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		12	%		40	%
B		21	%		60	%
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.)

b. Could the equilibrium r_ƒ be greater than 15.60%?

• Yes

Answer 1

Given that 2 stock are available with following details:

Expected return on stock A Ra = 12%

Standard deviation of stock A SDa = 40%

Expected return on stock B Rb = 21%

Standard deviation of stock B SDb = 60%

Correlation between the stock Corr(a,b) = -1

When correlation between two stock is -1, it is possible to create a risk free portfolio, where weight of stock A is calculated as:

Weight of stock A, Wa = SDb/(Sda+SDb) = 60/(40+60) = 60% or 0.6

So, weight of stock B, Wb = 1-Wa = 1-0.6 = 0.4 or 40%

So, risk free rate is weighted average return on this portfolio created.

So, risk free rate rf = Wa*Ra + Wb*Rb = 0.6*12 + 0.4*21 = 15.60%

b). At equilibrium, when there is no arbitrage opportunity, best estimate of risk free rate is 9.6 as calculated above. So, It can not be greater than 15.6% at equilibrium.