Question

Q.8      Consider the following assets:

asset	Expected return	Standard deviation	Beta
Risk-free asset	0.06	0	0
Market portfolio	0.22	0.20	1
Stock E	0.24	0.25	1.25

An investor wants to earn 24%, which one of the following strategies is optimal? Explain why suboptimal strategies should not be chosen.

1. Borrow at the risk-free rate and invest in stock E because the risk –free asset will offset some of the risk of stock E.
2. Borrow at the risk-free rate and invest in the market portfolio, even though this strategy is riskier than investing all of the available funds in the market portfolio.
3. Invest 100% of the available funds in stock E since its expected return is appropriate for its beta.
4. Invest 100% of the available funds in the market portfolio.

Answer 1

Let w be the weight in market portfolio and 1-w in risk free rate

w*0.22+(1-w)*0.06=0.24
=>w=(0.24-0.06)/(0.22-0.06)
=>w=1.12500

Borrow 12.5% at risk free and invest own as well as borrowed money in market portfolio

Borrow at the risk-free rate and invest in the market portfolio, even though this strategy is riskier than investing all of the available funds in the market portfolio.

Suboptimal strategies mean they provide either higher risk for the same return or lower return for the same risk. Thus they provide lower utility and hence should not be chosen