## Thursday, January 7, 2010

### Perverse Incentives for Hedge Fund Managers

While mutual funds usually just charge a fixed percentage management fee, such as 2% of assets under management, hedge funds add a “performance fee”. One of the supposed benefits of paying a hedge fund manager more if the fund performs well is that it aligns the manager’s interests with the investors’ interests. However, in reality, their interests are actually very poorly aligned.

Consider the hypothetical Hyper-Uber-Growth Engine (HUGE) fund. It has a typical “2 and 20” arrangement where management fees are 2% of assets under management plus 20% of any profits above a threshold return of 4%. So, the manager gets 2% plus one-fifth of any returns above 4%.

To model the amount of risk a hedge fund manager is willing to take, HUGE is run in the following unusual way. The assets are invested in some conservative way throughout the year, and on the last day of the year, the manager takes some fraction of the fund to Las Vegas and bets it all at the roulette wheel on red.

The odds are 18/38 that a red number will come up (fund investors win), and 20/38 that the result will be black or zero or double-zero (fund investors lose). Obviously, this is a bad bet from the fund investors’ point of view, but it is the HUGE manager who gets to decide whether to place the bet and how much to wager.

As of the last day of 2009, HUGE had made a 4% gain on its mix of investments and had \$100 million in assets. This amount includes the HUGE manager’s entire personal assets of \$1 million. The fact that the HUGE manager has all of his personal fortune in the hedge fund can only increase the alignment of his interests and those of the investors, but as we’ll see it won’t help much.

A \$1000 Bet

Suppose that the manager decides to bet only \$1000. From the investors’ point of view, either the fund will lose \$1000, or it will gain \$800 (after removing the 20% performance fee). Taking into account the roulette probabilities, the investors’ expected loss on this bet is \$147.

The manager’s personal wealth is 1% of the fund. So, the bet will cause him to lose \$10 or win \$8. But that’s not the end of the story for the manager. If he wins the roulette bet he will also get the \$200 performance fee. In total he has a 20/38 chance of losing \$10 and an 18/38 chance of winning \$208. His expected gain works out to \$93.

So, this is a bad bet for investors, but a very good bet for the manager. If the manager chooses to bet \$10 million of investor money, his personal wealth of \$1 million will either drop to \$900,000 or it will rise to \$3,080,000. This is a great bet for him, but investors will either lose 10% with probability 20/38 or gain 8% with probability 18/38. Investors’ expected loss is 1.47% of the fund.

Conclusion

Of course no hedge fund would be run the way that this hypothetical fund is run with the roulette betting. But this example does illustrate why hedge fund managers have a strong incentive to take big chances with investor money, even if those chances have a negative expectation.