Past public presentation is no warrant of future public presentation. This disclaimer is reminded to each investor for about all fiscal merchandises. It supposed that investings public presentations are really hard to foretell. Hence a fund director ‘s public presentation is non relentless over several clip periods. However, that premise is non obvious. In term of comparative returns, our hypothesis straight implies that any fund is able to pull out dependable information from the market in the long tally. This inquiry refers to the public presentation continuity analysis: is a fund able to crush the market over consecutive clip periods? If so, are past consequences a good calculator of future consequences?

One type of fund has aroused many economic experts ‘ involvement for its repute of over-performer, peculiarly highlighted after the 2007 market ‘s prostration of the sub-primes crisis, Hedge financess. The explosive growing of Hedge Fund during the 1990 ‘s resulted in a fecund literature about their public presentations. Hedge financess are largely defined by their freedom from the regulative controls based on the Investment Company Act of 1940.

This flexibleness irrespective the fiscal ordinance enables them to set about a wider scope of investing activities, which eventually achieve a better market clocking than classical common financess. This survey contributes to this literature in several ways. First, while there has been a important sum of research on the predictability of traditional plus categories, there are few about returns exhibiting by alternate vehicles such as hedge financess. All the same, analyzing Hedge Fund public presentation predictability as done in Martellini ‘s papercite { predictability } has led to important consequences, peculiarly in footings of benefits. Second, due to the trouble of obtaining informations about hedge financess, there is limited academic research in this area.

We study the public presentation of hedge fund and the continuity over a clip window that encompasses comparatively long bullish and bearish period. As the definition of hedge financess covers a battalion of investing allotment, we distinguish four classs of hedge financess harmonizing to their investing scheme. As the importance of happening public presentation continuity remainders on the fact that it would enable investors to crush the market norm, consistence of the public presentation continuity raises therefore inquiries about market efficiency. We confront this hypothesis to historical returns of our four schemes. It consists in proving if these schemes can ensue in a public presentation significantly greater than those of the whole market, on a semi-permanent footing. Consequently, we use benchmarked returns against the S & A ; P500 for our four schemes to analyze their kineticss comparatively to the hypothesis of market efficiency.

hspace* { 1cm } Efficiency theory suggests that any new information is outright incorporated into monetary values, doing over-performance merely a ephemeral measure. It besides implies the non-existence of inefficiencies that could take to arbitrage chances. This phenomenon so faces Efficiency belongings as more a series is relentless, more it will be possible to set up a moneymaking scheme. The figure of Runs trial denied weak-form market efficiency in several survey, M. Borges found important consequences over the European Stock Market

In add-on, aware of the fiscal markets world, which is normally defined as weakly-efficient harmonizing to Famafootnote { Fama ( 1970 ) defines, in the article extit { Efficient Capital Markets: A Review of Theory and Empirical Work } , three degrees of market efficiency: a strong efficiency signifier mentioning to a market where all the information is knew, a semi-strong efficiency signifier which merely implies public information, and a weak efficiency signifier matching to the past information. } , and giving the definition of hedge financess, we can supposed that their strategic freedom irrespective fiscal ordinance gives them the possibility to take advantages of these imperfections.

hspace* { 1cm } Ardian Harri and B. Wade Brorsencite { beginning } have highlighted this mechanism. The consistence of returns is an of import issue in the context of hedge financess because unlike the traditional common financess, investing in hedge financess involves normally a lock-up period. Wholly, this constrains means that investors need to hold sufficient information about the public presentation over a long period before wagering their money. Furthermore, as hedge financess exhibit a much higher abrasion rate compared to common financess, phenomenon examines by Browncite { brown } and Liangcite { liang } who estimated hedge fund annualized abrasion rates in a scope from 4.3 % to 15 % , the issue of public presentation continuity becomes particularly of import in this instance. Analyzing the continuity of hedge fund public presentation is therefore legitimate through above mentioned elements.

hspace* { 1cm } We develop our analysis into three parts. First, we define the alternate environment of hedge fund and present our database. Particularly, we insist on the chosen classification and explicate the consistence of our attack. We besides describe the economic environment of the studied period and explicate the information excavation employed. Second, we present the chief bing trials of consecutive correlativity. In this portion, we use autocorrelation trial as a first attack to place our procedure kineticss. Then, we present more specific processs recognized for their adequateness with fiscal series: the execution of the Runs trial and the computation of the Hurst advocate. Third, by utilizing the above mentioned processs, we present their consequences and place hedge fund schemes public presentations in footings of continuity. }

To stand for the alternate investing existence, we chose to utilize informations from HFR Hedge fund indexes. The HFR indexes have been used in a assortment of surveies on hedge fund public presentation and look to be dependable indexs of the alternate investing existence. We use a decomposition of the existence into four representative schemes of the major investing procedure.

Into our informations choice procedure, we confront several constrains. Hedge Fund existence is dark and we face the issue of deceit. Particularly, we chose our database in regard with recent surveies about prejudice bing on Hedge Fund indexes to guarantee the dependability of our trials consequences.

Hedge Fund informations are hard to obtain and normally non extremely dependable. This can be explained because of the freedom of this fund to supply or non their consequences. This girl of ordinance enables hedge fund to show their consequences merely when it is relevant for their ain involvement. There is accordingly a important information prejudice between that we can obtain and world. Besides, we can detect a subsister prejudice in some database.

Survivor prejudice refers to the fact that over a long clip period, the index observed represents merely lasting financess. As the poorest performing artists are non represented, there is an unreal addition of the index public presentation. Consequently, the inquiry of the abrasion consequence. Carpenter and Lynchexamine the job of subsister prejudice and abrasion consequence and conclude that they could take to false consequences, and peculiarly, to incorrect continuity hypothesis credence. The pick of the informations to utilize is accordingly non obvious and lead to arguments.

In the visible radiation of these informations we chose to utilize informations from HFR Hedge fund indexes to stand for the alternate investing existence. We think that HFR indexes respond to the constrain we mention. In the facts, Fundss are re-selected quarterly, as necessary, and in order to minimise the survivor-ship prejudice, they are non excluded until they liquidate or fail to run into the fiscal coverage demands. This makes these indexes representative of the assorted hedge fund investing manners and utile for tracking and comparing hedge fund public presentation against other major plus categories. In add-on, the HFR indexes have been used in a assortment of surveies on hedge fund public presentation. They offer several advantages with regard to their rivals: we can state that they are crystalline both in their computation and composing, and constructed in a disciplined and nonsubjective manner.

Finally, our sample is composed of the four schemes indexes returns cyberspace of direction fees. We use monthly informations from January 2000 to December 2012 stand foring 154 observations.

subsubsection { Strategy Classification }

As the definition of Hedge Funds covers a battalion of different types of investing allotment, we distinguish four classs of hedge financess harmonizing to their investing scheme. To function this intent, we use the scheme categorization constructed by HFR. Hedge Fund Research has constructed a Strategy Classification System representative of the alternate investing existence. The categorizations reflect the contemporary development in the Hedge Fund industry. This categorization is in changeless development to reflect the world of the industry. The aim is to specify scheme which can be used to qualify Hedge Fund return. This categorization leads to the building of dependable quantitative index. The Hedge Fund industry is therefore divided into four schemes: Equity Hedge, Event Driven, Macro and Relative Value. We define these schemes as follows:

The Equity Hedge scheme refers to investing places both long and short in equity and equity derivative securities. The investing processes included are every bit good quantitative as cardinal techniques and the investing existence loosely diversified or narrowly focused on specific sectors.

The Event Driven Hedge Fund apply a scheme that attempts to take advantage of events such as amalgamation and restructuring that can ensue in the short-run mispricing of a company ‘s stock.

The Macro scheme is a scheme that bases its retentions, such as long and short places in assorted equity, fixed income, currency, and hereafters markets, chiefly on overall economic and political positions. The investing procedure is predicated on motions in underlying economic variables.

The Relative Value scheme consists in buying a security that is expected to appreciate, while at the same time selling short a related security that is expected to deprecate. Managers employ a assortment of cardinal and quantitative techniques to set up investing theses, and security types range loosely across equity, fixed income, derivative or other security types.

We study the public presentation of hedge fund and the continuity over a clip window that encompasses comparatively long bullish and bearish period to separate between schemes the most acting.

As public presentation continuity raises inquiries about market efficiency, we confront this hypothesis to historical returns of our four schemes. Therefore, the more direct manner to see this theory is to utilize benchmarked returns against the S & A ; P500.

Our sample encompasses informations from January 2000 to December 2012. The hedge Fund industry grown exponentially during the 90 ‘s. Therefore we start our sample in 2000 as the industry was more stable and perennial and some schemes were non good develop yet earlier. This period is besides interesting because of its macro-economic context. Financial markets experienced alternation of enlargement and recession with the cyberspace bubble in 2000. Between 2002 and 2007 with the sub-primes crisis the emergent markets grew. These information will look helpful for the reading of our consequences.

Specifically, we use the indexes of four Hedge Fund market subdivisions which the amalgamation represents the full industry. Then we calculate returns for each. Benefit of utilizing returns, versus monetary values, is standardization. The simple returns are defined such that:

First of wholly, a brief history of the period studied is necessary. The information set begins with the engineering bubble inflated from 1998 to late 2000, which precipitated the market interrupt down until 2003. Then, there is a 5 back-to-back old ages period of euphoric from 2003 to 2007 that starts with the 2nd Gulf War and stoping in the summer of 2007. From 2007, it is a bearish period for overall industry, accelerated by the fiscal crisis and the ensuing by the planetary economic crisis. The four historical secret plan of the log-returns show good the context we mentioned.

First, we study the log-returns development against the S & A ; P500 log-returns. Graphically speech production, hedge fund indexes behaviour is less volatile than market. During market prostrations, the four schemes minimize their losingss. These findings suggest that there is potentially a determining procedure behind. Second, the volatility of the information set is germinating and altering from bearish to bullish period. In bearish province, market and overall industry is more volatile than during bullish province. In decision, the discrepancy of the series seems to alter over clip and there are second-order dependance. However, we can construe descriptive statistics table because as our informations set is monthly, the beaks-down are lifted.

The talk of the two descriptive statistics confirms that the hedge fund existence is really heterogenous: some hedge fund schemes have comparatively high volatility compare to others. The Equity Hedge Strategy seems to be the more volatile. On the other manus, some other hedge fund schemes have lower volatility, the Relative value scheme peculiarly is really stable comparison to the S & A ; P500.

Similarly, the distribution analysis indicates that the schemes are less volatile than market and that, in add-on their expected returns are higher. In term of Mean-Variance analysis these schemes are therefore better investing than the market. However, the comparing with the normal jurisprudence indicates big negative lopsidedness for Equity Hedge and Event Driven. The Macro scheme seems the closest of the normal distribution which would bespeak entropy. However, most of the schemes exhibit high kurtosis bespeaking utmost loses event. Finally, monthly returns are non usually distributed, because they are negatively skewed and leptokurtic.

To find if public presentation persists, one of the usual processs employed is to pattern current returns on past returns. We proceed in this survey in the same manner than Fama and Solnik. Fama and Solnik used the analysis of autocorrelation to observe dependance dealingss. Then, to corroborate their consequences, they used a Runs trial. In add-on, we decided to run a 3rd trial consisting in the computation of the Hurst coefficient to formalize our consequences.

Usual trials for efficient market hypothesis attempt to foreground independency into consecutive monetary value fluctuations. As autocorrelation is the cross-correlation of a signal with itself, one of these trials consists in gauging the correlativity coefficient between returns and lagged returns. In finance, the autocorrelation of a series of returns describes the correlativity between returns of the procedure at different times.

Some past empirical surveies on fiscal series have run autocorrelation analysis as the Cootner ‘s studybut the major portion found undistinguished coefficient. The best known and more dependable one is the Fama ‘s studyon stock monetary values walk in 1965. He examines day-to-day returns of Dow-Jones equity from 1957 to 1962. His survey does non propose any past dependence into monetary value kineticss. The same survey has been undertook by Solnik but this clip utilizing European market informations. Solnik ‘s survey besides confirms the weakly-efficient market hypothesis. By running the same process, we try to place dealingss of dependance in our returns which would corroborate the continuity of the scheme ‘s public presentation.

The relation of dependence between times s and T of our series is the autocorrelation

Finally, the autocorrelation coefficient is a step of the dependance of a clip series. Articles from the International Research Journal of Finance and Economics test the weak-form market efficiency though a Wald-Wolfowitz Trial for entropy. Therefore, a manner to prove for the significativity of this coefficient is to run this process.

The Runs trial for entropy is used to prove the hypothesis that a clip series is random. Runs trial have been used in several surveies about foretelling the Directional Movement of Index Returns. A tally is a set of consecutive values that are either all above or below the mean. To simplify calculations, the informations are foremost centered to their mean. To transport out the trial, the entire figure of tallies is computed along with the figure of positive and negative values. A positive tally is so a sequence of values greater than zero while a negative tally is a sequence of values less than zero. We can so prove if the figure of positive and negative tallies is distributed every bit in clip.

The intuitively fractal nature of fiscal information has lead a figure of mathematicians to use the fractal mathematics to fiscal clip series. These fractal belongingss have been good described by Kale Butar who have applied the Hurst coefficient on fiscal series. They explain that as the Hurst Index coefficient is a dimensionless calculator for the self-similarity of a clip series therefore, we can mensurate for consecutive correlativity in footings of the Hurst advocate which is a convenient sum-up of statistics of continuity in time-series informations.

Stochastic procedures with long-run dependance have been introduced foremost in the context of hydrology and geophysical sciences by Hurst. Recently the technique has been popularized in economic sciences by B. B. Mandelbrot. Due to its visual aspect in E. E. Peters works it is now popular for analysis of fiscal markets.In Finance, the Hurst advocate was used as the measuring of the grade of efficiency in several surveies about anticipation based on weak-form efficient market hypothesis.

Using the Hurst advocate we can place clip series kineticss and applied to fiscal informations, it can be interpreted as a step for the trendiness. Here, we use the method presented for gauging the Hurst Index of our benchmarked hedge fund indexes returns.

The Hurst exponent $ H $ can be calculated by rescaled scope analysis such that:

that can, for several subsets, be solved by a least square tantrum whose the incline of the obtained arrested development is the calculator of $ H $ .

This method of execution is the original one proposed by Harold Hurst. There exists a broad scope of computation techniques of the Hurst advocate. Some surveies have found a important prejudice in this appraisal method. Bo Qian and Khaled Rasheed place that the attack is reasonable to the window size of the subsets used and to the length of the clip series tested. Notwithstanding their findings, the convergence belongingss of our calculator are non contradictory with our involvement due to the comparative low size of our series.

As we said at the beginning of this portion, the impression of market efficiency is closely linked to the absence of memory: the efficiency hypothesis is so associated with the random walk theoretical account. The Hurst advocate enables to specify the tendency of our series. We can distinguish three instances of kineticss type. With $ H $ by building in the scope a Hurst advocate towards 0 represents a high fractal dimension, therefore the procedure displays anti-persistence. On the reverse, an advocate towards 1 represents a little fractal dimension and thereby the procedure exhibits continuity. By tax write-off, the hypothesis of efficient market is validated for a Hurst advocate closes to 0,5, matching to a White Noise procedure.

We run trials on all benchmarked and non-benchmarked schemes. We expect though each process find important and dependable consequences.

First of wholly, we present an autocorrelation analysis that gives an intuition about the kineticss of our series. Then, we except confirm these consequences by running a Runs Test.

The observation of the autocorrelogram enables to observe for consecutive correlativity. We run the process for our four series benchmarked and non-benchmarked. The consequences of this graphical analysis are helpful in the designation of the procedure. The analysis of autocorrelograms does non give signals of dependance for the benchmarked series, Pearson ‘s coefficient of autocorrelation are all non important. Reversely, the non-benchmarked series exhibit dependance of first and 2nd order. These signals are peculiarly accentuated for Relative Value and Event Driven which the Pearson coefficients are both important. The correlativity coefficients for Relative value are at the first order 0.55 and 0.23 at the 2nd order. The Event Driven coefficient for the first slowdown is 0.41 and non important at the 2nd slowdown. Equity Hedge seems besides weakly autocorrelated at first order with a coefficient of 0.24 and eventually Macro autocorrelogram shows independency with a Pearson coefficient at the first and 2nd order both non important. The spread secret plan of the four series show graphical groundss of these dealingss of dependance.

In add-on, harmonizing to the minutes distribution analysis, the series are likely heteroskedastic. We propose to run the ARIMA process on the Macro scheme which fits the most to the normal jurisprudence. This analysis concludes that HFR Macro can non be model by ARIMA procedure and the theoretical account ill explains the autocorrelation. In fact the discrepancy of the series changes excessively much. We can non make illation in this series. Finally, both heteroskedasticity and autocorrelation consequences represent a legitimation for the execution of Runs and Hurst process which are foremost, steps of continuity and most of all, robust to heteroskedasticity.

The Runs Test statistics is a step of the goodness of tantrum with a random distribution such that the p-value of the Runs trial describes the chance to suit with a random distribution. The tabular array shows consequences of the Bilateral Runs Test for a degree of hazard

First, the consequences on the benchmarked schemes are all consistent with the theory that comparative returns do non exhibit continuity. We already highlight randomness though statistical illation. We suppose that the usage of benchmark deletes the volatility of the information set. In decision, even if the benchmarked series perform better than market in footings of mean returns, we can non state that the series persist.

Reversely, we find consistent consequences about continuity with the non-benchmarked information set. Indeed, $ H0 $ is significantly rejected for the Event Driven Strategy with a p-value of $ 0.0009 $ . The same decision is given for Equity Hedge and Relative Value, with severally p-value of $ 0.0184 $ and $ 0.00094 $ . The $ H0 $ Hypothesis of entropy is rejected for most of informations set. There is still non-reject of $ H0 $ for the Macro Strategy with a p-value of 0.25. In add-on, the tabular array shows that the Runs statistics for the trials rejecting $ H0 $ is negative. The point is that the bilateral Runs trial can every bit good reject for continuity than for anti-persistence. In this instance, by sing a degree of hazard $ alpha=0.05 $ for the one-sided trial:

The rejecting zone is $ W=left [ Zvert { Z } & lt ; 1.64

ight ] $ .

In decision, we can prove straight for continuity with the tabular array. Particularly, in the instance of the three others schemes Equity Hedge, Event Driven and Relative Value ; the talk of the consequences table intuitively shows continuity. For illustration, while Event Driven p-value is the lowest, peers to $ 0.0009 $ certifying of non-randomness, the figure of tallies is 56 over 153 observations. As the figure of tallies is low comparison to the length of the sample, it means that there is a continuity of the performance.

Finally, the trial of figure of Runs gives strong signals of continuity for Equity Hedge, Event Driven and Relative, which is consistent with our statistical illation. However, these consequences do non enable to mensurate the continuity.

The statistical illation and the Runs trial have provided consequences about continuity public presentation but no step of it. The Hurst advocate solves this issue as it is a step of continuity.

The R/S statistic is the scope of partial amounts of divergences of a clip series from its mean, rescaled by its standard divergence. A log-log secret plan of the R/S statistic versus the figure of points of the aggregative series should be a consecutive line with the incline being an appraisal of the Hurst advocate. In order to back-test our process, we run the Hurst advocate calculation over foremost a fake random variable and secondly over the S & A ; P500. We conclude on the dependability of the method, the Random variable Hurst advocate is peers to 0.503 and the S & A ; P500 Hurst advocate is peers to 0.504, which is consistent with Fama ‘s findings about entropy of the market.

Hurst method discloses the undermentioned belongingss of the statistical informations: bunch, continuity, blending, anti-persistence, presence of periodical or non-periodical rhythms. In our instance, by analyzing the distribution of the series, we conclude to heteroskedasticity. Covering with heteroskedasticity normally appears hard and leads to meaningless consequences. Giving the constrains we face, the Hurst advocate is a manner to prove the hardiness of our last findings. Indeed, the biggest involvement of utilizing the Hurst advocate is its hardiness to heteroskedasticity.

As we expected, the Hurst advocate of benchmarked series is for each of them inferior or peers to $ 0.5. Most of them exhibit blending belongingss which is consistent with our Runs Test consequences The Hurst coefficient for benchmarked Equity Hedge scheme is $ 0.30 $ , for Event Driven $ 0.41 $ , for Macro $ 0.36 $ and for Relative Value $ 0.43 $ . Reversely, in the instance of the non-benchmarked schemes, most of them exhibit constellating characteristic. The most impressive consequence is the Relative Value Hurst advocate peers to $ 0.77 $ . Then, The Event Driven coefficient is $ 0.59 $ and eventually the Equity Hedge scheme with a $ H=0.55 $ . In add-on, systematically with our findings for Macro scheme with the Runs Test, the Hurst advocate is inferior to $ 0.5 $ peers to $ 0.42 $ . Nevertheless, we prevent about these consequences that there is non statistical illation bing in the Hurst advocate. The intervals distinguishing relentless and anti-persistent characteristic is therefore arbitrary. In this instance, we consider a conservative interval of $ 0.01 $ points of preciseness.

To sum up, foremost, the Hurst advocate calculation confirms that there is no continuity in the benchmarked log-returns. The benchmarked returns represent the excess of the scheme in comparing to the market. Therefore, we can reason that the extra returns are non relentless and that the anticipation of the addition over the market is impossible. These consequences mean that the chance of overperfoming is random and eventually, the hedge Fund industry, whatever the scheme considered, does non crush the market with predictability. Second, Hurst advocate reversely confirms that there is a continuity characteristic of the Hedge Fund strategies. This characteristic is peculiarly underlined for the Relative Value Strategy. The schemes which exhibit continuity are therefore plenty elaborated to observe dependable information from the market. This is non the instance for the Macro scheme. We suppose that as this scheme is extremely dependent of the market, this correlativity could be the cause of its anti-persistence. The confrontation of these statements draws to the stopping point that puting in Hedge Fund is rational and that past public presentations are correlated to future public presentations. To travel farther, the mold of the most relentless scheme with ARFIMA process could be a development of this survey.

Using informations from four HFR hedge fund indexes, we find that there is strong grounds of really important predictability in hedge fund returns. The processs run among the benchmarked and non-benchmarked log-returns lead to contrary decisions. We accept the weak-form market efficiency for the S & A ; P500 dataset. Therefore, the benchmark we use is random. This fact could explicate the consequences over the benchmarked schemes. Besides, we find dependence dealingss for the scheme Relative Value, Event Driven and Equity Hedge. However, this dealingss are non found for the same benchmarked series. We conclude that the extra returns are random because of the entropy of the benchmark. Even if the series are autocorrelated, the minus by a random walk lead to an unpredictable procedure. Therefore these consequences do non reprobate the Fama ‘s hypothesis.

Our overall decisions confirm that there is a mid-term dependance of returns. In sum we concluded that the monthly monetary values do non follows random walks. Furthermore, the rejection of the random walk for monthly returns does non back up a mean-reverting theoretical account of indexes procedure. We note that these consequences are closed to Lo Mackinlay ‘s decision, utilizing the discrepancy ratio on stock market. The investors can take the watercourse of benefits through arbitrage procedure from profitable chances across these markets. Finally, the survey shows that it is possible to foretell future public presentation with past public presentation for the most autocorrelated schemes.

The cognition of the past so provides information to foretell future returns. We find mid-term memory, therefore an interesting extension would be to prove for longer term continuity. We besides suggest to prove for shorter-term continuity. Several surveies show that the continuity tend to increase with the lessening of the sing clip window. Then, the first development we propose is to cover with heteroskedasticity by break uping our sample between bull and bear market period as in the Cappocci, Corhay and Hubner ‘s survey cite { BullBear } . Efficaciously, the statistical analysis suggest structural interruptions caused by the economic environment. As the decomposition leads to stationary procedure, running a such process could enable to pattern our series.

Our analysis can be farther improved in a figure of ways. Due to the fractal belongingss of the relentless schemes, we can pattern a self-similar procedure utilizing the Hurst coefficient. These belongingss come from the Fractal Brownian gesture theory. The first category of procedure to see is the ARMA procedure. It is frequently called “ short memory procedure ” in visible radiation of the rapid lessening of their autocorrelation map. A 2nd category of theoretical accounts related to the fractional brownian gesture is the ARFIMA theoretical account which is more altered to longer dependance relation.

Overall, we find that the continuity is linked with the investing

aims of the different hedge fund schemes. Efficaciously, among the directional

scheme, Macro does non exhibit significant dependence while, among the non-directional schemes, Event Driven, Relative value and Equity Hegde, we find important autocorrelation. Finally, we believe that these groundss of predictability for the non-directional scheme well better our apprehension of hedge financess. Besides, our empirical consequences provide the first geographic expedition of the features of hedge fund schemes through non-restrictive processs, a subject that needs more attending in the field of investing direction.