Question

In: Finance

One of Philip’s investments is going to mature, and he wants to determine how to invest...

One of Philip’s investments is going to mature, and he wants to determine how to invest the proceeds of $50,000. Philip is considering two new investments: a stock mutual fund and a one-year certificate of deposit (CD). The CD is guaranteed to pay a 3% return. Philip estimates the return on the stock mutual fund as 11%, 2%, or -9%, depending on whether market conditions are good, average, or poor, respectively. Philip estimates the probability of a good, average, and poor market to be 35%, 40%, and 25%, respectively.

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

(Question 2) What decision should be made according to the optimistic approach?

(Question 3) Create a regret table for Philip. What decision should be made according to the minimax approach?

(Question 4) What decision should be made according to the expected value approach?

(Question 5) How much should Philip be willing to pay to obtain a market forecast that is 100% accurate?

ANSWERS I'VE CALCULATE ALREADY

1.)

Decision Alternatives

Market Condition

Good

(p=.35)

Average

(p=.40)

Poor

(p=.25)

Stock Mutual Fund

$50,000 * .11*.35 = $1,925

$50,000 * .02*.40 = $400

$50,000 * -.09*.25 =

-$ 1,125

1 yr CD

$50,000*.03 =

$1,500

$50,000*.03 =

$1,500

$50,000*.03 =

$1,500

2. The optimistic approach involves selecting the alternative that maximizes the maximum payoff available. Therefore, the highest payoff is under stock when the market is in good condition.

Solutions

Expert Solution

Your solution to question (1) is not correct. While developing the payoff matrix, you have to simply mention the payoff and not the expected payoff. And hence, you should not multiply the payoff by the probabilities. I am rectifying the solution below.

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

Your payoff table should be as shown below. Individual values had been calculated in each cell for you to understand.

Decision Alternatives

Market Condition

Good

(p=.35)

Average

(p=.40)

Poor

(p=.25)

Stock Mutual Fund

50,000 x 0.11 = 5,500

50,000 x 0.02 = 1,000

$50,000 x (-0.09) = - 4,500

1 yr CD

50,000 x 0.03 =1,500

50,000 x 0.03 =1,500

50,000 x 0.03 =1,500

(Question 2) What decision should be made according to the optimistic approach?

Your answer is correct.

(Question 3) Create a regret table for Philip. What decision should be made according to the minimax approach?

In order to create a regret table, let's first pick up the payoff in the best scenario. You have already identified it in Question 2 to be "stock when the market is in good condition" with payoff of $ 5,500.

The regret table is a measure of opportunity loss. So, in order to create a regret table, you will have to create an opportunity loss table. Opportunity loss = Best case payoff - payoff in a given state. So if the market is doing average and you have invested in stock, then your opportunity loss = 5,500 - 1,000 = $ 4,500.

Thus the complete regret table will look like as shown below:

Decision Alternatives

Market Condition

Good

(p=.35)

Average

(p=.40)

Poor

(p=.25)

Stock Mutual Fund

5,500 - 5,500 = 0

5,500 - 1,000 = 4,500

5,500 - (-4,500) = 10,000

1 yr CD

5,500 - 1,500 = 4,000

5,500 - 1,500 = 4,000

5,500 - 1,500 = 4,000

Please note that it's a regret or opportunity loss table, hence lower the number, better it is.

Minimax: Refer the regret table above

  • Calculate the maximum regret (loss) under each action i.e. across each row. Maximum loss under stock mutual fund is $ 10,000. Maximum loss under 1 year CD is 4,000
  • Next calculate the minimum of these maximum losses, that is min(10000, 4000) = 4,000

So, as per minimax criterion, my decision will be to invest in 1 year CD.

(Question 4) What decision should be made according to the expected value approach?

Expected value = Sum of probability weighted return under each alternative.

Expected value under stock mutual fund = 0.35 x 5,500 + 0.4 x 1,000 + 0.25 x (-4,500) = 1,200

Expected value under 1 year CD = 1,500 > Expected value under stock mutual fund

Hence, the decision will be to invest in 1 year CD.

(Question 5) How much should Philip be willing to pay to obtain a market forecast that is 100% accurate?

Expected value under 1 year CD - Expected value under stock mutual fund = 1,500 - 1,200 = $ 300


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