投资学第10版习题答案06.docx

1、投资学第10版习题答案06CHAPTER 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 ratios are not an indica

2、tion 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, this increment wou

3、ld 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 (c) is not correct b

4、ecause 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 equation for the opti

5、mal investment in the risky portfolio (Equation 6.7). The proportion invested in the risky portfolio will therefore decrease.4. a. The expected cash flow is: (0.5 $70,000) + (0.5 200,000) = $135,000.With a risk premium of 8% over the risk-free rate of 6%, the required rate of return is 14%. Therefor

6、e, the present value of the portfolio is:$135,000/1.14 = $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 equate

7、 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:$135,000/1.18 = $114,407d. For a given expected cash flow, portfolios that command greater risk premiums m

8、ust sell at lower prices. The extra discount from expected value is a penalty for risk.5.When we specify utility by U = E(r) 0.5A 2, the utility level for T-bills is: 0.07The utility level for the risky portfolio is: U = 0.12 0.5 A (0.18)2 = 0.12 0.0162 AIn order for the risky portfolio to be prefer

9、red to bills, the following must hold:0.12 0.0162A 0.07 A 0.05/0.0162 = 3.09A must be less than 3.09 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 = 0.05 = E(r) 0.5A2 = E(r) 1.52The values of E(r), given the value

10、s of 2, are therefore: 2E(r)0.000.00000.050000.050.00250.053750.100.01000.065000.150.02250.083750.200.04000.110000.250.06250.14375The bold line in the graph on the next page (labeled Q6, for Question 6) depicts the indifference curve.7. Repeating the analysis in Problem 6, utility is now:U = E(r) 0.

11、5A2 = E(r) 2.02 = 0.05The 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 next page, labeled Q7 (for Question 7). 2E(r)0.000.00000.05000.050.00250.05500.100.01000.07000.150.02

12、250.09500.200.04000.13000.250.06250.1750The 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 additio

13、nal . 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 (se

14、e 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 labe

15、led 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 Portfolio0.05%1.013.0% 13.0% = 0.130 20% = 0.200.04000.250.813.0 11.4% = 0.114 16% = 0.160.02560.450.613.0 9.8% = 0.098 12% = 0.120.01440.650.413.0 8.2% = 0.082 8% = 0.080.00640.850.213.0 6.6% = 0.066 4% = 0.040.00161.050.013.0 5.0% = 0.050 0% = 0.000.000011. Com