Question

Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, r_f . The characteristics of two of the stocks are as follows:

Stock	Expected Return				Standard Deviation
A		10	%			35	%
B		16				65

Correlation = –1

Required:

(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?) (Omit the "%" sign in your response. Round your answer to 2 decimal places.)

Rate of return

%

(b)	Could the equilibrium rf be greater than 12.1%?

Answer 1

(a) Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio in equilibrium will always be the risk-free rate. To find the proportions of this portfolio [with wA invested in Stock A and wB= (1 – wA) invested in Stock B], set the standard deviation equal to zero. With perfect negative correlation, the portfolio standard deviation reduces to:

?P= Abs[wA*?A?wB*?B]

0 = 0.35*wA? 0.65*(1 – wA)

Wa=0.65

Wb =(1-0.65) = 0.35

Expected return of this risk-free portfolio is:

E (r ) = 0.65*10% +0.35*16% = 12.1%

Therefore, risk free rate of return = 12.1%

(b) NO. Equlibrium rf cannot be grater than 12.1% since risk free rate should be 12.1% and not greater.