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 21% chance for being good, a 52% chance for being fair, and a 27% 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	11 %	28 %
Fair	8 %	7 %
Poor	−6 %	−12 %

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

Answer 1

The probability distribution of the state of the U.S. Economy is

State of the U.S. Economy	Probability
Good	0.21
Fair	0.52
Poor	0.27

Let X be the Return (%) in Europe. The distribution of X is

Returns in Europe (%) (x)	P(x)
11	0.21
8	0.52
-6	0.27

The expected value of X is

The expected value of is

The variance of X is

The standard deviation of returns in Europe is

Let Y be the Return (%) in Asia. The distribution of Y is

Returns % in Asia (y)	P(y)
28	0.21
7	0.52
(12)	0.27

The expected value of Y is

The expected value of is

The variance of Y is

The standard deviation of returns in Asia is

ans:

	Returns in Europe	Returns in Asia
Expected value	4.85%	6.28%
standard deviation	6.70%	13.77%