Suppose two investments have the same three payoffs but the probability associat

Question

Suppose two investments have the same three payoffs but the probability associated with each payoff differs, as illustrated in the table below:

Payoff Probability (Investment A) Probability (Investment B)

$300 0.10 0.30

$250 0.80 0.40

$200 0.10 0.30

Find the expected return and standard deviation of each investment. Jill has the utility function U=5I, where I denotes the payoff.

Which investment will she choose?

Ken has the utility function U=5I. Which investment will he choose?

Laura has the utility function U=5I^2. Which investment will she choose?

Explanation / Answer

Answer:

a)

Investment A:

Expected return = (300*0.1) + (250*0.8) + (200*0.1) = 250

Standard deviation: Sqrt [ [(3002 *0.1) + (2502 *0.8) + (2002 *0.1)] – 2502 ] = sqrt 500 = 22.36

Investment B:

Expected return = (300*0.3) + (250*0.4) + (200*0.3) = 250

Standard deviation: Sqrt [ [(3002 *0.3) + (2502 *0.4) + (2002 *0.3)] – 2502 ] = sqrt 1500 = 38.72

b)

Investment A:

EU = (5*300*0.1) + (5*250*0.8) + (5*200*0.1) = 1250

Investment B:

EU = (5*300*0.3) + (5*250*0.4) + (5*200*0.3) = 1250

Outcome: Indifferent between both option

c)

Investment A:

EU = ((5*300)0.5*0.1) + ((5*250)0.5*0.8) + ((5*200)0.5*0.1) = 35.32

Investment B:

EU = ((5*300)0.5*0.1) + ((5*250)0.5*0.8) + ((5*200)0.5*0.1) = 35.25

Outcome: Investment A

d)

Investment A:

EU = (5*300*300*0.1) + (5*250*250*0.8) + (5*200*200*0.1) = 315000

Investment B:

EU = (5*300*300*0.3) + (5*250*250*0.4) + (5*200*200*0.3) = 320000

Outcome: Investment B

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