Question

Katie has $220,000 to invest. there are three possible investment options: The first option is a savings account at the local Bank. This savings account has a 2.5% return rate regardless the condition of the future economy. The second option is a technology stock with a return rate of 9%, 7%, or -18%, depending on whether the future economy condition is good, average, or poor, respectively. The third option is a mutual fund with a return rate of 5%, 2%, or 1%, depending on whether the future economy condition is good, average, or poor, respectively. A business analyst at a well-respected business journal estimates the probability of a good, average, or poor future economy to be 25%, 35%, and 40%, respectively.

(Question 1) Construct a payoff table (in dollars) for Katie.

(Question 2) Explain which investment option Katie should select according to the optimistic approach.

(Question 3) Create a regret table for Katie.

(Question 4) Explain which investment option Katie should select according to the minimax approach.

(Question 5) Explain which investment option Katie should select according to the expected value approach.

Answer 1

Payoff from Savings account=220000*2.5%=$5500

Payoff from Technology stocks, if economic condition is good=220000*9%=19800

Payoff from Technology stocks, if economic condition is average=220000*7%=15400

Payoff from Technology stocks, if economic condition is poor=220000*(-18)%=-39600

Payoff from Mutual Fund , if economic condition is good=220000*5%=11000

Payoff from Mutual Fund, if economic condition is average=220000*2%=4400

Payoff from Mutual Fund , if economic condition is poor=220000*1%=2200

Construct a payoff table (in dollars) for Katie.:

Economic Condition	Probability	Savings Account	Technology Stock	Mutual Fund
Good	0.25	5500	19800	11000
Average	0.35	5500	15400	4400
Poor	0.40	5500	-39600	2200

Explain which investment option Katie should select according to the optimistic approach:

Optimistic approach will be to select the option which maximizes the maximum Payoff available which is called Maximax approach.

Maximum Payoff for Savings account investment =$5500

Maximum Payoff for Technology Stock investment =$19800

Maximum Payoff for Mutual  account investment =$11000

Under Optimistic approach, Katie should select Technology Stock investment which maximizes maximum payoff

Create a regret table for Katie:

If the Economic Condition is good, the maximum payoff is=19800

If Katies chooses Savings bank, her regret will be=19800-5500=14300

If Katies chooses Mutual Fund, her regret will be=19800-11000=8800

If Katies chooses Technology Stock, her regret will be=19800-19800=0

If the Economic Condition is Average, the maximum payoff is=15400

If Katies chooses Savings bank, her regret will be=15400-5500=9900

If Katies chooses Mutual Fund, her regret will be=15400-4400=11000

If Katies chooses Technology Stock, her regret will be=15400-15400=0

If the Economic Condition is Poor, the maximum payoff is=5500

If Katies chooses Savings bank, her regret will be=5500-5500=0

If Katies chooses Mutual Fund, her regret will be=5500-2200=3300

If Katies chooses Technology Stock, her regret will be=5500-(-39600)=45100

MINIMAX REGRET TABLE :

Economic Condition	Probability	Savings Account	Technology Stock	Mutual Fund
Good	0.25	14300	0	8800
Average	0.35	9900	0	11000
Poor	0.40	0	45100	3300

Explain which investment option Katie should select according to the minimax approach

Under this Strategy Katie will minimize the maximum regret.

Maximum regret if she chooses Savings account=14300

Maximum regret if she chooses Technology stock=45100

Maximum regret if she chooses Mutual Fund =11000

Hence Katie would select MUTUAL FUND which minimizes the maximum regret.

Explain which investment option Katie should select according to the expected value:

Expected Value of Savings Account =5500*0.25+5500*0.35+5500*0.4=5500

Expected Value of Technology Stock=19800*0.25+15400*0.35-39600*0.4=-5500

Expected Value of Mutual Fund=11000*0.25+4400*0.35+2200*0.4=5170

Katie would Select Savings account