Question

Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening, while Normal economy has 70% chance of happening. For each scenario (Boom and Normal), stock ABC has a return of 25%, and 4%, respectively; stock XYZ has a return of 10% and 6.5%, respectively; the market portfolio has a return of 12% and 5% respectively.

Requried:
a. Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ.
b. Based on your results in part (1), can you decide which stock to invest?
c. Calculate Beta for stock ABC and XYZ.

Answer 1

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