Question

Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rƒ. The characteristics of two of the stocks are as follows: Stock Expected Return Standard Deviation A 6 % 20 % B 10 % 80 % 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 rƒ be greater than 6.80%?

Yes or No

Answer 1

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 thisportfolio [with wAinvested in Stock A and wB= (1 – wA) invested in Stock B], set the standard deviationequal to zero. With perfect negative correlation, the portfolio standard deviation reduces to:

?P= ABS[wA?A– wB?B]

0 = 20 wA– 80(1 – wA) ,wA= 0.80

The expected rate of return on this risk-free portfolio is:

E(r) = (0.80 ×0.06) + (0.20 ×0.10) = 6.80%

b.No

E(r) = 6.80%Therefore, the risk-free rate must also be 6.80%.

Thanks