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 5 % 45 % B 10 % 55 % 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.)

Answer 1

For two stock with a correlation of -1, it is possible to form an risk free portfolio without borrowing.

Weight of asset A in such portfolio Wa = SDb/(SDa + SDb)

standard deviation of stock A SDa = 45%

standard deviation of stock b SDb = 55%

=> Wa = 45/(45+55) = 45%

And weight of asset B Wb = 1-Wa = 1 - 0.45 = 55%

Expected return on this portfolio is weighted average return on its assets

=> E(p) = Wa*Ra + Wb*Rb = 0.45*5 + 0.55*10 = 7.75%

So,  expected rate of return on this risk-free portfolio = 7.75%