CFA QUANT ASSESSMENT TEST
The future value of $5,000 that is continuously compounded at a 10 percent stated rate for 18 months is closest to:
$5,810
It is Jim's birthday and he has thrown a party for his friends. Everyone except Henry has arrived. George states that the chances of Henry showing up on the party are only 10%. According to George the odds of Henry showing up at the party are:
1 to 9
A mortgage has an annual quoted interest rate of 12%. If mortgage payments are made monthly, then the effective annual interest rate is closest to:
12.68%.
There is a competition in which there are six fund advisors and you need to pick winners for first, second, and third places. How many ways can they be selected?
120
Four shares are going to be labeled as "buys" and they are to be selected from nine shares in a sector. How many ways can they be selected?
126
If a die is thrown four times, what is the probability of throwing exactly one 6? (Assume the die has an equal chance of showing a 1, 2, 3, 4, 5, or 6.)
38.6
Which of the following statements concerning a multivariate distribution is least accurate?
A multivariate distribution describes the outcomes for a single random variable under different scenarios.
In hypothesis testing a test statistic is:
A value that will decide whether to accept or reject the null hypothesis.
Robert received $150,000 and invested it at 6% compounded annually. He wants to purchase a piece of property worth $200,000 after 7 years. He will most likely:
Be able to purchase the property and have excess funds amounting to $25,544
A smaller sample size:
Increases the size of the "fail‐to‐reject‐the‐null" region, increases the probability of a Type II error, and reduces the power of a test.
Which of the following distributions is most likely to have a modal value greater than the mean?
Negatively skewed
Which of the following is least likely to be a valid visualization for a 5 ×3 contingency table?
Pareto chart
Which of the following statements is least accurate?
Type I error is accepting the null hypothesis when it is false
It is Jim's birthday and he has thrown a party for his friends. Everyone except Henry has arrived. George states that the chances of Henry showing up on the party are only 10%. If Jim bets a dollar against George that Henry will show up, his expected return from the bet would be:
$0
An investor is evaluating an insurance product that promises to pay a $1,000 monthly benefit for 20 years beginning 10 years from now. The investor is required to make payments at the end of each month for the next five years. Assuming a five percent discount rate and monthly compounding, the minimum monthly payment required to finance the benefit is closest to:
$1,743
Brian will receive $1,000 at the end of each year for the next 21 years. Given that the interest rate is 8%, the value of these payments 43 years from today is closest to:
$274,126
An investor puts $3,000 in a bank account that offers an annual interest rate of 11% compounded daily. The account balance at the end of Year 1 will be closest to:
$3,348.78
An investor puts $3,000 in a bank account that offers an annual interest rate of 11% compounded daily. The account balance at the end of Year 1 will be closest to:
$3,348.78 PV = −$3,000 I/Y = 11/365 N = 365 CPT FV; FV = $3,348.78
Mrs. Doherty wants to gift a car worth $24,000 to her son for his 18th birthday. She has 40% of the funds, and borrows the rest for 4 years at 8% compounded monthly. The fixed monthly payment that she will have to make to retire the loan in 48 months is closest to:
$352
A company pays a $2 per share annual dividend on its preferred stock. Given that the required rate of return is 5% and that this dividend policy will continue forever, the value of the preferred stock today is closest to:
$40
John and Paula Smith are expecting a baby girl. They've decided to set up a college fund, contributing $100 per month for the next 18 years. If they can achieve an average return of seven percent on the account, the expected future value is closest to:
$43,000
The following income streams will be paid from an investment: End year 1- $15,000 End year 2- $25,000 End year 3- $10,000 At the end of year 3 the investment will have no remaining value. If the discount rate is 8% the present value of the investment is closest to:
$43,260.
A technology sector analyst is considering two competing companies that she follows. A patent lawsuit was filed by PhoneWise (PW) against DyleTone (DT). If PW wins the suit, there is a 70 percent chance that its revenues will climb to $600 million within two years and a 30 percent chance that they will reach $1 billion. If PW loses the suit, the probability of revenues falling to $300 million is 0.60 and of plummeting to $150 million is 0.40 as competition from DT and new entrants intensifies. After consulting legal experts, the analyst is convinced that the chances of winning or losing the suit are 50‐50. Based on this information, the expected revenue for PW within the next two years is closest to:
$480 million
David Johnson knows that he must accumulate $180,000 five years from now to finance his daughter's college fees. David can make a quarterly contribution of $5,000. He is considering an investment that will return him the forecasted amount when required. Given an annual interest rate of 5%, compounded quarterly, how much should he invest today?
$52,405
An investor is offered a two‐year lump sum investment of $500 with annual compounding at four percent. The future value of this investment is closest to:
$541
An investment of $500 will be made 3 years from today. Given an interest rate of 7.25%, the value of this investment 40 years from today will beclosest to:
$6,663
Alex Sunarto is legally obliged to pay a sum of $40,000 to Lisa Mathew as part of their divorce settlement after three years. Lisa is planning to invest in a financial instruments that yields 5% semiannually. Calculate the value of the investment 15 years from now assuming interest payments are reinvested.
$72,350.
An investor is interested in purchasing a retirement annuity from an insurance company. The annuity pays $10,000 per year for 30 years beginning 10 years from now when the investor plans to retire. Using a discount rate of six percent, the fair value of this annuity today is closest to:
$81,000
A manufacturer claims that the life of its batteries is normally distributed with a mean of 20 hours. For a random sample of 64 batteries, it is observed that the average life of the batteries in the sample is 19 hours with a standard deviation of 3.25 hours. Determine whether the average life of batteries manufactured by this company is greater than 20 hours at the 5% significance level. Assuming that the t‐distribution is used for this hypothesis test, the critical value(s) is/are:
+1.67
An analyst states "... the odds against the company increasing its dividend are 12 to 1." This means that the analyst believes that the probability of it increasing the dividend is closest to:
0.0769.
After the first female president of the United States was elected into office, 27 inspired citizens decided to run for mayor in the City of Pines. With the vote resulting in a 17‐way tie, the city has decided to determine the eventual winner by chance. A number from 1 to 17 was assigned to the top 17 candidates and a wheel will be spun. The candidate whose number matches the result of the spin will be declared the winner. Given these facts, what is the probability the candidate assigned to number 11 or a candidate assigned to an even number will win?
0.53
The probability function for a random variable is given as p(x) = x/100. The set of possible values that the random variable, X, can take is given by X = (10, 20, 30, 40). For other values of x, p(x) = 0. F(35) equals:
0.6
The standard error of a sample that has an arithmetic mean of 11, a standard deviation of 3, and 20 observations is closest to:
0.67
An analyst wishes to identify whether there is a significant relationship between home sales and interest rates at the 5.0 percent significance level. The correlation between home sales and interest rates has been found to be 0.35 based on a sample of 25 observations. Using a student's t‐distribution table, the critical value of t was determined to be 2.069 for a sample of this size and for this level of significance. The t‐statistic for testing the null hypothesis that there is no relationship between home sales and interest rates is closest to:
1.79 and we can conclude at a 0.05 significance level that a relationship does not exist between home sales and interest rates.
An investment of $1,000 appreciates to a value of $1,450 in 3.5 years. What is the continuously compounded annual return on this investment?
10.62%
Test the accuracy of a claim made by AB Associates that the investment strategies they follow result in standard deviation of monthly returns of 0.58%. Use the 5% level of significance. ZX performance data for the last 31 months has a standard deviation of 0.55%. For this hypothesis test, the critical value(s) is/are:
16.79 and 46.98
Given the following information: Expected annual return of an investment: 10% SD of the annual returns: 5% The returns follow a normal distribution. What is the probability that the return will be greater than 20% in any given year?
2.28%
A trader uses a statistical model to estimate the probabilities of her BUY limit orders executing. A limit order executes at the stated price or lower. Based on the model, she places two limit orders on the same stock, which is currently trading at $57.00. One order is placed at $56.00 per share and has a 15 percent probability of executing before the end of the day. The second order is placed at $56.25 and has a 20 percent probability of executing before the exchange closes. The probability that either order will execute is closest to:
20 percent
The risk manager at a bank is reviewing its loan default data. He finds that the 5‐year average default rate for the bank was 4.76 percent of outstanding principal. In the event of a default, the bank has been able to recover an average of $0.35 per dollar outstanding. Based on this data, the odds against a default on one of the bank's loans are closest to:
20 to 1
A binomial distribution model is created to analyze the performance of a fund relative to an index over 36 trial periods. In each period there is a 60% probability of success which is defined as the fund matching or outperforming the index, in each period the performance is assumed to be independent. The mean of the binomial random variable is closestto:
21.6
A pension's investment committee commissioned a study of the significance of past performance in selecting asset managers. The research looked at a universe of managers over several periods, defining those in the top 50 percent of the group's annual returns as winners for the period and the bottom 50 percent to be losers. If a manager's performance in one period is independent of his performance in the next period, one would expect the probability of being classified as a winner in two consecutive periods to be:
25 percent.
In a nightclub, there are 22 male smokers to 16 female smokers. On the other hand, there are 18 female nonsmokers and 14 male nonsmokers. What are the odds of not meeting a female nonsmoker?
26/9
The data for a sample includes 2, 4, 6, 18, 6, 4, 2. The mean absolute deviation for this data is closest to:
3.43
An analyst has calculated the mean and standard deviation for a company's net profit margin and wants to forecast a one‐standard deviation range around the mean. Assuming the mean is a normal random variable, the likelihood that a net profit margin will fall outside the range is approximately:
32%
A sample of 150 new CPA board passers are chosen to take part in a survey to determine whether the average starting salaries of Certified Public Accountants equal to or exceed $78,500 annually. If the mean starting salary of the selected samples equals $82,500, and if the standard deviation is determined to be 1,500, how much is the test statistic?
32.66
A company's annual sales figures over the last four years are as follows: $2.6 million; $3.1 million, $5.3 million, $7.0 million. The firm's compound annual growth rate over the period is closest to:
39%
The effective annual rate for an automobile loan that has an interest rate of 7%, compounded monthly, is closest to:
7.23%
A mutual fund manager intends to replace three stocks in her portfolio. She has narrowed down the list of possible additions to nine stocks. How many three‐stock groups can be created from the prospect list?
84
Which of the following statements is most likely?
A portfolio with a higher SF Ratio also has a higher probability of attaining returns higher than the threshold level.
A sample containing the monthly returns for 75 U.S. stocks has a mean of 5% and a standard deviation of 12%. The standard error of the sample mean:
Approximately equals 1.39%
A portfolio manager is trying to develop an optimal asset allocation using mean‐variance optimization, which requires that she compute the variance of the portfolio under a variety of asset weightings. The investable universe includes 12 distinct asset classes. Which of the following is the appropriate counting formula and how many individual covariances must be derived to compute the variance of one prospective portfolio allocation?
Combination formula is used to compute 66 covariances.
Which of the following statements is most likely?
For a discrete distribution, p(x) equals 0 when x cannot occur, while for a continuous distribution, p(x) equals zero even though x can occur.
Which of the following is least likely regarding Student's t‐distribution?
It has a lower peak and thinner tails than the normal distribution.
The Central Limit Theorem states that if the sampling distribution of the sample mean is calculated using samples of equal size from a population that is not normal, then:
It is approximately a normal distribution.
Conditional probability refers to the probability:
Of a particular event occurring given that another event has already occurred.
Consider the following statements: Statement 1: Linear regression computes the line of best fit that minimizes the sum of the differences between actual and predicted values of the dependent variable. Statement 2: Increasing the significance level lowers the probability of a Type II error. Which of the following is most likely?
Only Statement 2 is correct.
A merger arbitrage hedge fund manager is considering using a scoring model to test the likelihood that a merger deal will close within six months. Back testing the model shows that 70 percent of all prospective mergers scored were closed within the allotted period. Of all mergers that were scored, 76 percent passed the test. Finally, the probability that a merger passed, given that it closed on time, was 82 percent. What is the probability that a merger passed the test, given that it did not close within six months?
P(passed|no close) = 0.62.
Which of the following is least likely a premium that compensates investors for bearing risk?
Payback premium
A hypothesis is a statement about a:
Population parameter.
The level of significance in hypothesis testing is the probability of:
Rejecting the null hypothesis when it is true.
Which of the following statements does not adhere to the rules for calculating different types of probabilities?
The addition rule is utilized in order to solve for the probability of two events occurring simultaneously.
Which of the following is least likely an assumption of linear regression?
The independent variable is random.
What does an observation's z‐score essentially represent?
The number of standard deviations away from the mean the given observation actually lies.
Steve York, CFA, wants to test a hypothesis concerning the mean returns of manufacturing companies. In which of the following cases is it equally appropriate for him to use the z‐test or the t‐test to make comparisons with the test statistic?
The population variance is unknown, and the sample size is large.
Which of the following statements is most accurate?
The shorter the time period until the future amount is received, the higher its present value
In a hypothesis testing, the probability of a true null hypothesis being rejected is 5% and the power of the test is 90%. Which of the following conclusions is most likely true?
The significance level of the hypothesis is 5%, and there is a 10% chance of the false null being accepted.
In using the F‐distribution test statistic, all of the following are assumed, except for:
The two random samples have the same sample size.
An analyst is asked to explain the strengths and weaknesses of using a Monte Carlo simulation to value a complex financial security. The analyst is most correct when she states that a Monte Carlo simulation:
allows "what if" analyses, which are not possible with historical simulation.
In comparison to a t‐distribution that has 10 degrees of freedom (df = 10), a t‐distribution with 22 degrees of freedom (df = 22) most likelywill:
be shaped more like the standard normal distribution.
An analyst wishes to present a distribution and comparison of various sample data using bar charts, heat maps, and tree maps. The data is most likely to be:
categorical.
Which stat is most likely used to test the equality of the variances of two normally distributed, independent populations?
f stat
An investment has stated annual interest rate (APR) of 7% with semiannual compounding. The effective interest rate (EAR) on the amount is most likely:
greater than 7%
An investment has stated annual interest rate (APR) of seven percent with semiannual compounding. The effective interest rate (EAR) on the amount is most likely:
greater than seven percent.
An analyst is considering a series of ratios with an extreme outlier. Wishing to give less weight to the outlier without interrupting the integrity of the data set, the analyst would most likely use the:
harmonic mean.
Chad Milhouse is arranging financing for a first‐time home purchase. He wants to borrow $200,000 for 15 years and is quoted a mortgage rate of 6.50 percent. The bank requires $2,000 in non‐interest fees due at closing. His mortgage broker explains the loan disclosures, which list both the mortgage rate and the APR (the implied interest rate including fees). Milhouse should expect the APR to be:
higher than the mortgage rate.
An analyst presenting the joint variation in GDP and hours worked four months ago would most likely use a:
line chart
An analyst wants to test whether the operating margin for Spanish companies that announce a restructuring is equal to the operating margin of Spanish companies in the same industry that do not restructure. Based on sampling and using a 5 percent level of significance, the hypothesis test indicated that the null hypothesis of equal operating margins could not be rejected. Subsequently, all Spanish companies were examined and it conclusively determined that the operating margin for companies announcing a restructuring is significantly different from the operating margin of non‐restructuring companies in the same industry. This subsequent analysis most likelyindicates that the analyst:
made a Type II error
A hypothesis test has been completed and the marginal significance level—the p‐value—is calculated to be 0.031. An analyst examining the test can most likely conclude that the:
null hypothesis will be rejected if the level of significance is 0.05.
An analyst is comparing the annual mean returns for the past 40 years on the S&P 500 index to the annual mean returns on the NYSE Composite index for the same period. The analyst believes that the indices are highly similar and wants to test her hypothesis that the difference in the annual returns is not significant—the difference in returns is really zero. The analyst assumes that the population variances are equal. The type of test that the analyst most likely will use is a:
paired comparison test because the two samples are dependent
The width of a prediction interval is most likely:
positively related to the standard error of estimate, but negatively related to the standard deviation of the independent variable.
A hypothesis test was completed and the test led the analyst to reject the null hypothesis. Subsequently, population data became available and it showed that the original null hypothesis was false. The probability of rejecting the false null hypothesis is the:
power of a test.
Which of the following describe lognormal distributions? A.Positively skewed- Prices B.Negatively skewed- Prices C.Negatively skewed- Returns
row a
Color in a word cloud most likely identifies:
sentiment
An analyst is completing a hypothesis test and wants to minimize the risk of a Type I error in making her decision. The analyst will most likely select a:
small alpha.
With respect to two variables that have a linear relationship, the correlation coefficient measures the:
strength of the relationship.
An analyst is describing the difference between a t‐distribution and the normal distribution. He is most likely correct when he states that:
the Student's t‐distribution is a family of distributions while there is only a single standard normal distribution.
Two random variables have a correlation of 0.04 with each other. This could best be described as:
the absence of a linear relationship.
A frequency distribution is least likely to assist an analyst in determining:
the tendency of observations to be clustered near the average of observed values.
A data table visualization in column and row format would most likely also be known as a:
two‐dimensional array.
An increase in the degrees of freedom will result in which of the following?
t‐distribution will become more peaked and have less fat tails.
The diagonal of a covariance matrix represents the:
variance of each fund.
A frequency distribution is least likely to assist an analyst in determining:
where most of the observations lie.
For tests concerning differences between the variances of two normally distributed populations based on two random, independent samples, the appropriate test statistic is based on a(n):
f test
A distribution with excess kurtosis of 1.5 would most likely be considered:
leptokurtic.
An analyst has developed a model to predict the GDP growth rate for countries. He started with 20 variables, eliminated those that did add predictive value, and then added new variables when necessary. The final combination of variables that worked best comprised 12 variables. The model has been tested on out‐of‐sample data and it was successful in predicting GDP growth. The next step for the analyst is to:
make sure that the 12 variables being used make sense from an economic standpoint.
A distribution with kurtosis less than 2.5 would most likely be considered:
platykurtic
A scatter plot matrix:
shows multiple bivariate scatter plots.