A bank can invest in 2 portfolios. Each requires $100 million to be raised either through debt or equity. One portfolio contains only safe assets and pays a certain gross return of $118 million.

The other portfolio is risky and will pay a gross return of $200 million with probability 1/5 or a return of $75 million with probability 4/5.

a. Which portfolio makes the most sense from society's standpoint? Why?

b. If they can borrow the entire 100 million at 10% which portfolio will they choose and why?

c. Suppose they can borrow 90 million at 10% but must raise the other 10 million from equity.

Which portfolio will they choose and why?

d. What if they must raise 20 million in equity and borrow only 80 million at 10%? Which portfolio will be chosen and why?

Explain how this problem illustrates the moral hazard associated with debt finance and what implications it has for bank regulation.