Question

Find beta, and determine the required rate of return. The market risk premium is 12%, and the risk-free rate is 5%.

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Comparative Returns in the Market	Returns on the Stock
8%	4%
9%	10%
2%	1%
10%	6%

Answer 1

Ans) According to CAPM model,

Beta = Covariance ( Re , Rm) / Variance ( Rm )

where,

Re - Returns on Stock

Rm- Market returns

Market returns (x)	Returns on stock (y)	xy	x^2	y^2
8%	4%	32	64	14
9%	10%	90	81	100
2%	1%	2	4	1
10%	6%	60	100	36
= 8+9+2+10 = 29	= 4+10+1+6 = 21	= 32+90+2+60 =184	= 64+81+4+100 249	=14+100+1+36 = 151

mean of X = 29/ 4 = 7.25

mean of y = 21/ 4 = 5.25

Beta = cov ( x , y) / Var ( x ) = {[sum ( xy)/ n ] - mean (x) * mean( y ) } / {x^2 /n - mean(x )^2}

= {184/4 - 7.25 * 5.25} / {249/4 - 7.25^2}

= {46 - 38.06} / {62.25- 52.56}

=7.94 / 9.69 = 0.819

Now, using CAPM formula,

Required rate of return = Risk free rate - Beta ( Market risk premium )

= 5% + 0.819 ( 12%)

= 14.828 %