Question 1 - Designing a risk-free asset (7+3)

Assume you have 2 risky assets: a bond fund & an equity fund.

w_D bond fund weight, with expected returns & variance: E(r_D) and s_D ²

w_E stock fund weight, with E(r_E) and s_E²

s_DE covariance between these funds = s_D. s_E with s_D ? s_E.

In what proportion do you have to mix these funds to create a risk-free portfolio? What is the risk-free rate in this market?

Question 2 Part I- Diversification & trading strategies: (2+3 points)

a)Suppose there are only 2 stocks x & y in the market and their returns are always related to one another by x=2y+0.05. Can an investor get any benefit from diversification in this market?

b)Can you design a long-short trading strategy in this market that will give you risk free returns? Elucidate.

Question 2 Part II - CAPM: (5 points)

We saw in class that the CAPM relates risk to expected returns for every security in the market, & Risk in CAPM is covariance. Suppose I told you that the relationship between risk and return given by the security market line was linear. That is, for any security x:

E(R_x)=a+b.?_Mx.

Use just this information to derive the CAPM equation/formula. (Hint: Two securities/portfolios that lie on the security market line are the risk-free asset & the market).

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