Question

You want to invest in two shares, X and Y. The following data are available for the two shares:

Share X

Expected Return: 9%

Standard Deviation :14%

Beta: 1.10

Share Y

Expected Return: 7%

Standard Deviation: 12%

Beta : 0.85

If you invest 70 percent of your funds in Share X, the remainder in Share Y and if the correlation of returns between X and Y is +0.7, compute the expected return and the standard deviation of returns from the portfolio.

Answer 1

Expected return of the portfolio= ?PiRi=Weight of x*return of x+ Weight of Y*return of Y

=0.70*9%+0.30*7%=6.3%+21%=8.4%

	Pi	Ri	PiRi
SHARE X	0.70	9	6.3
SHARE Y	0.30	7	2.1
			8.4

Variance of portfolio =(Weight of X)² *(Standard deviation of x)²+ (Weight of B)²*(Standard deviation of B)²+(2Correlation

Of And B *standard deviation of A*standard deviation of B*weight of A*weight of B)

=0.7²*0.14²+0.3²*0.12²+ (2*0.7*0.14*0.12*0.7*0.3)=0.49*0.0196+(0.09*0.0144)+(1.4*0.0168*0.21)

=0.009604+0.001296+0.0.0049392=0.0158392

Standard deviation of the portfolio=?variance of the portfolio=?0.015839=0.125854=12.5854%

Thus expected return of the portfolio=8.4% and standard deviation of the portfolio=12.59%