You need to invest $30M in two assets: a risk-free asset with an expected return of 6% and a risky asset with an expected return of 15% and a standard deviation of 35%

Finance Dec 22, 2020

You need to invest $30M in two assets: a risk-free asset with an expected return of 6% and a risky asset with an expected return of 15% and a standard deviation of 35%. You face a cap of 25% on the portfolio's standard deviation. What is the maximum expected return you can achieve on your portfolio? (4 marks) What is the corresponding Sharpe ratio of the portfolio with the maximum expected return?

Expert Solution

Weight of market portfolio=Desired standard deviation/Standard deviation of market portfolio=25%/35%=0.71429

Weight of risk free asset=1-weight of market portfolio=1-0.71429=0.28571

Maximum expected return=Weight of market portfolio*Returns of market portfolio+Weight of risk free asset*Returns of risk free asset=25%/35%*15%+(1-25%/35%)*6%=12.4286%

Sharpe ratio=(portfolio returns-risk free rate)/portfolio standard deviation=(12.4286%-6%)/25%=0.25714

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