Question

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

Stock	Expected Return			Standard Deviation
A		8	%		55	%
B		4	%		45	%
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

Correlation = -1

So,

Standard Deviation = WaSa - WbSb

for risk free standard deviation = 0

0 = Wa(0.55) - (1 - Wa)0.45

0 = 0.55Wa - 0.45 + 0.45Wa

Wa = 45.00%

Expected Return = 0.45(0.08) + 0.55(0.04)

Expected Return = 5.80%