Question

3. Suppose you are thinking of investing $100,000 in stock indexes. You are currently considering investing either in the financial sector or the technolgy sector but the returns will depend on the state of the economy. The following table summarizes the estimated net profts that would be realized during the next two years for each of the two investment alternatives you are considering.

		State of the Economy
		Good Economy	Poor Economy
	Healthcare	$60,000	$-10,000
Decision Alternative	Technology	$90,000	$-50,000
	Probability	0.45	0.55

1. What decision would maximize expected profit for you? Show the necessary steps.
2. What is the maximum amount you should be willing to pay for a perfect forecast of the state of the economy? Show the necessary steps.                    

1. Since perfect forecast of the state of the economy is impossible suppose you are considering hiring a financial analyst to help you forecast the state of the economy for the next two years. In the past the analyst accurately predicted a good economy 92% of the time. The analyst also has a history of incorrectly predicting a poor economy 20% of the time. She charges $10,000 for the forecasting service. Please calculate the expected value of survey information (EVSI) for the financial analyst you are considering hiring and briefly explain what your result means. Given your results will you hire the financial analyst? Please justify your answer and show all the necessary steps. Also calculate the efficiency of the financial analyst and explain what it means.                                                                                 

Answer 1

(a) We draw a decision tree and calculate expected values for each investing decision.

From the above, it is clear that the decision to invest in Healthcare sector (also called financial sector in the question) will maximize the expected profit.

(b) Let us first calculate the expected value with perfect forecast from the above decision map,

If it is known that the state of the economy will be good, then the best decision alternative would be to invest in the Technology sector as it will provide a profit of $90000.

If it is known that the state of the economy will be bad, then the best decision alternative would be to invest in the Healthcare sector as it will help minimize the loss. We can say that the profit will be -$10000.

Thus, expected value of the decision strategy with perfect forecast (EVPF) = 0.45*90000+0.55*(-10000)

= $35000

From part(a), we get the expected value of the decision strategy without perfect forecast (EVWOPF) = $21500

Subtracting the two above, we get the Expected value of perfect forecast = EVPF-EVWOPF

= 35000 - 21500

=$13500

Thus, the maximum amount you should be willing to pay for a perfect forecast of the state of the economy is $13500.

(c) This is the case of decision tree with sample information. The decision tree is shown below:

In the above diagram, we have made the assumption that the analyst predicts the good or bad economic scenario with equal probability 0.5 in the absence of any given information.

Calculating expected values at different nodes,

EV (Node4) = Max [EV(Node6), EV(Node7)] =Max [0.92*60000-0.08*10000, 0.92*90000-0.08*50000)] =Max[54400,78800] = $78800

EV (Node5) = Max [EV(Node8), EV(Node9)] =Max [0.20*60000-0.80*10000, 0.20*90000-0.80*50000)] =Max[20000,58000] = $58000

EV (Node3) = $21500 {calculated in part(a) of the question}

EV (Node2) = 0.5*EV (Node4) + 0.5*EV (Node5) = $136800

EVSI = 136800-21500 = $115300

EVSI shows that hiring the financial analyst for prediction adds $1,15,300 to the expected value of net profit over the alternative of investing without the sample information provided by the analyst.

Hence, we will hire the analyst.