Sunday, January 8, 2012

The wonders of hedge fund accounting: incentive fees "reduce" volatility

The mechanics of hedge fund incentive fee accounting tends to lower returns during positive performance months while raising them during negative months, making hedge fund performance seem less volatile than it actually is.

Let’s take a hypothetical fund with a starting NAV of $1,000 on Jan-1 that charges the traditional 2/20 (2% management fee per year on NAV and 20% incentive fee on performance.) To make it more realistic, assume all numbers are in millions. Also assume the fund made $23 in the month of January and then lost $12 in the month of February. Here is how the accounting will work from the investor’s perspective:

Hedge fund accounting example
At the end of January, once you account for the management fees and expenses, the fund is left with $21.21 in P&L, corresponding to 2.1% gross return for the month. The manager would accrue $4.24 (20% of 21.21) of incentive allocation against the fund, producing a net return of 1.7%. So far so good.

It gets tricky at the end of the next month when the fund lost money. The year-to-date P&L for the fund (including the management fee and fund expenses) is now $7.39 ($21.21 minus $13.82). 20% of that is $1.48 of year-to-date incentive fee. But back in January the fund was charged $4.24 in incentive allocation. Now with the loss in February the fund should be credited back what it was overcharged. So the accrual reversal of $2.76 is applied against the losses, making the February loss less than it actually was. Therefore the -1.4% of gross return for February is converted into -1.1% net. Note that if the year-to-date P&L turns negative, the entire incentive fee for the year is reversed, and as long as it stays negative, gross and net returns become the same.

This dampening effect both on the up-side and the down-side reduces the fund volatility as measured by monthly net returns – which is how most hedge funds are analyzed. The chart below shows net and gross returns for our hypothetical fund with the dampening clearly visible on both sides.

Net and gross returns of a hypothetical hedge fund

The standard deviation (effectively the monthly volatility) of the gross returns here is 2.61% (9.03% annualized), while the same for the net returns is 2.09% (7.23% annualized). The higher the incentive fee, the lower the volatility of net returns. Thus if one were to use something like the Sharpe Ratio to compare two funds, the fund with the higher incentive fee may actually look better on a risk adjusted basis.  Our hypothetical fund for example has gross return for the full year of 5.2%, while the net is 4.2%. Therefore the fund’s Sharpe Ratio is 0.585 (4.23% divided by 7.23% – assuming “riskless rate” is zero). However if this fund did not charge any incentive fees at all, its Sharpe Ratio would actually be lower: 0.579 (5.23% divided by 9.03%).  Lower Sharpe Ratio is typically interpreted as an inferior performance on a risk adjusted basis - yet here it's the same fund without the incentive fees.

This accounting trick that perversely favors funds with higher incentive fees makes is difficult to compare the “quality” of returns across hedge funds who charge different incentive fees. It also makes it difficult to perform risk adjusted comparison between hedge funds and other asset classes such as indices or mutual funds. So if you are looking at a hedge fund that has high incentive fees and claims low volatility, ask for gross returns to perform your analysis.
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