Question

(a) Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows Stock A B Expected Return Standard Deviation 10% 5% 15% 10% Correlation =-1 Suppose that it is possible to borrow at the risk-free rate, If. What must be the value of the risk-free rate? Explain. HINT!!! The stocks are perfectly negatively correlated. (b) Calculate the expected return and standard deviation of an equally weighted portfolio of Stock A, Stock B and the risk-free asset. What is the optimal portfolio? Assume the investors risk aversion coefficient is given by A=4. Provide all the relevant portfolio weights for all three assets. The utility function is given below. HINT: The formula sheet contains a formula for the optimal risky portfolio for the special case of two risky assets. Uị = E(ri) - 0.5A0?

Answer 1

Risk-free rate is the rate at which the standard deviation is zero.

	A	B	Risk-free
Returns	10%	15%	11.67%
S.D.	5%	10%	0.00%
Weight	66.65%	33.35%

We need to find weights of A and B such that the standard deviation of the portfolio is zero. With 66.65% in A and balance in B, we get risk-free rate = 11.67% as the standard deviation for that portfolio is zero.

Expected Return = 50% x 10% + 50% x 15% = 12.50%

Std. Dev. = [(50% x 5%)^2 + (50% x 10%)^2 + (2 x 50% x 50% x 5% x 10% x -1)]^(1/2) = 2.50%