Question

Briefly, explain the minimax regret criterion for decision making. Is this criterion an optimist, conservative, or middle of the road approach? Give a real-world example where the minimax regret criterion can be useful.

Answer 1

In the minimax regret problem, you are required to minimize your highest regret when you choose one stock over the other.

Step 1: We look at the first payoff time in this case Year 1, and find the stock with the highest payoff. In this case it is the Disney stock which has a payoff of 0.6.

Stock	Year1	Year2	Year3	Year 4
Intel	-0.3	0.9	0.4	0.5
Microsoft	0	0.5	0.1	0.4
Disney	0.6	0.4	0	0.6
Shell	0.3	-0.1	-0.7	0.7
Barclay	-0.2	-0.6	0.4	0

Now we ask ourselves, suppose we bought Intel Stock instead of Disney Stock, how much I would have lost (or regretted) making this decision.

Since Disney Stock is 0.6 and Intel Stock is -0.3, then the amount we regret will be:

0.6 – (-0.3) = 0.9

We have thus potentially lost a 0.9 payoff.

Similarly, we would ask how much I would regret buying Microsoft Stock with 0 payoff versus Disney Stock with a 0.6 payoff in the first year. Payoff: 0.6 - 0 = 0.6

My regret will thus be 0.6 if I bought Microsoft stock.

We continue similarly for the rest of the stocks in that year. You will note there is no regret in buying Disney stock.

I.E. Regret for Disney Stock in Year 1: 0.6 - 0.6 = 0