An investor has funds available to invest in one of three choices: a high-risk s

Question

An investor has funds available to invest in one of three choices: a high-risk stock, a low-risk stock, or a savings account that pays a sure $500. If he invests in the stocks, his payoff for the two stocks depends in part on what happens to the market as a whole. if the market goes up he can expext to earn $1500 from the high risk stock and $1000 from the low-risk stock. If the stock market goes down he will lose $1000 with the high risk stock and $100 with the low risk stock. The situation is as shown by the decision tree below. If t and v represents the probabilities of the market going up or down respectivitely then:

a. conduct sensitivity analysis using expected monetary value and determine the regions over which each option is better.

b. if t=0.35 and v=0.65, which option is the best.

Hint: use t+v=1 in your analysis and the dimension of the problem will reduce to one. The regions of interest will be segments over the line defined on t where 0<=t<=1

Market goes up ! 1.500 Market goes down V-1000 High-Risk Stock Market goes up 1 1,000 Low Risk Stock Market goes down 0 -100 500 Savings Account

Explanation / Answer

a) assume probability for market going up = t

probability for market going down = 1- t

for low risk zone to attractive: return from low risk > savings account

we calculate at equality: 1000*t + (1-t)*-100 = 500

1000t +100t - 100 = 500

1100t = 600

t= 0.5455

Hence above probability of 54.55% market going up low risk stock is prefered, probability of market going down:

1 - 0.5455 = 45.45%

comparing high risk and low risk:

the returns of high risk and low risk are equal at:

1500t + (1-t)*(-1000) = 1000t + (1-t)*(-100)

1500t + 1000t - 1000 = 1000t + 100t - 100

1400t = 900

t = 0.6429

hence above 64.29% high risk stock becomes attractive at low risk stock.

for market going up, From probability of 0% to 54.55% savings account should be preffered, from 54.55% to 64.29% low risk stock to be preffered and above 64.29% high risk stock to be preferred.

b) if t = 0.35 = 35% it is less than 54.55% hence savings account should be preffered.

lets verify with calculation.

expected return of low risk = 1000*0.35 - 100*0.65 = 350 - 65 = 285

expected return of high risk = 1500*0.35 - 1000*0.65 = 525 - 650 = -125

hence expected return of savings is higher at 500.

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