Quantification of Hedge Fund Default Risk

Finding the path to financial prosperity?

Originally published in the April 2007 issue

By their very nature, hedge funds allow the investor to be exposed to different risk factors such as volatility, counterparty or liquidity risk. Exposure to these risk factors is not only a source of superior risk-return trade-off but also the very essence of hedge funds’ extensive diversification possibilities compared with traditional investments. More importantly, it is interesting to note that the exposure to these risk factors is also a diversifiable risk, as it has been demonstrated that hedge funds exhibit low correlations amongst themselves.

These advantages do not come without a downside. Gaining exposure to alternative risk factors usually requires trading activities that can be considered less conventional than in the long only universe.

These include high leverage, investments in illiquid instruments, potentially high portfolio turnover and non-vanilla OTC contracts. While these technicalities do not represent an issue in themselves, they do however carry a level of operational risk for which the investor receives no premium.

Operational risk vs investment risk?

In addition to the very specific nature of their trading activity, hedge funds have developed as a new industry segment at a very significant pace over the last decade and the regulatory environment in which they operate is being updated accordingly. Nevertheless, hedge funds, by their very entrepreneurial nature, remain relatively small financial organisations where issues such as independent risk control, governance or the four eyes principle are not yet the norm.

It is interesting to note that the reporting on hedge fund risk exposure focuses on financial risks, when it is not limited to volatility only. A recent study from Edhec shows that in the case of blow-ups, operational risk greatly exceeds the risk related to the investment strategy, with more than half of hedge fund collapses directly related to a failure of operational processes.

Hedge fund operational risk has attracted enormous attention from the public, probably because of several fraudulent and high profile cases highlighted by the financial press. Not only does involvement in a hedge fund scandal result in possibly significant financial losses, the reputation aspect of the event may carry even greater weight for investors and third parties such as the administrators, auditors and prime brokers involved.

The objective of this article is to investigate the statistical properties of hedge fund failures further and attempt to identify essential risk factors that can tentatively explain why one fund is more likely to default on its investors and lenders than another. This attempt to quantify hedge fund operational risk will allow the reader to better assess the importance of extreme non-financial risks and understand what mitigation techniques beyond naïve diversification could be of use.

We will investigate two statistical methods in order to shed some light on the risk profile of hedge funds. In an initial stage, we will explore the mechanisms behind a hedge fund failure in more detail and propose a causal model that could explain the various scenarios that can occur when ahedge fund defaults.

A second stochastic analysis of a sample database of 100+ fund failures will allow a loss model for operational failures to be proposed. This model will allow us to better understand the limitations of a naïve diversification that aims to reduce the loss of a single event by reducing its share of the overall portfolio.
The data collection

The first phase in any analytical process is to collect data. In order to model and measure default risk, we need to construct two distinct databases: the first one includes hedge fund defaults; the second one contains the full universe of hedge funds. We define a default as a loss large enough to stop the manager from investing. Such defaults are usually widely publicised and are different from dissolutions. We constructed this database exclusively using publicly available information. We obtained a database that included 109 defaults between 1994 and 2005.

In order to get a full picture we need to assess the full universe of available hedge funds. We aggregated the information from six commercial sources and the EIM proprietary database. To obtain a consolidated database summarising each fund in a unique way we need to clean the dataset. All databases have about 15–25% of unique funds except the specialised Barclay CTA database. We were then able to associate the two databases in order to obtain the number of funds present each year. There were 751 funds in 1994 and 5563 in 2004, ten years later.

The Causal Model

A causal model is an advanced form of dependency model that allows the various scenarios that can lead to a defined state to be modelled. In our case, the scenario is the winding down of a hedge fund. Causal models are built on the basis of a bottom-up historical qualitative analysis of actual failures and attempt to identify the various situations and events that can lead to bankruptcy.

The causal model will allow both causal drivers and correlations between these drivers to be analysed in a second step to allow for better consideration of these factors in the portfolio construction model. In order to gain a better understanding of the drivers of hedge fund failures, the analysis of the causal model has been structured into three sections. In an initial step we will introduce a causal model that will allow us to factor information for the following steps. Secondly, we will analyse the overall breakdown of risk factors given defined default scenarios. This analysis will allow us to identify criteria that can easily be assessed prior to investing in the funds. In a third step, we will compute conditional probabilities based on certain realisations of risk factors in order to understand whether a given factor may lead to some specific scenarios.

Dynamics of default

Based on the analysis of our 109 actual cases, we have identified six different routes that lead to bankruptcy

  • Straight fraud leading to collapse
  • Straight fraud revealed by the authorities leading to forced liquidation
  • Undisclosed operational loss leading to collapse
  • Undisclosed financial loss leading to collapse
  • Disclosed operational loss leading to managed liquidation
  • Disclosed financial loss leading to managed liquidation

It is important to stress that the overall simplicity of the model is deliberate in order to allow specific risk factors to be clearly identified and, if possible, quantified to compute an overall likelihood of default.

We have analysed each of the 109 cases and assessed whether the dynamics of the winding down did fit one of the six scenarios. This has proven to be the case each time. The distribution of defaults across scenarios is described in Figure 2.

Actually quantifying the likelihood of each scenario for a fund does require the risk factors/events likely to trigger the various scenarios to be identified and, possibly, quantified.

Three key risk factors

We have highlighted three factors on the 109 cases analysed likely to provide an appropriate level of explanation as risk factors: location of the management company, assets under management, complexity of instruments.

The location of the management company is considered as a potentially significant risk factor for several reasons. First of all, the location of the management company can be considered to provide a good reflection of the level of regulation applied to the fund/company. Secondly, the location of the management company is a reflection of the level of visibility the manager is ready to accept. We found that 88% of the defaults we analysed occurred in the US.

The idea that the size of the fund and its ‘maturity’ explain a large part of the operational risks incurred by the investor is a hypothesis often put forward. The distribution of fund defaults according to the level of assets under management prior to the collapse validates this hypothesis. 49.5% of defaults concerned funds with less than US$100 Million of AUM. Over US$500 Million, the percentage goes down to 16.5%.

We have derived an average instrument complexity based on the investment style of the manager. Three levels (simple, complicated and opaque) have been designed to reflect the relative complexity of the instruments likely to be present in the fund. The resulting distribution of hedge fund failures across this segmentation reveals that the overall likelihood of default does not seem to be directly influenced by instrument complexity or at the very least that complex funds do not constitute the bulk of hedge fund failures. 56% of the defaults concern funds with simple instruments.

Analysing the distribution of defaults according to several possible risk factors makes it possible to identify which risk factors need to be considered when preparing the due diligence process.

In the case of fraud

It is therefore interesting to perform a similar analysis using conditional probabilities based on the scenario under which the funds have defaulted. We have conducted a detailed analysis for hedge fund defaults related to fraud and analysed the distribution of frauds by geographic location and assets under management. These factors have been chosen in order to allow for an easy comparison with the non-conditional probabilities discussed in the previous section.

Hedge fund failures included in this analysis include all situations where fraud was detected. Bearing in mind the various biases possibly limiting the relevance of an analysis by country (hedge fund market development stage), it is interesting to see that the percentage of failures in the US progresses from 88% (all scenarios) to 92% when restricted to frauds only, highlighting a potentially higher risk of fraud with funds managed in the US.

Several explanations may be put forward to justify this finding. There are fewer US funds that outsource NAV calculation to a third party administrator compared to European funds. A detailed analysis of other risk factors such as independent pricing and/or independent administration is likely to provide a more relevant explanation than the country itself.

Interestingly, the analysis of hedge fund defaults distribution by AUM shows that when it comes to fraud, investors in small and medium-sized organisations are more likely to be victims of deliberate initial or secondary fraud. Again, figures provided in this analysis confirm the significant importance to be given to fund size when it comes to assessing the likelihood of fraud.

We have also analysed the distribution of hedge fund failures by instrument complexity, following an operational issue.

This conditional analysis highlights a possible relationship between the instrument complexity and the likelihood of a hedge fund defaulting as a consequence of operational issues. Understanding this relationship is straightforward, as increased instrumentcomplexity involves more complex operations support and a higher level of possible errors in processing the trades.

We construct a loss model without considering the mechanism underlying the default and study the possibility of diversification by dilution.

We consider a frequency model (Bernoulli Variable) and a severity model (Loss Given Default LGD). The parameter p (probability of default) of the frequency model is estimated using historical annual frequencies. We weight each year’s result with the number of funds available that year in our database. The result is: p = 0.30%

The severity of the loss is modelled with the LGD:

Where L stands for the amount of the loss and AUM for the assets under management. When no loss is incurred LGD is 0% and when all assets under management vanish LGD is 100%.

A widely used distribution to describe such a quantity is the Beta distribution (see Lugman et al. [1998]). The Beta distribution with parameters a and b is defined through its probability density function:

Where B(a,b) is the usual Beta function and the indicator function I[0,1] (x) ensures that only values of x in the range [0,1] have non-zero probability.

To estimate the parameters of the Beta distribution we consider the 85 defaults for which we collected the loss incurred and the assets under management. Using maximum likelihood estimation (see Casella and Berger [1990]) we obtain: a = 0.82, b = 0.52.

In Fig.4 we show a rescaled histogram for the 85 realisations of LGD (full rectangle) and the probability density function of the Beta distribution with the estimated parameters.

To study the impact of default risk on a portfolio of hedge funds we consider an equally weighted portfolio of N hedge funds. The loss due to defaults DL is described by the random variable:

Where wi is the weight of fund i, Bi its default indicator and Li its LGD. For an equally weighted portfolio wi = . All Bi and Li are considered independent and are distributed following the above model.

We consider as risk measures, the standard deviation, the value at risk and the Expected Shortfall (see Artzner et al. [1999]) at level = 90%. Assuming each year is independent = 90% would represent the worst year out of 10 years.

To construct the distribution of DL and evaluate these risk measures we run a Monte Carlo simulation using importance sampling. The risk measures are plotted as a function of N.

Considering only the standard deviation as a risk measure we would conclude that the default risk is easily reduced by taking more than 20 hedge funds. However, since the losses are potentially extreme, the risk measure that takes this tail risk into account correctly is the Expected Shortfall. This risk measure has been proven to be the correct one to use in cases of discontinuous distribution functions, as is the case here. We see that the Expected Shortfall is not sensitive to the number of funds for portfolios with fewer than 40 funds. In fact, for all these portfolios the VaR at 90% is exactly 0.

Our analysis allows us to conclude that the extreme operational risk of hedge funds is a risk that is difficult to diversify through the naïve method of adding funds to minimise the possible loss of one single default. This conclusion reinforces the importance of appropriate due diligence being performed on hedge fund investments to significantly reduce the risk of being exposed to a failure. Investors will keep in mind that an increased number of funds also implies less time to investigate each individual fund and the inclusion of funds with lower standards of operations, hence possibly increasing the final likelihood of default of individual funds.

The cost and complexity of hedge fund operational due diligence can be significantly reduced by performing an ‘informed’ due diligence process. This ‘informed’ process will take into consideration the relative importance of the main risk factors to hedge funds in general(such as fraud), and the level of complexity/risk of the specific fund and management company under scrutiny, in order to determine the extent of operational review required.

The final version of this article was published in the Fall 2006 issue of the Journal of Alternative Investments