You have invested 10% of your wealth in a hedge fund; the other 90% is in cash and there is no time value of money. One year from now the hedge fund will cease operations; it will either fail and give you back only half of your investment, or succeed and give you back 1.85 times your investment. You know that 15% of hedge funds fail every year.

You find a hedge fund evaluation model that correctly identifies hedge funds that will fail 95% of the time, and correctly identifies hedge funds that will succeed 90% of the time. You run this model on your hedge fund and it says it will fail. You can get your money out now for a 2% exit fee. If you have a logarithmic utility function, should you exit now or stay for the remaining year? Explain.