Question

Suppose there are only two risky assets in the world (or some people are restricted to invest in only
two assets), the stock of an oil company with expected return equal to 10% and a volatility of 30%,
and the stock of an alternative energy company with expected return of -1% and volatility of 10%.
The covariance is equal to -0.01. a) What is the portfolio with lowest volatility? b) What is the
expected return and volatility of this portfolio? c) Suppose there is a risk-free asset with risk-free rate
equal to 1%, does it make sense for a rational and risk-adverse person to ever invest in an asset with
negative expected return? Why?

Answer 1

1.
weight of oil company=((10%)^2-(-0.01))/((30%)^2+(10%)^2-2*(-0.01))
=0.166666667

weight of energy company=1-0.166666667=0.833333333

2.
Expected return=0.166666667*10%+0.833333333*(-1%)=0.8333%

Volatility=sqrt((0.166666667*30%)^2+(0.833333333*10%)^2+2*0.166666667*0.833333333*(-0.01))=8.1650%

3.
Yes, for diversification when correlation is negative