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

State	Probability	ABC	XYZ	Market return
BOOM	0.3	25%	10%	12%
NORMAL	0.7	4%	6.5%	5%

1. Calculation of Expected return, Variance & Standard Deviation(SD)-

Expected Return(ER) =

ER (ABC) = (25%*0.3) +(4%*0.7) =10.3%

ER(XYZ) = (10%*0.3) + (6.5%*0.7)= 7.55%

ER(Market) = (12%*0.3) +(5%*0.7) = 7.1%

Variance (ABC) = [(25%-10.3%)^2 * 0.3] +[(4%-10.3%)^2*0.7] = 64.827 + 27.783 = 92.61

Variance (XYZ) = [(10%-7.55%)^2 *0.3] + [(6.5%-7.55%)^2 *0.7] = 1.80075 + 0.77175 = 2.5725

Variance (Market) =[(12%-7.1%)^2 *0.3] + [(5%-7.1%)^2*0.7] = 7.203 + 3.087 = 10.29

SD(ABC) = = 9.623%

SD(XYZ) = = 1.604%

SD(Market) = = 3.208%

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2.

	Expected Return	SD or standard Deviation	Co efficinet of Variation = SD/Expected Return
ABC	10.3%	9.623%	9.623/10.3 = 0.934
XYZ	7.55%	1.604%	1.604/7.55 = 0.212

Co efficient of Variation show the relationship between the SD & Expected return.

Stock wilth less Coefficient of variation to be choosed as lower Coefficient of variation show lower risk in relation to the return.

Hence stock XYZ to be choosed.

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3.

Cov (A, M) = Covariance of Asset and the Market return.

Cov(ABC & Market) = [(25%-10.3%)* (12%-7.1%) *0.3] +[(4%-10.3%) * (5%-7.1%) *0.7] = 21.609 + 9.261 = 30.87

Cov(XYZ & Market) = [(10%-7.55%)* (12%-7.1%) *0.3] +[(6.5%-7.55%) * (5%-7.1%) *0.7] = 3.6015 + 1.5435 = 5.145

Variance of market =10.29

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4.

AS per CAPM or Capital Asset pricing Method,

Fair return on stock = Risk free return + Beta(Expected return on market - Risk free return)

It is also know as the Minimum return

If the Expected return from the stock is more than the Fair return or Minimum return then the Investor should buy the Asset

If the Expected Retun is Less than the Fair return or Minimum return then the investor should not buy the stock or Should sell the stock

	ABC	XYZ
Risk Free return	3%	3%
Beta	3	0.5
Expected Market Return	7.1%	7.1%
Fair value Expected Return	=3% + 3*(7.1%-3%) =15.3%	=3% +0.5(7.1%-3%) =5.05%
Expected Return	10.3%	7.55%
Investment Decision	Dont buy as the Expected return is less than the Fair Return.	Buy the stock as Expected Return is more than the fair return.