# FINANCE-BMGT 343: Problem Set 2

BMGT 343: Problem Set 21. Mean-variance analysis tells us what expected returns and covariances should be. True or False?2. If portfolio A has a higher Sharpe ratio than portfolio B, then an investor with mean-variance preferences will prefer investing all his wealth A vs all in B. True or False?3. Can indiﬀerence curves for the same person cross?4. Why is there systematic risk? That is, why can’t all risk be diversiﬁed away?5. YouAssetE [r]observetheRisk-freeABP5%10% 12% 11%0%10% 15% 13%Someone proposes that P is the global MVE portfolio. Is this possible?following:6. YouAssetE [r]observethefollowing:Risk-freeAB5%8% 20%0%25% 50%⇢AB = 0.5. Let P ⇤ be the portfolio formed from A and B with the highest possible Sharpe ra2tio. An investor has the following utility function: U [rp ] = E [rp ]2 p . That investor’s optimal⇤⇤combination of P and the risk-free asset puts 80% weight on P and invests 20% in risk-free. Whatis ? (Assume A and B are the only risky assets)7. You are given the following information (all returns and standard deviations are per year unless otherwise speciﬁed):• E [rA ] = 9%, E [rB ] = 13%, rf = 3%•A= 40%,B= 50%• The optimal (MVE) combination of A and B puts 1/3 weight on asset A and 2/3 on B(a) What is ⇢A,B (the correlation between rA and rB )?2(b) An investor has the utility function U [rp ] = E [rp ] 2 p , with = 0.25. If the only assets in theworld are A, B, and risk-free, how should he invest his wealth?

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