Question

Investment advisors recommend risk reduction through international diversification. International investing allows you to take advantage of the potential for growth in foreign economies, particularly in emerging markets. Janice Wong is considering investment in either Europe or Asia. She has studied these markets and believes that both markets will be influenced by the U.S. economy, which has a 16% chance for being good, a 47% chance for being fair, and a 37% chance for being poor. Probability distributions of the returns for these markets are given in the accompanying table.

State of the U.S. Economy Returns in Europe Returns in Asia

Good 15% 25%

Fair 5% 9%

Poor -10% ?10%

a. Find the expected value and the standard deviation of returns in Europe and Asia. (Round intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Europe Asia

Expected value % %

Standard deviation

b. What will Janice pick as an investment if she is risk neutral? Investment in Europe Investment in Asia

Answer 1

(a)

Let X is a random variable shows the return in Europe. Following table shows the calculations for mean and expected value:

X	P(X=x)	xP(X=x)	x^2P(X=x)
0.15	0.16	0.024	0.0036
0.05	0.47	0.0235	0.001175
-0.1	0.37	-0.037	0.0037
Total		0.0105	0.008475

The expected value is:

The standard deviation is

---------------

Let Y is a random variable shows the return in Asia. Following table shows the calculations for mean and expected value:

Y	P(Y=y)	yP(Y=y)	y^2P(Y=y)
0.25	0.16	0.04	0.01
0.09	0.47	0.0423	0.003807
-0.1	0.37	-0.037	0.0037
Total		0.0453	0.017507

The expected value is:

The standard deviation is

(b)

Investment in Europe