Decision Analysis P.341

Volunteer Exercise # 1 Problem 3-41

De Jesus, Angelo J. Page 127

De Jesus, Jedediah Marie M. June 26, 2013

A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation:

| States of Nature |

Investment | Good Economy | Fair Economy | Poor Economy |

Fund A | $10,000.00 | $2,000.00 | $-5,000.00 |

Fund B | $6,000.00 | $4,000.00 | $0.00 |

Probability | 0.2 | 0.3 | 0.5 |

(a) Draw the decision tree to represent this situation.

(b) Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value?

(c) Suppose there is question about the return of Fund A in a good economy. It could be higher or lower than $10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (i.e., the EMV’s would be the same)?

Answer:

a. Decision Tree

b. EMV (Fund A) = 10,000(0.2) + 2,000(0.3) + (-5,000)(0.5) = 100

EMV (Fund B) = 6,000(0.2) + 4,000(0.3) + 0(0.5) = 2,400

Fund B is better and should be chosen to maximize the expected value.

c. Let X = Return of Fund A in a good economy

Indifferent between A and B: EMV (Fund A) = EMV (Fund B)

X(0.2) + 2,000(0.3) + (-5,000)(0.5) = 2,400

0.2X = 4,300

X = $21,500

The return of Fund A in a Good Economy should be $21,500 in order for a person to be indifferent between Fund A and Fund B.