The comptroller of the Macrosoft Corporation has $100 million of excess funds to

The comptroller of the Macrosoft
Corporation has $100 million of excess funds to invest. She has been instructed
to invest the entire amount for one year in either stocks or bonds (but not
both) and then to reinvest the entire fund in either stocks or bonds (but not
both) for one year more. The objectives is to maximize the expected monetary
value of the fund at the end of the second year.The annual
rates of return on these investments depend on the economic environment as
shown in the following table:Rate of ReturnEconomic
EnvironmentStocksBondsGrowth20%5%Recession-1010Depression-5020The probabilities of growth recession and depression for
the first year are 0.7 0.3 and 0 respectively. If growth occurs in the first
year these probabilities remain the same for the second year. However if a
recession occurs in the first year these probabilities change to 0.2 0.7 and
0.1 respectively for the second year.