Question

QUESTION 2:
Following are the probability distributions of annual returns of ABC Enterprises and TSX Composite Index (market).
Probability RABC RTSXComp
0.20 -5 2
0.50 11 6
0.30 14 10
a. Compute the expected annual returns, variances, and the standard deviations for ABC
and the TSX Composite Index.
b. Compute the covariance.
c. Compute the coefficient of correlation and interpret it.
d. Compute the Beta for ABC and interpret it.
e. Using CAPM determine the required rate of return for ABC if the risk free rate of
return is 4%.

Answer 1

a. Computation of expected annual returns, variances, and the standard deviations for ABC
and the TSX Composite Index.

1) Expected annual returns

-Expected annual returns for ABC = (.2*-5)+(.5*11)+(.3*14) = 8.70%
-Expected annual returns for TSX Composite Index. = (.2*2+(.5*6)+(.3*10) = 6.40%

2) Variance and standard deviation

-ABC Enterprises

Probability	Return(%)	Deviation from expected return of 8.70%(D1)	PD1^2
0.2	-5	-13.7	37.538
0.5	11	2.3	2.645
0.3	14	5.3	8.427

Variance = PD1^2

= 37.538+2.645+8.427

= 48.61

Standard Deviation = Variance

= 48.61

= 6.97

-TSX Composite Index.

Probability	Return(%)	Deviation from expected return of 6.40%(D2)	PD2^2
0.2	2	-4.4	3.872
0.5	6	-0.4	0.08
0.3	10	3.6	3.888

Variance = PD2^2

= 3.872+.08+3.888

= 7.84

Standard Deviation = Variance

= 7.84

= 2.80

b. Computation of covariance.

Probability(P)	Deviation (D1)	Deviation (D2)	P*D1*D2
0.2	-13.7	-4.4	12.056
0.5	2.3	-0.4	-0.46
0.3	5.3	3.6	5.724

Co-Variance = P*D1*D2

=12.056+-.46+5.724

= 17.32

c. Computation of coefficient of correlation and interpretation

Correlation = Covariance/(SD ofABC*SD of TSX)

= 17.32 / (6.97*2.8)

= 17.32 / 19.516

= .8875

Correlation is a measure of closeness of the relationship between two random variables and has a value between -1 and +1. In this case correlation is .8875. That means the stocks are positively correlated, both moves in the same direction.

d. Computation of the Beta for ABC and interpretation

Beta = (SD of ABC * correlation between returns from stock and market) / SD of market

= (6.97 * .8875) / 2.8

= 6.1859 / 2.8

= 2.21

Beta of 2.21 means the stock is 121% (2.21*100 -100) more risky than the market.

e. Computation of required rate of return for ABC

According to CAPM

Required Return = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return (4%)

b – Beta (2.21)

Rm – Expected return on market portfolio (6.40%)

Required Return = 4+ 2.21 (6.4-4)

= 4 + 5.304

= 9.30%