Question

Problem 2. Warren Buffy is an enormously wealthy investor who has built his fortune through his legendary investing acumen. He currently has been offered three major investments and he would like to choose one. The first one is a conservative investment that would perform very well in an improving economy and only suffer a small loss in a worsening economy The second is a speculative investment that would perform extremely well in an improving economy but would do very badly in a worsening economy. The third is a counter-cyclical investment that would lose some money in an improving economy but would perform well in a worsening economy. Warren believes that there are three possible scenarios over the lives of these potential investments: (1) an improving economy, (2) a stable economy, and (3) a worsening econ- omy. He is pessimistic about where the economy is headed, and so has assigned probabil- ities of 0.57, 0.29, and 0.14, respectively to these three scenarios. He also estimates that his profits (in millions of dollars) under these respective scenarios are those given by the following table:

Answer 1

Answer

A) For Maximin approach we will find minimum payoff for each investment and then we select the investment with maximum payoff.

So Minimum Payoff for

Conservative=-30

Speculative=-10

Counter cyclical =-20

So from above investments maximum payoff is for Speculative investment.So according to Maximin approach Warren will choose Speculative investment.

B)

Expected payoff= probability of improving economy*Payoff for improving economy+probability of Stable economy*Payoff for Stable economy+probability of worsening economy*Payoff for worsening economy

Expected payoff for Conservative Investment=0.57*20+0.29*10+0.14*(-30)=10.1

Expected payoff for Speculative Investment=0.57*10+0.29*10+0.14*(-10)=7.2

Expected payoff for cyclical Investment=0.57*10+0.29*15+0.14*(-20)=7.25

From above calculation we find that maximum payoff is for Conservative investment.So according to expected payoff approach Warren will choose Conservative investment.

C)

For Minimax approach we will find maximum  payoff for each investment and then we select the investment with minimum payoff.

So Maximum Payoff for

Conservative=20

Speculative=10

Counter cyclical =15

So from above investments Minimum payoff is for Speculative investment.So according to Minimax approach Warren will choose Speculative investment.

D

Given Utility function U(t)=C*ln(t)=C*ln (t^2)

where C= 4

t=Payoff

So utility Table

Investment	Improving Economy	Stable Economy	Worsening economy
Conservative	11.98	9.21	13.60
Speculative	9.21	9.21	9.21
Counter Cyclical	9.21	10.83	11.98

Expected utility for investment=probability of improving economy*utility for improving economy+probability of Stable economy*utility for Stable economy+probability of worsening economy*utility for worsening economy

Expected utility for Conservative Investment=0.57*11.98+0.29*9.21+0.14*13.60=11.41

Expected utility for Speculative Investment=0.57*9.21+0.29*9.21+0.14*(9.21)=9.21

Expected utility for cyclical Investment=0.57*9.21+0.29*10.83+0.14*(11.98)=10.07