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.

1) Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ

2) Based on your results in part (1), can you decide which stock to invest?

3) Calculate Beta for stock ABC and XYZ

4) If the T-bill rate is 3%, what does the CAPM say about the fair expected rate of return on the two stocks? How does this result influence your investment decision?

Answer 1

Given,

Bhoom economy probabiity = 30%

Normal eonomy probability = 70%

ABC's return = 25% or 4%

XYZ's return = 10% or 6.5%

Market return = 12% or 5%

Risk free rate = 3%

Computation of expected return and standard deviation for ABC and XYZ

ABC expected return = (25%30%) + (4% 70%) = 10.3%

ABC standard deviation = square root of [(25%-10.3%)30%] + [(4%-10.3%)70%]

= squareroot of [64.827] + [27.783] = 9.6234

XYZ expected return = (10%30%) + (6.5%70%) = 7.55%

XYZ standard deviation = square root of [(10%-7.55%)30%] + {(6.5%-7.55%)70%]

= square root of [1.80075] + [0.77175] = 1.6039

Particulars	ABC	XYZ
Expected return	10.3%	7.55%
Standard deviation	9.6234	1.6039

On observing the above results, it is better to invest in XYZ as it gives higher return with lower risk compared ABC higher return with higher risk.

Computation of beta for stock ABC and XYZ

Beta = Change in security return / change in market return

ABC's beta = (25% - 4%)/(12%-5%) = 3

XYZ's beta = (10%-6.5%)/(12%-5%) = 0.5

Computation of required rate of return for ABC and XYZ

Expected market return = (1230%) + (5%70%) = 7.1%

Required rate of return as per CAPM = Rf + (Rm - Rf)

ABC's required rate of return = 3% + 3(7.1% - 3%) = 15.3%

XYZ's required rate of return = 3% + 0.5(7.1% - 3%) = 5.05%

Computation of jenson's alpha for ABC and XYZ

Jenson's alpha = Expected return - Required rate of return

ABC's aplha = 10.3% - 15.3% = -5%

XYZ's alpha = 7.55% - 5.05% = 2.5%

ABC's alpha is negative,Therefore it's share is overpriced. It is not recommended to invest in ABC's shares.

XYZ's alpha is positive. Therefore it's share is underpriced. It is advisable to invest in XYZ's shares.