Answer:
A) Expected Return of Stock ABC = Probability of Boom * Return of ABC in boom+Probability of Normal * Return of ABC in norma
ER = 30% * 25% + 70% * 4% = 10.30%
Expected Return of Stock XYZ = Probability of Boom * Return of XYZ in boom+Probability of Normal*Return of XYZ in norma
ER = 30% * 10% + 70% * 6.5% = 7.55%
Variance of Stock ABC = 30% * (25%-10.30%)^2 + 70% * (4%-10.30%)^2 = 0.9261%
Variance of Stock XYZ = 30% * (10%-7.55%)^2 + 70% * (6.5%-7.55%)^2 = 0.02573%
Standard Deviation of ABC =0.9261%^0.5 = 9.62%
Standard Deviation of XYZ =0.02573%^0.5 = 1.60%
B) Coefficient of Variation of ABC=Standard Deviation of ABC/Expected Return of ABC =9.62%/10.30%=0.93
Coefficient of Variation of XYZ=Standard Deviation of XYZ/Expected Return of XYZ =1.60%/7.55%=0.21
Stock with less Coefficient of variation to be chosen as lower Coefficient of variation show lower risk in relation to the return.
Hence stock XYZ is best for investment.
C) Expected Return of Market =30% *12% + 70% * 5% = 7.1%
Variance of Market =30% * (12% - 7.1%)^2 + 70% * (5%-7.1%)^2 = 0.1029%
Covariance of Stock ABC and Market = 30% * (12% - 7.1%) * (25% - 10.30%) + 70%*(5% - 7.1%) * (4% - 10.30% )= 0.0030870
Beta of ABC = Covariance of Stock ABC and Market / Variance of Market
Beta ABC = (0.0030870 / 0.1029%) = 3.00
Covariance of Stock XYZ and Market =30% * ( 12% - 7.1%) * (10% - 7.55%) + 70% * (5% - 7.1%) * (6.50% - 7.55%) = 0.000515
Beta of Stock XYZ = Covariance of Stock XYZ and Market /
Variance of MarkeT
Beta XYZ = (0.000515 / 0.1029%) = 0.5
