Suppose that many stocks are traded in the market and that it is possible to bor

Question

Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rf. The characteristics of two of the stocks are as follows: Stock Expected ReturnStandard Deviation 8% 15% 35 % 65 % Correlation =-1 a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be substituted for the risk-free asset?) (Round your answer to 2 decimal places.) Rate of return b. Could the equilibrium rf be greater than 10.45%? Yes No

Explanation / Answer

Variance of portfolio:

p^2 = w1^2*1^2 + w2^2*2^2 + 2*w1*w2*1*2*

Given = -1

p^2 = w1^2*1^2 + w2^2*2^2 + 2*w1*w2*1*2*(-1)

p^2 = (w1*1 - w2*2)^2

p = |w1*1 - w2*2|

To make this portfolio risk-free, put p = 0

w1/w2 = 2/ 1 = 0.65/0.35 = 13/7, w1 = 13/20, w2 = 7/20

Return on risk-free portfolio = (13/20)*8 + (7/20)*15 = 10.45%

Equilibrium rf equals to 10.45%

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