Question

Mary Johnson recently received a lump sum of $240,000 after selling her old house in upstate New York. Mary would like to invest this amount of money. Her local bank offers Mary an available Gold Client account for her entire $240,000 deposit that guarantees 3.75% return regardless of the future market climate. Mary is also interested in investing her $240,000 in two stock options. The first one is to spend the entire $240,000 to purchase stocks from EliteCure, an upcoming pharmaceutical manufacturer. The projected return for EliteCure stock is 17%, 9%, -2%, -20%, respectively, depending on the future market climate to be excellent, good, poor, or disastrous. The other one is to spend her $240,000 to purchase stocks from AcutePro, a well-established pharmaceutical manufacturer. The projected return for AcutePro stock is 11%, 10%, 7%, -5%, respectively, depending on the future market climate to be excellent, good, poor, or disastrous. The stock industry considers many current economic events and estimates 40% chance to have an excellent future market while the remaining 60% chance to be evenly distributed among the other three (good, poor, or disastrous) possible future markets. Show how you derive your answers and support your answers with correct explanations.

(Question ) What decision should Mary make according to the expected value approach?

Answer 1

There are 3 alternative investment options for Mary

• Invest the entire amount in Gold Client account @ 3.75%.
• purchase stocks from EliteCure.
• purchase stocks from AcutePro

Note: The value of the investment is $240,000. Since the entire amount is invested every time, we can just compare the return % for the 3 alternatives and pick the alternative with the highest return.

The state of nature, the  future market climate, to be excellent, good, poor, or disastrous

The estimates 40% chance to have an excellent future market.

This is same as

The probability that the future market climate is Excellent is 0.40

P(Excellent) = 0.40

while the remaining 60% chance to be evenly distributed among the other three (good, poor, or disastrous) possible future markets. This is same as

The probability that the future market climate is Good is 0.60/3=0.20

P(Good) = 0.20

The probability that the future market climate is Poor is 0.60/3=0.20

P(Poor)=0.20

The probability that the future market climate is Disastrous is 0.60/3=0.20

P(Disastrous)=0.20

The payoff table (in terms of %return) for the 3 alternatives is given below

Payoff table in terms of % return. along with the probabilities is

	State of Nature (future market climate)
Decision Alternatives	excellent	good	poor	disastrous
Gold Client account	3.75%	3.75%	3.75%	3.75%
Purchase EliteCure	17.00%	9.00%	-2.00%	-20.00%
Purchase AcutePro	11.00%	10.00%	7.00%	-5.00%
Probability	0.40	0.20	0.20	0.20

Alternative 1: Invest in Gold Client account

• The payoff is 3.75% for certain

Alternative 2: Purchase EliteCure.

the expected value of the return is

Alternative 3: Purchase AcutePro.

the expected value of the return is

The expected return for 3 alternative investment options for Mary are

• Invest the entire amount in Gold Client account @ a return of 3.75%.
• purchase stocks from EliteCure @ an expected return of 4.2%
• purchase stocks from AcutePro @ an expected return of 6.8%

We can see that the expected return for purchase stocks from AcutePro is the highest and hence is the optimum decision.

ans: According to the expected value approach, Mary should purchase stocks from AcutePro

Note: This is the optimum decision irrespective of the value of the investment. Since the entire amount is invested every time, we can just compare the return % for the 3 alternatives and pick the alternative with the highest return.