*Performance fees.* No other words in the hedge fund lexicon seem to generate so much passion among both managers and investors. But while the concept seems simple enough, it actually has implications well beyond the size of the manager’s bonus.

For example, a performance fee reduces return volatility. In an up-month, the fee reduces the size of the return that might otherwise have been realized. But in a down-month, the unrealized performance fee is essentially paid back to the fund – as if a negative performance fee had been charged. Of course, after the fee is paid out at the end of the year, its gone for good and the worst a manager can do is to earn no performance fee the next year (see related posting for more discussion on intra-year negative performance fees).

Accounting for a performance fee can be a difficult task when conducting a back-test of a new trading model since the accrued performance fee in, say, December, would more than likely have impacted the manager’s strategy at that point. So applying the same trading rules across the board and ignoring downside risk for the manager is unrealistic.

An academic study released last week illustrates that the presence of performance (incentive) fees can also confound the factor-modeling conducted by those attempting to replicate hedge fund returns. It turns out that reversing out the performance fees from net returns is like unscrambling the proverbial egg.

**Evidence of the Effect of Performance Fees**

The authors, Chris Brooks of the University of Reading and Andrew Clare & Nick Motson of the Cass Business School, use a simple example to make this point. They compare the after fee (net) returns for two funds with identical before-fee (gross) returns (1% return per month and a 5% per month standard deviation). They find that a management fee-only version of the fund maintained the same standard deviation and had monthly return 0.17% lower than the original fund. However, the version of the fund with a 2 and 20 fee had a return 0.30% lower per month (no surprise there), but a standard deviation that was 33 basis points per month lower than that of the original fund.

While a fund has its own set of beta correlations, the performance fee itself also has a set of beta correlations. The authors say the beta of the fund is simply the sum of the two betas – a beta of gross returns (less management fees) and a beta of performance fees.

As we have discussed on this website (see related posting), performance fees amount to a call option written by the investor to the manager with no associated fee. The authors of this paper propose using the delta of that option to calculate the beta of the incentive fee.

**An Example**

Amazingly, when they apply this concept to a 2 and 20 fund with gross return beta of 1.0 (called Beta Partners), they find that the after-fee returns have a beta that actually fluctuates between 0.80 and 1.0 depending on whether or not the performance fee kicks-in (i.e., if the fund is above its high water mark). In other words, when the performance fee wasn’t charged during the bear market the fund was 100% correlated to the index.

Comment the authors:

On the basis of this information an investor might conclude that Beta Partners is varying its exposure to the market over time but by construction, the actual beta of the fund is 1.0 at all times. All of the variation in exposure is actually coming from the change in the delta of the incentive fee option.

So what happens when you reverse-engineer the gross returns for hedge funds? Apparently, you find that hedge funds don’t have the statistical characteristics we all thought they did. Say the authors:

gross hedge fund returns look far more normal than net returns and in fact, contrary to Brooks and Kat [2002], for our sample it would appear that on average hedge fund returns display positive skewness and do not exhibit significantly excess kurtosis.

**Implications for Calculating Embedded Fees**

Using this method of calculating gross returns, the authors then turn their attention to deriving the average costs associated with various hedge fund strategies. To accomplish this, they use the methodology first proposed by Ibbotson and Chen (see related posting).

They conclude that the gross returns of hedge funds are actually higher than one would find if they used the net after-fee results in their calculations (the Ibbotson & Chen approach). The corollary: implicit fees are actually a little lower than previously assumed.

**Implications for Factor Replication**

The authors also suggest that their approach will also produce more accurate results when used in factor models. Thankfully, while their results are arguable more accurate, we won’t have to re-write our understanding of hedge funds. When they reproduce the factor model first proposed by Jasmina Hasanhodzic and Andrew Lo (see related posting), they find no significant difference between the net and gross clones in either correlation or R-squared.

**Impact on Manager Behavior**

So how exactly do performance fees impact manager risk-taking behavior? The authors of this paper argue that a performance fee

encourages managers to maximise the value of this fee option; their motivations could be different depending upon the delta of the option. When the delta is high, the bulk of the value in the option comes from its moneyness and little from its volatility. But when the delta is low, the reverse is true.

So is it true that managers swing for the fences when they’re in trouble? Apparently, yes, on average. The authors find that the standard deviation of returns when a fund’s embedded option is in the money is much lower than the standard deviation of the returns when a fund is out of the money.

**The Tools to Unscramble the Performance Fee Egg**

The bottom line here seems to be that at least a portion of the characteristics what we have always ascribed to hedge funds actually may have always been from their unique fee model, not from their underlying investment strategies.

In retrospect, this makes a lot of sense. Hedge funds have been sliced and diced so many ways according to so many risk factors. But performance fees â€“ an equally significant influence on returns â€“ have rarely been examined explicitly. Thanks to this paper, we now have a framework to do this. We now have the tools to unscramble the egg.

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