Question

Consider the following information on returns and probabilities:

Invest 1/2 of your money in Asset A and 1/2 in Asset B.

State      Probability           A             B                           

Boom         .25                   12%       4%         

Bust            .75                   6%         18%      

what is the standard deviation of the return on the portfolio?

		a. 1.7
		b. 2.9
		c. 3.9
		d. 4.6
		e. 5.5
		f. 6.9
		g. 7.5
		h. 9.0
		i. 8.2
		j. 11

Answer 1

Answer is 1.7%

Weight of Asset A = 0.50
Weight of Asset B = 0.50

Boom:

Expected Return = 0.50 * 12% + 0.50 * 4%
Expected Return = 8%

Bust:

Expected Return = 0.50 * 6% + 0.50 * 18%
Expected Return = 12%

Expected Return on Portfolio = 0.25 * 0.08 + 0.75 * 0.12
Expected Return on Portfolio = 0.11 or 11.00%

Variance on Portfolio = 0.25 * (0.08 - 0.11)^2 + 0.75 * (0.12 - 0.11)^2
Variance on Portfolio = 0.0003

Standard Deviation on Portfolio = (0.0003)^(1/2)
Standard Deviation on Portfolio = 0.017 or 1.7%