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 objective 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:

The 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.
(a) Construct the decision tree for this problem by hand.
(b) Analyze the decision tree to identify the optimal policy.

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Rate of Return Economic Environment Stocks Bonds Growth Recession Depression 2096 10 5% 10 20 -50