Question

Rand Inc. and McNally Corp. have the following probability distribution of returns: Probability Rand Returns McNally Returns

0.3 15% 12% 0.4 9 5 0.3 18 20

Sudha Krishnaswami Lecture Notes

Page 1 of 3

Homework-6

a) Calculate the expected rates of return for the two stocks.

b) Calculate the standard deviation of returns for the two stocks.

c) Calculate the expected return and standard deviation on a portfolio P made up of 75%

invested in McNally stock and the remaining invested in Rand stock.

Answer 1

Solution:

Rand Inc. Returns denoted as (X) &

Mcnally Corp returns denoted as (Y)

Probability(P)	X	P*X	Y	P*Y	(X- mean of X)	(Y- mean of Y)	P(X-mean of X)2	P(Y-mean of Y)2	P[(x- mean of x) * (Y-mean of Y)
0.3	15	4.5	12	3.6	1.5	0.4	0.675	0.04	0.18
0.4	9	3.6	5	2	-4.5	-6.6	8.1	17.42	11.88
0.3	18	5.4	20	6	4.5	8.4	6.075	21.16	11.34
Total		Mean of X = 13.5		Mean of Y =11.6			Variance=14.85	Variance= 38.62	23.4

a) Expected rate of return for Rand Inc. = 13.5% &

For Mcnally Corp = 11.6%

b) Stanadard Deviation of return of Rand Inc. = Square root of Variance i.e 14.85 = 3.85% &

Stanadard Deviation of Mcnally Corp. = 6.21%

c) Weight of X (Wx) = 0.25 & Weight of Y (Wy)= 0.75

So, Expected return on portfolio = 0.25 * 13.5 + 0.75 * 11.6

= 12.075%

& Variance of portfolio = (Wx2 * Variance of X) + (Wy2 * Variance of Y) + 2*Wx*Wy*Covariance(X,Y)

= (0.252 * 14.85) + (0.752 * 38.62) + 2*0.25*0.75*23.4

=0.92 + 21.72 +8.77

= 31.41 %2

Therefore Standard Deviation of Portfolio = 5.60%