Question

Suppose that many stocks are traded in the market and that it is possible to borrow at the riskfree rate. The characteristics of two of the stocks are as follows. Stock A has an expected return of 6% and a standard deviation of 45%. Stock B has an expected return of 10% and a standard deviation of 75%. The correlation between the returns of the two stocks is -1. What should be the equilibrium risk-free rate in the market?

Answer 1

There is perfect negative correlation between Stock A & Stock B. So we can create a risk free portfolio and rate of return for this portfolio in equilbrium will always be risk free

Let weight of stock A in this Portfolio is WA

Let weight of stock B in this Portfolio is 1 - WA

We will set standard deviation equal to 0

0 = 45% * WA - 75% * (1 - WA)

WA = 75%/ 120%

WA = 62.50%

WB = 1 - 62.50% = 37.50%

Expected return on risk free portfolio = 62.50% * 6% + 37.50% * 10%

Expected return on risk free portfolio = 7.50%