# Performance Fees

Institutional investors continue to allocate a significant and growing fraction of their portfolios to alternative investments such as hedge funds, private equity, and real estate, notwithstanding the challenges these relatively illiquid assets posed to them during the financial crisis. We suspect that investors now pay considerable attention to their liquidity needs and factor these needs into their decision to invest in alternative investments.

We are fairly confident, though, that most investors do not fully appreciate the consequences of a second feature of alternative investments. They typically charge performance fees. It turns out that the expected return of a group of funds that charges performance fees is less than the average of the funds’ expected returns. And it also true that an individual fund’s standard deviation or the standard deviation of a group of funds, net of performance fees, understates risk. Together, these oversights lead investors to allocate more to alternative investments than they should, if they base their allocations on expected return and risk.

## The Expected Return of the Average is Less Than the Average of the Expected Returns

Managers of alternative investments typically charge a performance fee that is a percentage of profits — but not losses — relative to a benchmark, along with a base fee that is a fixed percentage of assets under management. Often the base fee is deducted from the profits before the performance fee is applied. If, for example, the base fee equals 2% and the performance fee equals 20%, a manager who produces a 10% return in excess of the benchmark on a $100 million portfolio will collect a $2 million base fee (2% × $100,000,000) and a $1.6 million performance fee (20% × ($10,000,000 – $2,000,000) for a total fee of $3.6 million. The investor’s return net of fees, therefore, is 6.40%.

Now suppose an investor hires two managers who each charge a base fee of 2% and a performance fee of 20%. Assume as well that these managers both have expected returns of 10% in excess of the benchmark. The expected fee for each manager is 3.60% (2% + 20% × (10% – 2%)). Therefore, the investor might expect an aggregate return net of fees from these two managers equal to 6.40%. This expectation would be justified, however, only if both managers’ returns exceed the base fee. If, instead, one manager produces an excess return of 30% and the other a –10% excess return, and an equal amount of capital is allocated to each manager, the investor would pay an average fee of 4.80% rather than 3.60%, and the average return to the investor would equal 5.20% rather than 6.40%, even though the managers still have an average excess return of 10%. The difference between 4.80% and 3.60% is known as the asymmetry penalty.

This result is specific to the assumptions of this example. Nevertheless, it is easy to determine the typical reduction in expected return by applying Monte Carlo simulation. Let’s consider investment in 10 funds, each of which has an expected excess return of 7%, a standard deviation of 15%, and a correlation of 0% with the other funds. Let’s also assume that LIBOR equals 4%. In order to estimate the impact of asymmetry, we proceed as follows:

We first draw 1,000 random returns for each fund, assuming their returns are normally distributed and uncorrelated.

Next, we apply the base fee and performance fee to the 1,000 returns for each fund and compute the average of their returns net of fees.

We then compute the average return across the 10 funds for the 1,000 random draws, and we apply the base fee and performance fee to these average returns. The average of these net returns reveals the performance that we should expect if we were reimbursed for underperformance or if we used a single multistrategy fund instead of separate funds.

Finally, we compute the difference between the results of steps 2 and 3, which equals the asymmetry penalty.

With the above assumptions, the asymmetry penalty equals about 0.70%. If the funds’ correlations were higher, the penalty would be smaller, and if they were lower, the penalty would be higher. This asymmetry penalty is a hidden fee arising from the fact that investors pay for outperformance but are not reimbursed for underperformance. This effect, in principle, would be somewhat muted because most performance fee arrangements include clawback provisions that require funds to offset prior losses before collecting performance fees. In most cases, though, underperforming managers are either terminated or the performance fees are reset without reimbursement for prior losses.

## Standard Deviation Understates Risk

There is yet another subtle and unpleasant feature of performance fees. The standard deviation of funds that charge performance fees understates risk, because it is reduced by the attenuation of upside performance. When a fund outperforms its benchmark, the upside return is cut by the amount of the performance fee, but because losses are not reimbursed, downside deviations are unaffected. Based on simulation, an individual fund that charges a 2% base fee and a 20% performance fee and that has a 15% standard deviation would produce about a 13% standard deviation net of performance fees. Thus, performance fees, given these assumptions, have the effect of understating risk by about 2%. If we treat these 10 funds as a group, the risk is understated by about 0.65%, because of the effect of diversification. These results are summarized as follows:

An investor who ignores these two effects would expect an individual fund, which is a member of a group of 10 funds, to have an expected return net of fees equal to 7.70% and volatility equal to 13%.By taking into account the asymmetry penalty and the mismeasurement of risk, this fund instead has an expected return of 7% and normalized downside volatility equal to 15%. If an investor treated the 10 funds as a single asset, the return comparison would remain the same, but the correct volatility estimate would equal 4.75% instead a presumed estimate of 4.10%. Either way, the correct return-to-risk ratio is more than 20% less than an investor would presume by ignoring the effects of performance fees.

These features of performance fees do not imply that investors should avoid alternative investments or other funds that charge performance fees. Rather, investors should account for these features, along with other considerations, such as illiquidity, when determining the appropriate allocation to such funds. We suspect most do not.

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