big quant pt 1

Q1. Three portfolios with normally distributed returns are available to an investor who wants to minimize the probability that the portfolio return will be less than 5%. The risk and return characteristics of these portfolios are shown in the following table: Portfolio Expected return Standard deviation Epps 6% 4% Flake 7% 9% Grant 10% 15% Based on Roy's safety-first criterion, which portfolio should the investor select?

Grant.

Q2. Lucy James, CFA, is constructing a hypothesis test using a 5% level of significance. If she is interested in increasing the "power of the test," she should consider:

keeping the significance level the same and increasing the sample size.

Q3. Which of the following statements about parametric and nonparametric tests is least accurate?

Nonparametric tests rely on population parameters.

Q4. Which of the following portfolios provides the best "safety first" ratio if the minimum acceptable return is 6%? Portfolio Expected Return (%) Standard Deviation (%) 1 13 5 2 11 3 3 9 2

2.

Q5. For two random variables, P(X = 20, Y = 0) = 0.4, and P(X = 30, Y = 50) = 0.6. Given that E(X) is 26 and E(Y) is 30, the covariance of X and Y is:

120.00.

Q6. An analyst decides to select 10 stocks for her portfolio by placing the ticker symbols for all the stocks traded on the New York Stock Exchange in a large bowl. She randomly selects 20 stocks and will put every other one chosen into her 10-stock portfolio. The analyst used:

simple random sampling.

Q7. For assets A and B we know the following: E(RA) = 0.10, E(RB) = 0.20, Var(RA) = 0.25, Var(RB) = 0.36 and the correlation of the returns is 0.6. What is the expected return of a portfolio that is equally invested in the two assets?

0.1500.

Q8. The following annualized monthly return measures have been calculated for an investment based on its performance over the last 72 months. Arithmetic mean 6.8% Geometric mean 6.0% 90% Winsorized mean 5.5% If for one month in the period the return was extremely high, which measure best reflects the central tendency of the investment's returns?

Winsorized mean.

Q9. A bond pays annual coupon interest of £40 and returns its face value of £1,000 in five years. The bond's yield to maturity is 4.5%. Its price today is closest to:

£978.

Q10. Assume that the following returns are a sample of annual returns for firms in the clothing industry. Firm 1 Firm 2 Firm 3 Firm 4 Firm 5 15% 2% 5% (7%) 0% The sample standard deviation is closest to:

8.0.

Q11. Consider the following statements about the geometric and arithmetic means as measures of central tendency. Which statement is least accurate?

The geometric mean may be used to estimate the average return over a one- period time horizon because it is the average of one-period returns.

Q12. Bo Rigley, CFA, is a financial analyst examining large-cap equity returns over a calendar year. His sample size is 252 trading days, and he observes a mean return of 0.07% and a standard deviation of 0.12%. With his null hypothesis that the daily portfolio return is equal to zero and a 10% level of significance, Rigley will:

reject the null because the test statistic is greater than the critical value.

Q13. The covariance of the returns on investments X and Y is 18.17. The standard deviation of returns on X is 7%, and the standard deviation of returns on Y is 4%. What is the value of the correlation coefficient for returns on investments X and Y?

+0.65.

Q14. The mean and standard deviation of returns for three portfolios are listed below in percentage terms. Portfolio X: Mean 5%, standard deviation 3%. Portfolio Y: Mean 14%, standard deviation 20%. Portfolio Z: Mean 19%, standard deviation 28%. Using Roy's safety-first criteria and a threshold of 4%, select the optimal portfolio.

Portfolio Z.

Q15. The returns on assets C and D are strongly correlated with a correlation coefficient of 0.80. The variance of returns on C is 0.0009, and the variance of returns on D is 0.0036. What is the covariance of returns on C and D?

0.00144.

Q16. Which of the following statements about hypothesis testing is most accurate? A Type I error is the probability of:

rejecting a true null hypothesis.

Q17. If a two-tailed hypothesis test has a 5% probability of rejecting the null hypothesis when the null is true, it is most likely that:

the confidence level of the test is 95%.

Q18. Assume that one- and two-year risk-free rates are 1.80% and 2.50%, respectively. Using the cash flow additivity principle, the one-year reinvestment rate, one year from now is closest to:

3.2%.

Q19. Bill Jones is creating a charitable trust to provide six annual payments of $20,000 each, beginning next year. How much must Jones set aside now at 10% interest compounded annually to meet the required disbursements?

$87,105.21.

Q20. Given the following annual returns, what are the geometric and arithmetic mean returns, respectively? 2002 2003 2004 2005 2006 15% 2% 5% -7% 0%

2.75%; 3.00%.

Q21. Given P(X = 2) = 0.3, P(X = 3) = 0.4, P(X = 4) = 0.3. What is the variance of X?

0.6.

Q22. If an analyst wants to perform hypothesis testing using a chi-square test, which of the following values is he most likely assessing?

The value of a population variance.

Q23. Michael Philizaire decides to calculate the geometric average of the appreciation/deprecation of his home over the last five years. Using comparable sales and market data he obtains from a local real estate appraiser, Philizaire calculates the year-to-year percentage change in the value of his home as follows: 20, 15, 0, –5, –5. The geometric return is closest to:

4.49%.

Q24. If given the standard deviations of the returns of two assets and the correlation between the two assets, which of the following would an analyst least likely be able to derive from these?

Expected returns.

Q25. A company reports its past six years' earnings growth at 10%, 14%, 12%, 10%, –10%, and 12%. The company's average compound annual growth rate of earnings is closest to:

7.7%.

Q26. The following data points are observed returns. 4.2%, 6.8%, 7.0%, 10.9%, 11.6%, 14.4%, 17.0%, 19.0%, 22.5% What return lies at the 70th percentile (70% of returns lie below this return)?

17.0%.

Q27. An investor has two stocks, Stock R and Stock S in her portfolio. Given the following information on the two stocks, the portfolio's standard deviation is closest to: σR = 34% σS = 16% rR,S = 0.67 WR = 80% WS = 20%

29.4%.

Q28. Compute the standard deviation of a two-stock portfolio if stock A (40% weight) has a variance of 0.0015, stock B (60% weight) has a variance of 0.0021, and the correlation coefficient for the two stocks is –0.35?

2.64%.

Q29. For a two-tailed test of hypothesis involving a z-distributed test statistic and a 5% level of significance, a calculated z-statistic of 1.5 indicates that:

the null hypothesis cannot be rejected.

Q30. An investor is considering investing in one of the following three portfolios: Statistical Measures Portfolio X Portfolio Y Portfolio Z Expected annual return 12% 17% 22% Standard deviation of return 14% 20% 25% If the investor's minimum acceptable return is 5%, the optimal portfolio using Roy's safety-first criterion is:

Portfolio Z.

Q31. An investor pays $726.27 for a zero-coupon bond with a face value of $1,000 and maturing in 10 years. Bonds with similar risk profiles and with similar terms yield 3.00%. The yield to maturity for this bond is closest to:

3.25%.

Q32. An investor is deciding whether to buy a 1-year bond two years in a row or lock in the rate on a 2-year bond today. The 1-year spot interest rate is 5.25%, and the 2-year spot interest rate is 6.50%. Which of the following statements is most accurate regarding implied forward rates and the investor's options?

The expected rate on a 1-year bond one year from today is equal to 7.76%.

Q33. A portfolio's monthly returns follow a distribution with a kurtosis measure of 4.2. Relative to a portfolio with normally distributed returns, this portfolio has a:

higher probability of extreme upside returns and higher chance of extreme downside returns.

Q34. Trina Romel, mutual fund manager, is taking over a poor-performing fund from a colleague. Romel wants to calculate the return on the portfolio. Over the last five years, the fund's annual percentage returns were: 25, 15, 12, -8, and –14. Determine if the geometric return of the fund will be less than or greater than the arithmetic return and calculate the fund's geometric return: Geometric compared to Geometric Return Arithmetic

4.96%; less than the arithmetic return.

Q35. The respective arithmetic mean and geometric mean returns of the following series of stock market returns are: Year 1 14% Year 2 6% Year 3 −5% Year 4 20%

8.75%; 8.34%.

Q36. An analyst is using the constant growth dividend discount model (DDM) to evaluate XYZ stock. The stock is currently trading at $20 per share and recently paid an annual dividend of $1.50. Assuming a constant growth rate of 4.5%, the implied required rate of return on the stock is closest to:

12.34%.

Q37. Assuming a constant rate of growth in dividends, we can estimate an equity share's:

required rate of return as the sum of its dividend yield and growth rate.

Q38. An investor has the following assets: $5,000 in bonds with an expected return of 8%. $10,000 in equities with an expected return of 12%. $5,000 in real estate with an expected return of 10%. What is the portfolio's expected return?

10.50%.

Q39. Wortel Industries has preferred stock outstanding that paying an annual dividend of $3.75 per share. If an investor wants to earn a rate of return of 8.5%, how much should he be willing to pay for a share of Wortel preferred stock?

$44.12.

Q40. An analyst calculates that the mean of a sample of 200 observations is 5. The analyst wants to determine whether the calculated mean, which has a standard error of the sample statistic of 1, is significantly different from 7 at the 5% level of significance. Which of the following statements is least accurate?:

The alternative hypothesis would be Ha: mean > 7.

Q41. The covariance of returns on two investments over a 10-year period is 0.009. If the variance of returns for investment A is 0.020 and the variance of returns for investment B is 0.033, what is the correlation coefficient for the returns?

0.350.

Q42. An investor looks at her monthly brokerage statement and notices that the yield to maturity on her 5-year corporate bond with a 4% annual coupon rate has gone from 4.2% last month to 3.8% this month. The statement will reflect a bond price that, over the last month, has:

increased.

Q43. An investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12%, what is the current market value of the bond?

$887.

Q44. A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $57,000 per year. Assuming a normal distribution, what is the test statistic given a sample of 115 newly acquired CFA charterholders with a mean starting salary of $65,000 and a standard deviation of $4,500?

19.06.

Q45. An investor spends $365,000 purchasing zero-coupon bonds with a total face value of $500,000 and maturing in 10 years. For the annualized rate of return to be above 3.20%, the bond's price will have to be:

lower than $365,000.

Q46. If Stock X's expected return is 30% and its expected standard deviation is 5%, Stock X's expected coefficient of variation is:

0.167.

Q47. Given a 5% discount rate, the present value of $500 to be received three years from today is:

$432.

Q48. Which of the following statements about hypothesis testing is least accurate?

A Type I error is the probability of rejecting the null hypothesis when the null hypothesis is false.

Q49. Which of the following statements regarding hypothesis testing is least accurate? 1

A type I error is acceptance of a hypothesis that is actually false.

Q50. A 5% trimmed mean ignores the:

highest and lowest 2.5% of observations.

Q51. Which of the following statements concerning skewness is least accurate? A distribution with:

positive skewness has a long left tail.

Q52. The power of the test is:

the probability of rejecting a false null hypothesis.

Q53. An investor purchases a stock on January 1. The annual dividend payments for a stock investment for the next four years, beginning on December 31, are $50, $75, $100, and $125. Based on the cash flow additivity principle, the present value of this series of cash flows will be equivalent to the present value of a $50 annuity and the present value of what series of cash flows?

$0, $25, $50, and $75.

Q54. If an analyst concludes that the distribution of a large sample of returns is positively skewed, which of the following relationships involving the mean, median, and mode is most likely?

Mean > median > mode.

Q55. The correlation between two variables is –0.74. The most appropriate way to interpret this correlation is that:

the two variables have a negative linear association.

Q56. For assets A and B we know the following: E(RA) = 0.10, E(RB) = 0.10, Var(RA) = 0.18, Var(RB) = 0.36 and the correlation of the returns is 0.6. What is the variance of the return of a portfolio that is equally invested in the two assets?

0.2114.

Q57. What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?

20%.

Q58. Given the following box-and-whisker plot: The interquartile range is:

0.5% to 5.2%.

Q59. A perpetual bond with a face value of $100,000 pays annual interest of 5%. The bond is quoted at a yield of 7%. The bond's price is closest to:

$71,500.

Q60. A financial advisor recommends to her client that he buy a 6-year, $1,000 face value bond that pays annual interest of 5%. The yield to maturity is 4.5%, and the client intends to hold the bond as an investment until it matures. The value of the bond today is closest to:

$1,025.

Q61. If a one-tailed z-test uses a 5% significance level, the test will reject a:

true null hypothesis 5% of the time.

Q62. Given the following annual returns, what is the mean absolute deviation? 2000 2001 2002 2003 2004 15% 2% 5% -7% 0%

5.6%.

Q63. What is the standard deviation of a portfolio if you invest 30% in stock one (standard deviation of 4.6%) and 70% in stock two (standard deviation of 7.8%) if the correlation coefficient for the two stocks is 0.45?

6.20%.

Q64. Abeta's stock is trading at $47. Abeta just paid a dividend of $1.50, and markets assume a constant growth rate in dividends of 4%. Abeta's required return on equity is closest to:

7.3%.

Q65. A 15-year zero-coupon German government bond has an annualized yield of –1.5%. Assuming annual compounding, the price of the bond per €100 of principal is closest to:

€125.

Q66. A distribution that is more peaked than a normal distribution is termed:

leptokurtic.

Q67. Consider the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%,15%. The third quartile is:

23%.

Q68. Which of the following portfolios provides the optimal "safety first" return if the minimum acceptable return is 9%? Portfolio Expected Return (%) Standard Deviation (%) 1 13 5 2 11 3 3 9 2

1.

Q69. A sample of returns for four randomly selected assets in a portfolio is shown below: Asset Return (%) A 1.3 B 1.4 C 2.2 D 3.4 What is the sample standard deviation of asset returns?

0.97%.

Q70. Expected returns and standard deviations of returns for three portfolios are shown in the following table: Portfolio Expected Return Standard Deviation 1 9% 5% 2 8% 4% 3 7% 3% Assuming the risk-free rate is 3%, an investor who wants to minimize the probability of returns less than 5% should choose:

Portfolio 1.

Q71. Which of the following statements about hypothesis testing is most accurate?

The probability of a Type I error is equal to the significance level of the test.

Q72. The following table shows the weightings and expected returns for a portfolio of three stocks: Stock Weight E(RX) V 0.40 12% M 0.35 8% S 0.25 5% What is the expected return of this portfolio?

8.85%.

Q73. For the last four years, the returns for XYZ Corporation's stock have been 10.4%, 8.1%, 3.2%, and 15.0%. The equivalent compound annual rate is:

9.1%.

Q74. An investor is choosing between two possible investments. Both have identical future cash flows in all situations, but the investor notices a slight discrepancy in price between the two. What action will this investor take based on the no-arbitrage principle?

Act quickly by buying the lower-priced investment, as the prices will quickly converge.

Q75. A test of whether a mutual fund's performance rank in one period provides information about the fund's performance rank in a subsequent period is best described as a:

nonparametric test.

Q76. For the past three years, Acme Corp. has generated the following sample returns on equity (ROE): 4%, 10%, and 1%. What is the sample variance of the ROE over the last three years?

21.0 (%²).

Q77. Which of the following statements concerning kurtosis is most accurate?

A leptokurtic distribution has fatter tails than a normal distribution.

Q78. What does it mean to say that an observation is at the sixty-fifth percentile?

65% of all the observations are below that observation.

Q79. A data analyst compares the P/E ratios for two companies over a period of 20 years and calculates a two-tailed F-statistic that exceeds the critical F-statistic value. As a result of her findings, she will:

reject the null hypothesis that the P/E ratio variances between the two companies are not significantly different.

Q80. Annual Returns on ABC Mutual Fund Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 Yr 6 Yr 7 Yr 8 Yr 9 Yr 10 11.0% 12.5% 8.0% 9.0% 13.0% 7.0% 15.0% 2.0% -16.5% 11.0% Assuming a mean of 7.2%, what is the sample standard deviation of the returns for ABC Mutual Fund for the period from Year 1 to Year 10?

9.1%.