Stock and bond indexes are expected to have the following returns (%) depending on the state of the economy next year:

State of the Economy Probability of State of Economy Stocks Bonds

Recession. 0.4 11% 8%

Normal 0.5 10% 5%

Boom 0.1 28% 15%

(a) Which of the two investments has more volatile returns? Would you (as a rational investor) prefer one of the two investments? Why or why not?

(b) Construct a portfolio that is 30% invested in stocks and 70% invested in bonds. Calculate the expected return and standard deviation of the portfolio and compare the three investment options (bonds, stocks and the 30/70 portfolio). Could the 30/70 portfolio be rationally chosen by some investors over the bond investment? Why or why not?