Comment: “Risk-based compensation” a more equitable approach
Jan 14th, 2010 | Filed under: Guest Posts, Today's PostOver the past few years, it has become clear to many that raw performance-based compensation for hedge fund managers has significant flaws – from its asymmetry to its inability to distinguish between skill and luck. Various tweaks have been proposed (as you can see in our section on fees). But here is one idea that integrates several dimensions of risk with traditional performance metrics. Eric Hirschberg is the CEO of the Bermuda-based fixed income manager Orion Investment Management. He also advises on compensation, resource allocation, portfolio structuring and risk management issues, and is the founder of the blog KapitalMarks.com.
Special to AllAboutAlpha.com by: Eric Stanhope Hirschberg, CEO, Orion Investment Management
The term Hedge Fund has become a misnomer, as more and more alternative and not so alternative assets find their way into the space. The term Hedge Fund has really become a proxy for an incentive based fee structure more than a statement about the investment enterprise that underlies it. The market settled on a 2% management fee with a 20% profit split for the manager. Of course there are variations on this theme, but they are more or less arbitrary structures.
The growing debate about the nature of Hedge Fund returns, coupled with the notion that many Hedge Fund returns are not in fact idiosyncratic are driving more institutions to revisit the issue of compensation.
I believe that an appropriate compensation scheme should take into account the following four rules.
- Managers should be rewarded for the volatility characteristics produced by their strategy P&L.
- Managers should be penalized for the inherent risk they undertake to achieve those returns.
- Investors should penalize Managers for the replicability of the return stream they generate.
- A Manager’s base compensation for “holding” an asset over its expected return horizon should be discounted by the expected horizon.
Armed with the above mentioned notions, we shall now attempt to construct a logical and equitable compensation framework.
Rule #1: A manager should be rewarded for the volatility characteristics produced by strategy P&L
The Sharpe ratio or is a measure of the excess return (or Risk Premium) per unit of risk in an investment asset or a trading strategy. But from the manager’s point of view, this measure is inferior to the Sortino ratio.
The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio or strategy. While the Sharpe ratio penalizes both upside and downside volatility equally, the Sortino ratio penalizes only those returns falling below a user-specified target, or required rate of return. Thus, the ratio is the actual rate of return in excess of the investor’s target rate of return, per unit of downside risk.
So let’s create a scalar that puts the 20% performance fee back in its rightful place.
In the early days of Hedge Funds (they actually did hedge back then) Sortino’s of 2 and above were the selling point. For argument’s sake, lets create a Scalar N, where N=0.1
Now let’s start to build a compensation equation, replacing 20% with C= N*S
Where N=0.1 and
Under our new compensation scheme, a manager with a Sortino of 2.0 would receive a compensation of 2.0*0.1, or 20% of performance. If on the other hand, the manager produced a return stream with a Sortino of 0.5, his compensation would be reduced to 5% of performance.
Rule #2: A manager should be penalized for the inherent risk undertaken to achieve those returns
The first flaw with “Version 1.0″ of our new compensation equation (above) is its failure to recognize the role of risk in creating a “false dawn” benchmark for the Sortino itself.
Our Sortino assumes that T = the risk free rate at a particular time. This creates the implicit assumption that T is also the appropriate rate benchmark for the Strategy return X. Holding a basket of risky debt will generally produce a return over the risk free rate as will selling a basket of out-of-the-money options. Both strategy return distributions are far from normal, yet the equation assumes a normal distribution.
The more fat-tailed and negatively skewed the underlying distribution, the more its return stream should be penalized. It is very difficult to know the underlying process distribution a priori. That said, we could use Conditional Value at Risk or CVaR.
As readers of AllAboutAlpha.com are aware from posts such as this one from Dr. William Shadwick, CVaR evaluates the value (or risk) of an investment in a conservative way - focusing on the less profitable outcomes. For high values of q (where q is the “threshold”), it ignores the most profitable – but also unlikely – possibilities. Unlike the discounted maximum loss even for lower values of q expected shortfall does not consider only the single most catastrophic outcome.
A value of q often used in practice is 5%.
ESq = E(x | x < ?,P(x < ?) = q)
where q is the threshold.
Now, a manager might argue that he should not be penalized for an outcome that did not occur. But nevertheless, he should not be incentivized to create a performance option by simply ramping up tail risk. After all he doesn’t share in the losses.
One suggestion would be ranking the q=0.05 across a range of strategies and creating a bucket penalty, e.g. if q(manager A) such that decile(qA) < 3 then V=.5. So under “Version 2.0″ of our new compensation scheme, a manager with a Sortino of 2.0 and a q=0.05 decile of 3 (v-0.5), would receive a compensation of 2.0*0.1*.5, or 10% of performance.
Rule #3: An investor should penalize a manager for the replicability of the return stream generated by that manager
Common sense and Modern Portfolio Theory would dictate that, the lower the covariance of strategy returns (with positive expected return), the more attractive the overall portfolio return. Therefore, the more idiosyncratic the manager’s return stream, the more he should get compensated to generate it for you.
The problem from the manager’s point of view is that this compensation scalar has potentially more to do with his investor’s portfolio construction skills, meaning that this element is investor specific. A work around involves the definition of common benchmarks (e.g. SP500, 10yr Bond, High Yield Index) with a penalty for correlation over a threshold ). To create a scalar against multiple benchmarks, one could consider covariance measure of returns. We can also consider conditional covariance (e.g. splitting negative SP500 months from positive SP500 months).
This way, the higher the (conditional) covariance of a manager’s return stream to an investable asset, the closer the compensation structure to the investable asset investment costs.
Rule #4: A Manager’s base compensation for “holding” an asset over its expected return horizon should be discounted by the expected horizon
There is a reason I’ve left this point for last. There are two linked issues at play, which are described below, and although I am convinced that a scalar penalty function is the answer, I’m not convinced that a single formula will work.
Firstly, the longer the manager subjects capital to risk to achieve a return, the less active the management. A counter argument would go something like this “Why shouldn’t I be compensated for all the background work that allows me to make that one correct decision?” My answer goes something like this: I believe all my managers do the work to make informed decisions. You will be compensated based upon your risk adjusted performance. As for base compensation, I am happy to pay you more if weeding the garden is needed, but watching the crop grow is another story. Less activity requires less application of resources. As active management requires more human and intellectual capital than passive management, it follows that an investor should pay an increasing scale within an agreed upon fee band to adjust for higher cost of goods.
Practically speaking, the investor needs to look at the range current range of fees charged across asset managers.
F( A) = (ATO(A)*(Tfr-Bfr))+(Bfr)
Where
- F(A)= fee to manager A
- ATO = annual percentage turnover normalized (0,1)
- Tfr = Top of market fee range
- Bfr =Bottom of market fee range
Secondly the longer the manager subjects capital to risk to achieve a return, the higher the probability of the occurrence of a negative tail outcome. Ask anyone who tells you differently to predict a 1 year return and a one year low and when that low will occur. Increasing exposure to risk results in decreased risk adjusted expected returns versus the Manager’s stated return target. This is particularly true if the Manager intends to liquidate the investment upon meeting stated target return regardless of holding period.
F(A) = F(A) – [ ( ( P(L>R) for duration(p) * RT(A) ) / RT(A) ) *F(A) ]
Where
- F(A)= fee to manager A
- P(L>R) = probability of loss greater than risk free rate
- Duration(p) = the expected holding period
- RT(A) = Manager A return target for portfolio
Obviously, none of the aforementioned concepts are particularly earth shattering. But having said that, I believe that new compensation structures need to integrate a variety of metrics, and thus reduce their reliance on simple raw returns.
- E. Hirschberg
The opinions expressed in this guest posting are those of the author and not necessarily those of AllAboutAlpha.com or the CAIA Association.
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