Question

You are interested in investing in two different shares. The anticipated annual return for a $1,000 investment in each share under different economic conditions is given below, together with the probability that each of these economic conditions will occur.

	State of	Returns
Probability	the economy	Share X	Share Y
0.25	Recession	$240	-$100
0.5	Slow growth	$150	$150
0.25	High growth	-$100	$240

1. Calculate the expected return for share X and for share Y.

2. Calculate the standard deviation for share X and for share Y.

3. Would you invest $1000 in share X or share Y or are they both equally desirable? Give a broad explanation of your answer.

Answer 1

Solution :

a) The expected return for share X is given as follows :

The expected return for share X is $110.

The expected return for share Y is given as follows :

The expected return for share Y is $110.

b) The standard deviation for share X is given as follows :

From part (a) we already have, E(X) = 110

Now,

The standard deviation for share X is $126.6886.

The standard deviation for share Y is given as follows :

From part (a) we already have, E(Y) = 110

Now,

The standard deviation for share Y is $126.6886.

c) The expected values of return for share X and share Y are equal and also the standard deviations for both the shares are equal. It means if we keep investing $1000 in each of the shares for long time, we can expect on an average same amount of return from both the shares and also the variation of the returns will be same.

Hence, both the shares are equally desirable.