A private equity manager has $3 million dollars to invest. After looking into dozens of companies, the manager short-listed two risky, but potentially very profitable potential in- vestments. For each of these investments, the manager expects that the investment will be successful with 50% probability, in which case the total return will be four times as much as what was invested. But with 50% probability, the company fails and the investment is worth zero. Because the companies are in very different industries, and the manager does not expect a recession or a boom in the near future, these two events are statistically independent. The manager considers three strategies: i. Invest all of the $3 million dollars in one of the firms.
ii. Invest $1.5 million in one firm and $1.5 million in the other.
iii. Not invest at all.

Required:
a. Calculate the expected value of the investments under each strategy.
b. Suppose the manager is risk averse: way more scared about ending up with a result of zero, in which case they will be fired, than they are excited about getting fantastic returns. Utility over the final value of investments is u(w) = -e-, where w is measured in millions. Calculate expected utility under each strategy. How are the strategies ranked in terms of manager preferences? Explain the intuition.