投资学第10版习题答案06.docx

1、投资学第10版习题答案06投资学第10版习题答案06(总13页)CHAPTER 6: CAPITAL ALLOCATION TO RISKY ASSETSPROBLEM SETS 1. (e) The first two answer choices are incorrect because a highly risk averse investor would avoid portfolios with higher risk premiums and higher standard deviations. In addition, higher or lower Sharpe ratio

2、s are not an indication of an investors tolerance for risk. The Sharpe ratio is simply a tool to absolutely measure the return premium earned per unit of risk. 2. (b) A higher borrowing rate is a consequence of the risk of the borrowers default. In perfect markets with no additional cost of default,

3、 this increment would equal the value of the borrowers option to default, and the Sharpe measure, with appropriate treatment of the default option, would be the same. However, in reality there are costs to default so that this part of the increment lowers the Sharpe ratio. Also, notice that answer (

4、c) is not correct because doubling the expected return with a fixed risk-free rate will more than double the risk premium and the Sharpe ratio.3. Assuming no change in risk tolerance, that is, an unchanged risk-aversion coefficient (A), higher perceived volatility increases the denominator of the eq

5、uation for the optimal investment in the risky portfolio (Equation . The proportion invested in the risky portfolio will therefore decrease.4. a. The expected cash flow is: $70,000) + 200,000) = $135,000.With a risk premium of 8% over the risk-free rate of 6%, the required rate of return is 14%. The

6、refore, the present value of the portfolio is:$135,000/ = $118,421b. If the portfolio is purchased for $118,421 and provides an expected cash inflow of $135,000, then the expected rate of return E(r) is as follows:$118,421 1 + E(r) = $135,000Therefore, E(r) = 14%. The portfolio price is set to equat

7、e the expected rate of return with the required rate of return.c. If the risk premium over T-bills is now 12%, then the required return is:6% + 12% = 18%The present value of the portfolio is now:$135,000/ = $114,407d. For a given expected cash flow, portfolios that command greater risk premiums must

8、 sell at lower prices. The extra discount from expected value is a penalty for risk.5.When we specify utility by U = E(r) 2, the utility level for T-bills is: The utility level for the risky portfolio is: U = A 2 = AIn order for the risky portfolio to be preferred to bills, the following must hold:

9、A = A must be less than for the risky portfolio to be preferred to bills.6. Points on the curve are derived by solving for E(r) in the following equation: U = = E(r) 2 = E(r) 2The values of E(r), given the values of 2, are therefore: 2E(r)The bold line in the graph on the next page (labeled Q6, for

10、Question 6) depicts the indifference curve.7. Repeating the analysis in Problem 6, utility is now:U = E(r) 2 = E(r) 2 = The equal-utility combinations of expected return and standard deviation are presented in the table below. The indifference curve is the upward sloping line in the graph on the nex

11、t page, labeled Q7 (for Question 7). 2E(r)The indifference curve in Problem 7 differs from that in Problem 6 in slope. When A increases from 3 to 4, the increased risk aversion results in a greater slope for the indifference curve since more expected return is needed in order to compensate for addit

12、ional . 8. The coefficient of risk aversion for a risk neutral investor is zero. Therefore, the corresponding utility is equal to the portfolios expected return. The corresponding indifference curve in the expected return-standard deviation plane is a horizontal line, labeled Q8 in the graph above (

13、see Problem 6).9. A risk lover, rather than penalizing portfolio utility to account for risk, derives greater utility as variance increases. This amounts to a negative coefficient of risk aversion. The corresponding indifference curve is downward sloping in the graph above (see Problem 6), and is la

14、beled Q9.10. The portfolio expected return and variance are computed as follows:(1)WBills(2)rBills(3)WIndex(4)rIndexrPortfolio(1)(2)+(3)(4) Portfolio(3) 20% 2 Portfolio5% % = 20% = 5 % = 16% = 5 % = 12% = 5 % = 8% = 5 % = 4% = 5 % = 0% = 11. Computing utility from U = E(r) A2 = E(r) 2, we arrive at

15、the values in the column labeled U(A = 2) in the following table:WBillsWIndexrPortfolio Portfolio 2PortfolioU(A = 2)U(A = 3).0700.0756.0764.0724.0636.0500The column labeled U(A = 2) implies that investors with A = 2 prefer a portfolio that is invested 100% in the market index to any of the other por

16、tfolios in the table.12. The column labeled U(A = 3) in the table above is computed from:U = E(r) 2 = E(r) 2The more risk averse investors prefer the portfolio that is invested 40% in the market, rather than the 100% market weight preferred by investors with A = 2.13. Expected return = 18%) + 8%) =

17、15%Standard deviation = 28% = %14.Investment proportions:% in T-bills 25% =% in Stock A 32% = % in Stock B 43% = % in Stock C15. Your reward-to-volatility ratio: Clients reward-to-volatility ratio: 16. 17. a. E(rC) = rf + y E(rP) rf = 8 + y (18 8)If the expected return for the portfolio is 16%, then

18、:16% = 8% + 10% y Therefore, in order to have a portfolio with expected rate of return equal to 16%, the client must invest 80% of total funds in the risky portfolio and 20% in T-bills.b.Clients investment proportions:% in T-bills 25% =% in Stock A 32% = % in Stock B 43% = % in Stock Cc. C = P = 28%

19、 = %18. a. C = y 28%If your client prefers a standard deviation of at most 18%, then:y = 18/28 = = % invested in the risky portfolio.b. 19. a. y*Therefore, the clients optimal proportions are: % invested in the risky portfolio and % invested in T-bills.b.E(rC) = + y* = + = or % C = 28 = %20. a. If t

20、he period 19262012 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(rM) rf = %, M = % (we use the standard deviation of the risk premium from Table . Then y* is given by:That is, % of the portfolio sh

21、ould be allocated to equity and % should be allocated to T-bills.b.If the period 19681988 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(rM) rf = %, M = % and y* is given by:Therefore, % of the comp

22、lete portfolio should be allocated to equity and % should be allocated to T-bills.c. In part (b), the market risk premium is expected to be lower than in part (a) and market risk is higher. Therefore, the reward-to-volatility ratio is expected to be lower in part (b), which explains the greater prop

23、ortion invested in T-bills.21. a. E(rC) = 8% = 5% + y (11% 5%) b. C = y P = 15% = %c. The first client is more risk averse, preferring investments that have less risk as evidenced by the lower standard deviation.22. Johnson requests the portfolio standard deviation to equal one half the market portf

24、olio standard deviation. The market portfolio , which implies . The intercept of the CML equals and the slope of the CML equals the Sharpe ratio for the market portfolio (35%). Therefore using the CML:23. Data: rf = 5%, E(rM) = 13%, M = 25%, and = 9%The CML and indifference curves are as follows:24.

25、 For y to be less than (that the investor is a lender), risk aversion (A) must be large enough such that: For y to be greater than 1 (the investor is a borrower), A must be small enough: For values of risk aversion within this range, the client will neither borrow nor lend but will hold a portfolio

26、composed only of the optimal risky portfolio:y = 1 for A 25. a. The graph for Problem 23 has to be redrawn here, with:E(rP) = 11% and P = 15%b. For a lending position: For a borrowing position: Therefore, y = 1 for A 26. The maximum feasible fee, denoted f, depends on the reward-to-variability ratio

27、.For y 1, the borrowing rate, 9%, is the relevant risk-free rate. Then we notice that, even without a fee, the active fund is inferior to the passive fund because:.11 .09 f= .13 .09= f = .004.15.25More risk tolerant investors (who are more inclined to borrow) will not be clients of the fund. We find

28、 that f is negative: that is, you would need to pay investors to choose your active fund. These investors desire higher riskhigher return complete portfolios and thus are in the borrowing range of the relevant CAL. In this range, the reward-to-variability ratio of the index (the passive fund) is bet

29、ter than that of the managed fund.27. a. Slope of the CMLThe diagram follows.b.My fund allows an investor to achieve a higher mean for any given standard deviation than would a passive strategy, ., a higher expected return for any given level of risk.28. a. With 70% of his money invested in my funds

30、 portfolio, the clients expected return is 15% per year with a standard deviation of % per year. If he shifts that money to the passive portfolio (which has an expected return of 13% and standard deviation of 25%), his overall expected return becomes:E(rC) = rf + E(rM) rf = .08 + (.13 .08) = .115, or %The standard devia