long-term growth, but she will need $30,000 by the end of the year to pay her son's college tuition and another $10,000 by year-end for her annual vacation. The investor is considering three alternative portfolios: *Portfolio=1 *Expected Return=--- *Standard Deviation of Returns=--- *Safety-First Ratio= 0.2290 *Portfolio=2 *Expected Return=---- *Standard Deviation of Returns=--- *Safety-First Ratio= 0.3300 *Portfolio=3 *Expected Return=14% *Standard Deviation of Returns=22% *Safety-First Ratio= ---- Using Roy's safety-first criterion, which of the alternative portfolios most likely minimizes the probability that the investor's portfolio will have a value lower than $700,000 at year-end? A. Portfolio 1 B. Portfolio 3 C. Portfolio 2

B. Portfolio 3 (Look at ebook question) Correct. The investor requires a minimum return of ($30,000 + $10,000)/$700,000, or 5.71%. Roy's safety-first model uses the excess portfolio's expected return over the minimum return and divides that excess by the standard deviation for that portfolio: Safety-first ratio = [E(RP) − RL]/σP, where E(RP) = the expected return of portfolio P RL = the minimum return required by the investor σP = the standard deviation of returns of portfolio P PortfolioSafety-First Ratio10.229020.33003(14% − 5.71%)/22% = 0.3768 The portfolio with the highest safety-first ratio minimizes the probability that the investor's portfolio will have a value lower than $700,000 at year end.

Quantitative Methonds (262 to 262) * Quantitative Methods: Practice Pack --(90 to 90) Which of the following factors is not used in the calculation of a confidence interval?\ A. Point estimate B. Sampling error C. Reliability factor

B. Sampling error

Which of the following visualizations is most appropriate for interpreting the correlation between two variables? A. Tree-map B. Scatter plot C. Clustered bar chart

B. Scatter plot Correct because scatter plots are a very useful tool for the sensible interpretation of a correlation coefficient. A scatter plot is a type of graph for visualizing the joint variation in two numerical variables. It is a useful tool for displaying and understanding potential relationships between the variables.

Ranked in ascending order, the 19th observation in a sample of 75 is in the second: A. decile. B. quintile. C. quartile.

B. quintile. (Look at study guide ebook) Correct because the 19th observation is located at the 25th percentile;;, which is in the second quintile. The second quintile includes observations that are above the 20th percentile and at or below the 40th percentile.

The minimum rate of return an investor must receive in order to accept an investment is best described as the: A. internal rate of return. B. required rate of return. C. expected return.

B. required rate of return. Correct. The required rate of return is the minimum rate of return an investor must receive in order to accept an investment.

A subset of a population is best described as a: A. statistic. B. sample. C. conditional distribution.

B. sample. Correct because we often need to infer information on a population (all members of a specified group) through samples (part of the population). Hence a sample is a subset of the population.

Samples are drawn from a population that follows a binomial distribution with a probability of success on a trial of 0.3. According to the central limit theorem, as the sample size increases, the distribution of the sample mean approaches a: A. negatively skewed distribution. B. symmetric distribution. C. positively skewed distribution.

B. symmetric distribution. Correct because, according to the central limit theorem, the sampling distribution of the sample mean will be approximately normal when the sample size n is large. The normal distribution has a skewness of 0 (it is symmetric). Since the binomial distribution has a mean of np and finite variance of np(1 - p), where n is the number of trials and p is the probability of success, the central limit theorem holds.

"Big data" is best described as: A. technology-driven innovation in the financial service industry. B. the collection of large quantities of financial data from a variety of sources in multiple formats. C. the use of technical models to describe patterns in financial markets and make trading decisions.

B. the collection of large quantities of financial data from a variety of sources in multiple formats. Correct. The collection of large quantities of data from a variety of sources in multiple formats is the description of big data.

In simple linear regression analysis, the total sum of squares best describes: A. a scatter plot. B. the variation of the dependent variable. C. a paired observation between variables.

B. the variation of the dependent variable. Correct because the variation of Y (the dependent variable) is often referred to as the sum of squares total (SST), or the total sum of squares.

An analyst estimates the probabilities of three possible economic scenarios and the probabilities of a stock having a positive or a negative return in each scenario. These scenarios are best represented by a: A. tree-map. B. tree diagram. C. probability density function.

B. tree diagram. Correct because probabilities for different scenarios and different outcomes are best represented using a tree diagram.

An investor deposits £2,000 into an account that pays 6% per annum compounded continuously. The value of the account at the end of four years is closest to: A. £2,525. B. £2,542. C. £2,854.

B. £2,542. (Look at ebook) Correct. The future value (FV) of a given lump sum, calculated using continuous compounding, is: FV = PVerN = 2,000 × e0.06 × 4 = £2,542.49 ~ £2,542.

A financial contract offers to pay €1,200 per month for five years with the first payment made immediately. Assuming an annual discount rate of 6.5%, compounded monthly, the present value of the contract is closest to: A. €61,330. B. €61,663. C. €63,731.

B. €61,663. (Look at study guide) Correct. Using a financial calculator: N = 60; the discount rate (I/Y) = (6.5%/12) = 0.54166667; PMT = €1,200; Future value = €0; Mode = Begin; Calculate present value (PV): PV = €61,662.62. Alternatively: Treat the stream as an ordinary annuity of 59 periods and add the current value of €1,200 to the derived answer. Using a financial calculator: N = 59; the discount rate (I/Y) = (6.5%/12) = 0.54166667; PMT = €1,200; Future value = €0; Mode = End; Calculate PV: PV = €60,462.62; Total PV = €1,200 + €60,462.62 = €61,662.62.

Over the past four years, a portfolio experienced returns of −8%, 4%, 17%, and −12%. The geometric mean return of the portfolio over the four-year period is closest to: A. 0.25%. B. −0.37%. C. 0.99%.

B. −0.37%. Correct. Add one to each of the given returns, then multiply them together and take the fourth root of the resulting product. 0.92 × 1.04 × 1.17 × 0.88 = 0.985121; 0.985121 raised to the 0.25 power is 0.996259. Subtracting one and multiplying by 100 gives the correct geometric mean return: [(0.92 × 1.04 × 1.17 × 0.88)0.25 − 1] × 100 = −0.37%.

A sample mean is computed from a population with a variance of 2.45. The sample size is 40. The standard error of the sample mean is closest to: A.0.039. B.0.247. C.0.387.

B.0.247. (Look at ebook) is correct. Taking the square root of the known population variance to determine the population standard deviation (σ) results in 𝜎=2.45⎯⎯⎯⎯⎯⎯⎯√=1.565σ=2.45=1.565. The formula for the standard error of the sample mean (σX), based on a known sample size (n), is 𝜎𝑋=𝜎𝑛⎯⎯√σX=σn. Therefore, 𝜎𝑋=1.56540⎯⎯⎯⎯√=0.247σX=1.56540=0.247.

*Statiistical Measures of Asset Returns (18 of 18) Consider the results of an analysis focusing on the market capitalizations of a sample of 100 firms: Exhibit 1: Market Capitalization of a Sample of 100 Firms *Bin 1, 2, 3, ,4 ,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,- 20 -Cumulative percentage of sample (%) 5, 10, ,15, 20, 25, 30, 35, 40 ,45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95,- 100 (Market Capitalization) - - euro billions *Lower Bound = 0.28, 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, 81.62 - 96.85 *Upper Bound = 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, 81.62 - 96.85 -Number of Observations 5 ....... -5 The tenth percentile corresponds to observations in bin(s): A.2. B.1 and 2. C.19 and 20.

B.1 and 2.

A fund had the following experience over the past 10 years: *Year 1 = 4.5% *Year 2 = 6.0% *Year 3 = 1.5% *Year 4 = -2.0% *Year 5 = 0.0% *Year 6 = 4.5% *Year 7 = 3.5% *Year 8 = 2.5% *Year 9 = 5.5% *Year 10 = 4.0% The target semideviation of the returns over the 10 years, if the target is 2 percent, is closest to: A.1.42 percent. B.1.50 percent. C.2.01 percent.

B.1.50 percent. (Look at ebook) B is correct. The target semideviation of the returns over the 10 years with a target of 2 percent is calculated as follows: YearReturnDeviation Squared below Target of 2%14.5% 26.0% 31.5%0.0000254−2.0%0.00160050.0%0.00040064.5% 73.5% 82.5% 95.5% 104.0% Sum 0.002025 The target semideviation is the square root of the sum of the squared deviations from the target, divided by n − 1: sTarget=0.002025(10−1)⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√0.00202510−1= 1.5%

*A fund had the following experience over the past 10 years: *Year 1 = 4.5% *Year 2 = 6.0% *Year 3 = 1.5% *Year 4 = -2.0% *Year 5 = 0.0% *Year 6 = 4.5% *Year 7 = 3.5% *Year 8 = 2.5% *Year 9 = 5.5% *Year 10 = 4.0% The fund's standard deviation of returns over the 10 years is closest to: A.2.40 percent. B.2.53 percent. C.7.58 percent.

B.2.53 percent. (Look at ebook) B is correct. The fund's standard deviation of returns is calculated as follows: YearReturnDeviation from MeanDeviation Squared14.5%0.01500.00022526.0%0.03000.00090031.5%−0.01500.0002254−2.0%−0.05000.00250050.0%−0.03000.00090064.5%0.01500.00022573.5%0.00500.00002582.5%−0.00500.00002595.5%0.02500.000625104.0%0.01000.000100Mean3.0% Sum 0.005750 The standard deviation is the square root of the sum of the squared deviations, divided by n − 1: 𝑠=0.005750(10−1)⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√s=0.00575010−1= 2.5276%.

An analyst has estimated a model that regresses a company's return on equity (ROE) against its growth opportunities (GO), defined as the company's three-year compounded annual growth rate in sales, over 20 years, and produces the following estimated simple linear regression: ROEi = 4 + 1.8 GOi + εi. Both variables are stated in percentages, so a GO observation of 5 percent is included as 5. Question Q. The residual in the case of a GO of 8 percent and an observed ROE of 21 percent is closest to: A.−1.8 percent. B.2.6 percent. C.12.0 percent.

B.2.6 percent. B is correct. The predicted value is ROE = 4 + (1.8 × 8) = 18.4. The observed value of ROE is 21, so the residual is 2.6 = 21.0 − 18.4.

Consider the results of an analysis focusing on the market capitalizations of a sample of 100 firms: Exhibit 1: Market Capitalization of a Sample of 100 Firms *Bin 1, 2, 3, ,4 ,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,- 20 -Cumulative percentage of sample (%) 5, 10, ,15, 20, 25, 30, 35, 40 ,45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95,- 100 (Market Capitalization) - - euro billions *Lower Bound = 0.28, 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, - 81.62 *Upper Bound = 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, 81.62 - 96.85 -Number of Observations 5 ....... -5 Q. The interquartile range is closest to: A.20.76. B.23.62. C.25.52.

B.23.62. B is correct. The interquartile range is the difference between the lowest value in the second quartile and the highest value in the third quartile. The lowest value of the second quartile is 34.72, and the highest value of the third quartile is 58.34. Therefore, the interquartile range is 58.34 − 34.72 = 23.62.

Exhibit 12 shows the annual MSCI World Index total returns for a 10-year period. Exhibit 1: MSCI World Index Returns *Year 1 = 15.25% *Year 2 = 10.02% *Year 3 = 20.65% *Year 4 = 9.57% *Year 5 = -40.33% *Year 6 = 30.79% *Year 7 = 12.34% *Year 8 = -5.02% *Year 9 = 16.54% *Year 10 = 27.37% The fourth quintile return for the MSCI World Index is closest to: A.20.65 percent. B.26.03 percent. C.27.37 percent.

B.26.03 percent. (Look at ebook) B is correct. Quintiles divide a distribution into fifths, with the fourth quintile occurring at the point at which 80 percent of the observations lie below it. The fourth quintile is equivalent to the 80th percentile. To find the yth percentile (Py), we first must determine its location. The formula for the location (Ly) of a yth percentile in an array with n entries sorted in ascending order is Ly = (n + 1) × (y/100). In this case, n = 10 and y = 80%, so L80= (10 + 1) × (80/100) = 11 × 0.8 = 8.8. With the data arranged in ascending order (−40.33 percent, −5.02 percent, 9.57 percent, 10.02 percent, 12.34 percent, 15.25 percent, 16.54 percent, 20.65 percent, 27.37 percent, and 30.79 percent), the 8.8th position would be between the eighth and ninth entries, 20.65 percent and 27.37 percent, respectively. Using linear interpolation, P80 = X8 + (Ly − 8) × (X9 − X8), P80= 20.65 + (8.8 − 8) × (27.37 − 20.65)= 20.65 + (0.8 × 6.72) = 20.65 + 5.38= 26.03 percent.

Consider the results of an analysis focusing on the market capitalizations of a sample of 100 firms: Exhibit 1: Market Capitalization of a Sample of 100 Firms *Bin 1, 2, 3, ,4 ,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,- 20 -Cumulative percentage of sample (%) 5, 10, ,15, 20, 25, 30, 35, 40 ,45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95,- 100 (Market Capitalization) - - euro billions *Lower Bound = 0.28, 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, - 81.62 *Upper Bound = 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, 81.62 - 96.85 -Number of Observations 5 ....... -5 The median is closest to: A.44.86. B.46.88. C.49.40.

B.46.88. B is correct. The center of the 20 bins is represented by the market capitalization of the highest value of the 10th bin and the lowest value of the 11th bin, which is 46.88.

Consider the results of an analysis focusing on the market capitalizations of a sample of 100 firms: Exhibit 1: Market Capitalization of a Sample of 100 Firms *Bin 1, 2, 3, ,4 ,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,- 20 -Cumulative percentage of sample (%) 5, 10, ,15, 20, 25, 30, 35, 40 ,45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95,- 100 (Market Capitalization) - - euro billions *Lower Bound = 0.28, 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, - 81.62 *Upper Bound = 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, 81.62 - 96.85 -Number of Observations 5 ....... -5 The second quintile corresponds to observations in bin(s): A.8. B.5, 6, 7, and 8. C.6, 7, 8, 9, and 10.

B.5, 6, 7, and 8. B is correct. The second quintile corresponds to the second 20 percent of observations. The first 20 percent consists of bins 1 through 4. The second 20 percent of observations consists of bins 5 through 8.

A investor in Abco stock forecasts the probability that Abco exceeded, met, or fell short of consensus expectations for free cash flow (FCF) during the prior quarter: P(FCF exceeded consensus) = 0.50 P(FCF met consensus) = 0.35 P(FCF fell short of consensus) = 0.15 While waiting for Abco to release last quarter's FCF data, the investor learns Abco will acquire a competitor. Believing that the upcoming acquisition makes it more likely that last quarter's FCF will exceed the consensus, the investor generates a list of FCF events that may have influenced the acquisition: P(Acquisition | FCF exceeded consensus) = 0.40 P(Acquisition | FCF met consensus) = 0.25 P(Acquisition | FCF fell short of consensus) = 0.35 Bayes' Formula, calculate the probability that Abco is likely to exceed consensus FCF expectations for last quarter given the acquisition. P(FCF exceeded consensus | Acquisition) is closest to: A.34%. B.59%. C.27%.

B.59%. (Look at ebook) Correct. The updated probability P(FCF exceeded consensus | Acquisition) is 59%. Calculate the unconditional probability that Abco will acquire the competitor firm:P(Acquisition) = (0.50 × 0.40) + (0.35 × 0.25) + (0.15 × 0.35) = 0.34, or 34%. Calculate the updated probability that Abco exceeded consensus expectations for FCF given that they acquire the competitor firm: P(FCF exceeded consensus | Acquisition) = [P(Acquisition | FCF exceeded consensus)/P(Acquisition)] × P(FCF exceeded consensus) = (0.40/0.34) × (0.50) = 0.59 or 59%.

Which of the following statements regarding the null hypothesis is correct? A.It can be stated as "not equal to" provided the alternative hypothesis is stated as "equal to." B.Along with the alternative hypothesis, it considers all possible values of the population parameter. C.In a two-tailed test, it is rejected when evidence supports equality between the hypothesized value and the population parameter.

B.Along with the alternative hypothesis, it considers all possible values of the population parameter. B is correct. The null and alternative hypotheses are complements of one another and must be both mutually and collectively exhaustive. Differently put: all possible values or outcomes need to be contained in either the null or the alternative hypothesis. A is incorrect because the null hypothesis must always include the equality sign (less than or equal to, equal to, or greater than or equal to). C is incorrect because, in a two-tailed test, the null hypothesis is generally set up as equality between the hypothesized value and the population parameter. If evidence supports equality, then the null hypothesis would not be rejected.B.Along with the alternative hypothesis, it considers all possible values of the population parameter.

An investor is evaluating the returns of three recently formed ETFs. Selected return information on the ETFs is presented in Exhibit 20: Exhibit 1: Returns on ETFs ETF = 1 *Time Since Inception = 125 days -Return Since Inception (%) = 4.25 ETF = 2 *Time Since Inception = 8 weeks -Return Since Inception (%) = 1.95 ETF = 3 *Time Since Inception = 16 months -Return Since Inception (%) = 17.18 Which ETF has the highest annualized rate of return? A.ETF 1 B.ETF 2 C.ETF 3

B.ETF 2 (Look at study guide) The annualized rate of return for ETF 1 annualized return = (1.0425365/125) - 1 = 12.92%ETF 2 annualized return = (1.019552/8) − 1 = 13.37%ETF 3 annualized return = (1.171812/16) - 1 = 12.63% Despite having the lowest value for the periodic rate, ETF 2 has the highest annualized rate of return because of the reinvestment rate assumption and the compounding of the periodic rate.

Which of the following tests should be used to test the difference between the variances of two normally distributed populations with random independent samples? A.t-test B.F-test C.Paired comparisons test

B.F-test B is correct. An F-test is used to conduct tests concerning the difference between the variances of two normally distributed populations with random independent samples.

*Hypothesis Testing (28 of 28) Q. An analyst suspects that, in the most recent year, excess returns on stocks have fallen below 5%. She wants to study whether the excess returns are less than 5%. Designating the population mean as μ, which hypotheses are most appropriate for her analysis? A.H0: µ = 5% versus Ha: µ ≠ 5% B.H0: µ> 5% versus Ha: µ < 5% C.H0: µ< 5% versus Ha: µ > 5%

B.H0: µ> 5% versus Ha: µ < 5% B is correct. The null hypothesis is what she wants to reject in favor of the alternative, which is that population mean excess return is less than 5%. This is a one-sided (left-side) alternative hypothesis.

An analyst observes the benchmark Indian NIFTY 50 stock index trading at a forward price-to-earnings ratio of 15. The index's expected dividend payout ratio in the next year is 50 percent, and the index's required return is 7.50 percent. If the analyst believes that the NIFTY 50 index dividends will grow at a constant rate of 4.50 percent in the future, which of the following statements is correct? A.The analyst should view the NIFTY 50 as overpriced. B.The analyst should view the NIFTY 50 as underpriced. C.The analyst should view the NIFTY 50 as fairly priced.

B.The analyst should view the NIFTY 50 as underpriced. (Look at study ebook) B is correct. Using Equation 24, the previous input results in the following inequality: 15<0.500.075−0.045=16.6715<0.500.075−0.045=16.67. The above inequality implies that the analyst should view the NIFTY 50 as priced too low. The fundamental inputs into the equation imply a forward price to earnings ratio of 16.67 rather than 15. An alternative approach to answering the question would be to solve for implied growth using the observed forward price to earnings ratio of 15 and compare this to the analyst's growth expectations: 15=0.500.075−𝑔15=0.500.075−g. Solving for g yields a result of 4.1667 percent. Since the analyst expects higher NIFTY 50 dividend growth of 4.50 percent, the index is viewed as underpriced.

Which of the following statements regarding arithmetic and geometric means is correct? A.The geometric mean will exceed the arithmetic mean for a series with non-zero variance. B.The geometric mean measures an investment's compound rate of growth over multiple periods. C.The arithmetic mean measures an investment's terminal value over multiple periods.

B.The geometric mean measures an investment's compound rate of growth over multiple periods. B is correct. The geometric mean compounds the periodic returns of every period, giving the investor a more accurate measure of the terminal value of an investment.

An analyst is examining the monthly returns for two funds over one year. Both funds' returns are non-normally distributed. To test whether the mean return of one fund is greater than the mean return of the other fund, the analyst can use: A.a parametric test only. B.a nonparametric test only. C.both parametric and nonparametric tests.

B.a nonparametric test only. B is correct. There are only 12 (monthly) observations over the one year of the sample and thus the samples are small. Additionally, the funds' returns are non-normally distributed. Therefore, the samples do not meet the distributional assumptions for a parametric test. The Mann-Whitney U test (a nonparametric test) could be used to test the differences between population means.

In contrast to normal distributions, lognormal distributions: A.are skewed to the left. B.have outcomes that cannot be negative. C.are more suitable for describing asset returns than asset prices.

B.have outcomes that cannot be negative. B is correct. By definition, lognormal random variables cannot have negative values (bounded below by 0) and have distributions that are skewed to the right.

With respect to simple linear regression, a residual is best described as the difference between the observed value of a dependent variable and: A. its mean. B. its estimated value using a fitted regression line based on the sample. C. its expected value based on the true underlying population relationship.

B.its estimated value using a fitted regression line based on the sample. Correct because the residual for the ith observation, ei, is how much the observed value of Yi differs from the estimated [value] using the regression line. Further, the residual refers to the fitted linear relation based on the sample.

A fund had the following experience over the past 10 years: *Year 1 = 4.5% *Year 2 = 6.0% *Year 3 = 1.5% *Year 4 = -2.0% *Year 5 = 0.0% *Year 6 = 4.5% *Year 7 = 3.5% *Year 8 = 2.5% *Year 9 = 5.5% *Year 10 = 4.0% Consider the mean monthly return and the standard deviation for three industry sectors, as shown in Exhibit 2: (Look at ebook) Based on the coefficient of variation (CV), the riskiest sector is: A.utilities. B.materials. C.industrials.

B.materials. B is correct. The CV is the ratio of the standard deviation to the mean, where a higher CV implies greater risk per unit of return. CV𝑈𝑇𝐼𝐿=𝑠𝑋⎯⎯⎯=1.23%2.10%=0.59CVUTIL=sX¯=1.23%2.10%=0.59,CV𝑀𝐴𝑇𝑅=𝑠𝑋⎯⎯⎯=1.35%1.25%=1.08CVMATR=sX¯=1.35%1.25%=1.08,CV𝐼𝑁𝐷𝑈=𝑠𝑋⎯⎯⎯=1.52%3.01%=0.51CVINDU=sX¯=1.52%3.01%=0.51

The probability of correctly rejecting the null hypothesis is the: A.p-value. B.power of a test. C.level of significance

B.power of a test.

The power of a hypothesis test is: A.equivalent to the level of significance. B.the probability of not making a Type II error. C.unchanged by increasing a small sample size.

B.the probability of not making a Type II error. B is correct. The power of a hypothesis test is the probability of correctly rejecting the null when it is false. Failing to reject the null when it is false is a Type II error. Thus, the power of a hypothesis test is the probability of not committing a Type II error.

Samples of size (n1,n2) are drawn respectively from two populations (X1,X2) with associated sample means and standard deviations of (𝑋⎯⎯⎯1,𝑋⎯⎯⎯2)(X¯1,X¯2) and (s1,s2) and associated population means and standard deviations of (μ1,μ2) and (σ1,σ2) where σ1 ≠ σ2. In addition, 𝑑⎯⎯d¯ is the sample mean of X1 − X2 with a standard error of 𝑠𝑑⎯⎯sd¯ and a population mean of μd0 and 𝑠2𝑝sp2 is a pooled estimator of the common variance. The most appropriate test statistic to determine the equality of the two population means assuming X1 and X2 are independent and normally distributed is: A. 𝑡=𝑑⎯⎯−𝜇𝑑0𝑠𝑑⎯⎯⎯t=d¯−μd0sd¯ B. 𝑡=(𝑋⎯⎯⎯⎯1−𝑋⎯⎯⎯⎯2)−(𝜇1−𝜇2)(𝑠2𝑝𝑛1+𝑠2𝑝𝑛2)0.5t=(X¯1−X¯2)−(μ1−μ2)(sp2n1+sp2n2)0.5 C. 𝑡=(𝑋⎯⎯⎯⎯1−𝑋⎯⎯⎯⎯2)−(𝜇1−𝜇2)(𝑠21𝑛1+𝑠22𝑛2)0.5

C. (Look at ebook) Correct. The most appropriate test statistic for the difference between two population means (unequal and unknown population variances) is 𝑡=(𝑋⎯⎯⎯⎯1−𝑋⎯⎯⎯⎯2)−(𝜇1−𝜇2)(𝑠21𝑛1+𝑠22𝑛2)0.5t=(X¯1−X¯2)−(μ1−μ2)(s12n1+s22n2)0.5 Hypothesis Testing • construct hypothesis tests and determine their statistical significance, the associated Type I and Type II errors, and power of the test given a significance level

A tree diagram contains the following information about the dividend per share payable by a company under two scenarios: *Scenario (Favorable) -Probability of Scenario = 0.60 -Dividend per Share = $2.00 , $1.25 -Probability of Dividend = 0.80 , 0.20 *Scenario (Unfavorable) -Probability of Scenario = 0.40 -Dividend per Share = $0.75 , $0.50 -Probability of Dividend = 0.30 , 0.70 The expected dividend per share under the favorable scenario is closest to: A. $1.14. B. $1.37. C. $1.90.

C. $1.90. (Look at ebook) Correct because the expected value of a random variable X given an event or scenario S is denoted E(X | S). Suppose the random variable X can take on any one of n distinct outcomes X1, X2, ..., Xn (these outcomes form a set of mutually exclusive and exhaustive events). The expected value of X conditional on S is the first outcome, X1, times the probability of the first outcome given S, P(X1 | S), plus the second outcome, X2, times the probability of the second outcome given S, P(X2 | S), and so forth. In our case, S = Favorable scenario, X1 = Dividend of $2.50, X2 = Dividend of $1.50, P(X1 | S) = 0.80, and P(X2 | S) = 0.20. Thus, the expected dividend given the favorable scenario = (0.80 × $2.00) + (0.20 × $1.50) = $1.90. Probability Trees and Conditional Expectations formulate an investment problem as a probability tree and explain the use of conditional expectations in investment application

An investment in 10,000 common shares of a company for one year earned a 15.5% return. The investor received a $2,500 dividend just prior to the sale of the shares at $24 per share. The price that the investor paid for each share one year earlier was closest to: A. $20.80. B. $20.50. C. $21.00

C. $21.00 (Look at ebook) Correct. Holding period return, HPR = (P1 − P0 + D1)/P0where P0 = initial investment P1 = price received at the end of holding period D1 = dividend paid by the investment at the end of holding period = $2,500/10,000 shares = $0.25/shares 0.155 = (24 − P0 + 0.25)/P0, and solving for P0 P0 = $20.99 ~ $21.00 Rates and Returns • calculate and interpret major return measures and describe their appropriate uses

Using a discount rate of 5%, compounded monthly, the present value (PV) of $5,000 to be received three years from today is closest to: A. $4,250. B. $4,319. C. $4,305.

C. $4,305. (Look at ebook) Correct. PV = FVN(1 + rs/m)−mN. In this case, PV = $5,000(1 + 0.05/12)(−12×3) = $4,304.88. Using a financial calculator: FV = $5,000, N = 36, I/Y = 5/12, PMT = 0, and solve for PV. Rates and Returns • calculate and interpret annualized return measures and continuously compounded returns, and describe their appropriate uses

Independent samples drawn from normally distributed populations exhibit the following characteristics: *Sample Size = 25 -Sample Mean = 200 Standard Deviation = 45 *Sample Size = 18 -Sample Mean = 185 Standard Deviation = 60 Assuming that the variances of the underlying populations are equal, the pooled estimate of the common variance is 2,678.05. The t-test statistic appropriate to test the hypothesis that the two population means are equal is closest to: A. 1.90. B. 0.29. C. 0.94.

C. 0.94. (Look at ebook question) Correct. The t-statistic for the given information (normally distributed populations, population variances assumed equal) is calculated as: 𝑡=(𝑥⎯⎯1−𝑥⎯⎯2)−(𝜇1−𝜇2)(𝑠2𝑝𝑛1+𝑠2𝑝𝑛2)0.5t=(x¯1−x¯2)−(μ1−μ2)(sp2n1+sp2n2)0.5 In this case we have: 𝑠2𝑝sp2 = 2678.05 𝑡=(200−185)−(0)(2678.0525+2678.0518)0.5t=(200−185)−(0)(2678.0525+2678.0518)0.5 = 0.93768 ~ 0.94 Hypothesis Testing • construct hypothesis tests and determine their statistical significance, the associated Type I and Type II errors, and power of the test given a significance level

A risk manager would like to calculate the coefficient of variation of a portfolio. The following table reports the annual returns of the portfolio and of the risk-free rate over the most recent five years: Year 1 *Portfolio Return = 4.0% -Risk-Free Rate = 2.0% Year 2 *Portfolio Return = -1.0% -Risk-Free Rate = 1.5% Year 3 *Portfolio Return = 7.0% -Risk-Free Rate = 1.0% Year 4 *Portfolio Return = 11.0% -Risk-Free Rate = 1.0% Year 5 *Portfolio Return = 2.0% -Risk-Free Rate = 0.5% The coefficient of variation of the portfolio is closest to: A. 0.74. B. 0.90. C. 1.00.

C. 1.00. (Look at ebook) Correct. First calculate the sample mean return as follows:𝑋⎯⎯⎯=∑𝑖=1𝑛𝑋𝑖𝑛X¯=∑i=1nXin where n = the number of observations in the sample i = the index for the year Xi = is the return in year i 𝑋⎯⎯⎯=(4.0%−1.0%+7.0%+11.0%+2.0%)5=23.0%5=4.6%X¯=(4.0%−1.0%+7.0%+11.0%+2.0%)5=23.0%5=4.6% Then calculate the sample standard deviation with the following formula: 𝑠=∑𝑖=1𝑛(𝑋𝑖−𝑋⎯⎯⎯⎯)2𝑛−1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√s=∑i=1n(Xi−X¯)2n−1 Year(𝑋𝑖−𝑋⎯⎯⎯)2(Xi−X¯)21(4.0% − 4.6%)2 = 0.000042(−1.0% − 4.6%)2 = 0.003143(7.0% − 4.6%)2 = 0.000584(11.0% − 4.6%)2 = 0.004105(2.0% − 4.6%)2 = 0.00068 s = 0.00004+0.00314+0.00058+0.00410+0.000685−1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√0.00004+0.00314+0.00058+0.00410+0.000685−1 = 4.62% The coefficient of variation (CV) is calculated with the following formula: CV = 𝑠𝑋⎯⎯⎯⎯=4.62%4.6%sX¯=4.62%4.6% = 1.0 Statistical Measures of Asset Returns • calculate, interpret, and evaluate measures of dispersion to address an investment problem

An investor purchases a stock for $100. Immediately after receiving a dividend of $7, the investor sells the stock for $107. The holding period return of the investment is closest to: A. 0% B. 7%. C. 14%.

C. 14% Correct because a holding period return is the return earned from holding an asset for a single specified period of time. This return can be generalized and shown as a mathematical expression in which P is the price and I is the income: R = (P1 − P0 + D1)/P0 Thus, R = ($107 - $100 + $7)/$100 = $14/$100 = 14%. Quantitative Methods calculate and interpret major return measures and describe their appropriate uses

An analyst produces the following joint probability function for the returns on two companies, X and Y: *Return of X = 20% -Return of Y = 15% ---- 0.2 --Return of Y = 10% ---- 0 ---Return of Y = 5% ---- 0 *Return of X = 15% -Return of Y = 15% ---- 0 --Return of Y = 10% ---- 0.4 ---Return of Y = 5% ---- 0 *Return of X = 20% -Return of Y = 15% ----- 0 --Return of Y = 10% ---- 0 ---Return of Y = 5% ---- 0.4 The expected returns of companies X and Y are 14% and 9%, respectively. The covariance of returns between X and Y (in percent squared) is closest to: A. 0. B. 5. C. 14.

C. 14. (Look at ebook) Correct because the formula for calculating the covariance between random variables RA and RB is Cov(RA,RB) = ΣΣP(RA,i,RB,j)(RA,i - E[RA])(RB,j - E[RB]). The expected return (given) for each company is: E[RX] = 0.2(20) + 0.4(15) + 0.4(10) = 4 + 6 + 4 = 14, E[RY] = 0.2(15) + 0.4(10) + 0.4(5) = 3 + 4 + 2 = 9. Hence, Cov(RX,RY) = 0.2(20 - 14)(15 - 9) + 0.4(15 - 14)(10 - 9) + 0.4(10 - 14)(5 - 9) = 0.2(6)(6) + 0.4(1)(1) + 0.4(-4)(-4) = 7.2 + 0.4 + 6.4 = 14. Quantitative Methods calculate and interpret the covariance and correlation of portfolio returns using a joint probability function for returns

An investor considers the following certificates of deposit (CDs) available for purchase at face value: *CD = 1 Interest Rate = 2.2% *CD = 2 Interest Rate = 3.3% *CD = 3 Interest Rate = 4.4% If each CD has the same maturity and default risk, the opportunity cost of investing in CD 1 is closest to: A. 0.0%. B. 1.1%. C. 2.2%.

C. 2.2%. Correct because all three securities have the same maturity and default risk so the investor is forgoing 2.2% (4.4% - 2.2%) by investing in CD 1 rather than investing in CD 3. Quantitative Methods interpret interest rates as required rates of return, discount rates, or opportunity costs and explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk

Consider a Swiss Confederation zero-coupon bond with a par value of CHF100, a remaining time to maturity of 12 years and a price of CHF89. In three years' time, the bond is expected to have a price of CHF95.25. If purchased today, the bond's expected annualized return is closest to: A.0.58 percent. B.1.64 percent. C.2.29 percent.

C. 2.29 percent. C is correct. The FV of the bond is CHF95.25, the PV is CHF89, and the number of annual periods (t) is 3. Using Equation 18, 2.29 percent = (92.25/89)(1/3)− 1. A is incorrect as the result is derived using t of 12. B is incorrect as this result is derived using a PV of CHF95.25 and an FV of 100.

An investor is considering buying a US T-bill. If the real risk-free rate is 1% and the inflation premium is 2%, the investor's opportunity cost of failing to make this investment is closest to: A. 1%. B. 2%. C. 3%.

C. 3%. Correct because interest rates can be considered opportunity costs. The real risk-free interest rate is the single-period interest rate for a completely risk-free security if no inflation were expected. In economic theory, the real risk-free rate reflects the time preferences of individuals for current versus future real consumption. The sum of the real risk-free interest rate and the inflation premium is the nominal risk-free interest rate. Many countries have governmental short-term debt whose interest rate can be considered to represent the nominal risk-free interest rate in that country. The interest rate on a 90-day US Treasury bill (T-bill), for example, represents the nominal risk-free interest rate over that time horizon. Therefore, the opportunity cost of this investment is 1% + 2% = 3%. Quantitative Methods interpret interest rates as required rates of return, discount rates, or opportunity costs and explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk

An investor records the following information and transactions for a stock: *Year 1 -Price per Share at Beginning of Year = $100 ^^Cash Flow at Beginning of Year = $100 used to purchase one share *Year 2 -Price per Share at Beginning of Year = $100 ^^Cash Flow at Beginning of Year = $9 used to purchase one share = $9 received in dividends and not invested *Year 3 -Price per Share at Beginning of Year = $100 ^^Cash Flow at Beginning of Year = $100 received from selling one share The investor's money-weighted rate of return is closest to: A. 4.4%. B. 4.5%. C. 4.6%.

C. 4.6%. Correct because it is the money-weighted return when the dividend is not reinvested. Calculator solution: CF0 = -100, CF1 = 9, CF2 = 100, compute IRR = 4.601% ≈ 4.6%. Quantitative Methods compare the money-weighted and time-weighted rates of return and evaluate the performance of portfolios based on these measures

An analyst observes that the historic geometric nominal return for equities is 9%. Given a real return of 1% for riskless Treasury bills and annual inflation of 2%, the real rate of return and risk premium for equities are closest to: A. 7.9% and 5.8%. B. 6.9% and 7.9%. C. 6.9% and 5.8%.

C. 6.9% and 5.8%. Correct. (1 + nominal return on risky asset) = (1 + real return on risky asset)(1 + inflation premium) Therefore, [(1 + 0.09)/(1 + 0.02)] - 1 = 6.9% real return on risky asset. (1 + real return on risky asset) = (1 + real risk-free rate)(1 + risk premium) Therefore, [(1 + 0.69)/(1 + 0.01)] - 1 = 5.8% risk premium. Rates and Returns • calculate and interpret major return measures and describe their appropriate uses

Mylandia Corporation stock trades at CAD60.00. The company pays an annual dividend to its shareholders, and its most recent payment of CAD2.40 occurred yesterday. Analysts following Mylandia expect the company's dividend to grow at a constant rate of 3 percent per year. Mylandia's required return is: A.8.00 percent. B.7.00 percent. C.7.12 percent.

C. 7.12 percent. C is correct. We may solve for required return based upon the assumption of constant dividend growth using Equation 21: 𝑟=2.40(1.03)60+0.03=0.0712r=2.401.0360+0.03=0.0712. B is incorrect as 7.00 percent is the result if we use the previous dividend of CAD2.40 instead of the next expected dividend. A is incorrect as 8.00 percent is simply the required return assumed from one of the Mylandia examples in Question Set 1 in which the price is solved to be a lower value.

The 15-month holding period return for a security is 12%. Its annualized return is closest to: A. 10.03%. B. 9.60%. C. 9.49%.

C. 9.49%. Correct. (1 + 0.12)12/15 - 1 = 9.49% Rates and Returns • calculate and interpret major return measures and describe their appropriate uses

Which of the following errors would most likely be a result of overfitting a machine learning model? A. Inability to recognize relationships within the training data B. A predictive model that treats true parameters as if they are noise C. The discovery of unsubstantiated patterns that lead to prediction errors

C. C. The discovery of unsubstantiated patterns that lead to prediction errors Correct. Overfitting a model can lead to the discovery of unsubstantiated patterns that lead to prediction errors and incorrect output forecasts.

Which of the following measures best quantifies the amount of risk per unit of mean return? A. Sharpe ratio B. Standard deviation C. Coefficient of variation

C. Coefficient of variation Correct because the coefficient of variation, CV, is the ratio of the standard deviation of a set of observations to their mean value. When the observations are returns, for example, the coefficient of variation measures the amount of risk (standard deviation) per unit of mean return.

In hypothesis testing, which of the following best describes a Type II error? A. Rejecting a true null hypothesis B. Rejecting a false null hypothesis C. Failure to reject a false null hypothesis

C. Failure to reject a false null hypothesis Correct because, when we make a decision in a hypothesis test, we run the risk of making either a Type I or a Type II error. These are mutually exclusive errors: If we mistakenly reject the null hypothesis, we can only be making a Type I error; if we mistakenly fail to reject the null, we can only be making a Type II error.

If you require an 8 percent return and must invest USD500,000, which of the investment opportunities in Exhibit 1 should you prefer? Investment Opportunities *Cash Flows (in thousands) t=0, Opportunity 1 (t=0) = -500, (t=1) = 195, (t=2) = 195, (t=3) = 195 Opportunity 2 (t=0) = -500, (t=1) = 225, (t=2) = 195, (t=3) = 160.008 A. Opportunity 1 B. Opportunity 2 C. Indifferent between the two opportunities.

C. Indifferent between the two opportunities. C is correct. Using cash flow additivity, compare the two opportunities by subtracting Opportunity 2 from Opportunity 1 yielding the following cash flows: Opportunity 1 - Opportunity 20−30034.992 Finding the present value of the above cash flows at 8 percent discount rate shows that both investment opportunities have the same present value. Thus, the two opportunities are economically identical, and there is no clear preference for one over the other.

Which of the following is most likely used to detect sentiment shifts in an analyst's commentary? A. Tokenization B. Data curation C. Natural language processing

C. Natural language processing Correct because NLP [natural language processing] may be used to monitor analyst commentary to aid investment decision making. Since analysts tend not to change their buy, hold, and sell recommendations for a company frequently, they may instead offer nuanced commentary without making a change in their investment recommendation. NLP can, therefore, be used to detect, monitor, and tag shifts in sentiment, potentially ahead of an analyst's recommendation change. Quantitative Methods describe applications of Big Data and Data Science to investment management

A Type I error is best described as the probability of: A. failing to reject a false null hypothesis. B. rejecting a true alternative hypothesis. C.rejecting a true null hypothesis.

C.rejecting a true null hypothesis. Correct. A Type I error is the mistake of rejecting the null hypothesis when it is, in fact, true. Hypothesis Testing • explain hypothesis testing and its components, including statistical significance, Type I and Type II errors, and the power of a test.

A portfolio manager will invest €100,000 and is presented with the following information about three portfolios with normally distributed returns: *Portfolio 1 -Expected Annual Return = 23% --Standard Deviation of Returns = 15% *Portfolio 2 -Expected Annual Return = 12% --Standard Deviation of Returns = 6% *Portfolio 3 -Expected Annual Return = 15% --Standard Deviation of Returns = 8% If the manager wants to withdraw €5,000 in one year without invading initial capital, the safety-first optimal portfolio is: A. Portfolio 1. B. Portfolio 2. C. Portfolio 3.

C. Portfolio 3. (Look at Ebook question) Correct because if returns are normally distributed, the safety-first optimal portfolio maximizes the safety-first ratio. SFRatio = [E(RP) - RL] / σP, where E(RP) is the expected portfolio return, RL is the investor's minimum acceptable return, and σP is the standard deviation of portfolio returns. The minimum acceptable return is 5% (= €5,000 / €100,000) as the investor needs to withdraw €5,000 without invading initial capital; SFP1 = (23% - 5%) / 15% = 1.20; SFP2 = (12% - 5%) / 6% ≈ 1.17; SFP3 = (15% - 5%) / 8% = 1.25. Therefore, Portfolio 3 is the safety-first optimal portfolio. "The portfolio for which E(RP) − RL is largest relative to standard deviation minimizes P(RP < RL). Quantitative Methods define shortfall risk, calculate the safety-first ratio, and identify an optimal portfolio using Roy's safety-first criterion

Which of the following is most likely an advantage of traditional financial advisers over fully automated digital wealth managers? A. Lower account minimums B. Dividend reinvestment options C. Solutions that better address the needs of complex portfolios

C. Solutions that better address the needs of complex portfolios Correct because as the complexity and size of an investor's portfolio grows, robo-advisers may not be able to sufficiently address the particular preferences and needs of the investor. In the case of extremely affluent investors who may own a greater number of asset types—including alternative investments (e.g., venture capital, private equity, hedge funds, and real estate)—in addition to global stocks and bonds and have greater demands for customization, the need for a team of human advisers, each with particular areas of investment or wealth-management expertise, is likely to endure. Quantitative Methods describe Big Data, artificial intelligence, and machine learning

A mutual fund manager wants to create a fund based on a high-grade corporate bond index. She first distinguishes between utility bonds and industrial bonds; she then, for each segment, defines maturity intervals of less than 5 years, 5 to 10 years, and greater than 10 years. For each segment and maturity level, she classifies the bonds as callable or noncallable. She then randomly selects bonds from each of the subpopulations she has created. For the manager's sample, which of the following best describes the sampling approach? A. Simple random B. Systematic C. Stratified random

C. Stratified random Correct. In stratified random sampling, one divides the population into subpopulations and randomly samples from within the subpopulations. Estimation and Inference • compare and contrast simple random, stratified random, cluster, convenience, and judgmental sampling and their implications for sampling error in an investment problem

Investor A and Investor B invest in a fund for two years: Fund Return *Year 1 = Positive *Year 2 = Negative Portfolio -Investor A *Money-Weighted Rate of Return = 7.5% Portfolio -Investor B *Money-Weighted Rate of Return = 8.2% Given the information in the table, which of the following is least likely to be an explanation for the difference between the two money-weighted rates of return? A. Investor A increased the investment in the fund at the end of year 1 whereas investor B did not make any additions or withdrawals. B. Investor B decreased the investment in the fund at the end of year 1 whereas investor A did not make any additions or withdrawals. C. The investors invested different amounts at inception and afterward did not make any additions or withdrawals.

C. The investors invested different amounts at inception and afterward did not make any additions or withdrawals. Correct. The money-weighted rate of return (MWR) is sensitive to the additions and withdrawals of funds in a portfolio over the course of an investment. If, at inception, investors A and B invest amounts of different size in the same fund but then neither add nor withdraw any cash for two years, they will obtain exactly the same MWR. In contrast, if investor A increases the investment in the fund at the end of year 1 and investor B does not make any additions or withdrawals, then Investor A will have a lower MWR than investor B because in year 2 the fund underperformed with respect to year 1. By the same token, if investor B decreases the investment at the end of year 1 and investor A does not make any additions or withdrawals, then investor B will have a higher MWR than investor A because she decreased the investment before an underperforming year. Rates and Returns • compare the money-weighted and time-weighted rates of return and evaluate the performance of portfolios based on these measures

Kenneth , CFA, is a challenging interviewer. Last year, handed each job applicant a paper w/the info in Exhibit 1, & he asked several questions about regression analysis. Some of McCoin's questions, along with a sample of answers he received to each, are given below. McCoin told the applicants that independent variable is the ratio of net income to sales for restaurants w/a market cap of more than $100 million & the dependent variable is the ratio of cash flow from operations to sales for those restaurants. Which of the choices provided is the best answer to each of McCoin's questions? Is the relationship between the ratio of cash flow to operations and the ratio of net income to sales significant at the 0.05 level? A.No, because the R2 is greater than 0.05 B.No, because the p-values of the intercept and slope are less than 0.05 C.Yes, because the p-values for F and t for the slope coefficient are less than 0.05

C. Yes, because the p-values for F and t for the slope coefficient are less than 0.05 C is correct. The p-value is the smallest level of significance at which the null hypotheses concerning the slope coefficient can be rejected. In this case, the p-value is less than 0.05, and thus the regression of the ratio of cash flow from operations to sales on the ratio of net income to sales is significant at the 5 percent level.

The standard error of the estimate in a simple linear regression is best described as: A. a relative measure of fit for the regression. B. the percentage of the variation of the dependent variable that is explained by the independent variable. C. a measure of the distance between the observed values of the dependent variable and those predicted from the estimated regression.

C. a measure of the distance between the observed values of the dependent variable and those predicted from the estimated regression. Correct because the standard error of the estimate is a measure of the distance between the observed values of the dependent variable and those predicted from the estimated regression.

All else being equal, when compared to non-probability sampling, probability sampling most likely yields: A. a less representative sample. B. an equally representative sample. C. a more representative sample.

C. a more representative sample. Correct because probability sampling gives every member of the population an equal change of being selected. Hence it can create a sample that is representative of the population. In contrast, non-probability sampling depends on factors other than probability considerations, such as a sampler's judgment or the convenience to access data. Consequently there is a significant risk that non-probability sampling might generate a non-representative sample. In general, all else being equal, probability sampling can yield more accuracy and reliability compared with non-probability sampling. Quantitative Methods compare and contrast simple random, stratified random, cluster, convenience, and judgmental sampling and their implications for sampling error in an investment problem

When working backward from the nodes on a binomial tree diagram, the analyst is most likely attempting to calculate: A. the number of potential outcomes. B. the probability of a given scenario. C. an expected value as of today.

C. an expected value as of today. Correct. In a tree diagram, a problem is worked backward to formulate an expected value as of today. Probability Trees and Conditional Expectations • formulate an investment problem as a probability tree and explain the use of conditional expectations in investment application

For a sample of 50 observations, in which of the following situations is a nonparametric test least likely to be appropriate? The data: A. contain outliers. B. are given in ranks. C. come from a population with a lognormal distribution.

C. come from a population with a lognormal distribution. Correct because a nonparametric test would be less appropriate compared to other answers as in this case a parametric test can be used. We may want to test a hypothesis concerning the mean of a population but believe that neither t- nor z-distributed tests are appropriate because the sample is small and may come from a markedly non-normally distributed population. In that case, we may use a nonparametric test. In our case, the data sample is large, thus a parametric test can be used instead. Quantitative Methods compare and contrast parametric and nonparametric tests, and describe situations where each is the more appropriate type of test

Assuming no short selling, a diversification benefit is most likely to occur when the correlations among the securities contained in the portfolio are: A. greater than +1. B. equal to +1. C. less than +1.

C. less than +1. Correct. As long as security returns are not perfectly positively correlated, diversification benefits are possible. Portfolio Mathematics • calculate and interpret the expected value, variance, standard deviation, covariances, and correlations of portfolio returns

An analyst is examining the annual growth of the money supply for a country over the past 30 years. This country experienced a central bank policy shift 15 years ago, which altered the approach to the management of the money supply. The analyst estimated a model using the annual growth rate in the money supply regressed on the variable (SHIFT) that takes on a value of 0 before the policy shift and 1 after. She estimated the values in Exhibit 1: Intercept -Coefficients = 5.767264 -Standard Error =0.445229 -t-Stat. =12.95348 Shift -Coefficients = −−5.13912 -Standard Error = −0.629649 -t-Stat. =−8.16188 The interpretation of the slope is the: A.change in the annual growth rate of the money supply per year. B.average annual growth rate of the money supply after the shift in policy. C.difference in the average annual growth rate of the money supply from before to after the shift in policy.

C. difference in the average annual growth rate of the money supply from before to after the shift in policy. C is correct. Whereas the intercept is the average of the dependent variable when the indicator variable is zero (i.e., before the shift in policy), the slope is the difference in the mean of the dependent variable from before to after the change in policy.

If the distribution of the population from which samples of size n are drawn is positively skewed and given that the sample size, n, is large, the sampling distribution of the sample means is most likely to have a: A. mean smaller than the mean of the entire population. B. variance equal to that of the entire population. C. distribution that is approximately normal.

C. distribution that is approximately normal. Correct. Given a population that has a finite variance and a large sample size, the central limit theorem establishes that the sampling distribution of sample means will be approximately normal, will have a mean equal to the population mean, and will have a variance equal to the population variance divided by the sample size. Estimation and Inference • explain the central limit theorem and its importance for the distribution and standard error of the sample mean

The failure of machine learning models to accurately predict outcomes can be the result of: A. overfitting, but not underfitting. B. underfitting, but not overfitting. C. either overfitting or underfitting.

C. either overfitting or underfitting. Correct because an ML model that has been overfitted is not able to accurately predict outcomes using a different dataset and may be too complex. Also, underfitted models will typically fail to fully discover patterns that underlie the data and thus may not be able to accurately predict outcomes. Quantitative Methods describe Big Data, artificial intelligence, and machine learning

Which of the following statements is most accurate? The first quintile generally exceeds the: A. first quartile. B. median. C. first decile.

C. first decile Correct. The first quintile is the 20th percentile (a percentile indicates the value below which a given percentage of observations in a group fall). The first decile is the 10th percentile, the first quartile is the 25th percentile, and the median is the 50th percentile. Although it is possible that these various percentiles or some subsets of them might be equal (for example, the 10th percentile possibly could be equal to the 20th percentile), in general, the order from smallest to largest would be: first decile, first quintile, first quartile, median. Statistical Measures of Asset Returns • calculate, interpret, and evaluate measures of central tendency and location to address an investment problem

The correlation coefficient: A. ranges from 0 to 1. B. is not affected by outliers. C. indicates the strength of the linear relationship between two random variables.

C. indicates the strength of the linear relationship between two random variables. Correct because the correlation coefficient expresses the strength of the linear relationship between the two random variables.

If a stock's continuously compounded return is normally distributed, then the distribution of the future stock price is best described as being: A. normal. B.a Student's t. C.lognormal

C. lognormal Correct. If a stock's continuously compounded return is normally distributed, then the future stock price is necessarily lognormally distributed.C.lognormal

When evaluating mean differences between two dependent samples, the most appropriate test is a: A.z-test. B.chi-square test. C.paired comparisons test.

C.paired comparisons test. C is correct. A paired comparisons test is appropriate to test the mean differences of two samples believed to be dependent. A is incorrect because a z-test is used to determine whether two population means are different when the variances are known and the sample size is large. B is incorrect because a chi-square test is used for tests concerning the variance of a single normally distributed population.

In its broadest sense, fintech is best described as: A. the vast amount of data being generated by the financial services industry. B. the execution of investment strategies through computer-generated algorithms. C. technological innovation in the design and delivery of financial services and products.

C. technological innovation in the design and delivery of financial services and products. Correct because in its broadest sense, the term 'fintech' generally refers to technology-driven innovation occurring in the financial services industry. For the purposes of this reading, fintech refers to technological innovation in the design and delivery of financial services and products. Note, however, that in common usage, fintech can also refer to companies (often new, startup companies) involved in developing the new technologies and their applications, as well as the business sector that comprises such companies.

The distribution of all the distinct possible values for a statistic when calculated from samples of the same size randomly drawn from the same population is most accurately referred to as: A. a discrete uniform distribution. B. a multivariate normal distribution. C. the sampling distribution of a statistic.

C. the sampling distribution of a statistic. Correct. The sampling distribution of a statistic (like a sample mean) is defined as the probability distribution of a given sample statistic when samples of the same size are randomly drawn from the same population. Estimation and Inference • compare and contrast simple random, stratified random, cluster, convenience, and judgmental sampling and their implications for sampling error in an investment problem

Which of the following statements is true in the use of ML: A.some techniques are termed "black box" due to data biases. B.human judgment is not needed because algorithms continuously learn from data. C.training data can be learned too precisely, resulting in inaccurate predictions when used with different datasets.

C. training data can be learned too precisely, resulting in inaccurate predictions when used with different datasets. C is correct. Overfitting occurs when the ML model learns the input and target dataset too precisely. In this case, the model has been "overtrained" on the data and is treating noise in the data as true parameters. An ML model that has been overfitted is not able to accurately predict outcomes using a different dataset and might be too complex.

To test whether a population's mean, µ, is greater than zero, the alternative hypothesis should be formulated as: A. µ ≤ 0. B. µ ≥ 0. C. µ > 0.

C. µ > 0. Correct because despite the different ways to formulate hypotheses, we always conduct a test of the null hypothesis at the point of equality, θ = θ0. We may have a 'suspected' or 'hoped for' condition for which we want to find supportive evidence. In that case, we can formulate the alternative hypothesis as the statement that this condition is true; the null hypothesis that we test is the statement that this condition is not true. Here, the "suspected" condition is that the population's mean is greater than zero (µ > 0). Quantitative Methods explain hypothesis testing and its components, including statistical significance, Type I and Type II errors, and the power of a test.

A bank offers a savings account with a stated annual rate of 3% in the first year and 5% in the second year. If returns are compounded quarterly and €90,000 is deposited in the account at the beginning of the first year, the account's value at the end of the second year is closest to: A. €97,200. B. €97,335. C. €97,455.

C. €97,455. (Look at ebook) Correct because the returns are compounded quarterly; Quantitative Methods calculate and interpret annualized return measures and continuously compounded returns, and describe their appropriate uses

Italian one-year government debt has an interest rate of 0.73 percent; Italian two-year government debt has an interest rate of 1.29 percent. The breakeven one-year reinvestment rate, one year from now is closest to: A.1.01 percent. B.1.11 percent. C.1.85 percent.

C.1.85 percent. C is correct. The one-year forward rate reflects the breakeven one-year reinvestment rate in one year, computed as follows: F1,1= (1+r2)2/(1+r1) - 1,F1,1= (1.0129)2/(1.0073) - 1 = 0.0185.

Consider the results of an analysis focusing on the market capitalizations of a sample of 100 firms: Exhibit 1: Market Capitalization of a Sample of 100 Firms *Bin 1, 2, 3, ,4 ,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,- 20 -Cumulative percentage of sample (%) 5, 10, ,15, 20, 25, 30, 35, 40 ,45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95,- 100 (Market Capitalization) - - euro billions *Lower Bound = 0.28, 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, - 81.62 *Upper Bound = 15.45, 21.22, 29.37, 32.57, 34.72, 37.58, 39.90, 41.57, 44.86, 46.88, 49.40, 51.27, 53.58, 56.66, 58.34, 63.10, 67.06, 73.00, 81.62 - 96.85 -Number of Observations 5 ....... -5 The fourth quartile corresponds to observations in bin(s): A.17. B.17, 18, 19, and 20. C.16, 17, 18, 19, and 20.

C.16, 17, 18, 19, and 20. C is correct. A quartile consists of 25 percent of the data, and the last 25 percent of the 20 bins are 16 through 20

*Simple Linear Regression (38 of 38) An analyst has estimated a model that regresses a company's return on equity (ROE) against its growth opportunities (GO), defined as the company's three-year compounded annual growth rate in sales, over 20 years, and produces the following estimated simple linear regression: ROEi= 4 + 1.8 GOi+ εi. Both variables are stated in percentages, so a GO observation of 5 percent is included as 5. The predicted value of the company's ROE if its GO is 10 percent is closest to: A.1.8 percent. B.15.8 percent. C.22.0 percent.

C.22.0 percent. C is correct. The predicted value of ROE = 4 + (1.8 × 10) = 22.

Kenneth McCoin, CFA, is a challenging interviewer. Last year, he handed each job applicant a sheet of paper with the information in Exhibit 1, and he then asked several questions about regression analysis. Some of McCoin's questions, along with a sample of the answers he received to each, are given below. McCoin told the applicants that the independent variable is the ratio of net income to sales for restaurants with a market cap of more than $100 million and the dependent variable is the ratio of cash flow from operations to sales for those restaurants. Which of the choices provided is the best answer to each of McCoin's questions? (Look T ebook) If the ratio of net income to sales for a restaurant is 5 percent, the predicted ratio of cash flow from operations (CFO) to sales is closest to: A.−4.054. B.0.524. C.4.207.

C.4.207. C is correct. To make a prediction using the regression model, multiply the slope coefficient by the forecast of the independent variable and add the result to the intercept. Expected value of CFO to sales = 0.077 + (0.826 × 5) = 4.207.

At the beginning of the year, an investor holds EUR10,000 in a hedge fund. The investor borrowed 25 percent of the purchase price, EUR2,500, at an annual interest rate of 6 percent and expects to pay a 30 percent tax on the return she earns from his investment. At the end of the year, the hedge fund reported the information in Exhibit 22: Exhibit 1: Hedge Fund Investment *Gross Return = 8.46% *Trading expenses = 1.10% ----------------------------------- *Managerial and administrative expenses = 1.60% The investor's after-tax return on the hedge fund investment is closest to: A.3.60 percent. B.3.98 percent. C.5.00 percent.

C.5.00 percent. (Look at ebook) C is correct. The first step is to compute the investor's net return from the hedge fund investment. The net return is the fund's gross return less managerial and administrative expenses of 1.60 percent, or 8.46% - 1.60% = 6.86%. Note that trading expenses are already reflected in the gross return, so they are not subtracted. The second step is to compute the investor's leveraged return (the investor borrowed EUR2,500 (25 percent) of the purchase), calculated as: follows 𝑅𝐿=𝑅𝑝+𝑉𝐵𝑉𝐸(𝑅𝑝−𝑟𝐷)RL=Rp+VBVERp−rD𝑅𝐿=6.86%+𝐸𝑈𝑅2,500𝐸𝑈𝑅7,500(6.86%−6%)RL=6.86%+EUR2,500EUR7,5006.86%−6%𝑅𝐿=6.86%+0.33×0.86%=7.15%RL=6.86%+0.33×0.86%=7.15%. The final step is to compute the after-tax return: After-tax return = 7.15% (1 - 0.30) = 5.00%.

If a researcher selects a 5 percent level of significance for a hypothesis test, the confidence level is: A.2.5 percent. B.5 percent. C.95 percent.

C.95 percent. C is correct. The 5 percent level of significance (i.e., probability of a Type I error) corresponds to 1 − 0.05 = 0.95, or a 95 percent confidence level (i.e., probability of not rejecting a true null hypothesis). The level of significance is the complement to the confidence level; in other words, they sum to 1.00, or 100 percent.

Suppose Mylandia announces that it expects significant cash flow growth over the next three years, and now plans to increase its recent CAD2.40 dividend by 10 percent in each of the next three years. Following the 10 percent growth period, Mylandia is expected to grow its annual dividend by a constant 3 percent indefinitely. Mylandia's required return is 8 percent. Based upon these revised expectations, The expected share price of Mylandia stock is: A.CAD49.98. B.CAD55.84. C.CAD59.71.

C.CAD59.71. (Look at study guide) C is correct. Following the first step, we observe the following expected dividends for Mylandia for the next three years: In 1 year: D1 = CAD2.64 (=2.40×1.10) In 2 years: D2 = CAD2.90 (=2.40×1.102) In 3 years: D3 = CAD3.19 (=2.40×1.103) The second step involves a lower 3 percent growth rate. At the end of year four, Mylandia's dividend (D4) is expected to be CAD3.29 (=2.40×1.103×1.03). At this time, Mylandia's expected terminal value at the end of three years is CAD65.80 using Equation 17, as follows: 𝐸(𝑆𝑡+𝑛)=3.290.08−0.03=65.80E(St+n)=3.290.08−0.03=65.80. Third, we calculate the sum of the present values of these expected dividends using Equation 16: 𝑃𝑉𝑡=2.641.08+2.901.082+3.191.083+65.801.083=59.71PVt=2.641.08+2.901.082+3.191.083+65.801.083=59.71.

Which of the following risk premiums is most relevant in explaining the difference in yields between 30-year bonds issued by the US Treasury and 30-year bonds issued by a small, private US corporate issuer? A.Inflation B.Maturity C.Liquidity

C.Liquidity C is correct. US Treasury bonds are highly liquid, whereas the bonds of small issuers trade infrequently and the interest rate includes a liquidity premium. This liquidity premium reflects the relatively high costs (including the impact on price) of selling a position. As the two bond issues have the same 30-year maturity, the observed difference in yields would not be solely explained by maturity. Further, the inflation premium embedded in the yield of both bonds is likely to be similar given they are both US-based bonds with the same maturity.

*The Time Value of Money In Finance (16 of 16) Grupo Ignacia issued 10-year corporate bonds two years ago. The bonds pay an annualized coupon of 10.7 percent on a semiannual basis, and the current annualized YTM is 11.6 percent. The current price of Grupo Ignacia's bonds (per MXN100 of par value) is closest to: A.MXN95.47. B.MXN97.18. C.MXN95.39.

C.MXN95.39 (Look at ebook) C is correct. The coupon payments are 5.35 (=10.7/2), the discount rate is 5.8 percent (=11.6%/2) per period, and the number of periods is 16 (=8×2). Using Equation 6, the calculation is as follows: 95.39 =5.351.058+5.351.058+5.351.0582+5.351.0583+5.351.0584+...+5.351.05814+5.351.05815+105.351.05816.5.351.0582+5.351.0583+5.351.0584+...+5.351.05814+5.351.05815+105.351.05816. Alternatively, using the Microsoft Excel or Google Sheets PV function (PV (0.058,16,5.35,100,0)) also yields a result of MXN95.39. A is incorrect. MXN95.47 is the result when incorrectly using coupon payments of 10.7, a discount rate of 11.6 percent, and 8 as the number of periods. B is incorrect. MXN97.18 is the result when using the correct semiannual coupons and discount rate, but incorrectly using 8 as the number of periods.

The strategy of using leverage to enhance investment returns: A.amplifies gains but not losses. B.doubles the net return if half of the invested capital is borrowed. C.increases total investment return only if the return earned exceeds the borrowing cost.

C.increases total investment return only if the return earned exceeds the borrowing cost. C is correct. The use of leverage can increase an investor's return if the total investment return earned on the leveraged investment exceeds the borrowing cost on debt. A is incorrect because leverage amplifies both gains and losses. B is incorrect because, if half of the invested capital is borrowed, then the investor's gross (not net) return would double.

A fund receives investments at the beginning of each year and generates returns for three years as follows: *Year of Investment - 1 *Assets Under Management at the Beginning of each year -USD 1,000 *Return during Year of Investment -15% *Year of Investment - 2 *Assets Under Management at the Beginning of each year -USD 4,000 *Return during Year of Investment -14% *Year of Investment - 3 *Assets Under Management at the Beginning of each year -USD 45,000 *Return during Year of Investment -4% Which return measure over the three-year period is negative? A.Geometric mean return B.Time-weighted rate of return C.Money-weighted rate of return

C.Money-weighted rate of return (Look at study ebook) The money-weighted rate of return considers both the timing and amounts of investments into the fund. To calculate the money-weighted rate of return, tabulate the annual returns and investment amounts to determine the cash flows. Solving for IRR results in a value of IRR = −2.22 percent. Note that A and B are incorrect because the time-weighted rate of return (TWR) of the fund is the same as the geometric mean return of the fund and is positive: 𝑅TW=(1.15)(1.14)(0.96)⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√3−1=7.97%RTW=1.151.140.963−1=7.97%.

Q. Which of the following statements about hypothesis testing is correct? A.The null hypothesis is the condition a researcher hopes to support. B.The alternative hypothesis is the proposition considered true without conclusive evidence to the contrary. C.The alternative hypothesis exhausts all potential parameter values not accounted for by the null hypothesis.

C.The alternative hypothesis exhausts all potential parameter values not accounted for by the null hypothesis. C is correct. Together, the null and alternative hypotheses account for all possible values of the parameter. Any possible values of the parameter not covered by the null must be covered by the alternative hypothesis (e.g., H0: μ ≤ 5 versus Ha: μ > 5). A is incorrect because the null hypothesis is what the researcher wants to reject; the "hoped for" or "suspected" condition is often set up as the alternative hypothesis. B is incorrect because the null (not the alternative) hypothesis is considered to be true unless the sample used to conduct the hypothesis test gives convincing evidence that the null hypothesis is false.

Probability Trees and Conditional Expectations An analyst developed two scenarios with respect to the recovery of USD100,000 principal from defaulted loans: -Scenario = 1 *Probability of Scenario (%) = 40 - Amount Recovered (USD) = 50,000... 30,000 *Probability of Amount (%) = 60....40 -Scenario = 2 *Probability of Scenario (%) = 60 - Amount Recovered (USD) = 80,000... 60,000 *Probability of Amount (%) = 90....10 The amount of the expected recovery is closest to which of the following? A.USD36,400. B.USD55,000. C.USD63,600.

C.USD63,600. C is correct. If Scenario 1 occurs, the expected recovery is 60% (USD50,000) + 40% (USD30,000) = USD42,000, and if Scenario 2 occurs, the expected recovery is 90% (USD80,000) + 10% (USD60,000) = USD78,000. Weighting by the probability of each scenario, the expected recovery is 40% (USD42,000) + 60% (USD78,000) = USD63,600. Alternatively, first calculating the probability of each amount occurring, the expected recovery is (40%)(60%)(USD50,000) + (40%)(40%)(USD30,000) + (60%)(90%)(USD80,000) + (60%)(10%)(USD60,000) = USD63,600.

An investment manager's gross return is: A.an after-tax nominal, risk-adjusted return. B.the return earned by the manager prior to deduction of trading expenses. C.an often used measure of an investment manager's skill because it does not include expenses related to management or administration.

C.an often used measure of an investment manager's skill because it does not include expenses related to management or administration. C is correct. Gross returns are calculated on a pre-tax basis; trading expenses are accounted for in the computation of gross returns as they contribute directly to the returns earned by the manager. A is incorrect because investment managers' gross returns are pre-tax and not adjusted for risk. B is incorrect because managers' gross returns do reflect the deduction of trading expenses since they contribute directly to the return earned by the manager.

Homoskedasticity is best described as the situation in which the variance of the residuals of a regression is: A.zero. B.normally distributed. C.constant across observations.

C.constant across observations. C is correct. Homoskedasticity is the situation in which the variance of the residuals is constant across the observations.

The best approach for creating a stratified random sample of a population involves: A.drawing an equal number of simple random samples from each subpopulation. B.selecting every kth member of the population until the desired sample size is reached. C.drawing simple random samples from each subpopulation in sizes proportional to the relative size of each subpopulation.

C.drawing simple random samples from each subpopulation in sizes proportional to the relative size of each subpopulation. C is correct. Stratified random sampling involves dividing a population into subpopulations based on one or more classification criteria. Then, simple random samples are drawn from each subpopulation in sizes proportional to the relative size of each subpopulation. These samples are then pooled to form a stratified random sample.C.drawing simple random samples from each subpopulation in sizes proportional to the relative size of each subpopulation.

Rates of Return Practice Packet (31 of 31) .The nominal risk-free rate is best described as the sum of the real risk-free rate and a premium for: A.maturity. B.liquidity. C.expected inflation.

C.expected inflation. C is correct. The nominal risk-free rate is approximated as the sum of the real risk-free interest rate and an inflation premium.

Text analytics is appropriate for application to: A.large, structured datasets. B.public but not private information. C.identifying possible short-term indicators of coming trends.

C.identifying possible short-term indicators of coming trends. C is correct. Through the text analytics application of NLP, models using NLP analysis might incorporate non-traditional information to evaluate what people are saying—through their preferences, opinions, likes, or dislikes— in an attempt to identify trends and short-term indicators—for example, about a company, a stock, or an economic event—to forecast coming trends that may affect investment performance in the future.

The lognormal distribution is a more accurate model for the distribution of stock prices than the normal distribution because stock prices are: A.symmetrical. B.unbounded. C.non-negative.

C.non-negative. C is correct. A lognormal distributed variable has a lower bound of zero. The lognormal distribution is also right skewed, which is a useful property in describing asset prices.C.non-negative.

Based on Exhibit 1, Olabudo should: A.conclude that the inflation predictions are unbiased. B.reject the null hypothesis that the slope coefficient equals one. C.reject the null hypothesis that the intercept coefficient equals zero. A.conclude that the inflation predictions are unbiased.

Doug Abitbol is a portfolio manager for Polyi Investments, a hedge fund that trades in the United States. Abitbol manages the hedge fund with the help of Robert Olabudo, a junior portfolio manager. Abitbol looks at economists' inflation forecasts and would like to examine the relationship between the US Consumer Price Index (US CPI) consensus forecast and the actual US CPI using regression analysis. Olabudo estimates regression coefficients to test whether the consensus forecast is unbiased. If the consensus forecasts are unbiased, the intercept should be 0.0 and the slope will be equal to 1.0. Regression results are presented in Exhibit 1. Additionally, Olabudo calculates the 95 percent prediction interval of the actual CPI using a US CPI consensus forecast of 2.8.

Which of Olabudo's observations of forecasting is correct? A.Only Observation 1 B.Only Observation 2 C.Both Observation 1 and Observations 2 B.Only Observation 2

Based on Exhibit 1, the standard error of the estimate is closest to: A.0.04456. B.0.04585. C.0.05018. B.0.04585. B is correct. The standard error of the estimate for a linear regression model with one independent variable is calculated as the square root of the mean square error: 𝑠𝑒=0.07147534⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√=0.04585.

Elena Vasileva recently joined EnergyInvest as a junior portfolio analyst. Vasileva's supervisor asks her to evaluate a potential investment opportunity in Amtex, a multinational oil and gas corporation based in the United States. Vasileva's supervisor suggests using regression analysis to examine the relation between Amtex shares and returns on crude oil. Vasileva notes the following assumptions of regression analysis: Assumption 1. The error term is uncorrelated across observations. Assumption 2. The variance of the error term is the same for all observations. Assumption 3. The dependent variable is normally distributed. Vasileva runs a regression of Amtex share returns on crude oil returns using the monthly data she collected. Selected data used in the regression are presented in Exhibit 1, and selected regression output is presented in Exhibit 2. She uses a 1 percent level of significance in all her tests.

Based on Exhibit 2, Vasileva should reject the null hypothesis that: A.the slope is less than or equal to 0.15. B.the intercept is less than or equal to zero. C.crude oil returns do not explain Amtex share returns. C is correct. Crude oil returns explain the Amtex share returns if the slope coefficient is statistically different from zero. The slope coefficient is 0.2354, and the calculated t-statistic is 𝑡=0.2354−0.00000.0760=3.0974,t=0.2354−0.00000.0760=3.0974, which is outside the bounds of the critical values of ±2.728. Therefore, Vasileva should reject the null hypothesis that crude oil returns do not explain Amtex share returns, because the slope coefficient is statistically different from zero.

Using information from Exhibit 2, the 99 percent prediction interval for Amtex share return for Month 37 is best described as: A.𝑌ˆ𝑓±0.0053Y^f±0.0053. B.𝑌ˆ𝑓±0.0469Y^f±0.0469. C.𝑌ˆ𝑓±0.1279Y^f±0.1279. C.𝑌ˆ𝑓±0.1279Y^f±0.1279. C is correct. The predicted share return is 0.0095 + [0.2354 × (−0.01)] = 0.0071. The lower limit for the prediction interval is 0.0071 − (2.728 × 0.0469) = −0.1208, and the upper limit for the prediction interval is 0.0071 + (2.728 × 0.0469) = 0.1350. A is incorrect because the bounds of the interval should be based on the standard error of the forecast and the critical t-value, not on the mean of the dependent variable. B is incorrect because bounds of the interval are based on the product of the standard error of the forecast and the critical t-value, not simply the standard error of the forecast.

The predicted net profit margin for a company with a fixed asset turnover of 2 times is closest to: A.1.1889 percent. B.1.8043 percent. C.3.2835 percent C is correct. The predicted natural log of the net profit margin is 0.5987 + (2 × 0.2951) = 1.1889. The predicted net profit margin is 𝑒1.1889=3.2835e1.1889=3.2835%.

Espey Jones is examining the relation between the net profit margin (NPM) of companies, in percent, and their fixed asset turnover (FATO). He collected a sample of 35 companies for the most recent fiscal year and fit several different functional forms, settling on the following model: ln(NPM𝑖)=𝑏0+𝑏1FATO𝑖.ln(NPMi)=b0+b1FATOi. The results of this estimation are provided in Exhibit 1.

The standard error of the estimate is closest to: A.0.2631. B.1.7849. C.38.5579. A is correct. The standard error is the square root of the mean square error, or 0.0692⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√=0.26310.0692=0.2631.

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