Modeling hedge fund exposure to risk factors

Economic Modelling 29 (2012) 1003–1018

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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod

Modeling hedge fund exposure to risk factors Fredj Jawadi a, b,⁎, Sabrina Khanniche c, 1 a b c

L@REM-Université d'Evry val d'Essonne, France Amiens School of Management, France Pictet Asset Management, Switzerland

a r t i c l e

i n f o

Article history: Accepted 6 February 2012 JEL classification: G12 G29 C22 Keywords: Hedge funds Style analysis Nonlinearity Switching Transition Regression models

a b s t r a c t This paper examines the adjustment dynamics of hedge fund returns and studies their exposure to risk factors in a nonlinear framework for several types of strategies over the last two decades. Nonlinearity is justified by distortions due to the use of short selling, leverage, derivatives and illiquid assets for hedge fund strategies. Among nonlinear models, switching regime (STR) models are applied to reproduce the dynamics of hedge fund returns. This nonlinear multivariate modeling has the advantage of capturing the time-varying exposure of hedge fund strategies to risk factors, and of specifying the asymmetric relationship between hedge fund returns and risk. The findings are interesting and provide several contributions to the hedge fund literature. First, we show that the dynamics of hedge fund returns exhibit significant asymmetry and nonlinearity, indicating that they evolve and vary asymmetrically in accordance with stages in financial cycles. Second, hedge fund exposure to risk factors also varies over time, depending on the strategy and the regime. Finally, our modeling captures the most important changes in hedge fund exposure to risk factors induced by the recent global financial crisis (2008–2009). © 2012 Elsevier B.V. All rights reserved.

1. Introduction The hedge fund industry has developed significantly over the last few years, accounting for $1.9 trillion in 2007, according to Hedge Fund Research. The prospect of double and triple-digit returns and the losses caused by the 2000 dot-com bubble led many investors to prefer hedge funds (Jawadi and Khanniche, 2012). By definition, the latter seek absolute positive returns. This implies taking up positions in complex financial markets that are sensitive to extreme losses, and making hedge funds a source of systemic risk. Hedge fund techniques can also induce distressed sales and contribute to systemic risk being widely disseminated (Aglietta et al., 2010; Khanniche, 2011). The institutionalization of hedge funds, which implies that public savings are concerned, and the way hedge funds affect financial stability, means that an in-depth understanding of the underlying risks is crucial. It is also important to note that even though the recent global financial crisis (2008–2009) illustrated how hedge funds fail to save investors and financial markets, investors are still interested in this form of investment. Consequently, it is essential to understand which factors impact most strongly on each hedge fund strategy in order to

⁎ Corresponding author at: Université d'Evry Val d'Essonne, Bâtiment La Poste, Bure 226, 2 rue Facteur Cheval, 91025 Evry, France. Tel.: + 33 1 69 47 78 98. E-mail addresses: [email protected] (F. Jawadi), [email protected] (S. Khanniche). 1 Université de Paris Ouest Nanterre La Défense, 200 Avenue de la République, 91000 Nanterre Cedex, France. 0264-9993/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2012.02.003

optimize asset allocation. An exploration of the linkage between hedge funds and risk factors is thus recommended if we are to better understand the hedge fund industry and its dynamics. Our paper therefore explores the dynamics of hedge fund returns with a particular focus on hedge fund exposure to risk in order to highlight the key risk-generating mechanisms and sources. The dynamics of hedge funds are, however, naturally complex because hedge funds are characterized by different ‘abnormal’ properties and have several ‘atypical relationships’ with macroeconomic and financial data, which also vary according to the hedge fund strategies adopted. Taking these different properties into account, this paper contributes to extending the investigation of hedge fund linkages in a nonlinear framework by its use of Smooth Transition Regression (STR) models by Granger and Teräsvirta (1993). While the introduction of nonlinearity is particularly interesting to capture asymmetry and complex linkages in the exposure of hedge funds to different types of risk, the use of STR is particularly innovative and not yet sufficiently applied to the hedge fund industry. This modeling enables us to capture the different changes associated with the relationship between risk and hedge funds, to apprehend asymmetry and nonlinearity linked to hedge fund adjustment dynamics and to reproduce the different asymmetrical feedback between macroeconomic and financial variables in hedge funds returns. It also helps us to capture the smoothness and inertia effects induced by the heterogeneity associated with hedge fund strategies. Our paper is organized as follows. Section 2 will discuss the main results of previous studies. Section 3 will briefly present the econometric modeling approach. The empirical results are discussed in Section 4. Section 5 will conclude.

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2. Literature review Several empirical studies in the literature have focused on the hedge fund industry to investigate the relationship between their returns and risk factors. Sharpe (1992) and Fung and Hsieh (1997) investigated mutual fund performance and hedge fund dynamics respectively. Their findings point to significant nonlinear dependencies of hedge fund returns with respect to risk factors. The authors justify this nonlinearity by the complexity of financial instruments and the dynamic strategies implemented by hedge funds to achieve absolute returns: i.e. short selling, leverage, derivatives, illiquid assets, etc. These instruments tend to involve a complex and asymmetrical relationship between hedge fund returns and traditional assets. Furthermore, the reaction of hedge funds may also be time-varying, depending on whether the market is bearish or bullish. In order to reproduce the nonlinearity that characterizes hedge funds, two approaches are proposed. The first enables the introduction of nonlinear regressors in a linear relationship with standard asset classes. The second approach focuses on nonlinear modeling for hedge fund adjustment dynamics. While the first approach has been widely studied in the past, the second is less commonly found in the literature. Lhabitant (2001), for example, introduced Tremont/ CSFB hedge fund indices to represent individual hedge fund returns in a nonlinear framework. Alexander and Dimitriu (2004) also investigated individual hedge fund returns. Various factors have been considered in order to capture the nonlinearity associated with hedge funds. Schneeweis and Spurgin (2000) introduced absolute value of traditional assets to apprehend managers' strategies. It seems logical that managers would take long positions when the market is bullish and the reverse when the market is depressed. Agarwal and Naik (2000) incorporated option-based factors and referred to put-and-call prices on traditional assets. They justified the use of these factors by the asymmetric fee structure that is similar to buy-a-call. Fung and Hsieh (2001) focused on trend-following funds and showed that their returns may be replicated with lookback straddle options. Gregoriou and Rouah (2001) point to evidence of a significant relationship between stock indexes and the ten largest hedge funds using cointegration tests. Overall, these studies retained nonlinearity to investigate the link between risk factors and hedge funds, at the same time implying that exposure to these risk factors is constant over time. However, the recent global financial instability and excess market volatility offers strong evidence that hedge fund exposure to risk factors is in fact time-varying. Investigating this time-variation in hedge fund risk exposure is crucial as it enables investors to identify less risky hedge fund strategies. In practice, several conditional models appear promising in a study of the dynamics of hedge fund risk exposure over time. Chan et al. (2005) introduced a threshold model to apprehend the asymmetry associated with hedge fund exposure when the market is up or down. Using the Markov switching regime model, Billio et al. (2006) also investigated dynamic hedge fund returns and conditionally analyzed the changes in hedge fund risk exposure in line with diverse market conditions. 2 Our paper aims to extend the previous literature while investigating the relationship between hedge fund returns and risk factors in a nonlinear framework. In particular, we suggest that hedge fund returns may be explained by linear factors, while exposure to these factors is considered to be nonlinear. This hypothesis—which is strongly supported by the characteristics of hedge funds (the use of leverage, short selling, derivatives, and asymmetrical performance fees inducing dynamic strategies)—has not been widely developed in the literature. In particular, using smooth transition regression models, we specify and identify regime-dependent hedge fund exposure to underlying risk factors. In a context of financial crisis, this is particularly important to

2

See Gregoriou, G., N., and Duffy for a summary of the literature on hedge funds.

explain the opportunities associated with hedge funds and their reactions and impacts in line with changes in the state of the financial market. Furthermore, STR models are preferred to linear models, abrupt threshold models or Marko switching models because they reproduce asymmetry, nonlinearity and structural breaks between regimes for which the transition is smooth rather than abrupt. STR models also offer a generalization of several nonlinear models such as threshold models and are then more informative. This smoothness can be justified by the heterogeneity associated with hedge fund strategies. Each strategy has its own factors and determinants in practice. For example, as in Billio et al. (2006), we would expect S&P500 to be strongly relevant for long short equity or dedicated short bias, but this is not true for other strategies such as fixed income arbitrage or global macro. 3. Nonlinear econometric modeling for hedge fund returns Threshold models have recently been applied to investigate the dynamics of several financial time-series (Anderson, 1997; Boswijk et al., 2007; De Grauwe and Grimaldi, 2005; Jawadi and Prat, 2011; Jawadi et al. (2010)). These models appear useful for apprehending asymmetry, structural breaks and switching regimes in financial data. Indeed, such modeling is widely used to specify different regimes and to characterize financial series adjustment dynamics where the adjustment may be abrupt or smooth. Prior literature has argued that the adjustment for financial series is smooth due to price rigidities, information asymmetry, transaction costs and behavioral heterogeneity (Anderson, 1997; De Grauwe and Grimaldi, 2005; Jawadi and Prat, 2011). To take the smoothness associated with price adjustment into account, Granger and Teräsvirta's (1993) Smooth Transition Regression (STR) models have often been preferred to Tsay's (1987) threshold models and Hamilton's (1994) Markov switching models. Indeed, STR models are interesting in that they can reproduce extreme regimes as well as a continuum of intermediate states. Such modeling is also useful for apprehending different hedge fund properties. Formally, STR models are a combination of two linear models. They can also be assimilated with the multivariate STAR (Smooth Transition Autoregressive) model developed by Teräsvirta and Anderson (1992), Granger and Teräsvirta (1993) and Teräsvirta (1994) as they enable the introduction of exogenous explanatory variables in addition to the lagged dependent variables in the STAR model. 3 As in STAR models, transition is carried out by a nonlinear function that is bounded between 0 and 1. It can either be a logistic or an exponential function, defining a Logistic STR (LSTR) model and an Exponential STR (ESTR) model respectively. Formally, an STR model corresponds to: yt ¼ φ′xt þ θ′xt  Gðb; c; st Þ þ ut

ð1Þ

where: xt = (1, x1t, ⋯, xpt)′ is a vector of explanatory variables, φ = (φ0, φ1, ⋯, φp)′ denotes the coefficients of the linear part, θ = (θ0, θ1, ⋯, θp)′ denote the parameters of the nonlinear part, G(.)is the transition function, and ut → iid(0, σ 2). A logistic function is defined as: −1

Gðb; c; st Þ ¼ ð1 þ expf−bðst −cÞgÞ

ð2Þ

while an ESTR corresponds to: n o 2 Gðb; c; st Þ ¼ 1− exp −bðst −cÞ

ð3Þ

where st is the transition variable, b is the transition speed and c denotes the threshold parameter. 3 For more details about STAR models and their recent developments, see Van Dijk et al. (2002).

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In this paper, we retain the following STR model to characterize the dynamics of hedge fund returns (rt): r t ¼ φ′xt þ θ′xt  Gðb; c; st Þ þ ut

ð4Þ

xt = (1, x1t, ⋯, xpt)′ denote the directional and non directional risk factor, 4 φ = (φ0, φ1, ⋯, φp)′are the coefficients of the first regime, θ = (θ0, θ1, ⋯, θp)′ are the coefficients of the second regime, G(.)is the transition function and ut → iid(0, σ 2). STR modeling provides asymmetrical and nonlinear dynamics and is conducted in a number of steps as for STAR models: Specification, Estimation and Validation. In practice, we firstly specify the risk factors for each hedge fund strategy using the stepwise approach. Second, we test for nonlinearity in hedge fund data through the linearity tests developed by Luukkonen et al. (1988). Third, we check for the appropriate transition function to characterize the transition between hedge fund regimes. Fourth, the estimate is carried out using the Nonlinear Least Square method. Finally, we apply several misspecification tests to check the validity of the estimation results. 4. Empirical results 4.1. The data Our data consist of hedge fund returns and risk factors. They concern different hedge fund strategies that may be classified into three groups: directional, arbitrage and specific strategies (see Table 1). Directional strategies entail a gamble on the overall market direction and involve taking positions on forward and option markets, and on global markets. Arbitrage strategy managers seek to exploit price discrepancies, while specific strategies tend to benefit from events affecting companies such as mergers or restructuring. For HF data, we use the 10 CSFB/Tremont monthly performance subindexes split by an investment style over the period January 1994– March 2009. The CSFB/Tremont indexes are asset-weighted indexes that measure the net of fee returns. They are based on the TASS database that tracks more than 5000 funds and they use data reported by 480 funds to compute the 10 indexes. Regarding risk factors, we consider a large and important set of variables (32 factors) that provide a reasonably broad cross-section of risk exposure for a typical hedge fund strategy (stocks, bonds, currencies, commodities, credit and volatility). In particular, directional factors encompass stocks, bonds, currency and commodity markets, 5 and characterize dedicated short bias and long/short equity strategies. These risk factors may also portray convertible arbitrage, and eventdriven and global macro strategies. Emerging market funds are mainly exposed to emerging stock markets. Global macro, emerging markets and fixed income arbitrage funds invest in fixed income markets. To capture all the exposures, we also consider Bond Market Indexes. Some fixed income arbitrage funds focus on a specific segment of the fixed income market. Therefore, we also retain indexes describing fixed income funds interested in investment grade issues, and high yield and Mortgage Backed Securities. We also consider the company default rate as it may have an impact on strategies based on company events such as event-driven strategies, distressed securities, and convertible and fixed income arbitrage. To portray managed futures style, we consider the currency and commodity markets. Finally, we introduce the VIX to depict strategies, in particular convertible arbitrage, as some funds take long positions on volatility. In addition, the use of non directional factors aims to replicate underlying risk factors in arbitrage strategies. These funds seek to

4 Directional factors refer to stock, exchange, obligation and commodities returns, while non directional factors refer to returns associated with derivatives. 5 An exhaustive list of risk factors is presented in Appendix B.

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Table 1 Hedge fund strategiesa. Directional strategies

Arbitrage strategies

Specific situation strategies

Long short equity Global macro Emerging markets Dedicated short bias Managed futures

Convertible arbitrage Equity market neutral Fixed income arbitrage

Event-driven

a

See Appendix A for more details about these strategies.

benefit from the evolution of a spread by simultaneously taking long and short positions on similar securities. A long position is taken on an underpriced security and a short position on an overpriced one. The factors under consideration are Small Minus Big (SMB) and High Minus Low (HML), identified by Fama and French (1992). These factors reflect a significant part of hedge fund returns associated with investment in stock markets. SMB is the spread between small cap and large cap returns. In practice, a long position is taken on a small cap as its return is expected to increase, and the same is true for value companies that are expected to gain value. However, growth company securities and large cap are more liquid and easier to sell, explaining why a short position is often preferred. We also consider the Momentum factor introduced by Carhart (1997). This is assimilated with the spread between the bestperforming securities on the NYSE, AMEX and NASDAQ over the last twelve months and the worst-performing securities on the same markets. A long position is taken on the best securities and a short position on the worst. To capture the underlying risks of fixed income arbitrage funds, we consider the variations of different return and interest rate spreads. We also introduce the one-month US Eurodollar deposit to consider deposits in cash. Indeed, most funds use short selling which largely involves a deposit in cash. All in all, these variables constitute the main risk factors for hedge funds and are also often referred to in the literature. Using stepwise regression, we selected only significant risk factors in order to eliminate further problems of colinearity (Agarwal and Naik, 2000). This method involves backward elimination through the introduction of whole variables, testing their significance and eliminating nonsignificant factors.

4.2. Preliminary results First, an analysis of the hedge fund return graphs (Appendix C) yields strong evidence of stationarity, shows cyclical movements inherent to hedge fund returns and indicates violent correction characterizing most hedge strategies over the last few years, reflecting further subprime effects. Second, from Appendix D, we note the high returns offered by hedge funds and their excess volatility. We also noted a leptokurtic and asymmetrical effect and the rejection of normality for several hedge fund strategies. The asymmetry, leptokurtic excess and non-normality are indicators of nonlinearity that can be induced by hedge fund characteristics (short selling, leverage, illiquid assets, etc.). This nonlinearity is also due to the fact that the performance fee structure is naturally asymmetrical as investors only have to pay it when returns exceed the previous high watermark. Gains are shared while losses are supported by investors. Our findings also point to evidence of strong heterogeneity between hedge fund strategies. In effect, while global macro is the most interesting strategy in terms of returns, fixed income arbitrage is the least interesting. The volatility associated with dedicated short bias and emerging markets is three times that of fixed income arbitrage and event-driven strategies. Leptokurtic and asymmetrical effects are more marked for certain strategies such as convertible arbitrage, and event-driven and fixed income arbitrage strategies.

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4.3. Nonlinear modeling of hedge fund return adjustment dynamics 4.3.1. Linear modeling First, the selection of risk factors for hedge fund returns by stepwise regression yields interesting results that are reported in Appendices E and F. Indeed, we note that the preselected factors are in line with each strategy but that they vary according to the strategy, confirming the heterogeneous nature of hedge fund investment and exposure to risk. Overall, we retain about 15 factors per strategy. Second, we investigate hedge fund exposure to risk in a linear framework and report the findings in Appendix E. For the Convertible Arbitrage Strategy, ML corporate and government master are significant and positive, suggesting significant exposure to the bond market. This is in line with managerial practices which tend to keep a long position on convertible bonds and particularly on investment grade bonds that represent a significant part of convertible bond issues. For the Dedicated Short Bias Strategy, managers tend to take a short position on stock markets, selling short overpriced securities and repurchasing later at a lower price. Thus, profits are made from negative shocks to the market, when prices fall, indicating that funds tend to have negative exposure to stock markets. This feature is depicted by negative exposure on S&P500 and SMB, but also positive exposure on HML. Indeed, managers tend to take a long position on small caps as their returns are expected to increase. Regarding the Emerging Market Strategy, here managers tend to invest in stocks and bonds from emerging market countries. As expected, funds are positively exposed on MSCI Emerging markets, SMB and HML indexes. Given that short selling is not permitted in emerging markets, we suppose that they sell short securities from developed countries. We also find positive exposure to investment grade bonds but negative exposure to junk bonds, which denotes a preference for less risky securities. It should be noted that emerging bonds are still considered risky compared to developed countries' bonds. In addition, funds are long on the JP Morgan EMBI global index and short on the JP Morgan US government bond index. They also exhibit negative exposure to the government bond spread, indicating that managers seek protection against interest rate risk. For the Equity Market Neutral Strategy, we note significant exposure to bond markets and spread returns rather than stock markets, while the Event Driven Strategy displays significant positive exposure to the S&P 500 and SMB indexes. Managers invest in undervalued securities that are expected to rise due to specific corporate events such as mergers, bankruptcies or restructuring. We also note negative exposure to government bond spread along with a positive weight on corporate bond spread. This suggests that funds are borrowed in the domestic market and invested in financially distressed firms internationally. The Fixed Income Arbitrage Strategy attempts to benefit from pricing inefficiencies between related fixed income securities while hedging exposure to interest rate risk. Fixed income arbitrage funds invest in convertible bonds, high yield bonds (i.e. non-investment grade debt) and mortgage backed securities. Managers may adopt a long-only strategy so they are naturally exposed to fixed income indexes. Our findings show positive exposure to high yield indexes. Managers also focus on spread trading, which means exposure to a difference between two bond index returns. They exhibit a negative weight to government bond spread, highlighting a convergence trading strategy, meaning that managers prefer to invest in US bonds rather than international ones. They also exhibit a positive weight to the corporate-treasury spread and a negative one to the mortgage-treasury rate. The Global Macro Strategy is specific in that it operates in international markets in addition to its exposure to domestic US equities. Thus, we show a significant and positive style weight to the JP Morgan global government, excluding the US index and investment grade

bonds. This strategy also displays positive exposure to the MOM factor, revealing its ability to act as market timers (Gregoriou, 2004). For the Long Short Equity Strategy, by definition managers keep a net long position. Our results are in line with this strategy as long exposure to S&P500, SMB and MOM indexes is highlighted. Managers take a long position to small caps as their returns are expected to increase. Furthermore, they prefer to invest in securities exhibiting past positive returns and going short on those displaying negative past returns. This strategy also points to negative exposure to HML, meaning that managers would rather invest in growth securities and short value securities. We also note long exposure to emerging market equities, which is consistent with a long-only strategy and with the prohibition of short selling. Regarding the Managed futures strategy, trend-following managers typically invest in different futures contracts, tracking various commodity, currency, fixed income and equity markets. As expected, we found exposure to stock, bond and currency markets. Funds are negatively exposed on the S&P500 and display positive weights on GSCI commodity spots, HML, MOM, and the US bond market, revealing the capacity to benefit from significant increases in the US stock market. Finally, with respect to the Multi-strategy, investors appear to take advantage of their ability to invest in several hedge fund strategies. We thus establish exposure to stock, bond and currency markets. A negative weight on the emerging bond markets is highlighted and we denoted a positive weight on high yield bonds, global stock markets, GSCI commodity spots, corporate-treasury spread and the MOM factor. After specifying the risk factors underlying hedge fund strategy exposures, we checked this relationship in a nonlinear framework. We tested whether the introduction of nonlinearity could improve the modeling of hedge fund exposure towards risk factors and whether this relationship would vary according to regime and over time. 4.3.2. Linearity tests In addition to the justification of nonlinearity by intrinsic hedge fund characteristics, the implementation of linearity tests is required to check nonlinearity in the data. To this end, we applied the linearity tests of Luukkonen et al. (1988) and report the main results in Table 2. 6 Our findings reveal strong evidence of nonlinearity for most hedge fund strategies. Therefore, linearity is not rejected against the STR model, but only for convertible arbitrage and event-driven strategies. The exposure of other hedge fund strategies towards risk seems a priori to exhibit nonlinearity and to be appropriately apprehended through STR modeling. All the preselected risk factors were candidates as transition variables for linearity tests. Table 3 reports the optimal values for which the rejection of linearity is strongest. Our findings indicate that transition variables also vary according to hedge fund strategy, but that they are often in line with the underlying strategy. Regarding the transition function, our findings show the superiority of exponential functions to characterize the transition between hedge fund regimes. We thus focused on ESTR modeling to characterize hedge fund exposure to risk factors. This result is in line with previous studies that often apply ESTR model to apprehend the dynamics and properties of financial time-series. 4.3.3. ESTR modeling 4.3.3.1. Estimated results. We estimated ESTR models using the NLS method and reported the main results in Appendix G. Overall, this

6

See also Van Dijk et al. (2002) for more details about these tests.

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018 Table 2 Linearity test (p-values). Hedge fund strategies

Probability

Convertible arbitrage Dedicated short bias Emerging markets Equity market neutral Event-driven Fixed income arbitrage Global macro Long short equity Managed futures Multi-strategy

0.43 0.00 0.00 0.09 0.57 0.02 0.07 0.10 0.00 0.01

Table 3 Transition variables. Hedge fund strategies

Transition variable

Dedicated short bias Emerging markets Equity market neutral Fixed income arbitrage Global macro Long short equity Managed futures Multi-strategy

MSCI WORLD MSCI EMERGING MARKETS MSCI WORLD ML CORP MASTER—JPM UNITED STATES GOVT BOND JPM EMBI GLOBAL JPM EMBI GLOBAL S&PCOMPOSITE ML CORP MASTER—JPM UNITED STATES GOVT BOND

modeling yields evidence of asymmetrical and nonlinear time-varying adjustment for hedge funds, while pointing to the presence of extreme regimes as well as a continuum of intermediate states for hedge funds. Indeed, the parameters associated with the transition speed and the threshold coefficient (b and c) are statistically significant either at 5% or 10% for most strategies, confirming the appropriateness of the ESTR model to characterize hedge fund return dynamics. Furthermore, the transition speed estimate is relatively weak for most hedge fund strategies, suggesting some smoothness in the transition between hedge fund regimes and showing the superiority of ESTR towards linear models and other nonlinear models. Emerging markets and long short equity, however, exhibit a high value of b, suggesting more abrupt adjustment. Our results also indicate significant structural breaks in hedge fund dynamics and thus in their exposure to risk factors. These findings confirm the fact that exposure to risk is time-varying and that managers continuously revise their strategies and positions according to the regimes and to evolutions in bond and capital markets. Furthermore, while attempting to locate the transition between regimes, we noted that the transition occurred on 12/31/1997 for dedicated short bias (Asian crisis), 7 on 03/31/1998 for the emerging markets, on 05/30/2008 for equity market neutral (global crisis), on 09/30/1999 for fixed income arbitrage (Russian crisis), on 11/30/2001 for global macro (US crisis), on 03/29/2002 for long short equity, on 06/30/1995 for managed futures and on 05/31/1995 for multi-strategy. The switching regime also varies according to hedge fund strategy, but is in line with its underlying determinants and corresponds to a financial crisis that occurred on the same date. For hedge fund exposure to risk, the relationship also varies according to the regime, and the introduction of nonlinearity improves the study significantly. Indeed, according to Appendix G, we show that some factors significantly and symmetrically affect the hedge fund industry as they are activated per regime, indicating that managers revise and adjust their strategies according to the stage in the economic cycle. Investors also tend to react differently in their arbitrage in periods of

7

We have noted the name of the crisis that occurred in the same year.

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crisis and in periods of growth. The main finding of this paper is the characterization of hedge fund exposure to risk factors through an on/off model that identifies an explosive local regime and a nonlinear mean-reverting cycle, for which the transition between these different regimes depends on the risk factor deviation size toward equilibrium. In particular, in the normal (central) regime, hedge funds can provide high returns, but an extreme event can make hedge funds vulnerable and a detachment from this normal regime is observed. To illustrate these regimes on a graph, we plotted the estimated transition functions against the transition variable and highlighted different regimes for hedge fund returns (Appendix I). Thus, the analysis of the estimated transition functions shows that the latter do not reach the unit for most strategies, also indicating the importance of persistence and nonlinearity associated with hedge fund adjustments. These results also indicate that the hedge fund returns dynamic and their exposure to risk varies according to regimes and this is specific to hedge fund strategy. All in all, our findings show that hedge fund adjustment dynamics exhibit nonlinearity, persistence, asymmetry and time-variance. They also indicate that ESTR modeling can supplant linear modeling to characterize hedge fund strategy exposure to risk factors, and identify the exposure of hedge funds to risk differently according to regimes.

4.3.3.2. Validation. Finally, we checked the robustness of our modeling while testing the robustness of ESTR modeling through the application of several misspecifications. We report the main results in Appendixes H and I. The nonlinear residuals show the appropriate statistical properties as they are stationary and do not reveal an ARCH effect. The ratio of residual variances is significantly less than one, indicating that the introduction of nonlinearity considerably reduced the residual variance and improved the study of hedge fund return dynamics. In addition, in Appendix I, we note that nonlinear residuals are less volatile than linear residuals, confirming the superiority of ESTR specification toward a linear model.

5. Conclusion This paper investigates hedge fund exposure to multiple sources of risk factors for several strategies and makes several contributions to the hedge fund literature. First, our findings enable us to specify the relationship between hedge fund returns and the risk factors occurring in diverse hedge fund strategies. Second, our results illustrate the fact that the dynamics of hedge fund returns and their relationship with risk factors exhibit nonlinearity and asymmetry. They also show that the extension of the study of these relationships to a nonlinear framework improves the modeling of hedge fund exposure to risk. In particular, our results show not only that the relationship between hedge funds and risk factors varies over time and depends on the regime: expansion, crisis, etc., but also that investors should keep a close eye on the variations in the main macroeconomic and financial time-series (interest rates, stock prices, etc.). Of course, improving this nonlinear specification in capturing the exposure of hedge funds to risk is particularly interesting and provides informative policy implications for investors while helping them to better understand the effects of economic changes and financial variables on the hedge fund industry, and to forecast their impact on the relationship between hedge funds and risk for the most important hedge fund strategies. Finally, this study supports the superiority of an on/off nonlinear adjustment model to capture the evolution of hedge fund exposure to risk and to prepare for the hedge funds reaction in periods of financial crisis. This study may also be extended by addressing whether ESTR models can over-fit the data and outperform linear model in terms of forecasting the future dynamics of hedge funds.

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Appendix A. Description of hedge fund strategies. The 10 CSFB/Tremont indexes are based on 10 different hedge fund investment styles: –Convertible arbitrage (CA): Managers typically build long positions of convertible bonds and then hedge the equity component of the long securities positions by shorting the underlying stock or options;

–Dedicated short bias (DSB): Managers take more short positions than long positions and earn returns by maintaining net short exposure in equities; –Emerging markets (EM): Managers invest in currencies, debt instruments, equities and other instruments of emerging countries; –Equity market neutral (EMN): Managers take both long and short positions in stocks while minimizing exposure to the systematic risk of the market (i.e. a beta of zero is desired); –Event-driven (ED): Managers invest in various asset classes and seek to benefit from potential mispricing of securities related to a specific corporate event such as mergers, bankruptcies or restructuring; –Fixed income arbitrage (FIA): Managers attempt to generate profit by exploiting inefficiencies and price anomalies between related fixed income securities; –Global macro (GM): Managers generate profit by correctly anticipating price movements in global markets, with the ability to hold positions in practically any market with any instrument; –Long/short equity (LSE): Managers invest in both long and short sides of equity markets, generally focusing on diversifying or hedging across particular sectors, regions or market capitalizations; –Managed futures (often referred to as CTAs or Commodity Trading Advisors) (MF): Managers focus on investing in listed bond, equity, commodity futures and currency markets; –Multi-strategy (MS): Managers are characterized by their ability to allocate capital based on perceived opportunities from several hedge fund strategies.

Appendix B. List of risk factors considered Factors Directional factors MSCI WORLD EXCLUDE US S&PCOMPOSITE MSCI EMERGING MARKETS JPM UNITED STATES GOVT BOND JPM GLOBAL GOVT BND exclude USA JPM EMBI GLOBAL ML CORP & GVT MASTER ML CORP MASTER ML US HIGH YIELD MASTER ML US MORT MASTER DEFAULT RATE-ALL CORPORATE BONDS US DEFAULT RATE-ALL US CORPORATE BONDS DEFAULT RATE-ALL NON US CORPORATE BONDS TRADE WEIGHTED DOLLAR INDEX S&P GSCI COMMODITY SPOT CBOE SPX VOLATILITY VIX US EURODOLLAR DEPOSIT: 1 MTH Non directional factors SMB (Small Minus Big) HML (High Minus Low) MOM (Momentum) JPM GLOBAL GOVT BOND exclude USA—JPM UNITED STATES GOVT BOND JPM EMBI GLOBAL—JPM UNITED STATES GOVT BOND ML CORP MASTER—JPM UNITED STATES GOVT BOND ML HIGH YIELD MASTER—JPM UNITED STATES GOVT BOND ML US MORT MASTER—JPM UNITED STATES GOVT BOND US BOND YIELD CORPORATE—US TREASURY 10 YEARS FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS US TREASURY 3 YEARS—US TREASURY 10 YEARS US BOND YIELD CORPORATE—US TREASURY 10 YEARS FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS US TREASURY 3 YEARS—US TREASURY 10 YEARS a

Description MSCI World exclude US S&P500 MSCI World Emerging Markets JP Morgan US Government Bond JP Morgan Global Government Bond exclude US JP Morgan Emerging Bond Market Merrill lynch Corporate and Government Master Merrill Lynch Corporate Master Merrill Lynch US High Yield Master Merrill Lynch US Mortgage Backed Securities Master Company default rate

Trade Weighted Dollar Index S&P GSCI Commodity Spot VIX One-month US Eurodollar deposita Small Minus Big High Minus Low Momentum Variations of different return spreads

Variations of different interest rate spreads

This factor is introduced so as to consider deposits in cash. Indeed, most funds use short selling, which involves a deposit in cash, in particular.

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018

1009

Appendix C. Hedge fund returns graphs

.25

.08

.20

.04

.15 .00 .10 -.04 .05 -.08

.00

-.12

-.05 -.10

-.16 1994

1996

1998

2000

2002

2004

2006

1994

2008

1996

1998

2000

2002

2004

2006

2008

2004

2006

2008

DSB

CA .04

.2

.1 .00 .0 -.04 -.1 -.08 -.2

-.3

-.12 1994

1996

1998

2000

2002

2004

2006

2008

1994

1996

1998

2000

2002 EM

ED .04

.04

.03 .00 .02 -.04 .01 -.08 .00 -.12

-.01

-.02

-.16 1994

1996

1998

2000

2002 EMN

2004

2006

2008

1994

1996

1998

2000

2002 FIA

2004

2006

2008

1010

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018

.15

.12

.10

.08

.05

.04

.00

.00

-.05

-.04

-.10

-.08

-.15

-.12 1994

1996

1998

2000

2002

2004

2006

1994

2008

1996

1998

2000

2004

2006

2008

2004

2006

2008

M

LS E .12

.04

.08

.02

.04

.00

.00

-.02

-.04

-.04

-.08

-.06

-.08

-.12 1994

1996

1998

2000

2002

2004

2006

1994

2008

1996

1998

2000

2002 MS

MF

Q11

2002

Appendix D. Descriptive statistics of hedge fund returns

Mean Median Maximum Minimum Std. Dev. Return Volatility Skewness Kurtosis Jarque-Bera Probability

CA

DSB

EM

EMN

ED

FIA

GM

LSE

MF

MS

0.01 0.01 0.06 − 0.13 0.02 5.87% 6.92% − 3.31 21.17 2852.52 0.00

0.00 0.00 0.23 − 0.09 0.05 − 0.69% 16.93% 0.75 4.61 37.19 0.00

0.01 0.01 0.16 − 0.23 0.05 6.58% 15.75% − 0.73 7.55 174.01 0.00

0.01 0.01 0.03 − 0.02 0.01 9.36% 2.89% 0.14 3.77 5.06 0.08

0.01 0.01 0.04 − 0.12 0.02 9.42% 6.08% − 2.65 17.31 1775.48 0.00

0.00 0.01 0.02 − 0.14 0.02 3.62% 5.96% − 4.62 32.47 7271.26 0.00

0.01 0.01 0.11 − 0.12 0.03 12.45% 10.49% − 0.03 6.00 68.70 0.00

0.01 0.01 0.13 − 0.11 0.03 9.58% 10.16% 0.03 6.46 91.10 0.00

0.01 0.00 0.10 − 0.09 0.03 6.89% 11.84% 0.01 3.11 0.10 0.95

0.01 0.01 0.04 − 0.07 0.02 7.25% 5.47% − 1.89 9.31 405.85 0.00

Appendix E. Stepwise regression results Stepwise regression CA Directional factors MSCI WORLD EXCLUDE US MSCI WORLD EXCLUDE US S&PCOMPOSITE MSCI EMERGING MARKETS JPM GLOBAL GOVT BND exclude USA JPM UNITED STATES GOVT BOND

DSB

EM

✓ ✓ ✓

EMN ✓ ✓ ✓

✓ ✓

✓

ED

✓ ✓

FIA

GM

LSE

MF

✓

✓ ✓ ✓ ✓

✓ ✓

MS

✓

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018

1011

Appendix (continued) E (continued) Stepwise regression CA JPM EMBI GLOBAL ML CORP & GVT MASTER ML CORP MASTER ML US HIGH YIELD MASTER ML US MORT MASTER DEFAULT RATE-ALL CORPORATE BONDS US DEFAULT RATE-ALL US CORPORATE BONDS DEFAULT RATE-ALL NON US CORPORATE BONDS TRADE WEIGHTED DOLLAR INDEX S&P GSCI COMMODITY SPOT CBOE SPX VOLATILITY VIX US EURODOLLAR DEPOSIT: 1 MTH Non directional factors SMB HML MOM JPM GLOBAL GOVT BOND exclude USA—JPM UNITED STATES GOVT BOND JPM EMBI GLOBAL—JPM UNITED STATES GOVT BOND ML CORP MASTER—JPM UNITED STATES GOVT BOND ML HIGH YIELD MASTER—JPM UNITED STATES GOVT BOND ML US MORT MASTER—JPM UNITED STATES GOVT BOND US BOND YIELD CORPORATE—US TREASURY 10 YEARS FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS US TREASURY 3 YEARS—US TREASURY 10 YEARS US BOND YIELD CORPORATE—US TREASURY 10 YEARS FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS US TREASURY 3 YEARS—US TREASURY 10 YEARS Note: “✓” denotes significant risk factors according to the stepwise test.

DSB

EM

EMN

ED

FIA

✓ ✓ ✓

✓ ✓ ✓

✓

✓ ✓ ✓

✓ ✓

✓ ✓

✓ ✓

✓ ✓ ✓

✓ ✓ ✓

✓ ✓

✓

✓ ✓ ✓ ✓

✓ ✓

GM

LSE

✓

✓

✓

✓

✓

✓

✓ ✓ ✓

✓ ✓ ✓ ✓

✓

✓

✓

✓

✓ ✓

✓ ✓

✓ ✓ ✓ ✓

✓

✓

✓

✓ ✓ ✓

✓ ✓

✓ ✓ ✓

MS

✓

✓ ✓

MF

✓ ✓

✓ ✓

✓

✓ ✓

1012

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018

Appendix F. Linear model estimations 8 Linear model

CA

DSB

EM

EMN

ED

FIA

GM

LSE

MF

MS

Centered-R² Regression-F Significance-Level-of-F Durbin–Watson-Statistic Constant

0.62 21.36 0.00 1.16 − 0.00 (− 0.22)

0.73 52.90 0.00 1.84 0.00 (0.67)

0.74 56.08 0.00 1.65 0.00 (0.17)

0.25 6.36 0.00 1.38 0.01 (10.44)

0.65 29.46 0.00 1.44 0.00 (4.40)

0.56 24.28 0.00 1.41 − 0.00 (− 1.12)

0.30 10.54 0.00 1.76 0.01 (3.11)

0.84 53.80 0.00 1.76 0.00 (1.88)

0.20 6.35 0.00 1.95 0.01 (3.98)

0.51 25.07 0.00 1.79 0.00 (4.43)

0.13 (4.31) 0.05 (2.21)

0.10 (2.36)

− 0.98 (− 1.90) 0.57 (2.09) 0.78 (3.12) 0.06 (2.05)

0.10 (3.37)

0.10 (1.38)

0.05 (1.48)

− 0.14 (− 5.20)

− 0.07 (− 1.05)

0.19 (3.23)

Directional factors MSCI WORLD EXCLUDE US MSCI WORLD EXCLUDE US S&PCOMPOSITE

− 0.27 (− 0.92) 0.17 (1.09) 0.18 (1.28)

0.18 (1.23) 0.07 (1.41) − 0.05 (− 1.06)

− 0.91 (− 6.33)

MSCI EMERGING MARKETS

0.45 (10.95)

JPM UNITED STATES GOVT BOND JPM EMBI GLOBAL 0.10 (1.11)

ML CORP MASTER − 0.24 (− 1.65)

ML US HIGH YIELD MASTER ML US MORT MASTER DEFAULT RATE-ALL CORPORATE BONDS US DEFAULT RATE-ALL US CORPORATE BONDS DEFAULT RATE-ALL NON US CORPORATE BONDS TRADE WEIGHTED DOLLAR INDEX S&P GSCI COMMODITY SPOT CBOE SPX VOLATILITY VIX US EURODOLLAR DEPOSIT: 1 MTH Non directional factors SMB

− 0.18 (− 1.78) 0.03 (1.60) 0.02 (2.12)

0.04 (1.13)

HML

JPM GLOBAL GOVT BOND exclude USA -JPM UNITED STATES GOVT BOND JPM EMBI GLOBAL—JPM UNITED STATES GOVT BOND

− 0.24 (− 4.10)

ML CORP MASTER—JPM UNITED STATES GOVT BOND

1.24 (9.83)

ML HIGH YIELD MASTER—JPM UNITED STATES GOVT BOND ML US MORT MASTER—JPM UNITED STATES GOVT BOND US BOND YIELD CORPORATE—US TREASURY 10 YEARS FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS

FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS US TREASURY 3 YEARS—US TREASURY 10 YEARS The values in brackets refer to the t-ratio statistics.

8

The values in brackets refer to the t-ratio statistics.

0.36 (1.65) − 0.13 (− 1.18) − 0.41 (− 1.20)

1.29 (1.43) − 1.16 (− 1.35) 0.14 (2.38)

0.11 (2.24) − 0.03 (− 0.79) − 0.24 (− 2.33)

− 0.15 (− 2.83)

0.05 (3.76)

− 0.47 (− 7.11) 0.19 (3.68)

0.01 (1.28)

− 0.38 (− 1.03)

− 0.22 (− 2.51) 0.07 (4.73) 0.02 (2.93)

0.01 (0.61)

0.03 (1.91) 0.02 (2.64)

0.13 (3.31) − 0.37 (− 3.90)

0.24 (6.52) − 0.18 (− 4.87) 0.15 (5.23) − 0.09 (− 1.70)

− 0.22 (− 4.35)

0.48 (5.40)

1.37 (2.74)

0.63 (4.01)

− 0.30 (− 1.01)

−

0.35 (− 2.36)

0.03 (1.24)

− 0.03 (− 2.49)

− 0.12 (− 1.96) 1.14 (3.75)

0.11 (1.96)

0.02 (1.48) 0.01 (2.29)

0.62 (3.07)

0.12 (4.16) 0.06 (1.93) 0.08 (3.22) − 0.09 (− 2.20)

MOM

US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS US TREASURY 3 YEARS—US TREASURY 10 YEARS US BOND YIELD CORPORATE—US TREASURY 10 YEARS

− 0.10 (− 1.33) 0.07 (1.36)

− 0.06 (− 1.70)

JPM GLOBAL GOVT BND exclude USA

ML CORP & GVT MASTER

0.08 (2.88)

0.13 (3.59) − 0.34 (3.96) 0.36 (5.55)

0.02 (1.61) − 0.02 (− 1.56) − 0.03 (− 1.12) − 0.00 (− 1.28)

− 0.04 (− 2.89) 0.02 (1.51)

0.07 (1.69)

0.09 (1.13) 0.13 (2.00) 0.21 (1.91)

0.04 (2.58) 0.01 (1.13)

0.04 (2.11)

0.58 (4.62) − 1.35 (− 4.64)

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018

1013

Appendix . Estimation results of ST model 9 ESTR model

DSB

EM

EMN

FIA

GM

LSE

MF

MS

Centered-R² Regression-F Significance-Level-of-F Durbin–Watson-Statistic B

0.80 30.48 0.00 2.02 0.25 (1.37) 0.01 (1.64) 0.01 (2.66) − 0.02 (− 1.11)

0.78 27.69 0.00 1.79 4.16 (2.14) 0.04 (7.60) 0.02 (1.96) − 0.02 (− 1.95)

0.36 4.36 0.00 1.49 0.66 (1.48) 0.01 (1.88) 0.01 (6.39) 0.00 (0.82)

0.71 18.66 0.00 1.41 0.33 (1.85) 0.01 (5.36) 0.01 (1.72) − 0.03 (− 3.40)

0.44 7.75 0.00 1.79 0.29 (1.22) − 0.01 (− 2.24) 0.01 (2.33) 0.01 (0.58)

0.87 26.98 0.00 1.76 41.92 (2.04) 0.00 (0.54) 0.01 (1.31) − 0.01 (− 0.79)

0.34 4.93 0.00 1.98 0.56 (1.93) 0.02 (2.10) 0.00 (0.52) − 0.00 (− 0.17)

0.56 12.34 0.00 1.83 0.89 (1.92) 0.02 (6.21) 0.02 (2.64) − 0.02 (− 2.39)

0.11 (2.15) − 0.24 (− 0.93)

7.14 (1.60) − 8.62 (− 1.89) − 3.87 (− 1.63) 4.72 (1.96) − 3.13 (− 1.38) 4.16 (1.80) 0.15 (1.15) − 0.10 (− 0.72)

0.15 (1.10) 0.03 (0.11)

− 1.51 (− 1.22) 1.53 (1.24)

− 0.09 (− 1.31) − 0.06 (− 0.65)

0.54 (1.03) − 0.60 (− 1.11)

0.19 (1.26) 0.02 (0.11)

C Constant (L) Constant (NL)

Directional factors MSCI WORLD (L) MSCI WORLD (NL)

− 0.24 (− 1.21) 1.68 (1.63)

− 0.49 (− 1.06) − 0.54 (− 0.56) 0.34 (1.38) 0.09 (0.19) 0.22 (0.98) 0.45 (0.90)

MSCI WORLD EXCLUDE US (L) MSCI WORLD EXCLUDE US (NL) S&PCOMPOSITE (L) S&PCOMPOSITE (NL)

− 0.69 (− 4.12) − 1.21 (− 1.21)

MSCI EMERGING MARKETS (L)

0.03 (0.12) 0.45 (1.77)

MSCI EMERGING MARKETS (NL) JPM GLOBAL GOVT BOND exclude USA (L)

JPM UNITED STATES GOVT BOND (L) JPM UNITED STATES GOVT BOND US (NL) JPM EMBI GLOBAL (L) JPM EMBI GLOBAL (NL) ML CORP & GVT MASTER (L) ML CORP & GVT MASTER (NL) ML CORP MASTER (L) ML CORP MASTER (NL)

ML US HIGH YIELD MASTER II (NL) ML US MORT MASTER (L) ML US MORT MASTER (NL)

− 0.29 (− 1.31) 0.35 (0.66)

− 1.65 (− 1.87) 2.55 (2.71) 0.81 (2.08) − 1.19 (− 2.87) 2.27 (1.68) − 3.30 (− 2.29)

DEFAULT RATE-ALL CORPORATE BONDS (L) DEFAULT RATE-ALL CORPORATE BONDS (NL) US DEFAULT RATE-ALL US CORPORATE BONDS (L) US DEFAULT RATE-ALL US CORPORATE BONDS (NL) DEFAULT RATE-ALL NON US CORPORATE BONDS (L) DEFAULT RATE-ALL NON US CORPORATE BONDS (NL) TRADE WEIGHTED DOLLAR INDEX (L)

− 0.10 (− 1.21) 0.43 (2.85) 0.09 (1.16) − 0.20 (− 1.89)

S&P GSCI COMMODITY SPOT (L) S&P GSCI COMMODITY SPOT (NL)

9

The values in brackets refer to the t-ratio statistics.

− 0.01 (− 0.49)

− 0.55 (− 0.52) 7.67 (2.44) 0.47 (0.47) − 6.67 (− 2.25) 0.18 (2.04) − 0.24 (− 1.12)

0.41 (1.22) 1.46 (1.20)

0.25 (0.47) − 3.71 (− 1.46)

− 0.01 (− 0.16) − 0.37 (− 2.02)

TRADE WEIGHTED DOLLAR INDEX (NL)

CBOE SPX VOLATILITY VIX (L)

0.33 (1.61) − 0.38 (− 1.22) 0.20 (2.92) − 0.44 (− 2.60)

0.04 (0.72) − 0.26 (− 2.12)

JPM GLOBAL GOVT BOND exclude USA (NL)

ML US HIGH YIELD MASTER (L)

0.18 (2.54) − 0.20 (− 2.22)

0.01 (1.22)

− 0.02 (− 0.23) − 0.51 (− 1.65) 0.01 (0.55) 0.23 (2.87) 0.01 (1.45)

0.02 (0.88)

0.01 (0.15) 0.02 (0.21) 0.06 (1.55)

0.08 (1.41) 0.07 (0.55)

− 0.04 (− 0.85) 0.11 (2.12) 0.01 (0.46)

1014

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018

Appendix (continued) (continued) ESTR model

DSB

CBOE SPX VOLATILITY VIX (NL) US EURODOLLAR DEPOSIT: 1 MTH (L) US EURODOLLAR DEPOSIT: 1 MTH (NL) Non directional factors SMB (L)

− 0.57 (− 6.91) 0.84 (1.58) 0.23 (3.43) − 0.26 (− 0.97)

SMB (NL) HML (L) HML (NL) MOM (L) MOM (NL) JPM GLOBAL GOVT BOND exclude USA—JPM UNITED STATES GOVT BOND (L) JPM GLOBAL GOVT BOND exclude USA—JPM UNITED STATES GOVT BOND (NL) JPM EMBI GLOBAL—JPM UNITED STATES GOVT BOND (L)

0.05 (0.63) − 0.61 (− 2.22) − 0.08 (− 0.15) 0.83 (0.74)

JPM EMBI GLOBAL—JPM UNITED STATES GOVT BOND (NL) ML CORP MASTER—JPM UNITED STATES GOVT BOND (L) ML CORP MASTER—JPM UNITED STATES GOVT BOND (NL) ML HIGH YIELD MASTER—JPM UNITED STATES GOVT BOND (L) ML HIGH YIELD MASTER—JPM UNITED STATES GOVT BOND (NL) ML US MORT MASTER—JPM UNITED STATES GOVT BOND (L)

EM

EMN

FIA

GM

LSE

0.09 (2.48)

− 0.01 (− 0.47)

0.02 (1.16)

− 0.05 (− 0.63)

− 0.04 (− 1.09)

0.12 (2.06) − 0.08 (− 0.40) 0.15 (1.03) − 2.72 (− 2.04)

0.18 (0.89) 0.06 (0.29) 0.40 (1.30) − 0.62 (− 1.95) 0.29 (1.31) − 0.18 (− 0.78) 0.37 (1.29) − 0.53 (− 1.78)

− 0.04 (− 0.31) 0.19 (1.03)

0.08 (0.87) 0.02 (0.14) − 0.35 (− 1.60) 0.03 (0.09) − 0.12 (− 0.68) 0.57 (2.85)

− 0.06 (− 1.16) − 0.78 (− 2.90)

0.13 (0.23) 4.17 (2.42)

− 1.54 (− 1.24) 1.12 (0.88)

US BOND YIELD CORPORATE—US TREASURY 10 YEARS (L) US BOND YIELD CORPORATE—US TREASURY 10 YEARS (NL) FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS (L)

− 0.02 (− 1.29) − 0.06 (− 1.42)

0.00 (− 0.11) 0.23 (1.31)

FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS (NL)

0.27 (2.23) − 0.36 (− 1.72) 0.19 (1.85) − 0.07 (− 0.34) 0.23 (1.52) 0.02 (0.04)

0.02 (0.63) − 0.01 (− 0.19)

− 1.36 (− 1.64) 2.02 (2.36)

− 1.49 (− 3.28) 0.40 (0.47)

− 0.10 (− 1.69) 0.06 (0.89) 0.07 (0.90) − 0.05 (− 0.67)

US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS (L) US CORPORATE BOND MOODYS S'ND BAA - US TREASURY 10 YEARS (NL) US TREASURY 3 YEARS—US TREASURY 10 YEARS (L) US TREASURY 3 YEARS—US TREASURY 10 YEARS (NL) US BOND YIELD CORPORATE—US TREASURY 10 YEARS (L) US BOND YIELD CORPORATE—US TREASURY 10 YEARS (NL) FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS (L) FHA MORTGAGE RATE—US TREASURY BOND 10 YEARS (NL) US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS (L) US CORPORATE BOND MOODYS S'ND BAA—US TREASURY 10 YEARS (NL) US TREASURY 3 YEARS—US TREASURY 10 YEARS (L)

MS − 0.01 (− 0.30)

1.34 (1.52) − 0.75 (− 0.81)

0.13 (0.33) 0.34 (0.23)

ML US MORT MASTER—JPM UNITED STATES GOVT BOND (NL)

MF

− 0.00 (− 1.46) 0.00 (0.16)

US TREASURY 3 YEARS—US TREASURY 10 YEARS (NL) The values in brackets refer to the t-ratio statistics.

Appendix H. Statistical properties of EST residuals ESTR model

DSB

EM

EMN

FIA

GM

LSE

MF

MS

Jarque-Bera P-value (Variance-ESTR/Variance-L) DF–T-test-statistic Chi-squared(2) P-value

2.60 0.27 0.75 − 9.28 1.94 0.38

18.95 0.00 0.85 − 7.39 3.14 0.21

0.30 0.86 0.85 − 5.85 19.37 0.00

326.48 0.00 0.66 − 7.13 19.34 0.00

22.02 0.00 0.79 − 9.62 0.64 0.72

8.20 0.02 0.67 − 8.00 0.12 0.94

7.16 0.03 0.83 − 10.80 0.42 0.81

22.15 0.00 0.89 − 5.86 10.14 0.01

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018

1015

Appendix I. Linear and nonlinear residual graphs

Transition Function

DSB 0.010

0.075

0.008

0.050

RESL RESESTR

0.025

0.006

0.000 0.004 -0.025 0.002 -0.050 0.000 -0.20

-0.15

-0.10

-0.05

-0.00

0.05

0.10

-0.075

Transition variable

1994

1996

1998

2000

2002

2004

2006

2008

fonction de transition

EM 0.40

0.100

0.35

0.075

0.30

0.050

0.25

0.025

0.20

-0.000

0.15

-0.025

0.10

-0.050

RES RESESTR

-0.075

0.05

-0.100

0.00 -0.3

-0.2

-0.1

0.0

0.1

0.2

-0.125

variable de transition

1994

1996

1998

2000

2002

2004

2006

2008

EMN 0.03

0.0225

RESL RESESTR

0.0200 0.02

Transition Function

0.0175 0.0150

0.01

0.0125 0.00

0.0100 0.0075

-0.01 0.0050 0.0025

-0.02

0.0000 -0.20

-0.15

-0.10

-0.05

-0.00

Transition variable

0.05

0.10

-0.03 1994

1996

1998

2000

2002

2004

2006

2008

1016

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018 FIA 0.03

1.00

RESL RESESTR

Transition Function

0.02 0.01

0.75

0.00 -0.01

0.50

-0.02 -0.03

0.25

-0.04 -0.05

0.00 -0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

-0.06

Transition variable

1994

1996

1998

2000

2002

2004

2006

2008

GM

Transition Function

0.0200

0.100

0.0175

0.075

0.0150

0.050

0.0125

0.025

0.0100

-0.000

0.0075

-0.025

0.0050

-0.050

0.0025

-0.075

RESL RESESTR

-0.100

0.0000 -0.3

-0.2

-0.1

0.0

0.1

0.2

-0.125

Transition variable

1994

1996

1998

2000

2002

2004

2006

2008

LSE 1.00

0.050

Transition Function

0.75

RESL RESESTR

0.025

0.50 0.000

0.25 -0.025

0.00 -0.3

-0.2

-0.1

0.0

Transition variable

0.1

0.2

-0.050 1994

1996

1998

2000

2002

2004

2006

2008

F. Jawadi, S. Khanniche / Economic Modelling 29 (2012) 1003–1018

1017

MF 0.0225

0.100

0.0200

0.075

0.0175

0.050

Transition Function

RESL

0.0150

RESESTR

0.025

0.0125 -0.000 0.0100 -0.025 0.0075 -0.050 0.0050 -0.075 0.0025 -0.100

0.0000 -0.20

-0.15

-0.10

-0.05

-0.00

0.05

0.10

-0.125 1994

Transition variable

1996

1998

2000

2002

2004

2006

2008

MS 0.6 0.04 RESL RESESTR

Transition Function

0.5

0.03

0.02

0.4

0.01 0.3 0.00 0.2 -0.01

0.1

-0.02

-0.03 0.0 -0.08

-0.06

-0.04

-0.02

0.00

0.02

Transition variable

eference s Agarwal, V., Naik, N., 2000. Generalized style analysis of hedge funds. Journal of Asset Management 1, 93–109. Aglietta, M., Khanniche, S., Rigot, S., 2010. Les hedge funds: entrepreneurs ou requins de la finance? Editions Perrin, Paris. Alexander, C., Dimitriu, A., 2004. The art of investing in hedge funds: fund selection and optimal allocations. In: Schachter, Barry (Ed.), Intelligent Hedge Fund Investing. Risk Publications. Anderson, H.M., 1997. Transaction costs and nonlinear adjustment towards equilibrium in the US treasury bill markets. Oxford Bulletin of Economics and Statistics 59, 465–484. Billio, M., Getmansky, M., Pelizzon, L., 2006. Dynamic Risk Exposure of Hedge Funds: A Regime-Switching Approach. Working Paper. CISDM. Carhart, M., 1997. On persistence of mutual fund performance. Journal of Finance 52, 57–82. Chan, N., Getmansky, M., Haas, S.M., Lo, A.W., 2005. Systemic risk and hedge funds. Research Paper, n°4535-05. MIT Sloan School of Management. De Grauwe, P., Grimaldi, M., 2005. Heterogeneity of agents, transactions costs and the exchange rate. Journal of Economic Dynamics and Control 29, 691–719. Fama, Eugene F., French, Kenneth R., 1992. The cross-section of expected stock returns. Journal of Finance 47, 427–465. Fung, W., Hsieh, D.A., 1997. Empirical characteristics of dynamic trading strategies: the case of hedge funds. Review of Financial Studies 10, 275–302. Fung, W., Hsieh, D.A., 2001. The risk in hedge fund strategies: theory and evidence from trend followers. Review of Financial Studies 14, 313–341.

0.04

-0.04 1994

1996

1998

2000

2002

2004

2006

2008

Granger, C.W.J., Teräsvirta, T., 1993. Modelling Non-linear Economic Relationships. Oxford University Press. Gregoriou, G.N., 2004. Are managers of fund of hedge funds good market timers? Journal of Wealth Management 7 (3), 61–76. Gregoriou, G.N., Rouah, 2001. Do stock market indices move the ten largest hedge funds? A cointegration approach. Journal of Alternative Investments 1, 61–66. Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press, Princeton. Jawadi, F., Khanniche, S., 2012. Are hedge fund clones attractive financial products for investors? Applied Economic Letters 19 (8), 739–743. Jawadi, F., Prat, G., 2011. Arbitrage costs and nonlinear stock price adjustment in the G7 countries. Applied Economics 1–22 (iFirst). Jawadi, F., Arouri, M., Nguyen, D., 2010. Global financial crisis, stock markets and efficiency of central banks interventions. Applied Financial Economics 20 (8), 669–680. Khanniche, S., 2011. Les hedge funds: quelles implications en termes de risque systémique ? Revue d'Economie Financière 101. Lhabitant, F.S., 2001. Hedge funds investing: a quantitative look inside the black box. The Journal of Financial Transformation 1, 82–90. Luukkonen, R., Saikkonen, P., Teräsvirta, T., 1988. Testing linearity against smooth transition autoregressive models. Biometrika 75, 491–499. Schneeweis, T., Spurgin, R., 2000. Quantitative Analysis of Hedge fund and Managed Futures Return and Risk Characteristics. Working Paper. CISDM. Sharpe, W.F., 1992. Asset allocation: management style and performance measurement. Journal of Portfolio Management 18, 7–19.

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Teräsvirta, T., 1994. Specification, estimation and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association 89, 208–218. Teräsvirta, T., Anderson, H.M., 1992. Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of Applied Econometrics 7, 119–136.

Tsay, R.S., 1987. Testing and modelling threshold autoregressive processes. Journal of the American Statistical Association 84, 1–240. Van Dijk, D., Teräsvirta, T., Franses, P.H., 2002. Smooth transition autoregressive models—a survey of recent developments. Econometrics Reviews 21, 1–47.