Portfolio Management and Measurements - Review Questions Flashcards
If you want to lower the risk of a portfolio of securities, you would want at least some of your securities to ______________?
Choose the best answer.
1) Have zero value for covariance
2) Have a positive covariance
3) Have a negative covariance
4) Covariance is unrelated to diversification
3) Have a negative covariance
Negative covariance helps diversification because at least some of the securities’ risks offset others within the portfolio.
According to the CAPM, which of the four is the most efficient?
Choose the best answer.
1) Asset A has a return of 14%; beta = 1.25; standard deviation = 18%
2) Asset B has a return of 10%; beta = 1.15; standard deviation = 14%
3) Asset C has a return of 19%; beta = 1.45; standard deviation = 24%
4) Asset D has a return of 17%; beta = 1.25; standard deviation = 21%
4) Asset D has a return of 17%; beta = 1.25; standard deviation = 21%
When the risk free rate is not known, you cannot use the Sharpe Index or the Treynor index. Based on the information provided, the risk assessment investment statistic under the CAPM that details relative efficiency is Coefficient of Variation, which is Standard Deviation, divided by return. Since the risk measure is the numerator, the lower the result - the better the risk return relationship; that is, it is more efficient. The CV for asset D is 1.235 which is the lowest. Simply, for every unit of return (for which Asset D has 17), there is 1.235 units of risk. Assets A, B, and C have CV of 1.286, 1.4, and 1.263, respectively.
Portfolio A has E(r) of 8% and a standard deviation of 16.6%. Portfolio B has E(r) of 13% and a standard deviation of 22.4%. The benchmark index (the S&P 500) has E(r) of 7.01% and a standard deviation of 17.9%. The risk-free rate is 4%. Which of the two portfolios performed better? How did they do against their benchmark?
SHARPE A - (.08−.04) / .1660 = .241
SHARPE B - (.13−.04) / .224 = .402
SHARPE sp500 - (.0701−.04) / .179 = .1682
The inequality SHARPEA < SHARPE B or 0.241 < 0.402 indicates that Portfolio B has a better risk-adjusted return than Portfolio A. Both portfolios outperformed the S&P 500. Portfolio B had the best risk-adjusted return for that time.
Which of the following stocks has less risk over time on a relative basis: Stock Y, with an average expected return of 20% and a standard deviation of 3; or Stock Z, with an average expected return of 27%, and standard deviation of 5?
1) Stock Z, because it has a higher expected return.
2) Stock Z, because it has a lower coefficient of variation.
3) Stock Y, because it has a lower coefficient of variation.
4) Stock Y, because it has a lower standard deviation.
3) Stock Y, because it has a lower coefficient of variation.
The important metric here in determining which security is more risky is the size of the standard deviation relative to the average returns. The coefficient of variation is this metric used. For stock Y, the coefficient of variation is: 3/20= 0.15. For stock Z, the coefficient of variation is: 5/27= 0.19. Therefore, stock Y is less risky by comparison.
Which of the following statements concerning correlation is (are) correct?
I) The returns of Security A would increase 5% when the returns of Security B increased 5% if the correlation coefficient for the returns of the two securities were +1.
II) A correlation coefficient of -1 for the returns of two securities indicates that both securities should be considered for inclusion in a broad portfolio since maximum risk reduction could be achieved by including both.
1) I only
2) II only
3) Both I and II
4) Neither I nor II
3) Both I and II
Both of these statements are correct regarding correlation.
David owns a stock that has a beta of -2.0 and a standard deviation of 16.3. If the market declines by 5%, he should expect his stock to:
1) Decline by 10%
2) Rise by 11.3%
3) Rise by 10%
4) Decline by 20%
3) Rise by 10%
If a stock has a beta of -2.0, it will move double in the opposite direction of the market. Therefore the stock will return 10% in this case.
The following information is available on Funds A and B:
Fund A Fund B Market Index Realized Return 16% 19% 17% Beta 0.75 1.25 1 Standard Deviation 3.3 5.5 4.2 R^2 85 80 100
The T-bill rate is 4.5%
Which of the following statements concerning Funds A and B is correct?
1) The investor should purchase Fund B because the Treynor Index is higher than for fund A.
2) The investor should purchase fund A because the Sharpe Index is lower than for Fund B.
3) The investor should purchase Fund A because the alpha is higher than for Fund B.
4) The investor should purchase Fund B because the realized return is higher than for Fund A.
3) The investor should purchase Fund A because the alpha is higher than for Fund B.
The high R^2 indicates that the funds are diversified. Beta is the measure of nondiversifiable risk. The Sharpe ratio uses the standard deviation to measure risk and the alpha measurement uses beta. Therefore, the investor should make use of the alpha index or the Treynor Index. For Fund A, alpha is calculated as follows:
Alpha for Fund A: 16- [4.5 + (17-4.5)0.75]= 2.125
Alpha for Fund B: 19- [4.5 + (17-4.5)1.25]= -1.125
Treadmar Corporation has an average return of 24% and a standard deviation of 10%. Assuming the historical returns for Treadmar are normally distributed, what is the probability that this stock will have a return greater than 4%?
Choose the best answer.
1) 2.5%
2) 34%
3) 95%
4) 97.5%
4) 97.5%
The mean is given as 24%. First, subtract the standard deviation of 10% to the left and to the right of the mean of the standard bell-shaped curve to find the first standard deviation of 14% through 34% probability of returns. Next, subtract the standard deviation of 10% to the left and right of the mean of the standard bell-shaped curve to find the second standard deviation of 4% through 44%. Therefore, to obtain the probability of a return greater than 4%, you add the 47% probability of the second standard found on the left of the mean plus the 50% that is greater than the mean for a probability of 97.5%.
In computing portfolio performance, the Sharpe Ratio uses ___________, while the Treynor Index uses ________ in terms of measuring risk.
I) Beta
II) Variance
III) Correlation coefficient
IV) Standard Deviation
1) IV and I
2) III and IV
3) I and III
4) II and IV
1) IV and I
The Sharpe ratio is calculated as the excess return divided by the standard deviation. The Treynor ratio is calculated by dividing the excess return by beta.
