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Assignment for Chapter 3宋逢明金融工程习题

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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

AssignmentforChapter3:1.Assumethattwosecuritiesconstitutethemarketportfolio.Thosesecuritieshavethefollowingexpectedreturns,standarddeviations,andproportions:S
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