Assignment for Chapter3:
1. Assume that two securities constitute the market portfolio. Those securities have the following
expected returns, standard deviations, and proportions: Security A B Expected Return 10% 15 Standard Deviation 20% 28 Proportion 0.4 0.6 The correlation between the two securities is 0.30. A risk free rate is 5%. Specify the equation of capital market line.
2. You are given the following information on two securities, the market portfolio, and the risk
free rate: Security 1 Security 2 Market portfolio Risk free rate Expected Return 15.5% 9.2 12.0% 5.0% Correlation with Market Portfolio 0.9 0.8 1.0 0.0 Standard Deviation 20% 9% 12.0% 0.0 (1) Draw the SML. (2) Plot the two securities on the SML.
3. Given that the expected return on the market portfolio is 10%, the risk free rate of return is
6%, the beta of stock A is 0.85, and the beta of stock B is 1.20: (1) Draw the SML.
(2) What is the equation for the SML?
(3) What are the equilibrium expected returns for stocks A and B? (4) Plot the two risky securities on the SML.
4. There are one risk-free bond and N stocks, no market friction. A is a stock. M is a stock
market portfolio
Month
1 31.5% 22%
2 27.5% 20%
3 25.5% 18%
4 19.5% 16%
5 31.5% 24%
rAi rM
Assume the yield of stocks follows rAi?E(rAi)??Ai, question:
(1) Please calculate the expected yield and its Standard deviation of A; (2) Please calculate the expected yield and its Standard deviation of M; (3) Please calculate the covariance cov(rA,rM);
(4) Please calculate the value of rf ? (under the market equilibrium)
22?S(5) Please calculate the system risk and the individual risk ?I(Assume the total risk
of stock A is ?2(rA)= ?2S+ ?2I)
5. There are two risky assets A and B.
Asset Expected yield Standard deviation （1） If
A 10%
0.15
B 6% 0.10
?(rA,rB)?0.5, How to use the two assets to get a portfolio, which expected yield
is 8%? What is the Standard deviation of the portfolio? （2） If
?(rA,rB)??0.5, How to use the two assets to get a portfolio, which expected
yield is 8%? What is the Standard deviation of the portfolio?
Assignment for Chapter 3宋逢明金融工程习题
