It is no secret that 2008 was one of Wall Street’s toughest years and perhaps the most challenging year ever for hedge funds. Evidence of this can be found in the dismal performance of the Barclay’s Hedge Fund and Fund of Funds indices, both down almost 21%. Many funds blew up, including Sailfish, Peloton and others. As the year closed, serious allegations of fraud were levied against one of the most famous and respected hedge fund managers, Bernard Madoff. While it is too early to count all of the casualties, the preliminary numbers paint a rather bleak picture. Using Barclay’s Global Data Feeder database, we estimate that about 18% of hedge funds either shut down or stopped reporting performance. Experts agree that the number of funds that go out of business will continue to increase throughout 2009. The widespread fallout from 2008 will provide firms that managed to survive with many learning opportunities, including the importance of proper risk management.

Effective risk management requires that firms establish the culture, policies and procedures that are specific to their operating model. Funds of funds, family offices and other hedge fund investors share a common need for a strong risk measurement infrastructure. Though there is no single blueprint for building a strong risk management process, there is one common need: accurate risk measurement.

**Back to the Basics**

Quantitative hedge fund analysis starts with taking the pulse of the fund by calculating some simple risk/reward measures. This analysis serves as a starting point in estimating the relative attractiveness of the investment. Few investors will invest with a fund that has consistently lost money over an extended period^{1}. There may be compelling reasons to consider such an investment, though one must have at least a starting picture.

Figure 1 illustrates industry standard statistics calculated within PackHedge™. Our analysis begins with a review of the top two tables. The table in the upper left hand corner, titled “Returns”, provides us with a snapshot of information covering the fund’s entire track record. The table in the upper right hand corner, titled “Annual Returns”, allows us to view the fund’s return consistency by looking at the annualised returns across several calendar years.

**Figure 1**

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At first glance, the above fund appears to be an attractive investment. During the period from January 2001 through December 2007, the fund produced an annualised return of 43.5%, with annualised volatility of 16.25%. The fund generated significant returns in four of the last five years and achieved positive, though modest, returns in 2007. While volatility appears high at 16.25% annualised, common skill ratios such as Sharpe, Sortino and Sterling indicate that the level or risk may be justified by high returns.

One type of statistic shown in Figure 1 deserves special attention –Value at Risk (VaR). VaR has received plenty of negative publicity in recent months. The media has been full of articles blaming risk management failures of the past 12 months on inadequate risk systems and methodology. Of all risk measures, VaR has received more than its share of the blame.

A common criticism of VaR has been that it does not measure the tail risk correctly. The criticism is correct to the extent that the VaR method could have predicted the dramatic losses seen in the markets. The fallacy of the argument is that VaR is not designed to predict tail events. VaR is defined as the “maximum/minimum loss that an investment is likely to suffer at most/least x% of the time.” VaR does not contain any information of the magnitude of the loss beyond the confidence interval, and thus cannot be used to estimate the tail loss.

Figure 1 shows three measures of VaR calculated within PackHedge™. Historical VaR is based on the actual performance of the fund. VaR Normal calculates the maximum loss assuming the fund’s returns follow the normal distribution. Another criticism of VaR is that too often people equate the use of VaR with the assumption of normal distribution. VaR can indeed be easily calculated using such an assumption:

**Formula 1: **

An investor, however, is not limited to this method of measuring VaR. A relatively simple way to calculate VaR without a normal distribution is to adjust the Z-score in Formula 1 according to Cornish-Fisher formula.

**Formula 2:**

Incorporating Skew and Kurtosis measures in a VaR calculation allows an analyst to account for asymmetries and fat tails present in the investment’s return distribution.

The result is shown as VaR Modified in Figure 1, as calculated by PackHedge™.

**Benchmark Analysis **

Benchmark analysis in Figure 1 also points to relative attractiveness of the fund vs several relevant benchmarks. The beta and correlation numbers do seem to indicate significant systemic risk, but the high level of alpha could potentially support the argument that the risk is justifiable.

**Less is Not Always More!**

One of my former managers loved to say that “less is more” and more often than not, he was correct. The simplest solution was often the best. In analysing hedge funds, however, simple is often insufficient.

While the statistics in Figure 1 provide a good starting point, they are not sufficient to make an informed investment decision. Relying solely on the basic analysis noted above introduces the following drawbacks:

- The analysis does not include a comparison of the fund performance to possible peers and a way to identify those peers.
- Basic risk/performance analysis does not account for different market environments.
- Univariate benchmark analysis does not account for interaction among factors.
- Historical drawdown analysis may be insufficient in forecasting tail risk.

**Peer Group Analysis **

In evaluating any investment, it is important to understand the investment’s performance relative to the universe of other similar investments. The long-held belief that all hedge funds are unique and thus have no peers does not hold up well, particularly in the face of recent market events. Peer group analysis can be performed in several steps:

- Qualitative Peer Identification
- Quantitative Peer Identification
- Peer Group Analysis

**Qualitative Peer Identification**

One way of identifying an appropriate peer group would be to select a number of funds, whose investment strategy and trading style most closely resemble that of the investment in question using qualitative criteria. This approach depends on a thorough understanding of each potential peer as well as a good understanding of the broader universe of funds since it is unlikely that any given investor may be familiar with all potential matches. The main benefit of this approach lies in the fact that it forces an investor to perform extensive due diligence and develop a good understanding of the potential investments. The obvious drawback to this approach is that it is highly subjective and peer selection can often be used to serve a particular purpose (eg making the investment appear superior to others by selecting weaker peers). That said, we do recommend using qualitative approach to identify a large group of peers, but supplement it with quantitative analysis.

**Quantitative Peer Identification**** **

The simplest quantitative way to identify a potential peer group is to perform correlation analysis between performance of the fund and that of the large universe of potential peers. The universe can be constructed by customising qualitative criteria that are based on the investor’s knowledge of the funds, or on simple selection from the hedge fund database that matches the fund’s strategy, AUM and other criteria. The adage that, in a stress environment, all correlations approach one is generally true, so when identifying potential peers we recommend performing correlation analysis in three steps:

- Calculate correlation over the entire overlapping period.
- Calculate correlations during the up market periods.
- Calculate correlation during the down market periods.

The three correlation analyses should provide investors with a good picture of the potential peer group.

If basic correlation analysis seems too simplistic, an investor may want to perform cluster analysis of the funds to identify groups (clusters) of funds that are most like each other. The advantage of this technique is that it can potentially incorporate both quantitative and qualitative (expressed numerically) information.

The advantage of quantitative approach is its objectivity. The approach removes user bias from the analysis and allows for honest evaluation of the investment. The downside is that blind quantitative analysis can sometimes produce spurious correlations. In an environment where the amount of data to analyse is often limited by minimal performance history, any quantitative analysis needs to be taken with a grain of salt.

**Peer Group Analysis**

With the peer group identified, several analyses are available. The simplest analysis produces a scatter plot of funds’ return vs volatility (Figure 2). The red diamond represents the fund in question. Other dots represent all funds within the same broad hedge fund strategy.

**Figure 2**

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Table 1 and Figure 3 show comparative analysis of our fund vs the most correlated peers. Figure 3 compares the fund’s performance in positive and negative market regimes to the peers. In our example, the sample’s fund down beta is higher than up beta, which implies that the fund’s potential losses in down markets are higher than its potential gains in up markets.

**Table 1**

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**Figure 3**

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This brings us to the second point – regime switching.

**Regime Switching**

On average, hedge funds have positive correlation to global equities and therefore are likely to produce positive performance during bull markets and lower or negative returns during bearish markets. Therefore, it is important to understand the fund’s behaviour during different market environments.

Table 2 shows the performance and correlation statistics of 12 hedge fund strategies relative to global equity markets (represented by MSCI World Index).

**Table 2**

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There are several ways to analyse a fund’s performance during various market environments.

**Up/Down Beta**

The most intuitive approach involves calculating two betas for the fund: one during the months when the benchmark index is positive, and the other for periods when the benchmark index is negative. This approach, referred to as the Up/Down Market Model (UDM), can be summarised by Formula 3.

**Formula 3**: Max(X,0)+Min(X,0).

The advantage of this approach is intuition. Generally speaking, an investment with higher positive up beta (and lower or negative down beta () would be considered attractive. The disadvantage of this approach is that depending on the time period used, the number of data points for calculating either up or down beta may be limited.

To adjust for that, an investor can use a model based on a Treynor-Mazuy (TMY) formula.

**Formula 4:**

Unlike the UDM approach, the TMY approach uses all available data. The squared component provides a way to account for convexity or gamma effects in the fund’s profile and can be thought of as the fund’s exposure to volatility of the underlying benchmark. Both approaches can be subjected to a nice graphical representation. Figures 4 and 5 show the fitted values generated by the two regression models.

**Figure 4 **

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**Figure 5 **

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In this example, the results of the two models are not consistent. The UDM model indicates that the fund has lower beta to the equity markets during the down months indicating positive results, while the TMY model shows a slight “frown”, indicating slightly negative results. The discrepancy between the results of the two models is not uncommon. An investor must be careful in selecting the appropriate model and benchmark to use. TMY analysis can be expanded to include more than one factor. Figure 6 shows the stress surface generated for the two most statistically significant factors of the sample fund.

**Figure 6 **

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**Regime Switching Models**

While market timing models do provide useful additional information about investments’ performance in up and down markets, it may also be desirable to evaluate investments from the perspective of normal/stress environments. A regime-switching model can be defined in a way similar to the UDM model, where the two environments may not necessarily be linked to the positive/negative periods but rather to some other definition. For example, one might define normal/stress environment based on market volatility. The VIX may be used as a proxy. Figure 7 shows the scatter plot of the sample fund vs S&P 500 in two different volatility regimes. The high/low volatility regimes are defined somewhat arbitrarily by choosing the time periods when VIX level was above/below 22.

**Figure 7 **

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**Benchmark Analysis**

In Figure 1, we saw simple analysis of the fund’s sensitivities to several benchmarks. While this analysis provides a good start, it is rarely sufficient. The analysis has two major drawbacks. First, it relies on specification of a single or several single factors that may or may not be relevant to the fund in question. Second, it ignores interaction among various factors. The analysis can be extended by using a multivariate regression model as shown by Formula 5.

**Formula 5:**

The numbers of factors chosen depend on the length of the track record being analysed, and the strategy of the manager. Factors may be chosen using a qualitative approach based on investor’s understanding of the fund’s strategy. Quantitative factors can also be chosen using the stepwise regression approach. In the stepwise regression approach, the factors are chosen based on their statistical significance. The downside of this approach is that it may, at times, result in selecting factors with spurious correlation to the investment in question and little economic significance.

**Table 3 **

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**Table 4 **

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Tables 3 and 4 show the results of the regression analysis that utilised two approaches. Table 3 reflects the results of the analysis based on qualitative specification of the factors that should be relevant to a large number of funds. The factors are part of our Global Market Model (GMM). Table 4 shows the results of the stepwise regression analysis. The results indicate that the latter approach has better explanatory power (as indicated by higher adjusted R-square). The factors identified by the approach are economically significant for the fund specialising in emerging markets, particularly Russia and CIS.

Factor analysis can be further enhanced by performing factor risk attribution. In this analysis, we try to understand the contribution of each risk factor to the monthly volatility of the investment. Figure 8 suggests that when using GMM, global equity factor accounts for about 20% of the fund’s volatility.

**Figure 8 **

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**Tail Risk**

Looking at historical drawdown analysis is useful, but unfortunately tells you nothing about future potential drawdowns. The following analysis can be performed to better understand the tail risk of an investment.

**Stress tests/Scenario Analysis**

As mentioned above, VaR does not provide information about the worst potential loss beyond a certain confidence level. Stress tests and scenario analysis can be used as a complement to VaR. Historical stress events such as the crash of 1997, September 11 and now the credit crunch of 2008 can be used along with other theoretical scenarios. Since in many cases a fund’s track record may not coincide with stress events, it is important to estimate the impact of such events on the fund’s performance.

It is not usually possible to calculate the fund’s NAV without having full transparency so regression models are often used to perform the stress analysis. The benchmark used in the analysis can include either market or hedge fund strategy indices. The analysis can be based on linear regression using one or more factors, but can also incorporate non-linear affects (by including squared factors such as in the TMY analysis described above).

**Maximum Drawdown Simulation**

Another technique for evaluating tail risk is the drawdown simulation. Using a distribution that best fits a particular fund, an investor may generate thousands of different scenarios and estimate the worst drawdown in each scenario. The resulting drawdown distribution may provide an investor with information about the likely losses beyond a single month loss. In such analysis, it is important to pick a distribution that would accurately represent not only the normal variation of the fund’s returns but also incorporate possible fat tails. Possible auto correlation effects should also be taken into account since significant positive auto correlation may result in extended drawdown periods. Figure 9 shows the graphical representation of such an analysis.

**Figure 9 **

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**Portfolio Analysis**

The process of portfolio management for funds of funds can be broken down into the following steps:

**Fund Selection.**Quantitative selection of hedge funds involves analysis of the universe of hedge funds using the tools described in the previous section, and selection of the funds that best satisfy portfolio objectives. The process results in the creation of a buy list of funds that are used in the portfolio optimisation step.**Portfolio Optimisation.**Various techniques can be used to allocate capital among the funds from the buy list. Optimisation can be performed using simple Markowitz style mean-variance optimisation. It can then be enhanced by changing either risk measure, return measure or both. Techniques based on the Black-Letterman approach can be used to incorporate forward-looking return expectations into the analysis. Other approaches may involve changing the risk measure from simple variance to more tail-oriented measures such as maximum drawdown and expected tail loss.**Risk Analysis.**To construct a strong portfolio, an investor needs to understand how individual funds, strategies and market factors contribute to the overall portfolio risk. Several analyses can be used to accomplish this goal.

**Portfolio Risk Analysis**

Contribution to Risk

Even in a portfolio with an equal fund allocation, individual funds can have unequal contribution to portfolio volatility. Table 5 shows an example of a portfolio equally allocated among ten funds, with one fund contributing more than 50% to the overall portfolio volatility. Figure 10 shows the aggregation of risk contribution by strategy.

**Table 5 **

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**Figure 10 **

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**Diversification Analysis**

There are various measures of diversification.

- Herfindahl Index can be used to measure the level of diversification relative to an equally-weighted portfolio. The index is calculated as a sum of squared weights of individual investments. The higher the value of the index, the more concentrated the portfolio is in a few names. For an equally weighted portfolio, the value of the index is always 1/N, where N is the number of investments.

- Average correlation among investments can be useful in estimating diversification. We recommend calculating three correlation numbers (overall, correlation in up markets, correlation in down markets).

- Factor diversification. Factor diversification analysis using principal component analysis (PCA) can provide additional information on diversification benefit of the portfolio. Figure 11 shows the Pareto chart representing the result of PCA analysis. We can see that in the portfolio with 20 managers, the first principal component accounts for almost 80% of the volatility, suggesting that a single factor is driving the performance and volatility of the portfolio. While the main disadvantage of PCA analysis lies in the difficulty in interpreting the factors, we can make a reasonable assumption that the single factor driving this portfolio is global equity factor.

**Figure 11 **

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**What Does It Take?**

With an understanding of the different aspects of hedge fund risk and portfolio analysis, we can now examine what it takes to build an infrastructure that is necessary to perform such an analysis.

First, at the heart of any analysis is the data, and three types of data are required to properly perform the analysis discussed herein.

- Access to a hedge fund database, which is required in order to identify the funds and perform peer group analysis.
- Hedge fund indexes
- Market Data

Second, it is critically important to possess a suitable warehouse for the information which is at your disposal. Too many investment businesses rely on Microsoft Excel to build the infrastructure. While Excel is a great tool for performing many types of analysis and building reports, it is not well suited for managing large amounts of complex data and analysis. To do that efficiently, one needs to use a relational database such as Microsoft SQL Server, Oracle or MySQL. Just designing the database by itself, however, is not sufficient. In order to efficiently manage the data, one needs to have a user-friendly application that would provide functionality to:

- Manage reference data (strategies, indexes, styles etc).

- Manage qualitative hedge fund data (management company, contacts, due diligence notes, other documents).

- Manage time series data (performance, NAV, AUM, etc).

- Run quick customizable queries.

- Produce professional reports.

Developing such an application in house requires a significant and expensive effort. Alternatively, one could leverage a commercially available “off the shelf” solution. Based on overall user experience, flexibility of data maintenance and sound database design, Risk-AI has chosen PackHedge™ by FinLab as its hedge fund data management software.

**Figure 12 **

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**Figure 13 **

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Once the data storage and maintenance parts are developed, an investor must build the infrastructure to perform the aforementioned statistical analysis. Once again, it is often tempting to build such infrastructure based on Microsoft Excel. While some of the analysis can be developed easily using Excel, the resulting application is unlikely to provide a robust and scalable solution. In order to develop such infrastructure outside of an Excel model, one needs:

- A state-of-the-art statistical library that supports basic statistics, time series analysis, factor analysis, multiple distributions. At Risk-AI we have chosen IMSL library provided by Visual Numerics (
__www.vni.com__).

- A modern development platform such as Microsoft.Net, Java or C++. FinLab has built its software in Java. Risk-AI’s software is built in C# 3.5.

- A robust reporting software. At Risk-AI we have chosen the flexible and customisable Report Publishing available within PackHedge™.

**BIBLIOGRAPHY**

- Francois-Serge Lhabitant, Hedge Funds, Quantitative Insights, Wiley Finance, 2004.
- Grinold & Kahn, Active Portfolio Management, McGraw Hill, 1999.
- Andrew W. Lo, Hedge Funds, An Analytic Perspective, Princeton University Press, 2008.

**ON LINE RESOURCES**

- Investment Performance Analysis & Risk Management.

http://www.andreassteiner.net/performanceanalysis/

**Footnote**

^{1}An investor could see the value in the fund that purchases out-of-the-money put options and consistently loses the principal payments but occasionally gets paid when extreme events happen.