1.8 Sarah, the manager of a bank, can make one of two types of loans. She can loan money to local firms, and have a 75% probability of earning $100 million and a 25% probability of earning $80 million. Alternatively, she can loan money to oil speculators, and have a 25% probability of earning

$400 million and a 75% probability of losing

$160 million (due to loan defaults by the speculators).

Sarah receives 1% of the bank’s earnings. She believes that if the bank loses money, she can walk away from her job without repercussions, although she will not receive any compensation.

Sarah and the bank’s shareholders are risk neutral.

How does Sarah invest the bank’s money if all she cares about is maximizing her personal expected earnings? How would the stockholders prefer that Sarah invest the bank’s money? (Hint: See Solved Problem 20.1.)