Question

Rate of Return Scenario Probability Stocks Bonds Recession .20 −9 % +20 % Normal economy .50 +21 +8 Boom .30 +31 +8 Consider a portfolio with weights of .6 in stocks and .4 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

WHAT IS THE STANDARD DEVIATION

Answer 1

a)
Return on portfolio = Weight of individual asset * Return of individual assets

Recession:
Rate of return = (0.6 * -9%) + (0.4 * 20%)
= -5.4% + 8%
= 2.6%

Normal economy:
Rate of return = (0.6 * 21%) + (0.4 * 8%)
= 12.6% + 3.2%
= 15.8%

Boom:
Rate of return = (0.6 * 31%) + (0.4 * 8%)
= 18.6% + 3.2%
= 21.8%

b)
Expected rate of return = sum of (Probability * return)
= (0.2 * 2.6%) + (0.5 * 15.8%) + (0.3 * 21.8%)
= 0.52% + 7.9% + 6.54%
= 14.96%

c)
Bond return = (0.2 * 20%) + (0.5 * 8%) + (0.3 * 8%)
= 4% + 4% + 2.4%
= 10.4%
Stock return = (0.2 * (-9%)) + (0.5 * 21%) + (0.3 * 31%)
= -1.8% + 10.5% + 9.3%
= 18%

Stocks gives highest return. So, investment in stock is preferable.