Master of Advanced Studies in Finance University Zurich

ETH Zurich A predictive model for Event Driven Hedge Fund

returns

Master Thesis December 2005

Karin Soosova

Supervisor: Dr. Pascal Botteron

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Acknowledgements I would like to thank Dr. Pascal Botteron, the supervisor of this thesis, for his help and for the insightful comments, support and suggestions, which have laid the foundation for this work. Special thanks go also to Deutsche Bank for having provided me with hedge fund data.

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Introduction A major part of the growing literature on hedge funds focused on the study of risk and return characteristics compared to other asset classes, style analysis, several authors tried to find explanatory factors on a contemporareus basis. However, up to now there were few attempts to predict hedge fund returns. One of them is the paper by (Amenc et al., 2002), which relies on a linear prediction model for hedge fund index returns based on variables known to have explanatory power for other types of securities, mainly stocks. Indeed, evidence for predictability in stock returns was found by many authors, for example by (Keim et al., 1986), (Fama et al., 1989), (Ferson et al., 1993), (Lo et al., 1997), and (Avramov et al., 2005). Based on the paper by (Amenc et al., 2002), this thesis is dedicated to the prediction of event driven hedge fund returns. The reason why the focus is on this type of hedge funds is twofold. First the relative importance of event driven hedge funds in the hedge fund universe is growing. A good example of the growth dynamics is the period between 1990 and 2002, when the relative portion measured by assets under management increased from 2.4% to 4.7% for distressed strategies, from 0.6% to 2.03% for merger arbitrage strategies and from 3.84% to 12.15% for event driven strategies (see (Nicholas, 2004)). Moreover, according to the Deutsche Bank Alternative Investment Survey (Dyment et al., 2005) the event driven strategy belongs to strategies with the deepest market penetration besides long/short equity and multi-strategy. About 60% of all investors involved in the survey have exposure to the event driven style. Second, strategies under the common description event driven are often claimed to be cyclical, resp. their return to be strongly dependent on the state of the aggregate economy. If this would be true, and if the relationship of event driven hedge fund returns and the business cycle would be stable, one might be able to utilize this fact in prediction of event driven hedge fund returns. The rest of the thesis is organized as follows. Section 1 defines the event driven hedge fund style and its substyles and provides an overview about the relationship of their returns to the business cycle as described by other authors. Section 2 compares event driven hedge fund returns and growth of industrial production (as a proxy for GDP growth) as a basis for further analysis. Section 3 contains the main methods and results from (Amenc et al., 2002), which are relevant for this theses. Section 4 explains the methodology, Section 5 is dedicated to a short description of data and data sources, Section 6 presents main results and the last Section concludes.

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Event Driven Hedge Funds and the business cycle

Definition of event driven hedge fund style and it’s substyles This section is to a large extent based on three books about hedge fund styles, namely (Lhabitant, 2002), (Ineichen, 2003) and (Nicholas, 2004). Joseph Nicholas defines event driven strategies in his book Hedge Fund of Funds Investing (Nicholas, 2004) as strategies that are based on investments in opportunities created by significant transactional events, such as spin-offs, mergers and acquisitions, industry consolidations, liquidations, reorganizations, bankruptcies, recapitalizations, share buybacks, and other extraordinary corporate transactions. The uncertainty about the outcome of these events creates investment opportunities for managers who can correctly anticipate them and the success or failure usually depends on whether the manager accurately predicts the outcome and timing of a concrete event. The most popular event driven strategies are distressed securities investing and merger arbitrage. Other strategies are often employed alongside these two strategies (Lhabitant, 2002). Distressed securities investing According to (Ineichen, 2003), distressed securities funds invest in the debt or equity of companies experiencing financial or operational difficulties or trade claims of companies that are in financial distress. These securities generally trade at substantial discounts to par value. The strategy exploits the fact that many investors are unable to hold securities that are below investment grade and it profits from the market’s lack of understanding of the true value of these securities. Hedge funds, investing in distressed securities, essentially attempt to profit from market pricing inefficiencies, which can be absolute or relative (Lhabitant, 2002). Absolute inefficiencies refer to differences between the market price and the intristic value of a distressed security. When the market price of a company’s security is lower than its fundamental value (e.g. due to temporary financial difficulties), distressed securities specialists will take positions in these securities and hold them through the restructuring process if they believe that the security will approach its fair value after the restructuring process is complete. Relative inefficiencies refer to price differences between two securities issued by the same distressed company. While a company is restructuring, the prices of its different financial instruments can become mispriced relative to one another. This is an opportunity called capital structure arbitrage. The distressed securities specialists purchase the undervalued security and take short positions in the overpriced security. Distressed securities investing is itself a quite heterogeneous group (Ineichen, 2003). Generally, one could classify distressed securities managers into active and passive. Active managers get involved in the restructuring process, while passive managers

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simply buy debt or equity of distressed companies at a discount and hold it until it appreciates. The market for distressed securities is quite illiquid and hedge funds operating in this field act to a large extent as liquidity providers. However the size of degree of activity in distressed markets differs strongly between regions (Lhabitant, 2002). United States clearly dominate the distressed securities landscape and it is the largest single source of corporate default. This market is much more liquid than the European distressed securities market. Even though the emergence of the European Union brought an improvement in the degree of development in this sector, and it experienced a high degree of expansion (100% growth in 2000), the European distressed securities market sill lags far behind the United States in terms of both experience and market size. The main reasons are the different bankruptcy legislations and the fact that European distressed securities are typically issued by holding companies (unlike United States, where issuers are operating companies), and this makes it harder to force default. The drawbacks of the European bankruptcy legislation are first, that there exist various national jurisdictions, regulatory rules and practices, what makes the system intransparent, and second, that the “bankruptcy is intended to end and not prolong the life of a company” (Ineichen, 2003). Default market opportunities outside United States and Europe tend to be quite dispersed around the globe. An interesting overview about the Asian hedge fund market in general can be found in (Douglas, 2003), who says that the characteristics of this market are different because of the youth of the industry (even though it is fast growing, 50% growth in 2003), the nature of the underlying capital markets and the cultural environment.. According to this study, most of the Asian managers are located in Australia, China, Japan and Singapore. For Japan some estimates mention trillion dollars of present nonperforming loans, but Japanese institutions are still extremely reluctant to disclose information on these activities(Lhabitant, 2002). This makes it difficult to take advantage of mispricings in the market by arbitrage. Douglas confirms this fact by the statement, that opportunities for event driven hedge funds in these markets are limited, because compared with developed markets, there is less corporate activity in public markets. Even though there is a sustainable supply of distressed securities, there are constraints on short availability and leverage. To ensure consistent profitability, many Asian managers are multi-strategy (what makes it hard to model their returns) and most of them are long/short equity. From more then 300 hedge funds considered only 7 belonged to the distressed and 6 to the event driven category (see Figure 3 on p.99 in (Douglas, 2003)). However, by the time, Asian managers become less directional and many new hedge funds are focusing on non-equity sectors. Merger Arbitrage Merger arbitrage (sometimes called risk arbitrage) is defined by (Nicholas, 2004) as a strategy, that involves investing in securities of companies that are the subject of some form of extraordinary corporate transaction, including acquisition or merger proposals, leveraged buyouts, recapitalizations, restructurings etc. When the event takes the form of a cash takeover, the strategy is based on the following (based on (Lhabitant, 2002)). The bid price of the acquirer usually includes a premium with respect to the target’s current share price on the market, to convince investors to tender their shares. Following the

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announcement of the acquisition bid, the market price of the target firm should naturally adjust upward. In practice it does, but it does not reach the bid price. The remaining gap is called the merger arbitrage spread and it will fluctuate over time, depending on the willingness of the market participants to take on the risk, that the transaction may not be completed. Merger arbitragers evaluate this transaction risk, and if they are confident about the success of the transaction, they buy the target company’s shares and wait to capture the corresponding spread. However, if the takeover is delayed or abandoned, the target’s share price usually falls and the arbitragers incur losses, usually much larger than the potential profits. In the case of a stock merger, the bidder offers its common stock in exchange for the target’s shares. Empirically, the bidder’s price is seen to fall while the target’s stock price increases. The arbitrage strategy consists of buying the target’s stock and short selling the bidder company’s stock. If the hedge fund manager considers the outcome of a merger to be doubtful, he may reverse the positions and short sell the target and buy the acquiring firm.

The event driven strategy in hedge fund style classification Due to the heterogeneity of hedge funds, and the fact that there are far less regulated than other investment vehicles, categorization of hedge funds is difficult, subjective and a generally accepted classification standard does not exist. Ineichen provides an overview of different classifications in (Ineichen, 2003). Looking at how event driven hedge funds are treated in different classification systems reveals information about their common characteristics and about features which differentiate between event driven substrategies. Some classification systems treat event driven strategies as one class, and put all substyles into the same category (e.g. Partners Group, Grosvenor Capital Management, Schneeweis and Spurgin (2000)). For example the classification by Partners Group (see Figure 5.1 on p.180 in (Ineichen, 2003)) positions event driven strategies as a separate class in the “middle” between relative-value (non-directional) and opportunistic (directional) strategies. Unlike classifications mentioned above, the Harcourt Investment Consulting AG and Morgan Stanley Capital management classification show distressed and merger arbitrage strategies in different style groups. The first mentioned considers distressed hedge funds as directional, invested mainly in fixed income securities. Merger arbitrage can be found in the relative value category with investments in equity. The separate classification indicates that risk and returns in both event driven substyles have different characteristics. Ineichen explains this separation by the fact, that distressed securities have a long “bias” whereas merger arbitrage has a long “bias” to a much smaller extent. But he says also that even though distressed are classified as fixed income, they are often involved also in equity, and that merger arbitrage, classified under equities, is essentially a hybrid strategy.

Relationship of event driven returns, the stock market and the business cycle Further evidence for different characteristics of distressed and merger arbitrage can be found in their different behavior during some periods in time. For example, according to

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(Ineichen, 2003), the year 2001 offered many investment opportunities for distressed styles, and at the same time it was not a good year for merger arbitrage. He explains this by the argument, that merger arbitrage does well when the economy expands and the merger activity is at its peak, unlike distressed strategies which offer many investment opportunities when the economy contracts. The first quarter of 2002 (see p.12 in (Nicholas, 2004)) can also serve as a good example for differences in distressed and merger arbitrage return patterns. During this period, opportunities in distressed area expanded dramatically and distressed strategies experienced one of the largest capital inflows of all hedge fund strategies. On the other hand, merger arbitrage experienced the larges outflow of all strategies in this quarter, mainly because merger activity decreased resulting in a lack of opportunities. This Section should provide a brief overview of how various authors see the relationship between event driven hedge fund strategies and the business cycle. Regarding the dependence on the state of the equity market, both(Ineichen, 2003) and (Lhabitant, 2002) say, that because event driven strategies try to take advantage of valuation disparities coming from major corporate events, their returns are influenced more by the uncertainty about the particular event than by general appreciation or depreciation of debt and equity in the market. As a result, they are (according to the above mentioned authors) less dependent on the overall stock market than traditional equity investment approaches. What immediately comes to ones mind is that, when the main risk in these strategies is the event risk, and if corporate activity (number of liquidations, mergers and acquisition etc.) depends on the state of the economy, event driven strategies might be more vulnerable to shifts in the business cycle. For distressed strategies, (Lhabitant, 2002) states that although the supply of defaulted and distressed securities (which is necessary for investment opportunities ) is cyclical, the returns of distressed strategies are only slightly cyclical, because bankruptcies are permanent in nature and each industry sector might be in a different cycle. For merger arbitrage he identifies two major factors for success. First, a sufficient volume of mergers and takeovers on the market to permit the construction of a diversified merger arbitrage portfolio, and second, a sufficient spread on each successful transaction to compensate failing transactions. Hence, merger arbitrage is essentially influenced by merger activity in the market, which is likely to be higher in expansion than in recession. For merger arbitrage strategies (Ineichen, 2003) confirms that their performance depends on the overall volume of merger activity, which has historically been cyclical in nature. The number of opportunities for distressed strategies is positively related to the number of defaults. Therefore the number of opportunities should be somewhat countercyclical to economic growth and as a result countercyclical to merger activity and merger arbitrage returns. A recession can lead also well-established companies into temporary financial difficulties, which mean good opportunities for distressed strategies in the years that follow the recession. However, in a recession there are fewer mergers and acquisitions and therefore fewer opportunities for merger arbitrage strategies. These do well when the economy is expanding, but at the same time there are fewer bankruptcies and companies in distresses, shortening the opportunity set for distressed styles. He claims, that this is the reason why many multi-strategy managers switch between distressed and merger arbitrage depending on investment opportunities.

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Before studying the dependence of event driven returns and the business cycle formally, one can see from Figures 1A and 2A in the Appendix, that most of the event driven indices and subindices returns reveal some kind cyclical structure. The pattern is most pronounced for the CSFB/Tremont event driven index from March 2000 to September 2005 (the lower part of Figure 1A) and for the Eureka United States distressed index (the middle part of Figure 2A). One of possible explanations for this behavior could be the dependence on the business cycle. The next section studies the correlation with industrial pattern to obtain more information about their relationship. There might be also alternative explanations for a pattern which appears to be cyclical, even though it might not be explained by the business cycle. Several authors have found serial correlation in hedge fund returns (Getmansky et al., 2003) and they stated that part of this autocorrelation (witch might result in a cyclical pattern) comes from return smoothing by hedge fund managers and illiquidity of securities traded in some hedge fund styles. Since event driven hedge funds are heavily involved in securities that are illiquid because of distresses or other reason, this explanation might make sense. However this effect is beyond the scope of this work, and will not be studied any further.

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Event Driven Hedge Funds and Industrial Production This section will examine the correlation of event driven returns with industrial production, to get a first insight into their relationship. Industrial production has been used rather than GDP, because GDP data are mostly available only in quarterly form, often with a delay and industrial production is used as a proxy for economic activity by major research institutions and data providers (e.g. OECD, see Section Data). Since the economies in different world regions follow individual business cycles, which although they are certainly correlated, do not move perfectly in line, it would be useful to know how event driven strategies behave in this regions. For this reason, the analysis of returns in this thesis will be performed on three sets of hedge funds data:

• A global hedge fund index (CSFC/Tremont Event Driven Index) • Three regional event driven indices(for Europe, Asia and United States, described

in the Section Data) • A selection of individual hedge fund (who’s regional focus in not known) which

claim to follow mainly event driven strategies. Correlation between hedge fund returns and industrial production has been studied only for index data (CSFB/Tremont and Eureka regional indices). A graphical comparison of event driven hedge fund returns and industrial production, resp. its annual change, can be found in Figures 3A – 5A in the Appendix. Even though it is not possible to draw general conclusions based on this graphical comparison, in some cases there seems to be a certain comovement in both series. In the case in Asia (where returns have been compared to the industrial production of Japan) it seems to be the case around the year 2003 for event driven strategies and 2002 for distressed strategies. In United States one can see similar patterns in the first and last years of the time period. The comparison of European hedge fund returns reveals the strongest comovement before and around the year 2001. Later on the overall tendencies of both series remain similar. Correlation of event driven hedge fund returns and the change in industrial production has been studied on a contemporareous basis and at 6 lags, to capture possible lags in the dependence of hedge fund return on the business cycle. Unlike financial returns, the growth in industrial production is characterized by a positive long term trend. It would therefore not be correct to compare these two series on an unadjusted basis. Hence, correlation was computed for both the unadjusted growth and growth adjusted by the change in the long term trend. Moreoever, the relationship might not be linear, therefore the correlation was measured also separately for periods with positive and negative industrial growth. This idea has been mentioned by several authors, who studied the behavior of default rates over the business cycle. (Helwege et al., 1996), (Keenan, 1999) and (Matos, 2000) claim that default rates behave nonlinearly with respect to the state of the economy. Since distressed strategies invest in distressed securities, their return might be affected by this property of default rates.

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Correlation of event driven index returns and the change in industrial production Table 1A in the Appendix presents results, which show a significant (negative) correlation (about -0.2) of the CSFB/Tremont event drive (ED) and distressed (D) index with the contemporaneous US-Industrial production. This is not surprising, since the majority of CSFB hedge funds are domiciled in the United States, therefore the impact of the U.S. economy is high. The fact that the correlation is negative supports the hypothesis that distressed hedge funds behave countercyclically. As mentioned before, the success of distressed strategies depends on the availability of investment opportunities. When industrial production decreases, the number of companies in distress might increase, therefore creating investing opportunities. This effect remains significant when industrial production growth is adjusted for the long-term trend, the correlation and its significance are even higher (Table 2A in Appendix). There is a positive significant (but not very high) correlation of the CSFB/ Tremont merger arbitrage (MA) index and the second lag of U.S. industrial production. This might be explained by the fact, that returns of these hedge funds are dependent on the success of the merger deals. When industrial production is growing, merger activity might be growing, hence influencing MA hedge fund returns. MA strategy is often claimed to be highly cyclical. Here we can find a cyclical pattern, but it is not very pronounced. The correlation is about 15% and is present with a 2 months lag. Moreover, the significance of the correlation disappears when industrial growth is adjusted for the growth in the long term trend. The correlation for Eureka U.S. distressed index has the expected negative sign, however it is significant only at 5 or 6 lags of change in Industrial production. Correlation of event driven index returns and the (adjusted) change in industrial production (for positive and negative changes). When comparing correlation for rising and falling industrial production, one can see strong differences between signs and significance of correlations. This indicates that it might be useful to differentiate between a positive and negative economic outlook in a predictive model. One interesting result for the good state in economy (increased industrial production) is the strong and significant negative correlation of all CSFB/Tremont ED indices with the contemporaneous value of U.S. industrial production. If this would be true, it would be bad news, meaning that ED hedge funds loose when industrial production is rising. The effect is even stronger with the adjustment for industrial production trend. The same is true for the US regional index and their regional industrial production. Surprising is the negative correlation of Europe ED index, because the database states that this index contains MA funds, which are claimed to be cyclical (see results for down period, there the correlation is positive). Correlation of event driven index returns and the (adjusted) change in industrial production (for positive and positive changes). In general correlation is lower in absolute value and less significant than in period with growing industrial production, at least for the CSFB/Tremont indices. For the distressed CSFB/Tremont index, the negative correlation (significant only if industrial production is unadjusted, not reported here) supports the result from the total period about

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countercyclicality. This would mean that distressed hedge funds earn positive return in periods when industrial is decreasing. However, the dependence is lower in absolute value than in the growth period, meaning that the countercyclicality of returns of distressed hedge funds is weaker in bad periods. The same is true for the US Distressed regional index and US industrial production. The strong positive correlation of the regional ED Europe index with contemporaneous industrial production supports the hypothesis of cyclicality in MA returns (unlike results for the growth period), because this indices include MA hedge funds. This would again be bad news, because it would mean that MA hedge funds returns move in line with industrial production when it is decreasing. It is not straightforward do draw clear conclusions about how returns of distressed and merger arbitrage strategies will behave with changes in the aggregate economy. The research on this issue is difficult, mainly because the strategies themselves are heterogeneous and their positions are not transparent. In fact, managers of hedge funds may employ multiple strategies and change their exposures dynamically and it is therefore not possible to separate the individual effects. Nonetheless, the evidence of dependence of event driven returns on the business cycle is worth the effort for further investigation. Even if we cannot make precise statements about the cyclicality or countercyclicality of event driven returns, it might be useful to include variables which are connected the business cycle (or variables which are believed to have predictive power for the performance of the economy) into the analysis besides those variables which have already been shown to have some predictive power for hedge fund returns.

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The model of Amenc, Bied and Martinelli The paper by (Amenc et al., 2002) builds the basis of this thesis both in terms of goals and methodology. It documents evidence of predictability of returns on nine hedge fund indices using linear (lagged) multi-factor models. The authors find strong evidence of very significant predictability in hedge fund returns, they also test the benefits in terms of tactical style allocation. The predictive variables in the model are selected on the basis of previous evidence of their ability to predict asset returns. These are:

• Yield on T-Bill 3-month rate, which serves (according to the authors) as a proxy for expectations of future economic activity. (Fama, 1981) and (Fama et al., 1977) showed that it is negatively correlated to stock market returns.

• Dividend yield on S&P stock, which has been shown to be associated with slow mean reversion in stock returns across several economic cycles (Keim et al., 1986). It serves as a proxy for time variation in the unobservable risk premium.

• Default spread (difference between the yield on long term Baa bonds and the yield on long term AAA bonds). This captures the effect of default premium, which tracks long-term business cycle conditions (higher during recessions, lower during expansions (Fama et al., 1998)).

• Term spread (difference between the yield on 3-month Treasuries and 10-year Treasuries)

• Volatility, proxied by the volatility index VIX (measures the volatility of the U.S. equity market)

• Market volume (monthly market volume on the NYSE). The last three factors have been identified by (Amenc et al., 2001) and (Schneeweis et al., 1999) as important factors explaining hedge fund returns

• Oil price, which, they say, is closely related to short-term business cycles • U.S. equity factor (return on the S&P500 index) • World equity factor (return on the MSCI World index ex US) • Currency factor (volume weighted exchange index of currencies versus US

dollar)

Besides raw values of these variables, the authors tested the explanatory power of several permutations (changes, lagged values up to 3 lags and the 3-month moving average). In a second step, they selected a subset of these variables (and their permutations) for each of the hedge fund indices, based on their explanatory power. The explanatory power was measured in terms of (at least 5%) in-sample R2 of regressions of the nine CSFB/Tremont indices on a subset of permutations of one of the 10 variables listed above. This resulted in a very limit set of factors (2 or3) that predict the return on the CSFB/Tremont index most closely. Based on tests on serial correlation (using the Hurst exponent), which revealed significant serial correlation for most of the hedge fund indices, they decided to include the lagged return in the model as a potential regressor.

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For the purposes of this thesis, only the results for the event driven CSFB/Tremont index are of interest. For this hedge fund style, the only factors present in the final model were:

• Lagged return of the CSFB/Tremont event driven index • Lagged value of the oil price.

The proposed linear multi-factor model for prediction was tested out-of-sample by using rolling windows of 60 months to calibrate (reestimate the factor loadings) the model end predict the next month’s return value. The out-of-sample performance was measured in terms of the hit ratio. This is the percentage of time predicted direction is valid, i.e., the index goes up (resp. down) when the model predicts it will go up (resp. down). Even though the in-sample performance of the lagged regression (measured by R2) for event driven return was only 15-16%, the hit ratio resulted to almost 80%. The authors consider this to be clear statistical evidence of predictability in hedge fund returns (in this case event driven hedge funds).

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Methodology Compared to the paper by (Amenc et al., 2002), this thesis focuses on following targets:

• Employ a broader range of variables (listed below) as the base set for the selection of factors with predictive power for event driven hedge fund returns, including

- business cycle variables and - regional market variables

• Perform the analysis for different regional event driven hedge fund indices • Test the predictive power of the resulting model for individual event driven hedge

funds Furthermore, the methodology used here has been modified, as this section will explain in detail. There are basically two possible approaches to prediction using regression models. The first approach is to construct a linear factor model of returns based on contemporaneous explanatory variables and then analyze the predictability of these factors. The problem with this model is, according to (Lo et al., 2002), that the set of factors, that best explains the cross-sectional variation in returns on a contemporaneous basis, can be relatively unpredictable, whereas other factors, that could be used to predict expected returns are not so useful in explaining the variation of these returns contemporaneously. Even though the approach described above can provide information on the nature of asset returns predictability when the risk factors (regressors) are known, when these factors are unknown in is better to employ a procedure like adopted by (Amenc et al., 2002), namely regress historical returns on lagged values of explanatory factors. The idea behind this is, that it is easier to predict the reaction of market participants on known variables, than predict the future values of risk factor themselves. Therefore the analysis in this thesis was performed in the following steps. Step 1: Base Set of Variables In comparison to the set of 10 variables used by (Amenc et al., 2002), the base set of variables which will be tested for explanatory, resp. predictive power is broader, mainly for two reasons:

• event driven hedge fund returns will be studies also on a regional level, therefore variables for regional asset markets are included

• Since previous literature and the correlation analysis confirmed the presence of a relationship between the state of the aggregate economy and the event driven hedge fund returns, one of the aims is to investigate, whether including variables which are believed to have predictive power for the business cycle, can improve the performance of the model in prediction.

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Additionally to variables listed in the short description of the paper of (Amenc et al., 2002), following variables have been included:

• Equity indices: - MSCI World - MSCI European Union - MSCI Asia - MSCI Emerging markets - MSCI Small cap

• Currency factors for all three regions (JP Morgan Trade weighted indices for the EUR, Japanese Yen, and USD)

• Price of gold • Market volume for all three regions (Trading volume on the NYSE, London Stock

Exchange and Tokyo Stock Exchange) • Volatility indices for the German (DAX), Japanese and U.S. market • Consumer price index (by OECD) for Europe, Japan and U.S. • Consumer confidence and manufacturing confidence • Composite leading indicators:

- 6-month rate of change of the trend restored series - 6-month rate of change of the trend restored series adjusted for long term

trend of industrial production (explained below) - CLI reference series

The decision to include the small cap MSCI index was based on a statement in (Keim et al., 1986). There the authors mention, that the risk premium of small stock are the most volatile, therefore when expected premiums on all assets change, the expected risk premium on small stocks change the most. They suggest that thereby the level of small stock prices may provide a sensitive ex ante barometer of expected risk premiums. The last two groups of variables are variables closely connected to the business cycle, as explained in the section Data. All of them have been employed in from of regional values (for Europe, U.S., Japan and Australia to represent the Asian region). The CLI reference series corresponds to the value of industrial production in each region. The 6-month rate of change of the trend restored series is computed (by OECD) as follows:

( )

126.5

12

1

CLI trend restored6-months rate of change 1 *100CLI trend restored

12

tt

t ii

−=

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟= −⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

∑

Therefore it stands for the change in the leading indicator (in a trend restored form) compared to its value during the last year. However this value does not account for the fact, that the industrial production is characterized by a positive long term trend. Hence if we want to compare hedge fund returns with this predictive indicator for changes in the economy, we have to eliminate the effect of the long term trend. For this reason a second

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variable (besides the raw value of this indicator obtained from the OECD) has been created. This is the 6-month rate of change of the trend restored series adjusted for long term trend of industrial production, which is the difference of the raw value of the indicator and the so called trend rate computed with the following formula (which has a similar form as the formula for the raw value, to be consistent).

( )

126.5

12

1

Longterm trendTrend rate 1 *100Longterm trend

12

tt

t ii

−=

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟= −⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

∑

6-months rate of change adjusted for trend 6-months rate of change trend ratet t t= − Data problems. Hedge fund data are well known for their characteristic distributional features. This is particularly true for event driven hedge funds, which to a large extent invest in illiquid securities. Since the analysis involves linear least squares regression, it is important to bear in mind how the distributional characteristics of the dependent variables (in this case hedge fund returns) correspond to the assumptions of this fitting method.

a) Non-normality of hedge fund returns. From Table 5A in the appendix one can see (as stated by several authors before), the data for hedge fund indices are skewed and have excess kurtosis (of various degrees). One of the assumptions of the OLS method is the normality of the distribution error, which is equivalent to the normality of the dependent variable data. The distribution of the OLS estimators, and therefore all test statistics (such as the t and F statistic) are crucially dependent on this assumption. A partial solution to this problem is a large dataset, because according to (Wooldrindge, 2003), the central limit theorem implies that the OLS estimators are at least asymptotically normal in large enough sample sizes. He says that some econometricians consider 30 observations to satisfactory. Therefore, in this thesis the regressions are performed on sets of at least 40 observations (40 for regional indices, 111 for CSFB/Tremont indices). Moreover, the regressions will be performed in a form robust to outliers, since the kurtosis in the return series is likely to be caused by outliers in returns. b) Serial correlation As it was already mentioned earlier, (Amenc et al., 2002) discovered serial correlation in the returns data and therefore included the lagged return in the predictive model. According to (Wooldrindge, 2003) and (Brooks, 2002), serial correlation does not lead to a bias in the OLS estimators, but the standard errors and test statistics are no longer valid and the problem is not resolved by a large sample size. However, one can overcome the problem by including the lagged value of the dependent variable (hedge fund returns) in the regression. In that case, the OLS method produces consistent and asymptotically normal estimates. There is no need to

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both include the lagged return and additionally use a particular model of serial correlation in the errors. c) Multi-collinearity of independent variables A further concern, which is often mentioned in case of financial series, is correlation of explanatory variables. This is not a real problem up to a certain degree. However, a high degree of linear relationship (a rule of thumb is a correlation above 0.7, see p. 655 in (Anderson et al., 2005)) between these variables can lead to large variances of OLS estimators (even though it is not a direct violation of the OLS assumptions, these would be violated only in case of perfect correlation). There are several ways to avoid this problem:

- Use a larger or different set of data, which is however often impossible in financial applications

- Drop some of the highly correlated variables, but this could lead to a certain loss of information

- Employ other estimators (e.g. the ridge estimator, which is however biased)

- Convert the original variables into orthogonal factors using principal component analysis (PCA)

The last mentioned approach is (according to (Alexander, 2001), p. 171 ff.) the most powerful solution for multi-collinearity. It will be employed here for historical series on the selected explanatory variables, because, as will be mentioned later, there was a significant level of correlation in several variables. PCA provides a means of performing regressions on totally uncorrelated variables, and it is a simple method to obtain estimates for the original model using nothing more than OLS. The original variables first have to be normalized, before they are passed through PCA, to obtain the principal component and their weights. Then the regression is performed on the principal components. The coefficient for the original variables can be obtained by a simple transformation using the intercept and slope from the regression with the principal components, and the means and variances of the original variables (see (Alexander, 2001) p. 173 for details).

Step 2: Variables selection Similarly to (Amenc et al., 2002), for each variable, a subset of permutations was tested for predictive power (the raw value, three lagged values, change and two lagged changes, 3-months moving average). For business cycle variables, an additional “permutation” was the product of the variable and an indicator variable for increasing and decreasing industrial production. The indicator takes the value 1 if the industrial production (based on the CLI trend restored series) is predicted to increase and 0 if it‘s predicted to fall. The reason for doing this is the observation form the correlation analysis that the relationship between event driven hedge fund returns and the state of the economy seems to be different in a growing and in a falling economy. The selection of variables started with individual stepwise regressions of each lagged variable and its permutations on all hedge fund indices (resulting in 10 regressions, 4 for CSFB/Tremont indices and 6 for regional indices). This resulted in a few selected

18

permutations for each variable, which were further considered for the prediction model. For each selection of permutations (for each variable) to be included in the final model, it was required to have at least 5% explanatory power in terms of the in-sample-R2 (from a regression of the selected permutations on the hedge fund index). The result of this procedure was a shortlist of variables for each hedge fund index for the final predictive model. Step 3: Check for multicollinearity (explain PCA) The remaining variables selected for at least one hedge fund index build a list of 53 variables. These were tested for collinearity (correlation higher than 0.7) because of the above mentioned potential consequences of high correlation. The correlation matrix will not be reported here because of its large size (53 x 53), however, it revealed high correlation (up to 0.9) in several cases. For this reason, following tests will be performed for both the raw values of the selected factors and for factors build by PCA. Step 4: Model calibration (with and without PCA) and out-of-sample testing The model was calibrated using rolling windows of 40 months for the regional indices (because their return history was much shorter, from January 2000 rather then 1994) and of 111 months for the CSFB/Tremont indices. These lengths of the rolling windows have been chosen such that the end of the first calibration period (April 2003) is the same for all indices and herefore the out-of-sample test starts with the same date (for better comparability). As it was mentioned above, the model was calibrated in two forms

• With raw values of the selected factors without adjustment for collinearity • With orthogonal principal components, build from the original variables

In the first case, the regression was simply performed for each rolling window and the resulting coefficients have been used to predict the next month’s return (based on current values of the involved factors). Results for the first calibration period can be found in Tables 6A – 8A in the appendix. These overviews contain, besides the list of variables for each index, their coefficients and p-values, also the average and standard deviation of the coefficients along all rolling windows. These statistics provide some information about how stable the model is over time and how the coefficients behaved. In the case, where data were adjusted for collinearity, there was one more issue to be considered. This is the fact, as (Alexander, 2001) mentions in her book, that if the principal components would have been build based on the entire time period, we would in essence use data “from the future” when using them in the prediction. In order to avoid building new principal components for each rolling window, she suggests to run the PCA only for the first calibration period, save the resulting weight, and construct the factors for later regressions (“principal components”) as a weighted average of the original variables (using weights form the first calibration period). Hence, after doing this, the rolling regressions were performed on this set of constructed principal components. Only the first principal components, which explained together at least 95% of the variation in the data, were used. This had a further advantage of reducing the dimension of the problem.

19

It was not necessary to convert the obtained regression coefficients into a form valid for the original data, because the main interest lies not in the relative influence on the variables, but in the predictive power of their linear combination (in form of the linear multi-factor model) for event driven hedge fund returns. For this reason it was simpler to predict the next month’s returns as follows. First, the original variables were transformed into factors (similar to the constructed principal components above) using the principal components weights from PCA. Then, the resulting values were used with the coefficients form the rolling windows regression with principal components to obtain the return prediction. The out-of sample-performance of all models for the prediction of event driven hedge fund returns was measured in terms of the so called hit ratio, used also by (Amenc et al., 2002). This it the percentage of time, the model predicted the right direction of the return change. Results are presented in the last section.

20

Data The database used in this analysis consists of three sets of data. These are data on:

• Event driven hedge funds • Business cycle indicators • Market variables

Data on event driven hedge funds Various commercial hedge fund databases, listed for example in (Al-Sharkas, 2005)or (Brooks et al., 2001), provide historical returns for hedge fund indices. The CSFB/Tremont Hedge Fund Index database provides monthly data for 10 hedge fund styles, among those the CSFB/Tremont Event Driven Hedge Fund Index. The advantage of using this index is that it is subdivided into subindices for strategies in distressed securities, risk arbitrage (or merger arbitrage) and multi-strategy. A further advantage is the effort of the data providers to avoid different kinds of biases. Using data on the entire event driven universe and substrategies allows one to draw conclusions on common features and differences in different event driven investment substyles. Monthly data for the entire time span available (January 1994 to September 2005) were used for the above mentioned indices. Furthermore, since one of the goals in this thesis is to investigate regional differences, return series for event driven hedge funds with different regional focus were needed. Two of commercial databases which provide regional data for hedge fund return histories are Eurekahedge and HedgeFund Intelligence. The later provides return histories for three index groups. The EuroHedge Indices for European hedge funds, the HSBC AsiaHedge Indices for Asian hedge funds and the Absolute Return Indices for the North-American hedge fund market. Even though two of this regional indices contain an event driven subindex (for the European and North-American region), the return numbers are median values of the peer group. However, using the median as a measure for the representative return causes most of the other observations to remain unconsidered and a lot of information contained in the data will be lost. For this reason, the analysis was based on the Eurekahedge database, which uses the median return and provides an event driven index for all regions (Europe, Asia, U.S.). Besides hedge fund index returns, data on individual hedge funds, provided by Deutsche Bank, were used. The database contained about 470 hedge funds with information about their strategy and returns. From all hedge funds, only those were considered, which had at least two years of track record, and reported to follow event driven strategies. In fact most of the funds claimed to follow these strategies among other investment styles. However, since it would be difficult to determine which part of the returns comes form the event driven activity, when the fund applied multiple styles, only two groups of funds have been selected for the analysis. One group is a group of 88 funds which reported to use only strategies from the event driven set (event drive, merger arbitrage, distressed). In second group are 24 funds which besides event driven strategies invest in fund of funds.

21

Both groups have been evaluated separately, since it is not known what kind of fund of fund investments the funds were involved in, and it would therefore not be correct to include them into the pure event driven group. In total the database consists of returns for 132 individual hedge funds, with different time series lengths (the longest from January 1996 to June 2005).

Business cycle data The Organization for Economic Cooperation and Development (OECD) maintains a comprehensive database on different economic indicators for member and some non-member countries. This thesis makes use of several sets of data provided by OECD in the periodical publication OECD Main Economic Indicators. Among these information are historical series on variables which are widely used as indicators for future development in the economy: Consumer confidence and manufacturing confidence (from Business and consumer tendency survey series): According to OECD Main Economic Indicators Explanatory Notes (2005): “Business and consumer opinion (tendency) surveys provide qualitative information that has proved useful for monitoring the current economic situation. Typically they are based on a sample of enterprises or households and respondents are asked about their assessments of the current situation and expectations for the immediate future .... Many survey series provide advance warning of turning points in aggregate economic activity as measured by GDP or industrial production.” Composite leading indicators (CLIs) The second set of data, Composite leading indicators “are constructed to predict cycles in a reference series chosen as a proxy measure for the aggregate economy. The index of industrial production is used as the reference series for aggregate economic activity … The OECD system of CLIs is designed to track changes in the “growth cycles” by tracking deviations from the long-term trend.” Figures 6A – 8A in the appendix show the leading relationship between the trend restored CLI series and the industrial production. There is a major difference between returns of financial instruments and changes in economic activity (GDP growth or change in industrial production). Unlike returns of hedge funds, the later have a long term positive trend, and it would not be correct to compare both figures directly. OECD provides data in both detrended and trend restored form. The following series (those publicly available) have been adjusted to account for this fact (see Section Methodology):

• CLI trend restored (leading indicator directly comparable to industrial production) • CLI long term tend (of industrial production, cyclicality is measured in deviation

from this long term trend) • 6-month rate of change of the trend restored series (change of trend restored CLI

compared to the last years average, provides early signal of turning points in the business cycle)

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Industrial production A third data series from this source is an index of industrial production, which serves as the reference series for the CLIs. Industrial production is a proxy for the aggregate economic activity, because, according to the OECD Main Economic Indicators Explanatory Notes (2005), “…besides constituting the most cyclical subset of the aggregate economy, it is available promptly and on a monthly basis for most OECD countries. In addition, the cyclical profiles of IIP and GDP in OECD countries have been found to be closely related so that the CLIs also serve as leading indicators for the GDP cycle.” In an earlier subsection, industrial production has been compared to hedge fund return, both graphically and in terms of correlation, to get an insight into their potential relationship. Data on consumer confidence, manufacturing confidence and CLIs (after adjustment described in Methodology) have been used as explanatory variables, resp. predictors, together with other market variables. Market variables A further predictive variable obtained from the OECD Main Economic Indicators publication was the CPI (consumer price index) for European Union, U.S. and Japan. Other market variables listed in the description of the methodology, which served as predictors for hedge fund returns were obtained from the Datastream Database.

23

Results First results to be presented are the sets of variables, which were selected by the procedures described above, for each event driven index (see Tables 6A – 8A in the Appendix). The number of selected variables and the composition of the variable sets differ strongly between hedge fund indices. Since the selection was done by means of a statistical procedure, the outcome is not always intuitive. What is important is, if a model of this composition allows to predict expected returns of event driven hedge funds, and what is its average performance. For the CSFB/Tremont indices (Table 6A in the appendix), the only variable from the set of composite leading indicators (which were supposed to capture the effect of the business cycle), is the trend restored CLI of Japan. A further variable from those believed to predict the performance of the economy selected based on its explanatory power for these indices is the consumer confidence for Europe and Great Britain. Even though their presence in the model provides some evidence for the idea, that predictors for the business cycle might be used also as predictors for event driven hedge fund returns, their regional origin is not very intuitive in this model. This is because the majority of hedge fund in the CSFB/Tremont indices (according to the index description) is domiciled in the United States and one would expect North-American business cycle predictors to have explanatory power rather then their European counterparts. A very strong position between the selected variables is taken by volatility indices (both for the U.S. and the European market). These variables appear in models for all CSFB/Tremont subindices and in several permutations (raw value, lagged values, changes and moving average). This observation is in line with the observation of (Adlersson et al., 2004), who also found the volatility index to be a significant predictor for the event driven and distressed strategy. Furthermore, variables from the stock market are often present in the models for CSFB/Tremont indices, in most cases in the moving average form. Among these is the MSCI small cap index (which was not included by (Amenc et al., 2002) in his tests), providing support for the hypothesis by (Keim et al., 1986), that the level of small stock prices may provide an ex ante barometer of expected risk premiums. For European Regional event driven index, the procedure resulted in a variable selection, where the Australian 6-month rate of change in the CLI indicator is present in several permutations. Since this variable take about half of the model, it leads to a high degree of collinearity, causing problems in the OLS procedure. For this reason, results for index in Table 7A are not really meaningful. One result that confirms the previous results is the presence of consumer confidence for Europe (with a highly significant coefficient) and the volatility of DAX in the model. The consumer confidence is present also in the model for European Distressed funds, besides market volume, currency, consumer price index and equity indices.

24

In the case of the Asian event driven index, only three variables with sufficient explanatory power could be found. It is not surprising, that one of them is the volatility index in Japan, given the strong presence of volatility in above mentioned indices. The last statement is true also for the Asian distressed index (although there were more variables selected), where volatility appears besides, consumer and manufacturing confidence (of Europe and US), the dividend yield, bond market variables and the price of gold (this is the only case where gold is included in a model.) There are no big surprises for the U.S. regional indices. Equity indices and volatility indices (for the U.S. market) are dominant variables in the models. Tables 1 and 2 presents measures for in-sample and out-of sample performance for the models presented above (without using PCA), for the CSFB/Tremont and Regional indices.

In-sample Performance(R2) Ou-of-sample performance (Hit ratio)

CSFB_ED 0.55 0.71CSFB_D 0.44 0.79CSFB_MA 0.5 0.79CSFB_multi 0.52 0.79

IN and OUT-of-sample performance of predictive models for CSFB indices

Table 1: In and out-of-sample-performance of models for CSFB/Tremont indices The results in table 1 might be compared with the results in (Amenc et al., 2002), because he performs the analysis on indices from the same data provider, even though he studies only the event driven index and not its subindices. Although the in-sample performance of the current model is much better then the in-sample performance of the (Amenc et al., 2002) model for the event driven index (15.7% in terms of R2), the out-of-sample performance is very similar. (Amenc et al., 2002) report a hit ration for the event driven index of 79.2%, which is similar to the value for CSFB/Tremont subindices obtained here. However, the hit ratio for the whole event driven CSFB/Tremont index is only 71%. The lower out-of-sample performance resulting from this model might be explained by the different time periods studied. (Amenc et al., 2002) performs the analysis for historical data from January 1994 to December 2000, whereas this study uses data up to September 2005.

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In-sample Performance(R2) Ou-of-sample performance (Hit ratio)

Eureka_Europe_ED 44.77 0.46Eureka_Europe_D 0.71 0.71Eureka_Asia_ED 0.2 0.54Eureka_Asia_D 0.54 0.68Eureka_US_ED 0.63 0.86Eureka_US_D 0.55 0.64

IN and OUT-of-sample performance of predictive models for Regional indices

Table 2: In and out-of-sample-performance of models for Regional indices For most of the regional indices, the out-of-sample performance is worse than the performance of the models for CFB/Tremont indices. An exception is the Asian distressed index, who’s hit ratio achieves a high of 86%. Some of possible reason for the weak hit ratios might be a shorter track record of returns or the fact that the table present results obtained without adjustments for collinearity. This is also the reason why the R2 of the model for the European event driven index is not meaningful, since, as has already been mentioned before, the collinearity for this model was severe, causing problems in the regression process. All results presented above are valid for the model without adjustment for collinearity. When PCA was applied to explanatory variables before the model was calibrated and tested out-of-sample, the results were the following. IN and OUT-of-sample performance of predictive models for CSFB indices using PCA

In-sample Performance(R2) Ou-of-sample performance (Hit ratio)

CSFB_ED 0.35 0.86CSFB_D 0.3 0.75CSFB_MA 0.32 0.79CSFB_multi 0.39 0.82 Table 3: In and out-of-sample-performance of models for CSFB/Tremont indices, using PCA Removing any dependence between the factors in the prediction model improved the performance of all but one CSFB/Tremont indices. This is particularly true for the total event driven CSFB/Tremont index and the multi-strategy subindex. However, the average in-sample R2 from the rolling time windows are lower than for the model with the original set of untransformed variables. Since we are more interested in predictive power than in in-sample performance, the employment of PCA analysis to orthogonalize the explanatory factors can be seen as an improvement.

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In-sample Performance(R2) Ou-of-sample performance (Hit ratio)

Eureka_Europe_ED 0.54 0.54Eureka_Europe_D 0.58 0.68Eureka_Asia_ED 0.33 0.61Eureka_Asia_D 0.47 0.61Eureka_US_ED 0.51 0.82Eureka_US_D 0.52 0.61

IN and OUT-of-sample performance of predictive models for Regional indices using PCA

Table 4: In and out-of-sample-performance of models for Regional indices, using PCA The effect of PCA on the performance of regional models in not so pronounced, as in the previous case. An improvement in the hit ration has been achieved only in the case of the European event driven index (the one with the high collinearity) and for the Asian event driven index. Results for individual hedge funds The model for the CSFB/Tremont event driven index is most general one. Hence it might be useful for predicting the returns for individual hedge funds. It is not possible to use regional models, because information about the regional focus of these hedge funds was not available. Similarly it would be difficult to assess the predictability for distressed and merger arbitrage separately, because most of the hedge funds in the database employ a mixture of event driven strategies. Table 5 presents hit ratios of the CSFB/Tremont event driven model when applied to returns of individual hedge funds, which report to be pure event driven in their strategy, and for a sample of hedge funds, who are involved in fund of funds besides direct event driven investments The out-of-sample performance of the model is surprisingly good, given that the model was calibrated on a different set of data then the data it is trying to predict. When the CSFB/Tremont event driven model was calibrated on principal components of variables, its performance for individual hedge funds improves slightly.

In Sample Performance: mean

R2

Out-of-sample performance: mean

Hit ratio STD of Hit ratios

Pure ED Hedge Funds 0.54 0.7 0.09ED and FoF Hedge Funds 0.54 0.7 0.09

IN and OUT-of-sample performance of CSFB ED predictive model for individual HFs

Table 5: In and out-of-sample-performance of models for a selection of individual hedge funds, based on the model for CSFB/Tremont event driven index (without adjustment for collinearity)

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In-sample Performance:

mean R2

Out-of sample performance: mean

Hit ratio STD of Hit ratios

Pure ED Hedge Funds 0.35 0.72 0.09ED and FoF Hedge Funds 0.35 0.72 0.08

IN and OUT-of-sample performance of CSFB ED predictive model using PCA for individual HFs

Table 6: In and out-of-sample-performance of models for a selection of individual hedge funds, based on the model for CSFB/Tremont event driven index (using PCA as an adjustment for collinearity) The values in the Tables 5 and 6 are average values. Figures 1 and 2 plot the hit ratios of all individual hedge funds (88 pure event driven and 24 event driven involved in fund of fund investments).

0 10 20 30 40 50 60 70 80 900

0.2

0.4

0.6

0.8

1Hit ratios for individual Hedge Funds with ED strategy

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1Hit ratios for individual Hedge Funds with ED and FoF strategy

Figure 1: Hit ratios for a selection of individual hedge funds, based on the model for CSFB/Tremont event driven index (without adjustment for collinearity)

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0 10 20 30 40 50 60 70 80 900

0.2

0.4

0.6

0.8

1Hit ratios for individual Hedge Funds with ED strategy using PCA

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1Hit ratios for individual Hedge Funds with ED and FoF strategy using PCA

Figure 2: Hit ratios for a selection of individual hedge funds, based on the model for CSFB/Tremont event driven index (using PCA as an adjustment for collinearity) As the above figures reveal, for the majority of individual hedge funds (using both model, with and without PCA) hit ratios are well above 50%, in some cases reaching a level of 90%. As it was already stated, these results are surprisingly good, and they would require further investigation, including tests on different subsets of hedge funds and different databases, to be able to draw clear conclusions on whether it is really possible to use a general model for the prediction of individual hedge fund returns. Unfortunately, this is a goal beyond the scope of this these. It would be certainly possible to calibrate the model for each fund separately, but it would be quite time consuming. However, this could be an interesting question for further research, to investigate, whether a separate model for each individual hedge fund would improve the predictive performance or not.

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Conclusions Event driven strategies are often claimed to have a cyclical behavior. The main goal of this thesis was to investigate this relationship and try to find a predictive model, which would utilize this dependence. The approach to the prediction of event driven hedge fund returns applied here is based on the model by (Amenc et al., 2002), who presented a predictive model for hedge fund returns in a form of a linear multi-factor model, based on variables, who’s ability to predict asset returns has already been proven. This thesis broadens the set of variables employed in the development of the predictive model by variables which are believed to have predictive power for the business cycle and by a set of regional variables, because, unlike in (Amenc et al., 2002), a separate model was fitted for three regional event driven indices. Although the investigation of the dependence structure between event driven hedge fund returns and the overall state of the economy, measured by the correlation of these returns with industrial production, did not reveal a clear dependence structure, certain tendencies were found, that provide support on the cyclical behavior of event driven hedge funds as described by several authors (e.g. (Lhabitant, 2002), (Ineichen, 2003) and (Nicholas, 2004)). Hedge funds employing the distressed style have been shown to behave countercyclically, whereas merger arbitrage hedge funds tend to behave cyclically. For each hedge fund index a subset of variables with the highest explanatory power has been selected using stepwise regression. The resulting models have been shown to have significant in and out-of-sample (predictive) performance. Using principal component analysis to remove potential correlation from the explanatory factors improved the predictive performance of the models in many cases. Moreover, the model developed for the CSFB/Tremont event driven index, has been tested for the ability to predict individual event driven hedge fund returns. This procedure is motivated by the fact, that when trying to predict individual performance, the calibration of a separate model for each individual hedge fund would be quite time consuming. It would therefore be a considerable advantage, if a general model could be, at least to a certain extent, used for prediction of individual hedge fund returns. The out-of-sample predictive performance of the CSFB/Tremont model for individual event driven hedge fund returns was found to be surprisingly good, for the subset of individual hedge fund available for analysis. However, further research would be needed to confirm these outcomes, for example by performing a similar test on a different set of hedge funds.

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Appendix

30-Mar-1994 29-Feb-1996 30-Jan-1998 01-Jan-2000-4

-3

-2

-1

0

1

2

3Monthly returns CSFB ED Indices 1994 to 1999 in %

CSFB EDCSFB DistressedCSFB RiskArbCSFB MultiStr

31-Mar-2000 30-Jan-2002 01-Dec-2003 01-Oct-2005-3

-2

-1

0

1

2

3Monthly returns CSFB ED Indices 2000 to 2005 in %

CSFB EDCSFB DistressedCSFB RiskArbCSFB MultiStr

Figure 1A: Monthly returns (quarterly averaged) for CSFB/Tremont event driven indices

31

31-Mar-2000 30-Jan-2002 01-Dec-2003 01-Oct-2005-2

0

2

4

6Monthly returns for regional indices in %

Eureka Asia EDEureka Asia D

31-Mar-2000 30-Jan-2002 01-Dec-2003 01-Oct-2005

-2

0

2

4

Eureka U.S. EDEureka U.S. D

31-Mar-2000 30-Jan-2002 01-Dec-2003 01-Oct-2005

-2

0

2

4

Eureka Europe EDEureka Europe D

Figure 2A: Monthly returns (quarterly averaged) for Eurekahedge regional event driven indices

32

31-Jan-2000 21-Dec-2001 11-Nov-2003 01-Oct-2005-6

-4

-2

0

2

4

Monthly Asian HF returns vs. annual trend adj. growth in Ind. Prod. Japan (%)

%change IP-%change trendAsia Event Driven

31-Jan-2000 21-Dec-2001 11-Nov-2003 01-Oct-2005-5

0

5

10

%change IP-%change trendAsia Distr.

Figure 3A: Comparison of monthly returns of the regional event driven and distressed indices for Asia and the annual change in industrial production

33

31-Jan-2000 21-Dec-2001 11-Nov-2003 01-Oct-2005-4

-2

0

2

4Monthly HF returns vs. annual trend adjusted growth in Ind. Prod. Europe (%)

%change IP-%change trendEurope Event Driven

31-Jan-2000 21-Dec-2001 11-Nov-2003 01-Oct-2005-5

0

5

10%change IP-%change trendEurope Distr.

Figure 4A: Comparison of monthly returns of the regional event driven and distressed indices for Europe and the annual change in industrial production

34

31-Jan-2000 21-Dec-2001 11-Nov-2003 01-Oct-2005-6

-4

-2

0

2

4

6Monthly HF returns vs. annual trend adj. growth in Ind. Prod. US (%)

%change IP-%change trendUS Event Driven

31-Jan-2000 21-Dec-2001 11-Nov-2003 01-Oct-2005-4

-2

0

2

4

6

%change IP-%change trendUS Distr.

Figure 5A: Comparison of monthly returns of the regional event driven and distressed indices for United States and the annual change in industrial production

35

31-Jan-1993 22-Apr-1997 12-Jul-2001 01-Oct-200575

80

85

90

95

100

105

110Comparison of Ind. Prod. and Trend restored Leading Indic. Europe

IP Europe%Leading ind. Europe

Figure 6A: The leading relationship between the trend restored composite leading index and industrial production for Europe

31-Jan-1993 22-Apr-1997 12-Jul-2001 01-Oct-200588

90

92

94

96

98

100

102

104

106Comparison of Ind. Prod. and Trend restored Leading Indic. Japan

IP Japan%Leading ind. Japan

Figure 7A: The leading relationship between the trend restored composite leading index and industrial production for Japan

36

31-Jan-1993 22-Apr-1997 12-Jul-2001 01-Oct-200565

70

75

80

85

90

95

100

105Comparison of Ind. Prod. and Trend restored Leading Indic. U.S.

IP US%Leading ind. US

Figure 8A: The leading relationship between the trend restored composite leading index and industrial production for Europe

37

HFIndex CSFB_ED CSFB_D CSFB_MA CSFB_multi Eureka_Europe_ED Eureka_Europe_D Eureka_Asia_ED Eureka_Asia_D Eureka_US_ED Eureka_US_DLAG0Europe 0.12 0.07 0.1 0.14 0.14 -0.08 0.05 -0.07 0.01 0Pvalues 0.17 0.39 0.22 0.09 0.25 0.58 0.68 0.59 0.92 0.99Japan 0.02 0.04 -0.04 0 0.02 -0.11 0.08 0.01 -0.1 -0.06Pvalues 0.79 0.61 0.65 0.96 0.89 0.44 0.52 0.96 0.41 0.62US -0.16 -0.22 -0.03 -0.08 0.08 0.03 -0.01 0.03 0.01 -0.06Pvalues 0.06 0.01 0.69 0.36 0.52 0.87 0.95 0.79 0.96 0.61

LAG1Europe -0.06 -0.07 -0.14 -0.04 0.09 0.03 -0.06 -0.15 -0.18 -0.18Pvalues 0.48 0.41 0.09 0.66 0.45 0.82 0.65 0.22 0.15 0.14Japan -0.03 -0.06 0.02 -0.01 0.11 0.22 -0.12 0.02 -0.03 -0.07Pvalues 0.75 0.51 0.86 0.94 0.39 0.13 0.32 0.84 0.8 0.56US -0.03 -0.07 -0.04 0 0.1 -0.29 -0.01 -0.1 -0.16 -0.15Pvalues 0.73 0.43 0.67 0.96 0.43 0.05 0.96 0.43 0.2 0.23

LAG2Europe 0 -0.08 0.18 0.06 0.07 -0.03 -0.12 -0.14 0.01 0.03Pvalues 0.98 0.32 0.03 0.48 0.55 0.83 0.34 0.25 0.96 0.84Japan 0.01 -0.02 -0.03 0.04 0.13 -0.34 -0.07 -0.12 -0.06 -0.01Pvalues 0.88 0.77 0.7 0.6 0.28 0.02 0.55 0.32 0.64 0.9US 0.09 0.03 0.15 0.12 0.17 -0.12 0.19 -0.07 -0.03 0.01Pvalues 0.28 0.75 0.08 0.14 0.18 0.41 0.11 0.59 0.82 0.95

LAG3Europe -0.01 -0.03 0.08 0 0.1 0.07 0.06 -0.04 0.01 0.09Pvalues 0.95 0.74 0.33 0.99 0.39 0.64 0.62 0.76 0.9 0.47Japan 0.02 0.01 0.03 0.02 0.15 0.01 -0.02 0.03 -0.01 0.04Pvalues 0.81 0.95 0.73 0.79 0.22 0.97 0.85 0.8 0.91 0.72US 0.04 0.01 0.1 0.04 0.1 -0.09 0.09 0.02 -0.08 -0.11Pvalues 0.63 0.89 0.23 0.63 0.39 0.55 0.44 0.9 0.5 0.38

LAG4Europe -0.03 -0.02 0.01 -0.03 0.02 -0.11 -0.16 -0.06 -0.05 -0.09Pvalues 0.75 0.85 0.93 0.7 0.87 0.45 0.19 0.6 0.67 0.47Japan 0.04 0.04 0 0.04 -0.09 -0.25 -0.04 -0.02 -0.13 -0.11Pvalues 0.6 0.65 0.96 0.65 0.46 0.09 0.74 0.86 0.28 0.36US 0.03 -0.02 0.06 0.07 0.04 -0.22 -0.18 -0.08 0.06 0.05Pvalues 0.7 0.83 0.49 0.42 0.77 0.14 0.14 0.52 0.6 0.69

LAG5Europe -0.01 -0.06 0.06 0.04 0 -0.14 -0.2 -0.12 -0.05 -0.05Pvalues 0.88 0.48 0.5 0.66 0.98 0.35 0.1 0.31 0.69 0.68Japan 0.06 0.03 0.11 0.08 0.09 0.13 -0.15 -0.08 0 -0.06Pvalues 0.46 0.76 0.21 0.33 0.47 0.37 0.22 0.51 0.97 0.64US -0.02 -0.03 -0.01 -0.01 0.01 -0.11 -0.17 -0.2 -0.21 -0.22Pvalues 0.83 0.69 0.93 0.87 0.95 0.44 0.15 0.11 0.08 0.06

LAG6Europe -0.09 -0.11 -0.04 -0.07 -0.01 -0.14 -0.05 -0.11 -0.07 -0.1Pvalues 0.29 0.18 0.65 0.4 0.93 0.34 0.68 0.38 0.58 0.42Japan 0.23 0.19 0.12 0.25 0.03 -0.02 0.04 -0.02 0.11 0.09Pvalues 0.01 0.03 0.16 0 0.83 0.9 0.73 0.85 0.35 0.44US -0.07 -0.09 0.03 -0.06 -0.16 -0.31 -0.24 -0.1 -0.23 -0.22Pvalues 0.4 0.31 0.72 0.47 0.18 0.03 0.05 0.41 0.05 0.07

Correlation of HF returns and lagged change of industrial production

Table 1A: Correlation of monthly hedge fund index returns with monthly (unadjusted) changes in industrial production at different lags

38

HFIndex CSFB_ED CSFB_D CSFB_MA CSFB_multi Eureka_Europe_ED Eureka_Europe_D Eureka_Asia_ED Eureka_Asia_D Eureka_US_ED Eureka_US_DLAG0Europe 0.11 0.07 0.1 0.14 0.14 -0.08 0.05 -0.07 0.01 0Pvalues 0.18 0.4 0.22 0.1 0.25 0.58 0.68 0.59 0.93 0.99Japan 0.03 0.04 -0.04 0 0.02 -0.11 0.08 0.01 -0.1 -0.06Pvalues 0.77 0.6 0.63 0.99 0.89 0.44 0.52 0.96 0.41 0.62US -0.2 -0.28 -0.09 -0.11 0.08 0.03 0.01 0.04 0.01 -0.06Pvalues 0.02 0 0.28 0.2 0.52 0.86 0.94 0.75 0.96 0.65

LAG1Europe -0.06 -0.07 -0.14 -0.04 0.09 0.03 -0.06 -0.15 -0.18 -0.18Pvalues 0.47 0.4 0.09 0.64 0.45 0.82 0.64 0.22 0.15 0.14Japan -0.03 -0.05 0.01 0 0.11 0.22 -0.12 0.02 -0.03 -0.07Pvalues 0.77 0.52 0.88 0.97 0.39 0.13 0.32 0.84 0.8 0.56US -0.07 -0.11 -0.1 -0.04 0.1 -0.29 0.01 -0.09 -0.16 -0.14Pvalues 0.42 0.21 0.26 0.65 0.43 0.05 0.91 0.47 0.19 0.25

LAG2Europe 0 -0.09 0.18 0.06 0.07 -0.03 -0.12 -0.14 0.01 0.02Pvalues 0.99 0.31 0.03 0.49 0.55 0.83 0.33 0.25 0.96 0.84Japan 0.01 -0.02 -0.03 0.05 0.13 -0.34 -0.07 -0.12 -0.06 -0.01Pvalues 0.87 0.77 0.68 0.58 0.28 0.02 0.55 0.32 0.64 0.9US 0.06 -0.01 0.09 0.1 0.16 -0.12 0.22 -0.05 -0.03 0.02Pvalues 0.5 0.93 0.31 0.26 0.18 0.41 0.07 0.67 0.83 0.89

LAG3Europe -0.01 -0.03 0.08 0 0.1 0.07 0.06 -0.04 0.01 0.09Pvalues 0.93 0.73 0.33 0.97 0.4 0.64 0.63 0.76 0.91 0.48Japan 0.02 0 0.03 0.02 0.15 0.01 -0.02 0.03 -0.01 0.04Pvalues 0.81 0.97 0.75 0.78 0.22 0.97 0.85 0.8 0.91 0.72US 0.01 -0.02 0.04 0.01 0.1 -0.09 0.12 0.03 -0.08 -0.1Pvalues 0.95 0.82 0.67 0.93 0.4 0.55 0.31 0.78 0.51 0.41

LAG4Europe -0.03 -0.02 0.01 -0.03 0.02 -0.11 -0.16 -0.07 -0.05 -0.09Pvalues 0.73 0.82 0.93 0.68 0.88 0.45 0.19 0.59 0.67 0.47Japan 0.05 0.04 0 0.04 -0.09 -0.25 -0.04 -0.02 -0.13 -0.11Pvalues 0.59 0.66 0.98 0.64 0.46 0.09 0.74 0.86 0.28 0.36US 0 -0.05 0 0.03 0.03 -0.22 -0.15 -0.06 0.07 0.06Pvalues 1 0.59 0.98 0.69 0.81 0.14 0.21 0.64 0.57 0.61

LAG5Europe -0.01 -0.06 0.06 0.04 0 -0.14 -0.2 -0.13 -0.05 -0.05Pvalues 0.86 0.46 0.5 0.68 0.97 0.35 0.1 0.31 0.69 0.67Japan 0.06 0.02 0.1 0.08 0.09 0.13 -0.15 -0.08 0 -0.06Pvalues 0.46 0.77 0.22 0.32 0.47 0.37 0.22 0.51 0.97 0.64US -0.05 -0.05 -0.07 -0.05 0 -0.11 -0.14 -0.18 -0.21 -0.22Pvalues 0.58 0.55 0.41 0.56 0.99 0.44 0.24 0.15 0.08 0.07

LAG6Europe -0.09 -0.11 -0.04 -0.07 -0.01 -0.14 -0.05 -0.11 -0.07 -0.1Pvalues 0.28 0.17 0.65 0.39 0.93 0.34 0.67 0.38 0.58 0.42Japan 0.23 0.18 0.12 0.25 0.03 -0.02 0.04 -0.02 0.11 0.09Pvalues 0.01 0.03 0.17 0 0.83 0.9 0.73 0.85 0.35 0.44US -0.1 -0.11 -0.03 -0.1 -0.18 -0.31 -0.21 -0.07 -0.24 -0.22Pvalues 0.23 0.2 0.7 0.26 0.14 0.03 0.08 0.55 0.05 0.08

Correlation o HF returns and lagged difference of changes inIP and longterm trend

Table 2A: Correlation of monthly hedge fund index returns with monthly changes in industrial production (adjusted by the change in the long term trend) at different lags

39

HFIndex CSFB_ED CSFB_D CSFB_MA CSFB_multi Eureka_Europe_ED Eureka_Europe_D Eureka_Asia_ED Eureka_Asia_D Eureka_US_ED Eureka_US_DLAG0Europe -0.16 -0.19 -0.08 -0.11 -0.31 -0.08 -0.12 -0.17 -0.18 -0.08Pvalues 0.16 0.11 0.5 0.37 0.09 0.72 0.5 0.35 0.32 0.65Japan 0.06 0.07 0.04 0.02 0.07 0.09 -0.02 0.12 0 0.17Pvalues 0.63 0.54 0.73 0.84 0.69 0.64 0.93 0.48 0.98 0.34US -0.51 -0.5 -0.34 -0.46 0.21 -0.04 0.02 -0.27 -0.24 -0.31Pvalues 0 0 0 0 0.24 0.82 0.9 0.12 0.18 0.07

LAG1Europe 0.04 0.02 -0.06 0.06 -0.18 0.1 -0.07 -0.25 -0.01 -0.12Pvalues 0.73 0.85 0.59 0.59 0.31 0.64 0.7 0.17 0.96 0.51Japan -0.08 -0.13 0.03 -0.05 0.07 -0.08 -0.01 -0.28 -0.27 -0.19Pvalues 0.48 0.26 0.8 0.7 0.69 0.7 0.94 0.1 0.12 0.28US -0.24 -0.21 -0.1 -0.23 0.03 -0.24 0.07 -0.17 0.03 -0.03Pvalues 0.04 0.06 0.37 0.05 0.86 0.21 0.71 0.33 0.87 0.85

LAG2Europe 0 -0.05 0.24 0.02 0.09 -0.27 -0.11 -0.14 0.08 0.04Pvalues 0.98 0.64 0.03 0.85 0.63 0.2 0.55 0.43 0.67 0.83Japan -0.21 -0.24 -0.23 -0.14 0.06 -0.32 -0.19 -0.29 -0.33 -0.3Pvalues 0.08 0.05 0.05 0.23 0.74 0.12 0.29 0.1 0.05 0.08US 0.05 -0.03 0.02 0.13 0.2 0.09 0.15 -0.03 0.15 0.22Pvalues 0.68 0.8 0.89 0.25 0.25 0.66 0.39 0.87 0.38 0.21

LAG3Europe 0.21 0.21 0.26 0.17 0.15 0.27 0.08 -0.15 0.31 0.34Pvalues 0.07 0.07 0.02 0.13 0.4 0.22 0.67 0.39 0.07 0.05Japan -0.24 -0.24 -0.28 -0.17 -0.02 -0.47 -0.11 -0.3 -0.18 -0.27Pvalues 0.05 0.04 0.02 0.16 0.91 0.02 0.54 0.08 0.31 0.13US 0.06 0.09 0.04 0.02 -0.14 -0.28 0.03 -0.09 -0.3 -0.38Pvalues 0.57 0.46 0.75 0.84 0.42 0.15 0.87 0.62 0.08 0.02

LAG4Europe 0.13 0.06 0.18 0.17 0.33 0.22 0.03 -0.22 0.25 0.06Pvalues 0.25 0.58 0.11 0.13 0.05 0.32 0.87 0.21 0.15 0.75Japan -0.1 -0.11 0.06 -0.09 -0.18 -0.17 0.08 -0.25 -0.04 0Pvalues 0.41 0.37 0.64 0.47 0.32 0.42 0.65 0.16 0.81 0.98US 0.02 -0.02 0.05 0.05 -0.29 -0.31 -0.13 -0.08 -0.11 -0.04Pvalues 0.88 0.84 0.64 0.65 0.1 0.12 0.46 0.66 0.53 0.84

LAG5Europe 0.04 0.02 0.16 0.04 0.17 -0.04 -0.14 -0.2 -0.04 -0.04Pvalues 0.73 0.9 0.15 0.7 0.35 0.87 0.42 0.25 0.83 0.81Japan -0.2 -0.18 -0.03 -0.18 -0.07 0.28 0.02 -0.27 -0.1 -0.14Pvalues 0.09 0.13 0.81 0.12 0.69 0.18 0.91 0.11 0.58 0.42US 0.14 0.16 -0.23 0.1 -0.05 -0.21 0.07 0.12 -0.17 -0.27Pvalues 0.24 0.18 0.04 0.38 0.79 0.31 0.69 0.49 0.32 0.12

LAG6Europe -0.05 -0.05 -0.03 -0.04 -0.01 0.03 0.01 -0.15 -0.07 -0.05Pvalues 0.66 0.64 0.79 0.73 0.98 0.89 0.94 0.39 0.7 0.77Japan 0.03 0.01 -0.06 0.06 -0.24 -0.24 0.06 0.04 0.05 -0.09Pvalues 0.8 0.93 0.6 0.64 0.17 0.27 0.72 0.83 0.79 0.61US -0.11 -0.13 -0.1 -0.06 -0.28 -0.5 -0.07 -0.04 -0.34 -0.26Pvalues 0.33 0.24 0.38 0.58 0.1 0.01 0.68 0.81 0.04 0.13

Correlation of HF returns and laged positive difference of changes in IP and longterm trend

Table 3A: Correlation of monthly hedge fund index returns with monthly changes in industrial production (adjusted by the change in the long term trend) at different lags – when the adjusted change in industrial production was positive

40

HFIndex CSFB_ED CSFB_D CSFB_MA CSFB_multi Eureka_Europe_ED Eureka_Europe_D Eureka_Asia_ED Eureka_Asia_D Eureka_US_ED Eureka_US_DLAG0Europe 0.14 0.14 0.08 0.1 0.37 0.05 0.25 -0.08 0.01 0.07Pvalues 0.27 0.26 0.52 0.43 0.02 0.81 0.14 0.63 0.98 0.7Japan 0.04 0.02 0.04 0.06 -0.07 -0.13 0.19 0.29 0 0.07Pvalues 0.75 0.9 0.74 0.65 0.67 0.56 0.28 0.1 0.99 0.7US -0.05 -0.15 0.01 0.02 -0.1 -0.46 0.07 0.09 -0.24 -0.4Pvalues 0.67 0.23 0.92 0.9 0.56 0.05 0.69 0.6 0.17 0.02

LAG1Europe -0.06 0 -0.03 -0.12 0.34 -0.06 -0.3 -0.26 -0.2 -0.2Pvalues 0.66 0.97 0.83 0.34 0.04 0.78 0.07 0.12 0.25 0.23Japan -0.05 -0.05 -0.14 -0.03 -0.02 0.26 -0.02 0.51 0.2 0.14Pvalues 0.7 0.66 0.27 0.81 0.9 0.24 0.93 0 0.25 0.41US 0.03 0.02 -0.08 0.03 -0.04 -0.33 0.01 -0.03 -0.17 -0.16Pvalues 0.82 0.87 0.55 0.82 0.84 0.17 0.95 0.86 0.34 0.38

LAG2Europe -0.02 -0.06 0.07 0.01 0.25 0.04 -0.14 -0.19 -0.14 0.01Pvalues 0.88 0.62 0.6 0.95 0.14 0.87 0.42 0.27 0.42 0.95Japan -0.07 -0.14 -0.08 0.01 0.04 -0.06 0.04 0.25 0.13 0.17Pvalues 0.57 0.24 0.5 0.96 0.84 0.77 0.82 0.15 0.46 0.34US 0.07 0.02 0.04 0.1 0 -0.32 0.21 0 -0.03 0.04Pvalues 0.61 0.9 0.74 0.42 1 0.17 0.23 0.98 0.88 0.84

LAG3Europe -0.12 -0.08 -0.06 -0.14 -0.07 0.06 0.01 -0.17 -0.15 -0.14Pvalues 0.36 0.52 0.63 0.28 0.68 0.77 0.97 0.32 0.38 0.41Japan -0.08 -0.1 -0.01 -0.07 0.13 0.03 -0.18 0.09 -0.19 -0.11Pvalues 0.52 0.43 0.9 0.54 0.45 0.88 0.31 0.59 0.27 0.54US -0.08 -0.05 -0.05 -0.1 0.01 0.07 0.01 0.3 0.01 0.06Pvalues 0.54 0.7 0.71 0.43 0.95 0.77 0.96 0.09 0.97 0.75

LAG4Europe -0.06 -0.05 -0.06 -0.05 -0.26 -0.3 0.22 0.06 0.1 0.12Pvalues 0.64 0.68 0.63 0.69 0.14 0.13 0.2 0.74 0.56 0.48Japan -0.06 -0.15 0.06 0.01 -0.06 -0.15 -0.03 -0.1 -0.12 -0.2Pvalues 0.62 0.22 0.64 0.93 0.72 0.47 0.86 0.56 0.48 0.26US -0.06 -0.07 -0.05 -0.05 -0.11 -0.46 -0.39 0.19 -0.04 -0.13Pvalues 0.64 0.6 0.7 0.73 0.53 0.03 0.02 0.28 0.82 0.46

LAG5Europe -0.04 -0.02 0.01 -0.06 0.09 -0.2 -0.08 0.28 0.17 0.16Pvalues 0.73 0.87 0.92 0.62 0.6 0.34 0.66 0.11 0.33 0.36Japan 0.12 0.05 0.29 0.14 0.04 0.19 -0.26 -0.19 0.03 -0.06Pvalues 0.34 0.66 0.01 0.25 0.81 0.36 0.14 0.29 0.85 0.75US -0.17 -0.17 -0.08 -0.18 0.02 -0.11 -0.15 0.04 -0.24 -0.15Pvalues 0.18 0.17 0.55 0.15 0.91 0.61 0.41 0.84 0.17 0.4

LAG6Europe 0.04 0 0.06 0.08 0.08 -0.25 0.03 0.22 0.11 0.12Pvalues 0.76 1 0.61 0.52 0.64 0.22 0.85 0.2 0.52 0.48Japan 0.36 0.26 0.34 0.41 0.29 0.16 0 -0.06 0.26 0.2Pvalues 0 0.03 0 0 0.09 0.43 0.98 0.72 0.14 0.26US -0.19 -0.15 -0.31 -0.21 -0.05 -0.05 -0.15 0.12 -0.26 -0.12Pvalues 0.13 0.23 0.01 0.1 0.79 0.84 0.41 0.51 0.15 0.5

Correlation of HF returns and laged negative difference of changes in IP and longterm trend

Table 4A: Correlation of monthly hedge fund index returns with monthly changes in industrial production (adjusted by the change in the long term trend) at different lags – when the adjusted change in industrial production was negative

41

Mean Median Volatility Skewness KurtosisCSFB_ED 0.93 1.03 1.64 -3.46 26.93CSFB_D 1.07 1.21 1.88 -2.84 20.75CSFB_MA 0.64 0.61 1.22 -1.26 9.33CSFB_multi 0.86 0.9 1.75 -2.6 20.03Eureka_Europe_ED 0.81 1.03 1.01 -1.39 8.08Eureka_Europe_D 0.9 1.21 1.2 -0.54 4.78Eureka_US_ED 0.62 0.75 1.19 -0.61 4.13Eureka_US_D 0.98 1.16 1.78 -0.31 3.14HFIntel_Europe_ED 1.14 1.15 1.61 -0.11 3.07HFIntel_US_ED 0.74 0.65 0.86 1.06 5.37HFIntel_US_D 1.2 1.27 1.72 0.29 4.1

Descriptive statistics for HF indices

Table 5A: Descriptive statistics for time series of hedge fund indices

42

CSFB ED

Constant Lagged Return CLI_TR_Japan Vol_DAX Vol_USVol_DAX L1 Vol_US L3

Conf_Cons_GB Change

Div_yield_SandP Change

Vol_US Change

Conf_Cons_GB ChangeL1

Vol_Jap ChangeL1

MSCI_W_mRet 3mMovAver

MSCI_WexUS_mRet 3mMovAver

SandP500_mRet 3mMovAver

MSCI_EU_mRet 3mMovAver

MSCI_Asia_mRet 3mMovAver

MSCI_EmM_mRet3mMovAver

MSCI_W_SmallC_mRet3mMovAver

Vol_DAX 3mMovAver

Vol_US 3mMovAver

Coefficients -11.008 0.042 0.113 0.016 -0.027 0.012 0.044 -0.005 -0.295 -0.027 0.041 -0.072 0.273 -0.562 0.002 0.214 0.074 0.040 0.166 -0.035 0.026P-values 0.074 0.716 0.072 0.809 0.778 0.787 0.130 0.913 0.905 0.631 0.404 0.267 0.822 0.521 0.998 0.482 0.663 0.557 0.125 0.631 0.807Average coefff. of all rolling windows -9.950 -0.095 0.106 0.011 -0.006 0.001 0.042 -0.017 -1.301 -0.019 0.045 -0.100 0.993 -1.163 -0.383 0.390 0.148 0.024 0.174 -0.020 -0.004STD of coeff. of all 2.171 0.104 0.019 0.011 0.018 0.005 0.006 0.012 0.813 0.012 0.007 0.020 0.412 0.430 0.229 0.176 0.090 0.030 0.025 0.016 0.025

CSFB D

Constant Lagged Return Vol_DAXVol_DAX L2

Conf_Cons_EUR Change

Div_yield_SandP Change

Vol_US Change

MSCI_W_mRet 3mMovAver

MSCI_WexUS_mRet3mMovAver

SandP500_mRet 3mMovAver

MSCI_EU_mRet 3mMovAver

MSCI_EmM_mRet 3mMovAver

MSCI_W_SmallC_mRet3mMovAver

Vol_DAX 3mMovAver

Coefficients 0.957 0.058 -0.001 0.042 -0.213 -1.015 0.012 -0.320 -0.187 0.279 0.228 0.077 0.143 -0.047P-values 0.096 0.546 0.991 0.174 0.048 0.734 0.803 0.814 0.804 0.683 0.161 0.248 0.261 0.416Average coefff. of all rolling windows 1.370 0.018 0.002 0.041 -0.160 -0.722 0.007 0.656 -0.660 -0.228 0.190 0.068 0.159 -0.058STD of coeff. of all 0.214 0.024 0.004 0.002 0.026 0.364 0.005 0.331 0.155 0.168 0.027 0.009 0.010 0.007

CSFB MA

Constant Lagged Return CLI_TR_Japan Vol_DAXTerm_spread_US L1 Vol_US L1

Tbill3M_yield L2

Div_yield_SandP Change

Vol_DAX Change

MSCI_W_mRet 3mMovAver

MSCI_WexUS_mRet 3mMovAver

SandP500_mRet 3mMovAver

MSCI_EU_mRet 3mMovAver

MSCI_Asia_mRet 3mMovAver

MSCI_EmM_mRet 3mMovAver

MSCI_W_SmallC_mRet3mMovAver

Vol_DAX 3mMovAver

Vol_US 3mMovAver

Coefficients -3.898 0.028 0.022 0.121 0.134 -0.019 0.353 -1.740 -0.060 -0.761 0.023 0.363 0.184 0.116 -0.020 0.181 -0.111 0.039P-values 0.412 0.765 0.653 0.012 0.591 0.662 0.100 0.364 0.112 0.425 0.973 0.453 0.434 0.367 0.701 0.033 0.051 0.541Average coefff. of all rolling windows -3.459 0.030 0.027 0.110 -0.003 -0.025 0.232 -0.672 -0.061 -1.290 0.325 0.659 0.180 0.106 -0.029 0.172 -0.099 0.031STD of coeff. of all 1.238 0.021 0.009 0.007 0.075 0.009 0.073 0.379 0.005 0.204 0.117 0.114 0.031 0.015 0.017 0.017 0.011 0.025

CSFB multi

Constant Lagged Return CLI_TR_Japan

MSCI_W_SmallC_mRetL1 Vol_DAX L1

Conf_Cons_GB Change

Div_yield_SandP Change

Vol_US Change

Currency_EUR Change

Conf_Cons_GB ChangeL1

Vol_Jap ChangeL1

MSCI_W_mRet 3mMovAver

MSCI_WexUS_mRet 3mMovAver

SandP500_mRet 3mMovAver

MSCI_EU_mRet 3mMovAver

MSCI_Asia_mRet 3mMovAver

MSCI_EmM_mRet 3mMovAver

MSCI_W_SmallC_mRet3mMovAver

Vol_DAX 3mMovAver

Coefficients -20.407 -0.138 0.209 0.063 -0.009 -0.033 -1.262 -0.054 -0.020 0.037 -0.110 1.102 -0.882 -0.420 0.122 0.054 0.017 0.258 0.045P-values 0.002 0.195 0.002 0.075 0.824 0.513 0.608 0.287 0.797 0.467 0.108 0.386 0.324 0.511 0.693 0.756 0.804 0.021 0.262Average coefff. of all rolling windows -16.293 -0.107 0.170 0.032 -0.005 -0.024 -1.012 -0.043 -0.032 0.079 -0.133 1.549 -1.143 -0.655 0.172 0.039 0.033 0.214 0.029STD of coeff. of all 2.299 0.041 0.022 0.015 0.006 0.011 0.612 0.012 0.013 0.027 0.020 0.362 0.295 0.206 0.107 0.052 0.022 0.031 0.008

Coefficients and P-values in predictive model for CSFB indices

Table 6A: Results from the first calibration period for CSFB/Tremont event driven indices. The first line of each table is the selected subset of variables in the final prediction model, the second and third lines are coefficients and p-values for this variables and the last two lines provide information about the mean and STD of coefficient over all rolling windows.

43

Eureka_Europe_ED

ConstantLagged Return

Australia_CLI_6M_rate_of_change

Australia_CLI_6M_rate_of_change_trend_adjusted

Australia_CLI_6M_rate_of_change L2

Australia_CLI_6M_rate_of_change_trend_adjusted L3

Australia_CLI_6M_rate_of_change_trend_adjusted *D

Conf_Cons_GB Change

Vol_DAX Change

Conf_Cons_EUR ChangeL2

Coefficients 36.992 0.289 28.727 -30.333 0.705 -0.457 1.325 0.060 -0.062 0.232P-values 0.365 0.042 0.383 0.357 0.085 0.144 0.021 0.282 0.015 0.037Average coefff. of all rolling windows NaN NaN NaN NaN NaN NaN NaN NaN NaN NaNSTD of coeff. of all rolling windows NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

Eureka_Europe_D

ConstantLagged Return

Conf_Cons_EUR L1

M_Volume_Mill_Asia L1

Conf_Cons_US L3

MSCI_Asia_mRet L3 Vol_DAX L3

Currency_EUR L3

CPI_Europe Change

M_Volume_Bill_US ChangeL1

MSCI_W_SmallC_mRetChangeL2

MSCI_W_SmallC_mRet3mMovAver

Coefficients -20.796 -0.068 -0.074 0.041 -0.117 -0.007 -0.072 0.319 -0.382 -0.099 0.112 0.242P-values 0.175 0.738 0.720 0.877 0.392 0.927 0.221 0.165 0.837 0.090 0.030 0.049Average coefff. of all rolling windows -5.563 -0.054 -0.238 -0.122 0.017 -0.019 0.001 0.038 0.106 -0.096 0.059 0.217STD of coeff. of all rolling windows 4.193 0.067 0.080 0.118 0.053 0.020 0.023 0.080 0.981 0.010 0.036 0.039

Eureka_Asia_ED

ConstantLagged Return

Vol_Jap ChangeL1

CPI_Europe ChangeL1

Tbill3M_yield ChangeL2

Coefficients -0.346 -0.014 -0.246 2.562 -0.285P-values 0.411 0.918 0.114 0.007 0.718Average coefff. of all rolling windows 0.552 0.142 -0.177 0.469 0.043STD of coeff. of all rolling windows 0.414 0.137 0.058 1.122 0.319

Coefficients and P-values in predictive model for Regional indices (1)

Table 7A: Results from the first calibration period for Regional indices (Europe event driven, Europe distressed, Asia event driven). The first line of each table is the selected subset of variables in the final prediction model, the second and third lines are coefficients and p-values for this variables and the last two lines provide information about the mean and STD of coefficient over all rolling windows.

44

Eureka_Asia_D

ConstantLagged Return Term_spread_US Tbill3M_yield L1 Vol_DAX L2 Vol_US L2

Conf_Manuf_EUR L3

Conf_Cons_US L3

Div_yield_SandP L3

Div_yield_SandP Change

Conf_Cons_EUR 3mMovAver

Gold 3mMovAver

CPI_Japan 3mMovAver

Coefficients 13.304 0.148 0.403 0.611 -0.062 0.212 -0.058 -0.027 0.506 -4.048 0.038 0.030 -0.255P-values 0.941 0.396 0.730 0.624 0.582 0.256 0.721 0.787 0.927 0.344 0.831 0.425 0.891Average coefff. of all rolling windows 8.550 0.120 0.520 -0.089 -0.037 0.073 0.099 -0.100 -1.723 -4.099 -0.004 0.003 0.027STD of coeff. of all rolling windows 126.457 0.287 0.440 0.908 0.044 0.074 0.071 0.066 2.240 2.020 0.101 0.018 1.334

Eureka_US_ED

ConstantLagged Return Vol_US Vol_US L1

Currency_JY Change

MSCI_W_mRet 3mMovAver

MSCI_WexUS_mRet 3mMovAver

SandP500_mRet 3mMovAver

MSCI_EU_mRet 3mMovAver

MSCI_Asia_mRet 3mMovAver

MSCI_EmM_mRet 3mMovAver

MSCI_W_SmallC_mRet3mMovAver

Vol_US 3mMovAver

Coefficients -1.336 -0.051 0.195 0.236 -0.087 -2.781 -0.497 1.316 1.221 0.485 -0.225 0.372 -0.365P-values 0.684 0.811 0.278 0.082 0.507 0.468 0.809 0.509 0.289 0.386 0.250 0.185 0.082Average coefff. of all rolling windows 0.755 -0.010 0.190 0.074 -0.042 3.549 -0.957 -2.155 -0.391 -0.146 0.021 0.298 -0.273STD of coeff. of all rolling windows 1.195 0.058 0.030 0.096 0.051 2.628 0.980 1.467 0.979 0.462 0.138 0.184 0.099

Eureka_US_D

ConstantLagged Return Vol_US L2

Div_yield_SandP Change

CPI_Europe ChangeL1

MSCI_W_mRet 3mMovAver

SandP500_mRet 3mMovAver

MSCI_EmM_mRet 3mMovAver

MSCI_W_SmallC_mRet3mMovAver

Coefficients -4.765 -0.317 0.186 -4.485 1.480 -0.982 0.327 -0.215 0.853P-values 0.007 0.061 0.004 0.186 0.156 0.044 0.339 0.064 0.000Average coefff. of all rolling windows -0.860 -0.098 0.079 -5.973 0.096 0.175 -0.171 -0.155 0.354STD of coeff. of all rolling windows 1.471 0.084 0.043 0.869 0.528 0.574 0.290 0.041 0.228

Coefficients and P-values in predictive model for Regional indices (2)

Table 8A: Results from the first calibration period for Regional indices (Asia distressed, US event driven, US distressed). The first line of each table is the selected subset of variables in the final prediction model, the second and third lines are coefficients and p-values for this variables and the last two lines provide information about the mean and STD of coefficient over all rolling windows.

45

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