Quantitative Methods: Practice Pack

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

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

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.

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

A. t-statistic

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.

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.

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.

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%.

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

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.

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.

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.

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.

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.

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.

An investor invests a fixed amount of money into a fund each year for three years as follows: Year. Price per Share 1: €14.00 2: €12.00 3: €17.00 The investor's average cost per share is closest to: A.€14.05. B.€14.33. C.€14.63.

A.€14.05.

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%

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

B. is asymmetrical.

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

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.

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.

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.

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%.

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%.

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

B.82.

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

B.82.

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

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

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

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.

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.

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.

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.

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.

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.

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

B.quintile.

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.

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.

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

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.

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.

A portfolio manager will invest €100,000 and is presented with the following information about three portfolios with normally distributed returns: Expected Annual Return. Standard Deviation of Returns Portfolio 1 23%. 15% Portfolio 2. 12% 6% Portfolio 3 15% 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.

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.

Which of the following is the most recent advancement in fintech? Applications that can: A.process data B.automate tasks C.make decisions

C.make decisions

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.

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.

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

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.

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.

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.

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.