You have $300,000 available in cash and you want to decide on how to invest this money. There are two main portfolios (collection of various financial instruments) that you can use for investment. The first portfolio, Portfolio A, requires $200,000 of initial investment. If the market conditions turn out to be good then Portfolio A will bring 20% of interest. However, if the market conditions turn out to be bad, then you will lose the initial investment. The second portfolio, Portfolio B, requires only $100,000 of initial investment. If the market conditions turn out to be good then Portfolio B will bring 10% of interest. However, if the market conditions turn out to be bad, then you will lose the initial investment. Because of regulatory reasons, you can only invest in one of the portfolios and only one unit of each portfolio. Besides these two portfolios, you can also use a safer option, investing in the bond market. This investment will bring 3% of interest if the market turns out to be good and only 1% of interest if the market turns out to be bad. You can invest as much as you want into the bond market up to your initial endowment $300,000. From your past experience, you estimate that the likelihood of having a good market is 0.90.

a) Solve for the optimal investment decision by constructing a decision tree.

b) Assume that you do not know the probability of having a good market (p). Provide a roadmap for yourself for the optimal investment decision based on the good market probability (p). In other words, write down the optimal investment decision(s) and the optimal value with respect to the good market probability (p).