solution-to-第三章-习题

1、1. You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%.(1) Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected value and standard deviation of the rate of retu

2、rn on his portfolio?(2) Suppose that your risky portfolio includes the following investments in the given proportion stock A 25%; stock B 32%; stock C 43%. What are the investment proportions of your clients overall portfolio, including the position in T-bill?(3) What is the reward to variability ra

3、tio(S) of your risky portfolio? Your clients(4) Draw the CAL of your portfolio on an expected return-standard deviation diagram, what is the slope of the CAL? Show the position of your client on your funds Cal(5) Suppose that your client decides to invest in your portfolio a proportion y of the tota

4、l investment budget so that the overall portfolio will have an expected rate of return of 16%. What is the proportion y? What are your clients investment proportions in your three stocks and the T-bill fund? What is the standard deviation of the rate of return on your clients portfolio?(6) Suppose t

5、hat your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolios standard deviation will not exceed 18%. What is the investment proportion y? What is the expected rate of return on the co

6、mplete portfolio?(7) Your clients degree of risk aversion is A=3.5. What proportion y of the total investment should be invested in your fund? What is the expected value and standard deviation of the rate of return on your clients optimized portfolio? Solution:(1) Expected return=0.3*8%+0.7*18%=15%

7、standard variance=0.7*28%=19.6%(2) Proportion: T-bill 30% A: 0.7*25%=17.5%;B:0.7*32=22.4%;C:0.7*43%=30.1%(3) My reward to variability ration=(18-8)/28=0.3571; clients=(15-8)/19.6=0.3571(4)(5) the expected return of portfolio= If the expected return of portfolio=16% then y=0.8 which means 80% must in

8、vested in risk fund and 20% in T-bill, the completely proportion as: T-bill 20%;A 0.8*25%=20%,B:0.8*32%=25.6%;C:0.8*43%=34.4%Standard variance=0.8*28%=22.4%(6) because the standard variance=y*28%, if it less than 18%, then y=18/28=64.29% and expected return=8+10y=14.429%(7) =(18-8)/(0.01*3.5*28*28)=

9、0.3644Expected return of optimal=8+10y=11.644%Standard variance=0.3644*28=10.20%2. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 8%.

10、The probability distribution of the risky funds is as follows: Expected return Standard deviation Stock fund (S) 20% 30% Bond fund (B) 12% 15% The correlation between the fund returns is 0.1. 1) What are the investment proportions in the minimum-variance portfolio of the two risky funds, and what is

11、 the expected value and standard deviation of its rate of return? 2) Tabulate and draw the investment opportunity set of two risky funds. Use investment proportions for the stock funds of zero to 100% in increments of 20%. 3) Draw a tangent from the risk-free rate to the opportunity set. Solve numer

12、ically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. 4) You require that your portfolio yield an expected return of 14% a) What is the standard deviation of your optimal portfolio? b) What is the proportion invested in the T-bill

13、 fund and each of two risky funds? 5) If you were to use only the two risky funds, and still require an expected return of 14%, what must be the investment proportions of your portfolio? Compare its standard deviation to that of the optimized portfolio in Problem 4). What do you conclude? Solution:(

14、1)Expected return=0.1739*20+0.8261*12=13.39%Standard variance=13.92%(2)Stock(%)Bond(%)Expected returnVariance0100121517.3982.6113.3913.92208013.613.94406015.215.7045.1654.8415.6116.54604016.8019.53802018.4024.4810002030(3)Max slope of Cal then proportion of stock=0.4516 and bond=0.5484Expected return of optimal portfolio=0.4516*20+0.5484*12=15.61Standard variance=16.54(4) A: because Now required return=14%, then standard variance=13.04% B: because then y=0.7884, 1-y=0.2116, the proportion