Question

Asset A has a mean return of 0.03 and a standard deviation of 0.04, while asset B has a mean return of 0.06 and standard deviation of 0.08. Their returns are perfectly negatively correlated (correlation coefficient of -1).

a. Assuming absence of arbitrage, what must the risk-free rate be?

b. Suppose that in fact the risk-free rate were 0.02. Describe how one would exploit the arbitrage situation (what would you buy, and what would you sell?)

Answer 1

1.
Risk free asset has zero standard deviation

A zero standard deviation portfolio can be created by combining two assets which are perfectly negatively correlated

Let w be the weight of Asset A and 1-w be the weight of Asset B

Hence,
w*0.04-(1-w)*0.08=0
=>w=0.08/(0.04+0.08)
=>w=0.666666667

Expected returns of the portfolio must be equal to the risk free rate

Hence, risk free rate=0.666666667*0.03+(1-0.666666667)*0.06=0.04

2.
Borrow money at risk free rate or sell a treasury bond
Buy Asset A and Asset B