Question

Suppose stock A has an expected return of 12% and stock B has an expected return of 17%. Stock A has a standard deviation of 5% and stock abs has a standard deviation of 10%. The correlation coefficient is -1. If it is possible to lend and borrow at the risk free rate. What will that rate be

Answer 1

Let w be the proportion in Stock A and 1-w in Stock B

For perfectly negatively correlated stocks, portfolio standard deviation=w1*s1-w2*s2

Risk free rate has zero standard deviation

Hence,
w*5%-(1-w)*10%=0
=>w=2/3
and 1-w=1/3

The portfolio has zero standard deviation i.e., zero risk and hence the returns of the portfolio must equal the risk free rate, to prevent arbitrage

Hence,
Expected returns=w1*R1+w2*R2=2/3*12%+1/3*17%=13.6667%

Hence, risk free rate is 13.6667%