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) Create a regret table for Mary. What decision should Mary make according to the minimax approach?

Answer 1

we will select the option that gives maximum payout in worst possible case :

1.

Gold Client account

worst case payout = payout (payout constant in all cases) = 3.75%*240000 $ = 9000$

2.

EliteCure stock

worst case payout = -20%*240000 $ = -48000 $

3.

AcutePro stock

worst case payout = -5%*240000 $ = -12000 $

worst case payout is maximum for gold client account so that should be chosen as per minimax approach

P.S. (please upvote if you find the answer satisfactory)