Question

16 Debbie Gibson is considering three investment options for a small inheritance that she has just received stocks, bonds, and money market. The return on her investment will depend on the per formance of the economy, which can be strong, average, or weak. The returns for each possible combination are shown in the following table: INVESTMENT STRONG AVERAGE WEAK Stocks 12% 6% -10% Bonds Money market 4% 3% 2% 7% Assume that Debbie will choose only one of the investment options. (a) Which investment should Debbie choose if she uses the maximax criterion? (b) Which investment should Debbie choose if she uses the maximin criterion? (c) Which investment should Debbie choose if she uses the equally likely criterion? (d) Which investment should Debbie choose if she uses the criterion of realism with a 0.5? (c) Which investment should Debbie choose if she uses the minimax regret criterion?

Answer 1

16

a)

In maximax criterion, we need to first choose the maximum value of the alternatives and then choose the maximum value among them.

Maximum value of each alternatives

Stock = 12%

Bonds = 7%

Money market = 4%

Among these, the best option is stocks. Thus we should choose stocks

b)

In maximin criterion, we need to first choose the minimum value of the alternatives and then choose the maximum value among them

Minimum value of each alternatives

Stock = -10%

Bonds = 1%

Money market = 2%

The best among these is Money market. Thus we should choose money market.

c)

In equally likely criterion, there is equal probability of each chance event. This means the probability of each event is 1/3. Thus we multiply the sum of the total chance event with 1/3.

Expected value

Stocks = (12 + 6 - 10)*(1/3) = 8/3

Bonds = (7 + 4 + 1)*(1/3) = 4

Money market = (4 + 3 + 2)*1/3 = 3

The highest value is 4 with Bonds and we should choose bond.

d)

In realism criterion, the best value of each alternative is multiplied with alpha and the worst value with (1-alpha).

Thus using Hurwicz criterion

Stock = 12*0.5 – 10*(1-0.5) = 1

Bonds = 7*0.5 + 1*(1-0.5) = 4

Money market = 4*0.5 + 2*(1-0.5) = 3

The best payoff is Bonds and we should choose that.

e)

We first have to create a regret matrix. This means we need to compare the payoff of each chance event and the amount of regrets against the best alternative for each chance event. The regret is

Stocks = 0 0 12

Bonds = 5 2 1

Money market = 8 3 0

Now the maximum regret for each alternatives is

Stocks = 12

Bonds = 5

Money market = 8

Among them minimum is Bonds. Thus we should choose bonds.