By: Roy Kouwenberg, Asian Institute of Technology & Erasmus University, William Ziemba, University of British Columbia
Published: July 2005

Lacking any common definition of the term “hedge fund” many use the moniker to refer to a fund that is a) is “unregulated” and b) involves some kind of unique fee structure such as a performance fee.

So this paper on the effect of management & performance fees on hedge fund risk aversion is particularly salient.  The authors studied both single manager funds and funds of funds to determine if the existence of a performance fee might change a manager’s views on volatility, skewedness and kurtosis (as expressed by the performance of their funds).

Kouwenberg & Ziemba draw heavily on “prospect theory“ that states that the decrease in utility from a loss is larger than the utility increase from a commensurate gain.  They describe the implication for hedge fund managers the following way:

“Once the fund value drops below the benchmark the manager tries to maximize the probability of beating the hurdle rate in order to avoid the negative consequences of a loss, i.e. the manager becomes risk seeking. On the other hand, when the fund value exceeds the benchmark, the manager expects to receive additional income from incentive fees and becomes risk averse to protect his gains.”

In theory, say the authors, a manager’s risk aversion a) should be lower when there is a high performance fee – i.e. as she “swings for the fences” and b) should be higher when the manager has a substantial stake in the fund - no matter what the performance fee.

Results for Single Strategy Funds

Empirical evidence seems to support these hypotheses – sort of.  When a large database of hedge funds was analyzed, it turned out that volatility was pretty stable across buckets of funds with different performance fees.  However, funds with a higher performance fee (e.g. over 20%) had a significantly more negative skewedness and a higher kurtosis.

Unfortunately for hedge fund manager, this study also corroborates common sense – that the existence of a performance fee does, in fact, reduce returns.  In other words, whatever incentive benefit there might be from charging a performance fee, it’s not large enough to make up for the cost of the fee.

Interestingly, while higher performance fees didn’t significantly increase volatility, higher management fees did.  In fact, higher management fees also increased kurtosis, suggesting more risk taking in these funds.

Results for Funds of Funds

The authors find that, unlike that of single-manager funds, the volatility of funds of funds does increase when performance fees are higher.  However, average returns also rise (although not on a risk-adjusted basis).  In other words, a higher incentive fee for a fund of funds might actually incent the manager.  Go figure.

But unfortunately, like single manager funds, funds of funds with higher management fees also produce lower returns.

Performance Fee as the manager’s option

We have touched on the optionality of a performance fee a little on this blog.  But this paper actually puts a value on that call option.  Naturally, the value of the fee to the manager is based on the particular level of performance fee.  But it’s also based on the portion of the fund owned (or more appropriately not owned) by the manager.  In other words, if a manager owns most of the fund, then charging herself a meaty performance fee is not that useful.

Under a series of complex assumptions regarding a manager’s utility curve and risk aversion, the authors come up with the following theoretical function that describes the value of 20% performance fee to a hedge fund manager.

Basically, this chart says that the performance fee “option” is worth a lot to a manager – as long as the manager doesn’t own a large chunk of the fund.  If he does, then the value to be gained by increasing volatility (to increase option value) is mitigated by the disutility of having to ride the resulting roller coaster along with clients.

Our conclusion: Ten bucks says Alfred Jones had no idea how complicated the addition of a performance fee could possibly be.

Read Full Paper