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2) A private equity manager has $3 million dollars to invest. After looking into dozens of companies, the manager shortlisted two risky, but potentially very protable 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 dierent 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 rms; ii Invest $1.5 million in one rm and $1.5 million in the other; iii Not invest at all. Za) [3) Calculate the expected value of the investments under each strategy. 2b) [b] Suppose the manager is risk averse: way more scared about ending up with a result of zero, in which case they will be red, than they are excited about getting fantastic returns. Utility over the nal value of investments is aka) 2 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