$2.$ A trust officer for a major banking institution is planning the investment of a $$1$ million family trust fund for the coming year. The trust officer has identified a portfolio of stocks and another group of bonds that might be selected for investment. The family trust can be invested in stocks or bonds exclusively, or a mix of the two. This trust officer prefers to divide the funds in increments of $10\%$; that is$,$ the family trust is split into the following alternatives:

$($a$)100\%$ stocks and $0\%$ bonds$$

$($d$)70\%$ stocks and $30\%$ bonds

$($b$)90\%$ stocks and $10\%$ bonds$($e$)0\%$ stocks and $100\%$ bonds

$($c$)80\%$ stocks and $20\%$ bonds

The trust officer has evaluated the relationship between the yields on the different investments and the general economic conditions. Her judgment is as follows:

$(1)$ If the next year is characterized by solid growth in the economy, bonds will yield $12\%$ and stocks $20\%$;

$(2)$ If the next year is characterized by inflation, bonds will yield $18\%$ and stocks $10\%$;

$(3)$ If the next year is characterized by stagnation, bonds will yield $12\%$ and stocks $8\%.$

$($A$)$ Constructs the payoff and the opportunity loss table.

$($B$)$ Determine the best decision using the maximax, maximin, Laplace, Hurwicz $(\backslash$alpha $=0\mathrm{.}40)$ and minimax regret criteria.

$($C$)$ Suppose that a leading economic forecasting firm projects P$($solid growth$)=0\mathrm{.}40,$ P$($inflation$)=0\mathrm{.}25$ and P$($stagnation$)=0\mathrm{.}35.$ Use the expected value criterion to select the appropriate strategy. What is the EVPI for this problem?