An investor can borrow or invest at a risk-free rate of 4%. The investor is a...

An investor can borrow or invest at a risk-free rate of 4%. The investor is a mean-variance utility maximize with a risk aversion coefficient A = 4. What is the expected return on an optimal allocation between the risk-free security and a risky portfolio with an expected return of 10% and a volatility of 20%?

Expert Solution

Investment proportio in risky portfolio = (Expected return on risky portfolio - Risk free rate) / (Risk Aversion * (Standard Deviation)²)

Investment proportio in risky portfolio = (10% - 4%) / (4 * (20%)²)

Investment proportio in risky portfolio = 37.5%

Investment proportio in risk free rate = 1 - Investment proportio in risky portfolio

Investment proportio in risk free rate = 1 - 37.5%

Investment proportio in risk free rate = 62.5%

Expected return of optimal porfolio = Investment proportio in risk free rate * Risk free rate + Investment proportio in risky portfolio * Return of Risky portfolio

Expected return of optimal porfolio = 62.5% * 4% + 37.5% * 10%

Expected return of optimal porfolio = 6.25%

jeff jeffy answered 2 years ago

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