Problem 2: Risk Aversion and Capital Allocation [10 points Standard Deviation 38

Question

Problem 2: Risk Aversion and Capital Allocation [10 points Standard Deviation 38% 34% 28% 27% Investment Expected Return 20% 24% 33% 34% 4 Consider an investor having the utility function U E(r)-0.5 A . A. [3 points] On a stand-alone basis, which investment would they select if they are risk-averse with A =37 B. [3 points] If they are risk-neutral, which investment would they pick? C. [4 points] If the investor with A-3 allocates their wealth between a risky portfolio P having expected return of 12% and standard deviation of 16% and the risk-free asset which returns 6% what fraction (y) of their wealth will they allocate to the risky portfolio?

Explanation / Answer

1.

U=20%-0.5*3*38%^2=-0.0166

U=24%-0.5*3*34%^2=0.0666

U=33%-0.5*3*28%^2=0.2124

U=34%-0.5*3*27%^2=0.23065

So choose option 4

2. Risk neutral would prefer return irrespective of risk and hence they would prefer 4

3.

Invested in risky portfolio, y*=(12%-6%)/(3*16%^2)=0.78125=78.125%

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