Question
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4.32 Investment risk analysis. The risk of a portfolio of financial assets is sometimes called investment risk. In general, in- vestment risk is typically measured by computing the vari- ance or standard deviation of the probability distribution that describes the decision maker's potential outcomes (gains or losses). The greater the variation in potential outcomes, the greater the uncertainty faced by the decision maker; the smaller the variation in potential outcomes the more predictable the decision maker's gains or losses The two discrete probability distributions given in the next table were developed from historical data. They describe the potential total physical damage losses next year to the fleets of delivery trucks of two different firms Firm A Firm B Loss Next Year Probability Loss Next Year 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 .01 .01 .01 .02 .35 30 .25 .02 .01 .01 .01 200 700 1,200 1,700 2.200 2,700 3,200 3,700 4,200 4,700 Probability .00 .01 .02 .02 15 30 .30 15 .02 01 NMa. Verify that both firms have the same expected total physical damage loss. b. Compute the standard deviation of each prob- ability distribution and determine which firm faces the greater risk of physical damage to its fleet next year.
Explanation / Answer
a) Both have same expected same total physical loss.
b) Firm B has greater SD so greater the risk.
S.No Loss Next year (xi) Probability (Pi) Pi * xi Pi*(xi)^2 1 0 0.01 0 0 2 500 0.01 5 2500 E(X) xi*Pi 2450 3 1000 0.01 10 10000 E(X^2) (Xi)^2*Pi 6440000 4 1500 0.02 30 45000 Variance E(X^2)-(E(X))^2 437500 5 2000 0.35 700 1400000 SD SQRT(VARIANCE) 661.44 6 2500 0.3 750 1875000 7 3000 0.25 750 2250000 8 3500 0.02 70 245000 9 4000 0.01 40 160000 10 4500 0.01 45 202500 11 5000 0.01 50 250000
Total 1 2450 6440000
