Finance论文模板 – Survival Analysis of a Hedge Fund

Abstract

In this paper, the survival analysis of the hedge fund is examined utilizing various survival models. The survival analysis model has been used extensively in the studies of marketing preferences, lifetime bonds and other areas within the financial marketble. Acloser look into the numerous predictor models indicates that some variables could be used in the prediction of the hedge fund mortality. The models used in the analysis of the hedge fund include; the product-Limit estimator, “ the Accelerated Failure Time Model”, Life table method and the Cox Proportional” Hazards models.

Analysis of the hedge fund rate of failure adapts a particular style of investment. The above mentioned models have been proved to be vital in the investigations of the the survival times of the hedge fund within a period of 12 years. This includes CA, equity market neutral, fixed income arbitrage, global macro, multistrategy, long/ short equity hedge, event driven and dedicated short bias. The medium survival time for hedge funds is exactly 5.50 years. It is worthy to note that some hedge fund classifications experience relatively higher survival times than others.

Among the factors that may have impacted the hedge fund mortality include the redemption period, performance fee, monthly returns, minimum purchase, e.t.c..The Lipper TASS database is a very useful resource for gaining the desired information used in the study. funds having higher intensive fees have higher probability for survival whilst those with low watermark have higher survival probability. It is also true that lower survival probabilities is associated with larger hedge funds. Additionally, the level of leverage has very low-frequency levels. Hence, to add on the previously mentioned models, the study shall utilize other empirical methods relevant to the study. The study shall combine a precise conclusion for the whole study.

To add on this, the leverage levels have very low frequency levels. This study utilizes empirical methods that are relevant and a precise conclusion is derived at the end

Introduction

Over the past decade, the hedge funds have experienced a sustained  growth, they have grown  from relative obscurity to being a topic of cocktail party chatter discussed all over the world.  Together with Investment banks and private equity firms, hedge funds are at the epicenter of a transformed landscape, coming up with new roles and looking for ways of creating new roles in an environment of lower risk and greater regulation (Seager and Slabaugh 2008).  This has seen the  number of estimated assets under management (AUM) increase to an estimated  $1.5 trillion (Adrian, 2007). Hedge funds have gathered a reasonable amount of assets from wealthy individuals and institutional investors especially in the developed economies. Albeit the hedge fund has grown substantially, it has been accompanied by quite a number of setbacks due to massive fund inflows that have impacted on its returns and risks.  These risks facing the funds are nonlinear and more complex than those facing the traditional asset classes. Due to the dynamic nature hedge fund investment strategies and the impact of the huge fund inflows on leverage and performance, the hedge fund risk model require sophisticated analysis and more sophisticated users. The paper seeks to identify the risk measurement mechanisms, for instance, the downside measures, which have proved proficient in measuring their survival rate. Secondly the paper will distinguish the real failure rate from the attrition rate of hedge funds.

Arguments have been fronted in favour of diversification of the traditional portfolio with hedge funds owed to the high volatility in stock, bond and currency markets. This has  led to the multiplication of dead hedge funds during the same period. The August 1998 Russian ruble crisis, followed by a collapse of the invalid Long-Term-Capital Management, claimed some victims. It was attributed to lack of liquidity in the global markets caused by the credit squeeze imposed on hedge funds (Gregoriou 2002). Numerous experts have carried out studies concerning the issue of survivorship bias in hedge funds albeit to my knowledge; the study on survival analysis of a hedge fund is still in its juvenile stage. The survivorship bias touches on the upward bias of the estimated returns, which gives a higher likelihood of occurrence among studies that leave out “defunct” hedge funds in their analyzes. The survivorship bias of hedge funds is assistive in this study since it outlines factors that lead to the collapse of hedge funds within the market. It plays a big role in the analysis of hedge funds (Baquero et al 2005). A registered survivor bias of close to 3% annually for hedge funds has was registered  ( Saha 2005) . Hsieh  observed 1.6% while other experts register rates of 2% consecutively. The studies aforementioned utilize a variety of databases with diverse period, for instance, hedge funds managers in the HFR and TASS offer some overlap. The average attrition rate for hedge funds was 8.6% and 8.3% during the period 1994-1998. The entire period witnessed surviving funds outperforming the non-surviving ones by an approximated value of 2.1% yearly. Large hedge funds survive a longer period and use of debt financing, leads to shortened survival times.  In this paper , the TASS database,  which began its fund tracking exits from January 1994 is used. The database consists of monthly returns, assests under management  which are divided into “Live” and “Graveyard” funds. Upto August 2004, the combined database of both the live and dead hedge funds had 4,781 funds with at least on monthly return observation (Carey and Stulz 2006).

Literature Review

The literature review begins by categorizing hedge funds. The first category is referred to as non-normality of hedge fund returns and AUM (Chan et al. 2006). The type of hedge fund is flexible in its strategies and cannot solely be judged using the standard deviation approach. The type of hedge fund is characterized by negative skewness and high kurtosis (Malkiel and Saha 2005). Category 2 is referred to as hedge-fund short-term capital outflows. The fund is highly motivated by the return-chasing investors’ behaviours. In this case, investors flock around funds, which have shown good performance and shun funds showing negative performance. Category 3 is the liquidity constraints characterize hedge funds with low liquidity hence they face high-level cancelations. The fund cancelation policies offer curative options such as redemption frequency, lockup period and notice period.

 An augmented TASS database was used to observe that hedge funds have a half-life survival of 30 months using the Cox PH model ( Brown et al. 2001). The study also discovered that young funds die faster (Amin and Kat 2002). The probability of hedge funds failing in their infancy was 7.4%, which increases to 20.3% in their second year. It is because the marginal funds with minimal amounts of assets under management will bring an additional risk to enhance returns and solicit for investors. They tend to use their performance, instead of their reputation in soliciting funds from investors. Approximately 30% of the hedge funds do not make it past their 3years due to poor performance ( Brooks and Kat 2001). The poor performing funds drop out of the database at a faster rate than the older funds, putting into consideration conditional failure. Additionally, volatility and manager tenure were utilized as covariates (Jen et al. 2001).

The  rate of hedge fund attrition since 1994 was 15% per year (Brown et al. 2001). However, the graveside probability increases with increasing risk and that fund with negative returns for two consecutive years have a higher risk of shutting down. The attrition rate also referred to as churn rate is the proportion of investors, who stop investing funds during a given period. It is also a determinant of hedge fund failure since hedge funds die once they lack funds.  While utilizing TASS data, the size and leverage have a profound effect on the on hedge fund survival (Amin and Kat 2002). It is also ascertained that less than 40% of hedge funds make it to their fifth year and the ones which make a representation of 60%. (Boyson 2002) acknowledges the stated conclusion and observes that the hedge fund size has a significant effect on their survival. Boyson relies on the TASS data by asserting that smaller hedge funds die faster than the large ones

In a study of 288 funds, 57 were considered dead hence, they could not report to their database (Boyson 2002). Out of the 57, a total of five had merged, 31 had died, and 21 closed. It was opined that most of them closed due to poor performance.  From the information provided, it can be ascertained that age, AUM, cumulative returns and fund flows have a significant effect on their survival ( Baquero et al 2005) . The studies rely on the data found in the Lipper TASS database, which uses logit and probit models.

In another study, the Zurich database was utilized to determine how it helps money managers and potential investors by giving reliable information and valuable results in forecasting death funds (Gregoriou 2002).  The hedge fund style is considered as an important factor in analyzing survival. It is because hedge funds perform as a portfolio with a reasonable survival time and variable diversification. Larger funds give a better return, and those with minimal leverage levels survive longer. 

The study utilizes the previously mentioned models to estimate hedge fund survival. The next part will describe the data and methodology and finally a description of the models. The results and ramifications are presented in the last part.

Data and Methodology.

This study shall utilize a sample of 1,222 in its cross-sectional analysis. The  cross-sectional time series analysis turns out to be 78,002. As mentioned previously, the study shall utilize data as from 1994-2005 of the TASS database, both the cross-sectional and time-series analysis.. The time-series status of sample funds between 1985 and Dec 1993 is “live” for the logit model

Empirical Methodologies

Under this section, a dissection of the utilized methods is studied indepth. This is in abid to address the questions like, ‘how long will the hedge fund survive?’, ‘what variables affect the probability of hedge funds survival’ and ‘what models and hazards are generally utilized?’.Comparisons and analysis from previous works and the empirical illustrations is taken into consideration. Hazard methods are used generally. There exists two models for hazard model estimation; a discrete time hazard model and duration model. Though the classe resemble each other statistically, each has its respective advantages and disadvantages. For instance, the duration model ia able to capture a non-monotic relationship between the duration of a fund and its probability of an exit. An assumption that the probability of an exit increases or dicreases mono-atomically with duration time is made when a duration time is introduced as an explanatory variable in a discrete time hazard model. Also, the  duration model is able to deal with the challenge of right censoring. There is a high chance that some hedge fund wouldn’t exist at the end of the sample period. The logit model cannot handle such a right-censoring problem properly. On the other hand, the semi-parametric duration model is dependent on  a limited hazard assumption that is proportional. This makes it difficult for estimation of robust parameters. The logit model doesn’t assume and incorporate time varying covariates which involve economic indicators and lagged changes of own fund flows with a lot more of computational efficiency as compared to the duration model. Referring to the mentioned merits and demerits, both types of models are used mutually and complementarily with an aim of maximizing on their key strengths (Gasko 1990).

The below models were discussed and results analysed for a better insight. The models are insighted below.

Duration model

This is a model used to estimate the hazard function for the hedge fund. Its interpretation is intuitive and the shape carries valuable information. Given that the hazard rate in t is homogeneous, each fund’s intensity to exit the database at a given date t, the higher the hazard rate, the more the likelihood of the fund to stop reporting its performance (Brown et al 2001). However, the parametric framework imposes predermined forms hence constraining the analysis. This leads to miss of critical information at specific moments of the fund. Below are the different approaches utilized by this model.under this model, the below approaches are utilized.

Non-parametric Approach: The Kaplan-Meier Analysis

This approach gives a good interpretation as a non-parametric maximum likelihood estimator. In this approach, we basically put into consideration the likelihood of the dying cases or those that are censored at a time t. For instance, if a phenomenon were censored at t, its contribution to the likelihood would be S (t). To maximize the likelihood, this is made as large as possible. Since the survival function  must not be increasing, the time t  is kept at constant. This is to mean that the survival fund doesn’t change during censoring times. When a subject dies at t then this is one of the distinct times of death t(i).To make the fund just before this distinct time as large as possible is a need. However, the biggest it can be is the previous time of death or 1 or whichever value is less. It is also important to make the survival at t (i) as small as possible an indicator that we need a discontinuity at t(i).

T= Random time

C= Censoring time

The random variable is written as T =min (T*, C).

Semi-parametric Approach: The Cox Proportional Hazard Analysis

The approach circumvents the problems of both the non-parametric estimator and the parametric estimator. (Cox 1972, 1975) observed durations from the smallest to the largest in a time series. The model assumes uncensored observation= n, from t1< t2…< tn. The condtional probability of t1 exiting, given that all of the n durations could have ended at time t1 is written as

        h(t1, x1, ß, h0)

Ʃni=1 h(t1, x1, ß, h0)

X= vector of explanatory variables; ß= parameter vector to be estimated and h0 is the baseline hazard i.e. the hazard function for the mean fund. The test is a nonzero slope in a generalized linear regression of the Schoenfield residuals on time functions.

The Accelerated Failure Time (AFT) Model

This model considers a specific relationship between the survivor functions of any two hedge funds. If Si (t) is the survivor function for hedge fund i, then for any other hedge fund j, the below equation relates the AFT model to the survival functions.

Si (t)= Sj(ϕijt) for all t,

ϕij = constant that is specific to the pair of funds (i,j).

The model assumes that hedge funds differ in aging rate. Ti is denoted as a random variable corresponding to the event time for the ith hedge fund in the sample and xi….xn to be the values of k covariates for the hedge fund, the AFT model is written as

Log Ti = ß0+ ß1xi +….+ ßkxtk + σԑi

ԑi= is a random disturbance term and ß0… ßk, σ are parameters to be estimated (ϕ is the scale parameter).

Plots based on life –tables estimates of the survival function Ŝ (t) help to differentiate between the different probability distributions for the AFT model. A plot of –log [Ŝ (t)] against time will be linear when the appropriateness of the exponential distribution is paramount. A plot of log [–log Ŝ (t)] against log (time) depicts a linear where a Weibull distribution is appropriate.

Semi-parametric Approach: The Cox Proportional Hazard Analysis

This is a hazard model used to detect multivariate effects and estimate effects in both a univariate and multivariate setting. It is a statistical technique for exploring the relationship between the survival of an item or system and several other explanatory variables. Such analysis deals with studying the time between entry to a study and the subsequent event like death or failure. The method is based on the modelling approach to the analysis of survival data. The purpose of the model is to explore simultaneously the effects of several variables on survival.

A regression method introduced by Cox is used to investigate several variables at a time. It does not assume a particular distribution for the survival times, but assumes that the effects of the different variables on survival are constant over time and are additive in a particular scale

The approach circumvents the problems of both the non-parametric estimator and the parametric estimator by model assuming uncensored observation= n, from t1< t2…< tn (Cox 1975). The conditional probability of t1 exiting, given that all of the n durations could have ended at time t1 is written as

        h(t1, x1, ß, h0)

Ʃni=1 h(t1, x1, ß, h0)

X= vector of explanatory variables; ß= parameter vector to be estimated and h0 is the baseline hazard i.e. the hazard function for the mean fund. The test is a nonzero slope in a generalized linear regression of the Schoenfield residuals on time functions.

Empirical analysis and Results

Explanatory variables

There exists six categories of explanatory variables for the cross-sectional hazard models, these include: AUM , return property , leverage, liquidity , fees, and minimum investment. Funds that perform better, with larger and more stable assets, have a less likelihood of liquidation. Hence, the results will have negative coefficients on mean and skewness of returns.  On the other hand, hedge funds have a high affinity for  leverage. Because of this, they utilize it heavily bringing a positive coefficient on the mean level average. The  use of management, incentive fees, and a high water mark dummy provides the effects of the incentive structure on the probability of liquidation. The current trend in the industry shows that incentive fees are attached to high water mark, which is conditioned on payment of the incentive when the maximum share value is achieved. As a result, it promotes risk taking by managers hence high probability of liquidation. (Casey et al. 2004) assert that high-water mark provisions avail incentives to the managers to facilitate more fund management than its absence.  The  research utilizes four variables that relate to cancelation policy of hedge funds, meant to confine liquidity constraints for the investors. These variables include;, lockp period payout period redemption frequency, and redemption notice period. The larger the variables, the longer the redemption period hence lower liquidity.

This discussion narrows down on two aspects regarding the stated variables. The first aspects signify lower liquidity  which is a contributing factor to the more stable hedge fund performancedue to the manager’s possibility to mitigate outflows. This  causes a negative coefficient.  On the other hand, the fund fund is less likely to gather capital from investors hence a higher likelihood of destabilization since investors have a low affinity for funds. This offers some inflexibility in liquidation. This causes a positive coefficient. The fifth aspect concerning the minimum investment for hedge fund investors gives the assertion that hedge funds with a larger minimum investment have a higher likelihood of withdrawal hence rendering the fund management fragile. Funds with a smaller minimum investment tend to attract smaller and risk- averse investors who go for safer strategies and fund management. 

Empirical Results

Non-parametric Kaplan-Meier Analysis of Hedge Fund Survival

Figure 1 below refers the Kaplan-meyer survival and the corresponding Nelson_Aalen hazard curves. There is a clear observation that the hazard and survival curves differ greatly by the graveyard status. The log rank and the generalized Wilcoxon tests were conducted to show the differences between the two curves.

Figure 1: Kaplam-meier survival curves by Graveyard Status

On the other hand, Table 1 below shows the 5 5 significant risk measures with a significance of 1% level. There are explanatory variables in the model. The age impact here is ascertains the fact that the longer the fund had been in existence, the higher its ability to survive (BGP 2001).  When the stated variables i.e. age, size, HWM, performance and lockup are included, the standard deviation losses the explanatory power while ES and TR stay significant at 5% level. It is to show that the downside risk measures can predict the survival of hedge funds while the SD does not. The impact of age signifies that the longer the fund has been in existence, the higher the likelihood of its survival. Funds with HWM are very likely to survive since the provision dictates that the fund managers collect their incentive fees after recovery of the previous losses hence acts as a signal to manager quality. The provision also lowers existing investors’ marginal cost for staying with the fund due to poor performance. This enables the fund managers to retain the investors when liquidation is costly. Funds with lockup provision also retain investors even after perfoming poorly. However, the survival of hedge funds is not explained by the manager’s personal investment and the power of size.

Table 1 below shows the total five significant risk measures with a significance of 1% level, when they are only explanatory variables in the model. When the stated variables i.e. age, size, HWM, performance, and lockup are included, the standard deviation losses the explanatory power while ES and TR stay significant at 5% level. It is to show that the downside risk measures can predict the survival of hedge funds while the standard deviation does not. The impact of age signifies that the longer the fund has been in existence, the higher likelihood of survival.

Survival Analysis Based on the Drop Reasons

The analysis refines the database to come up with funds which might not have failed. As previously mentioned, successful hedge funds might be moved to the graveyard and classified as defunct if they do not report to the database since reporting to the database is not mandatory. Only  liquidated funds should be regarded as failed ( Baquero et al2005). The analysis shows that some hedge funds were regarded as graveyard yet they were still alive. In this case, if such funds experience downward trends, the action settles on the fund managers to come up with appropriate strategies to save them for instance liquidating before “market crash” to avoid losses.

A Survival Analysis to predict Real Failure

The “real failure” concept follows the following guidelines in determining the survival of hedge funds. Once listed in the database but stopped reporting, negative average rate of return for the last six months and a decrease in AUM for the last 12 months. Table 1 shows the five risk measures inclusive of the SD, which is significant at 1% level. The HWM and other dummy variables in place, only the ES and TR maintain the explanatory power. The SD, SEM, and VaR do not change. Hence, SD is unreliable in measuring the total risk, which calls for consideration of downside risk. Older hedge funds with huge AUM will be the best option if staying in business is the only criterion for defining failure. The high hazard rate of equity market neutral and CA funds is undetectable when failure is defined as attrition..

Attrition rate versus failure rate

Table 2 shows the annual attrition rate between 1995 and 2004 as 8.7%. The annual average rate of failure is 3.1% within the same period.  The table 2 below provides adequate basis and failure rate. The hedge fund failures should be differentiated from discretionary fund closures. It is because they are frequent to failures and always driven by business or market expectations of fund managers.

The hedge funds have high attrition rates due to flexibility in portfolio adjustments, when the market environment moves in a detrimental direction.

Table 2: Attrition Rate” versus “Failure Rate” of Hedge Funds (1995–2004)

Conclusion

The  hedge fund survival over the 1994-2005 periods using the Lipper TASS database was inestigated in this paper. The downward risk measures for instance the ES and TR are advantageous to the standard deviation, when predicting hedge fund failures. The standard deviation is too juvenile when estimating the left-tail risk in hedge funds . Liquidation of hedge funds does not necessarily mean failure of the funds. Liquidated ones averagely have lower downside risk than the average hedge fund in the graveyard. Finally, clarifying the roles of performance, age, size HWM and lockup provision in predicting hedge fund failure is paramount. Probit and logit regression models with dichotomous dependant variables can also be used. The performance and HWM are essential in determining fund failure. Performance has always been significant at 1% level after risk control, age, size, style, leverage, personal capital, HWM and the lockup provision. Funds having HWM provision are less likely to fail. The lockup provision at times prevents attrition by preventing redemption in a set period albeit it plays no role in the prevention of hedge funds failure.

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