Investment Expected Return Standard Deviation 1 20% 38% 2 24% 34% 3 33% 28% 4 34

Question

Investment Expected Return Standard Deviation

1 20% 38%

2 24% 34%

3 33% 28%

4 34% 27%

Consider an investor having the utility function U = E(r) – 0.5 A 2 .

A. On a stand-alone basis, which investment would they select if they are risk-averse with A = 3?

B. If they are risk-neutral, which investment would they pick?

C. 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

A=3

Investment 1: 20%-0.5*3*38%^2=-0.0166

Investment 2: 24%-0.5*3*34%^2=0.066

Investment 3: 33%-0.5*3*28%^2=0.212

Investment 4: 34%-0.5*3*27%^2=0.2365

So, highest is investment hence he will choose Investment 4

2

In case of risk neutrality, only concern is return not risk hence choose Investment 4

3

U=w*12%+(1-w)*6%-0.5*3*w^2*16%^2

Differentiating U w.r.t. w, we get 12%-6%-1.5*16%^2*2*w

Setting it to 0, we get

2w*0.0384=0.06

=>w=0.78125

78.125% will be invested in risky portfolio

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