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Q11. Chris McDonald, CFA, is a portfolio manager for InvesTrack, a firm that seeks to closely track a selected index or indexes with each of its funds. McDonald is analyzing the returns of several of InvesTrack’s managed funds. The primary fund, Marketrack, or the MT portfolio, tracks a combination of a major stock index, bond index, real estate index, and a precious metals index. The stock index in the MT portfolio closely follows the S& 500. The weights on each of the indexes in the MT target portfolio are approximately the same as the weights that the analysts at InvesTrack have estimated for these assets in the overall economy. McDonald believes that the MT portfolio is more likely to lie on the efficient frontier than a portfolio of only stocks. In a recent discussion with his assistants, Joseph Kreager and Maria Ito, McDonald said the low correlations between classes such as precious metals and real estate in the portfolio will improve the diversification of the portfolio. Kreager proposes that the ultimate goal should be to combine assets to achieve the minimum variance portfolio on the efficient frontier. ffice ffice" />
McDonald proposes that the returns of the MT portfolio can serve as a better representation of a market portfolio than an index like the Dow Jones Industrial Average or the S& 500, which many analysts and portfolio managers use as a market proxy. For example, he asserts that betas estimated using the MT portfolio will be a more realistic representation of systematic risk, and this will make the betas more reliable in decisions concerning the effects of diversification. Furthermore, he suggests that the capital asset line (ffice:smarttags" />CAL) based upon the MT portfolio should be steeper than that based upon the S& 500 alone. Kreager claims that that the MT portfolio will only have steeper CAL if the average returns of the indexes other than the stock index in the MT tracking portfolio are higher than the S& 500. Ito responds that MT portfolio CAL will be higher than the S& 500 CAL only if the standard deviation of the returns of the other indexes in the MT tracking portfolio are lower than the S& 500.
Recently a customer holding a position in TTX stock wanted to explore the purchase of shares in a real estate investment trust (REIT). McDonald ran a regression of the return of the stock on the return of the MT portfolio, and he also ran a regression of the REIT’s return on the return of MT portfolio. Using monthly returns over three years, the results of the market model regressions are:
(Return of the TTX stock)t = ?0.006 + 1.28 × (Return of MT portfolio)t + εt
(Return of the REIT) t = 0.014 + 0.60 × (Return of MT portfolio) t + ηt
The annualized standard deviations of the monthly returns for each of these investments are σTTXstock = 38, σREIT = 24, and σMT = 16. McDonald asks Kreager to compute the variance covariance matrix based upon these results. He also asks Kreager to compute the standard deviation of the unexplained risk for each of the assets.
After performing the regressions, Kreager investigates the property of beta drift. Using a monthly time-series, he finds that the betas of both the TTX stock and the REIT both follow an AR(1) process:
βt+1 = 0.1 + 0.9 × βt-1
Using this AR(1) process, Kreager tries to determine if the covariance between the two assets will increase or decrease in the next time period. He assumes the variance of the MT portfolio will remain the same.
After viewing the statistics, Ito gathers information on the S& 500 and finds that its average return is 12%, and the standard deviation is 20%. The current risk-free rate is 5%. She wants to investigate whether McDonald’s assertion that the MT portfolio CAL is steeper than the S& 500 CAL is true.
In Kreager and Ito's responses to McDonald’s proposition that the CAL of the MT portfolio should be steeper than that of the S& 500:
A) only one is correct.
B) both are correct.
C) both are incorrect.
Correct answer is C)
Kreager asserts that the CAL will be steeper if the average returns on the non-stock indexes are greater than the S& 500. The fact is that the slope, which is also called the Sharpe Ratio, also depends upon the standard deviation of the MT portfolio. Without further information, it is impossible to know if Kreager is correct, but his statement is clearly not correct taken in isolation.
Ito asserts that the CAL will be steeper if the standard deviations of the non-stock indexes are less than the S&P 500. The fact is that the slope, which is also called the Sharpe Ratio, also depends upon the return of the MT portfolio. Without further information, it is impossible to know if Ito is correct, but her statement is clearly not correct taken in isolation.
Q12. In response to Kreager’s assertion that the goal is to try to achieve the minimum variance portfolio on the efficient frontier, McDonald should:
A) disagree under any circumstances.
B) agree.
C) agree only if it can be achieved with long positions in assets.
Correct answer is A)
Any portfolio on the efficient frontier with a return greater than the minimum variance portfolio can be combined with the risk-free asset to create a portfolio that has a superior risk-return tradeoff when compared with the minimum variance portfolio. Thus, achieving the minimum variance portfolio would not be a worthwhile goal.
Q13. With the given information, Ito finds that the CAL of the S&P 500 is equal to the CAL of the MT portfolio if the return of the MT portfolio equals:
A) 10.6%.
B) 8.6%.
C) 11.4%.
Correct answer is A)
The CAL of the S&P 500 is 0.35 = (12 ? 5) / 20. To find the return that gives this slope for the CAL, Ito would solve for R in the expression 0.35 = (R ? 5) / 16. This gives 5.6 = R ? 5, R = 10.6.
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发表于 2009-4-2 11:06
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