Consider the following scenario analysis:

Rate of Return

Scenario: Probability, Stocks, Bonds

Recession $0\mathrm{.}20,8\%,19\%$

Normal economy $0\mathrm{.}50,20\%,10\%$

Boom $0\mathrm{.}30,25\%,6\%$

a$.$ Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?

b$.$ Calculate the expected rate of return and standard deviation for each investment.

c$.$ Which investment would you prefer?