Rate of Return Scenario Probability Stocks Bonds Recession .30 4 % +16 % Normal

Question

Rate of Return Scenario Probability Stocks Bonds Recession .30 4 % +16 % Normal economy .50 +17 +10 Boom .20 +28 +9 Consider a portfolio with weights of .7 in stocks and .3 in bonds. a. What is the rate of return on the portfolio in each scenario? (Do not round intermediate calculations. Round your answers to 1 decimal place.) Scenario Rate of Return Recession % Normal economy % Boom % b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected rate of return % Standard deviation % c. Which investment would you prefer? Portfolio Bonds Stocks

Explanation / Answer

Rate of return:

Recession = 0.7 * -0.04 + 0.3 * 0.16

= -0.028 + 0.048

= 0.02 or 2%.

Normal economy = 0.7 * 0.17 + 0.3 * 0.1

= 0.119 + 0.03

= 0.149 or 14.9%.

Boom = 0.7 * 0.28 + 0.3 * 0.09

= 0.196 + 0.027

= 0.223 or 22.3%.

Expected return = 0.3 * 0.02 + 0.5 * 0.149 + 0.2 * 0.223

= 0.006 + 0.0745 + 0.0446

= 0.1251 or 12.51%.

Variance = 0.3 (0.02 - 0.1251)2 + 0.5 (0.149 - 0.1251)2 + 0.2 (0.223 - 0.1261)2

= 0.0033138 + 0.0002856 + 0.0018779

= 0.0054773

Standard deviation = 0.074 or 7.4%.

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