An investment analyst is studying three different bond mutual funds given below

Question

An investment analyst is studying three different bond mutual funds given below using a forecast for 1 year. The investment amount is $8,000.

Fund 1 Fund 2 Fund 3

Return Payoff Prob Payoff Prob Payoff Prob

Favorable $800 .40 $1000 .5 $1,500 .45

Stagnant $100 .35 $100 .2 $ 300 .35 Unfavorable -$100 .20 (i) .3 (ii) .20

Disaster -$400 .05

(i) In Fund 2 if the return is unfavorable, the investor can either hold the mutual funds and incur a loss of $500 at the end of the year, or sell the prior to the end of the year and incur a loss of only $100.

(ii) In Fund 3 if the return is unfavorable, the investor can either hold the mutual funds and incur a loss of $50 at the end of the year, or sell after 6 months and invest in a high tech stock for a gain of $100.

a) Illustrate the decision of selecting a fund using a decision tree. Label the decision alternatives, the states of nature, the probabilities and payoffs appropriately. Be sure to distinguish between square nodes and round nodes where appropriate.

b) Analyze the tree to determine which fund is best based on maximizing expected payoff.

Explanation / Answer

Maximum expected payoff from Fund A = (0.4 x 800 + 0.35 x 100 - 0.2 x 100 - 0.05 x 400) = 315 $


Maximum expected payoff from Fund B = (0.5 x 1000 + 0.2 x 100 - 0.3 x 100) = 490 $


Maximum expected payoff from Fund C = (0.45 x 1500 + 0.35 x 300 + 0.2 x 100) = 800 $

Fund C gives the best pay-off provided that you sell the stock in this fund after 6 months and invest in a high tech stock for a gain of $100, when the conditions are unfavorable.

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