The possible annual percentage returns of Alpha, Inc, and Beta Inc. are distribu

Question

The possible annual percentage returns of Alpha, Inc, and Beta Inc. are distributed as follows: Annual return of Alpha Annual return of Beta Probability 40.3 -18.8 0.05 37.9 -9.5 0.15 30.1 1.3 0.3 24.6 6.9 0.22 19.7 13 0.13 7.5 22.6 0.09 -2.3 35.8 0.06 a)      What is the expected annual return of Alpha The possible annual percentage returns of Alpha, Inc, and Beta Inc. are distributed as follows: Annual return of Alpha Annual return of Beta Probability 40.3 -18.8 0.05 37.9 -9.5 0.15 30.1 1.3 0.3 24.6 6.9 0.22 19.7 13 0.13 7.5 22.6 0.09 -2.3 35.8 0.06 a)      What is the expected annual return of Alpha

Explanation / Answer

I would prefer to buy Alpha as the Expected Return is high and the SD (i.e Risk) is low.

Covariance

1758.14

Corealtion Coefficient=1758.14/(38.92*45.87) =0.984 (So positively corelated)

Expected Return of Alpha=0.05*40.3+0.15*37.9+0.3*30.1+0.22*24.6+0.13*19.7+0.09*7.5+0.06*(-2.3) 25.24 Variance of Alpha=(40.3-25.24)^2+(37.9-25.24)^2+(30.1-25.24)^2+(24.6-25.24)^2+(19.7-25.24)^2+(7.5-25.24)^2+(-2.3-25.24)^2 1514.959 SD of Alpha=Square Root(1514.959) 38.92 Expected Return of Beta=0.05*(-18.8)+0.15*(-9.5)+0.3*(1.3)+0.22*(6.9)+0.13*(13)+0.09*(22.6)+0.06*(35.8) 5.415 Variance of Beta=(-18.8-5.415)^2+(-9.5-5.415)^2+(1.3-5.415)^2+(6.9-5.415)^2+(13-5.415)^2+(22.6-5.415)^2+(35.8-5.415)^2 2104.067 SD of Beta=Square Root(2104.067) 45.87

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