Question

Suppose that many stocks are traded in the market and that it is possible to borrow...

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 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 rƒ be greater than 15.60%?

  • Yes

Homework Answers

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.

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