Question

Finance

3. Suppose that there are many stocks in the security market and that the characteristics of stocks A and B are given as follows: Stock Expected Return 10% 15% Standard Deviation 5% 10% The correlation between the stock returns is -1. Suppose that it is possible to borrow at the risk-free rate, rf. What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from stocks A and B.)

Answer 1

Given for Stocks

E(A) = 10%

SD(A) = 5%

E(B) = 15%

SD(B) = 10%

Corr(A,B) = -1

Desired standard deviation = 0

let assume weight of stock A is w, then weigh of stock B is (1-w)

standard deviation of a portfolio with p = -1 is w1*sd1 + w2*sd2

So here 0 = w*5 + (1-w)*10

So, w = 2

so weight of A is 2 and weight of B is -1

with these weight risk free rate = 2*10 - 1*15 = 5%

So, risk free return = 5%