The Alternative Investment Management Association

Alternative Investment Management Association Representing the global hedge fund industry

Hedge fund asymmetry

Cedric Dingens and Herve Burger

Notz Stucki & Cie

Q1 2006


Hedge Funds (HFs) are different from standard investment vehicles because their behaviour is considered as asymmetric in terms of relative performance to traditional stock or bond indices. The goal of most HF managers is to capture positive returns in bull markets and avoid negative returns in bear markets.

This asymmetric pattern warrants us to consider HFs as important and revolutionary vehicles in the asset class universe.

But how does one investigate the return asymmetry? Many academic papers have tested the issue of HF return asymmetry in terms of absolute performance by examining the skew-ness of the return distribution.

The problem is different when looking at relative performance. In this case, the use of Beta statistics (which measures the sensitivity of the fund return distribution to a benchmark return) seems more appropriate for three reasons:

- Even though HFs have an absolute performance objective, their performance is compared implicitly to the performances of stock indices. Moreover, Equity Long/Short managers lost money on their short book and the performance was achieved on the long side.
- More than 70% of the total AUM in the HF industry is invested in equity markets.
- Beta statistics seem particularly natural when investigating the performance of HFs because of this strong stock bias: Equity Long/Short, Equity Market Neutral, Event-Driven exposure, Equity Trading.

An interesting way to catch asymmetry is to compute Beta Bull and Beta Bear statistics. By definition, Beta Bull is calculated as the coefficient of the least squared binary regression of HF monthly returns relative to positive monthly stockmarket returns. (The opposite Beta Bear is calculated with the negative monthly stockmarket returns).

The great game for HF managers is trying to outperform stocks indices having a Beta Bull greater than 1 and a Beta Bear close to 0 (or even negative!).

From our point of view, Beta Bull and Beta Bear statistics are too schematic. They have basic limitations, since the strategies used by HF managers are more and more diversified and complex. Consequently, we have developed the following model: Monthly HF returns are regressed against stock index returns and classified by intervals. The correlation factors are defined as the Beta factors (we obtain n Beta statistics corresponding to n intervals).

For each interval, the combination of the Beta factor value, the quality of the linear correlation (measured by the coefficient of determination) and the intensity of the index moves, generates a matrix converted to a continuum of colour, what we call the Beta Spectrogram.

It is important to note that the use of the intensity of the market moves is justified in this framework by the fact that a Beta close to 1 is more crucial in intervals corresponding to strong positive returns of the stock index, than for intervals corresponding to small positive moves.

Green colours indicate favourable situations; a Beta close to 1 in a given interval of positive stock returns or a negative Beta in a given interval of negative stock returns with a good quality of correlation. A darker green colour shows an increasingly favourable situation.
Red indicates an unfavourable situation; a Beta close to 0 in an interval of positive returns or a Beta close to 1 in case of negative index returns. Dark red indicates an increasingly unfavourable situation. Light-blue means that there is no effective correlation. A good HF manager will have a dark-green Beta Spectrogram: he tracks the benchmark in bullish months and does not lose or perhaps makes money in bearish months

Figure 1: FoHF Beta Spectogram
Hedge Fund Asymmetry - Figure 1 

The Beta Spectrogram of a FoHF composed of European Equity Long/Short HFs relative to European small caps stocks is represented in Figure 1. The upper band is the benchmark band (here the MSCI Europe small caps index) characterised by a regular continuum of colour going from the red (on the left) to the green (on the right) as the Beta is, by definition, equal to 1 for each interval.

The second band represents the FoHF. It is a useful tool to actively monitor the performance profile and to study the impact of the addition/removal of a single HF, relative to small caps stocks. The FoHF performs well when small caps stocks perform well (+, ++ & +++), and is not sensitive to a small negative performance (- & --) but suffers slightly in the case of a very sharp decline (---).

The following bands (from single HF A to single HF P) represent the pattern of 16 single HFs included in the FoHF ranked by weight. HF F is very sensitive to small caps whereas HFs L, M, N and O can lose money when small caps show negative performances (- & --) but then protect capital in case of sharp declines (---). HFs B, D, J and P only suffer in case of sharp declines in the small caps (---) whereas HFs A, C, G, H and K are agnostic to small caps stocks decline. The Beta Spectrogram optically captures the managers’ style and is a simple method of evaluating the added value of the manager, when compared to a passive stock management.

FoHF Duration Spectrogram

For single HFs and FoHFs whose performance depends on bond market returns, or is compared to bond indices, an equivalent process is implemented. This process concerns strategies like Fixed Income Arbitrage, Credit Long/Short and High-Yield/Distressed. Moreover the performance of low volatility FoHFs is in general compared to the performance of long or medium Treasury bonds.

In a first step we have selected short-, mid- and long-term maturity US T-Bond indexes. As we have seen before, index returns are classified by intervals and the HF returns are regressed against the bond index return for each interval. With this method, the n correlation factors can be defined as n Beta factors. Another alternative would be to use the yield moves instead of price moves. In this case, the Beta factor would correspond to an empirical duration. This method gives the same result. The figure 3 shows an example of single HF Duration Spectrogram.

Figure 2: HF Beta Spectrogram

Hedge Fund Asymmetry - Figure 2


With the spectrogram, we can now analyse the behaviour of a single HF relative to different market factors. First we analyse the sensitivity of a European Equity Long/Short Hedge Fund through the Beta Spectrogram in Figure 2.

We take into account the five following factors : MSCI Europe Index, Value stocks, Growth stocks, small caps stocks and European market volatility (VDAX Index).

On the right side of the spectrogram (stocks are performing well and volatility declines), the HF performs fairly well in all cases. We find three results: 1. Low sensitivity to global stock- markets, value stocks and stockmarket volatility: 2. High sensitivity to small caps when they are in negative territory (- & --) but less sensitivity when there is real stress on the small caps stocks: 3. Low correlation to growth stocks as we can assume that the only sensitivity we see is due to correlation between the different markets.

To conclude, this is a HF which captures much of the upside of the market, is more exposed to small caps and which manages to protect capital to some extent.

Figure 3: HF Duration Spectrogram

Hedge Fund Asymmetry - Figure 3


The figure 3 refers to the Duration Spectrogram of a Fixed-Income Arbitrage HF. The six following factors are taken into account: 1-3Y US T-Bond Index, 5-7Y US T-Bond Index, 10Y+ US T-Bond Index, JP Morgan Global Govt Bond Index, US High-Yield Bond Index and US 10Y-3M Govt Bond Spread.

The HF performs well when US T-Bond yields decrease regardless of the maturity. The HF does not react to increases in US T-Bond LT yield but can lose some money when the US T-Bond ST & MT yields rise sharply (---). The HF shows a good performance when HY spreads narrow, suffers a little when they widen at a certain point (--) but manages to deliver a positive performance and to protect the capital when they widen substantially (---). Finally, whether the yield curve widens or tightens, the HF reacts favourably.


The Beta/Duration Spectrogram is a useful quantitative tool to analyse HFs and FoHFs. On the one hand it allows a manager to check and analyse HF exposure relative to what a HF manager says. Additionally it helps construct the portfolio at the FoHF level as it shows global exposure at a glance and quick decisions can be taken with regards to what we expect in the market (favour large caps versus small caps, growth stocks versus value stocks or changes in interest rates) or at least to be protected against huge market movements. The Beta/Duration Spectrogram has to be seen as a complementary tool to your HF analysis, selection and portfolio construction.

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