Date post: | 06-Apr-2018 |
Category: |
Documents |
Upload: | kostas-iordanidis |
View: | 229 times |
Download: | 0 times |
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 1/49
Time-Varying Coefficient Model for Hedge Funds∗
Gilles CRITON†and Olivier SCAILLET‡
Second version, September 2009
Abstract
We propose a time-varying coefficient model in order to analyze the dynamic in estimated
alpha and betas. We showed that the proportion of “skilled”funds are higher with our model
than with a static linear factor model. Indeed, our time-varying coefficient model captures the
dynamic part of alpha that reflects the dynamic strategy that we can find within Hedge Funds.
Furthermore this model is not only capable of looking into anticipation for Hedge Fund managers
but is equally well suited for the analysis of beta exposure. We show that whatever the strategy,
the increase in risk behavior is mainly concentrated on the credit spread risk factor and bond
risk factor.
∗We thank Jerome Teiletche as well as seminar participants at Pictet, Unigestion, SoFiE (2009).†
‡
1
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 2/49
1 Introduction
Nowadays, it is well known that investing in Mutual Funds, on average, underperform passive
investment strategies. One class commonly called Hedge Funds are defined as pooled invest-
ment vehicles that are privately organized, and not widely available to the general investing
public. Hedge Funds are private partnerships that use advanced investment strategies and can
use derivatives, leverage and short selling. Over the last few years, Hedge Funds have become
the favorites of many private as well as institutional investors. Hedge Funds follow investment
strategies that are substantially different from the non-leveraged, long-only strategies conven-
tionally followed by investors. During alternative investment seminars and conferences, Hedge
Fund managers boast about their ability to produce something they refer to as “alpha”or “ab-
solute return”in the sense that performance is not due to primary asset classes performance.
They do not aim to track and try to beat a certain benchmark, but instead are focused on
pure return generation. Hence Hedge Funds generate alpha, as opposed to depending on beta
and performance should normally result from active management decisions combined with the
skills of their advisors. However statistical analysis shows that many of them retain significant
exposure to different types of market risk factors.
Consequently, it is essential for qualified investors to determine whether or not these strategies
are sensitive to the market and whether they can find alpha through the manager’s skill. For
these reasons, an increasing focus has been directed to the performance of Hedge Funds and
their factor exposures.
Mostly, owing to the theory of CAPM or APT, fund performances are assessed by a parametric
model with the hypothesis of normality and linearity of coefficients, as well as, the non-dynamic
behavior of beta. Some researchers expanded the parametric model to the world of Hedge
Funds. Fung and Hsieh (2001, 2004a) developed factors used to replicate trend-following
strategies. Agarwal and Naik (2000) suggested an approach using option-based returns in
order to capture the non-linearity in beta. Recently, Bollen and Whaley (2008) tested for
structural change and used two econometric models in order to capture the dynamic in beta.
In this paper, we attempt to go a step further than the previous research.
First, by developing the result from Bollen and Whaley (2008) by testing up to five multiple
structural changes. We showed that the relative number of breaks by fund has increased over
the last few years, resulting in the increase of the use of leverage.
2
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 3/49
Secondly, by developing a new model1 for Hedge Funds which can take into consideration their
distinctly non-normal characteristics, the dynamic in manager skill, as well as, the dynamic
trading represented respectively by alpha and beta. This model allows us to relax traditional
parametric models and to exploit possible hidden structure. For example, what manager skillis the most important? Is it the skill to pick and choose the right stocks, bonds, any other
financial products, or is it the skill to anticipate market events? If we consider that alpha
estimated from a linear model contains the two skills, how can we separate and study them?
Can we find a different proportion of positive-alpha funds? This model specifically allows us to
look into how managers behave in relation to strong events and whether or not they succeed
to generate alpha. Moreover, Hedge Fund managers are likely to change trading strategies
in order to obtain “absolute return”2. Therefore, the exposure to a risk factor can change
during special events and can have some deep implications for a Fund of Funds or a portfolio.
Often it has been merely stated that during an event, risk to a specific factor can increase or
decrease. Our study also portrays how the beta exposure or risk behaves in relation to market
reaction, as well as, alpha during two agitated periods; the equity bubble crisis (the Equity
Bubble hereafter)3 and LTCM crisis (LTCM hereafter) 4.
Thirdly, with the methodology used for mutual Funds by Barras, Scaillet and Wermers (2008)
called False Discovery Rate, we look into the proportion of the fund’s population which has
an increase in different market exposures, as well as, the proportion of skilled, unskilled and
zero-alpha funds.
We showed that the proportion of “skilled”funds are higher with our model than with a static
linear factor model. We explained such a difference by our model’s ability to capture the
dynamic part of alpha that reflects Hedge Fund managers’ market timing ability. We found
that the quantity of new alpha substantially increased the proportion of positive and negative
alpha funds. Nevertheless, we showed that the majority of Hedge Funds are zero-alpha funds
as Barras, Scaillet and Wermers (2008) portrayed for Mutual Funds. Furthermore, we look
into the possibility for a strategy to have a common increasing trend to a market exposure
during a crisis. For all strategies, the main result was a common trend to an increase in the
credit spread risk factor.
1This time-varying coefficient model has been fully explored by the seminal work of Cleveland, Grosse and Shyu(1991).
2positive returns in all market conditions, up or down.3February, March 20004July, Auguste, and September 1998
3
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 4/49
To the best of our knowledge, this is the first paper which tries to look into how the risk of
Hedge Funds and CTAs exposure changes. This paper also looks into the skill of manager
anticipation, part of alpha.
The rest of our paper is organized as follows; Section 2 reviews related literature about Hedge
Funds modeling, and the dynamic in beta5. The data is described in section 3. Section 4
summarizes the risk factors defined in Fung and Hsieh’s paper (2001, 2004). Section 5 tests
for structural change by applying the method of Bai and Perron (1998). Section 6 defines
our time-varying coefficient model. Our methodology in which we apply our model is defined
in section 7. Section 8 provides results of our time-varying coefficient model, as well as, the
application of the False discovery Rate (FDR hereafter) to alpha and beta bringing, in this
way, a new tool for Hedge Fund analysis. Section 9 presents our conclusion.
2 Literature review
It is well-known that there are some drawbacks to model Hedge Funds. Various fundamental
and statistical multifactor models for Hedge Funds have been analyzed by Agarwal and Naik
(2000), Edwards and Caglayan (2001), Fung and Hsieh (1997, 2001, 2004a), Lhabitant (2001),
Liang (2001), Schneeweis and Spurgin (1998), among others.
Research has specifically been focused on identifying dynamic trading strategies in order to
mimic the actual trades of Hedge Funds (for example: Fung and Hsieh (1997), Agarwal and
Naik (2000)). Contrary to mutual funds, performance analyzes of Hedge Funds are completely
different. One reason for this, concerns the returns of Hedge Funds which usually have low
correlations with market indices, and therefore a traditional CAPM analysis using the Jensen
measure is typically non-appropriate. Another reason concerns the linear regression which
works well for mutual funds because its strategies tend to follow a buy-and-hold pattern.
Brown, Goetzmann and Ibbotson (1999) have shown that Hedge Funds pursue many different
styles which are completely different to the buy and hold strategy followed by Mutual Funds
and therefore can put the hypothesis of linearity to question. Liang (2001) also documents
that Hedge Fund investment strategies are dramatically different from those of Mutual Funds.
To the best of our knowledge, the first paper which suggested another approach in order to bet-
ter analyze the returns of Hedge Funds was written by Fung and Hsieh (1997). They attempted
5the readers can find a detailed literature review into the book from Agarwal and Naik (2005).
4
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 5/49
to analyze the returns to Hedge Funds by applying the factor or style analysis conducted by
William Sharpe with respect to Mutual funds. As we will be using their methodology in this
paper we will introduce and develop it further later on in our work. In their paper, they found
that the amount of variation in Hedge Fund returns that is explained by asset class return islow 6. Schneeweis and Spurgin (1998) confirm this result by conducting a regression analysis
of the returns of stocks, bonds, commodities, and currency returns. They found that R-square
measures that range from near zero for relative value Hedge Funds to 0.67 for Hedge Funds
that pursue primarily a long equity investment strategy, which concludes that Hedge Fund
return patterns do not map as well to the financial asset as do mutual fund returns. In order
to ameliorate the explanation of Hedge Fund returns by asset class, Fung and Hsieh (1997)
applied a factor analysis based on a Hedge Fund’s trading style. They found that five dif-
ferent trading style (system/opportunistic, global/macro, value, systems/trend following and
distressed) explain about 45 percent of the cross-sectional variation in Hedge Fund returns.
Following Fung and Hsieh (1997), a lot of articles have been developed which seek to under-
stand the trading strategies and characteristics of Hedge Funds by regressing their returns
on explanatory factors (Agarwal and Naik (2000), Brown and al. (2001), Mitchell and Pul-
vino (2001)). Agarwal and Naik (2000) extended this analysis of Hedge Fund performance by
recognizing that funds may follow dynamic non-linear trading strategies. They used stepwise
regression to identify the independent variables, and found that a put or a call option on
an underlying variable is the most significant factor in the case of 54 percent of their funds.
Also, Fung and Hsieh (2002) incorporated option strategies into a Sharpe style model, but
they focused on exploring the risk of fixed income Hedge Fund styles and did not consider
performance explicitly. In contrary to Agarwal and Naik’s (2000) discoverers, Fung and Hsieh
found that in most cases their option strategies only played a marginal role. One reason
given by the authors for the varied results mentioned above is due to the fact that Fung and
Hsieh (2002) used active and advanced straddle strategies. The paper written by Mitchell and
Pulvino (2001) on merger-arbitrage strategies are also begun to produce useful explicit links
between Hedge-Fund strategies and observable asset returns. Mitchell and Pulvino (2001) sim-
ulated the returns of a merger arbitrage strategy applied to announced takeover transactions
from 1968 until 1998. In summary, Fung and Hsieh (1999,2000,2001), Mitchell and Pulvino
(2001) and Agarwal and Naik (2004) show that Hedge Fund returns relate to conventional6R-Square measures were less than twenty five percent for almost half of the Hedge Fund studied
5
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 6/49
asset class returns and option-based strategy returns. They relate another strong difference
between Mutual Funds and Hedge Funds which concerns the problem of managers changing
their investment style over time. This problem is less acute for Mutual Funds than for Hedge-
Funds. Brealey and Kaplanis (2001) presented evidence that within each category funds tendto make similar changes to their factor exposures. Their interest is in the broader issue of how
well data on Fund returns can be used to measure “changes”in factor exposure. Indeed they
found that their CUSUMs’ tests of the stability of factor loadings rejected the null hypothesis
of stable coefficients at the 5 percent level in the case of three quarters of the funds. In a
similar way, Fung et al.(2006) paper was concerned with estimating factor exposures at the
time of particular crises. They study vendor-provided fund-of-fund indices, and performed
a modified-CUSUM test to find structural break points in fund factor loadings. They found
that the break points coincide with extreme market events7. Recently, the paper from Bollen
and Whaley8 studied 2 econometric techniques that accommodate changes in risk exposure.
The primer methodology was developed by Andrews, Lee, and Ploberger (1996). They stud-
ied a class of optimal tests9 for multiple changes. The latter, uses maximum likelihood and
a Kalman filter under an AR(1) model. They found significant changes in the risk factor
parameters in about 40 percent of their sample of Hedge Funds.
Nevertheless the 2 precedent methodologies use a hypothesis of normality which is not adapted
to the world of Hedge Funds. With strong evidence of non normality (Agarwal and Naik, 2001;
Amin and Kat, 2003; Fung and Hsieh, 1999; Lo, 2001), the mean and standard deviations are
not sufficient to describe the return distribution, and higher moments need to be considered.
Kat and Lu (2002), Brooks and Kat (2002) show that although Hedge Funds offer high mean
returns and low standard deviations, the returns also exhibit third and fourth moment at-
tributes10 as well as positive first-order serial correlation11.
Furthermore these results about the distribution of Hedge Funds could be different depending
on their strategies (Anson, 2006).7the collapse of Long-Term Capital Management in September 1998, and the peak of the technology bubble in
March 20008At the moment where we write this article, we do not know when this paper will be publish in Journal of Finance.9In the sense that they maximize a weighted average power, namely the Avg-W and Exp-W.
10Skewness and kurtosis.11They showed (as Lo & al. (2004)) that monthly Hedge Fund returns may exhibit high levels of autocorrelation.
6
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 7/49
3 Database
For this study, we use the Center for International Securities and Derivatives Markets (CISDM)
and HedgeFund.Net database. The primer covers the period from January 1994 through to
July 2007 with the advantage of the inclusion of dead funds. One of the main studies in this
article is to analyze whether or not Hedge Funds and CTA were able to generate alpha during
market events or on the contrary, whether they generated negative alpha. In order not to
create a bias we have included all funds in our analysis even though dead funds mean that
they did not necessarily generate alpha or worst, generate negative alpha. The sample with
all funds contains approximately 9800 funds (Hedge Funds, CTA and Fund of Funds), and
approximately 3000 live funds. The latter is the largest commercial database of active Hedge
Fund, Fund of Fund and CTA products with over 8500. It covers the period from May 1975
through to October 2008 but we are only concerned with the period from January 1991 until
October 2008. It has approximately 3000 Funds of Funds, 4900 Hedge Funds, and 600 CTAs.
For every fund, we have collected the returns, the strategy and fund type12. Returns are net
of management and performance based fees. We select funds for a minimum of 30 months
covering the period May 1998 until June 2000. We have created 2 groups in order to analyze
them separately; one for Hedge Funds and the other for CTAs. Nevertheless, it is more
pertinent to study Hedge Funds and CTAs depending on their strategies. There is a vast
selection of academic literature on how to classify Hedge Funds. Fung and Hsieh (1997)
and Brown and Goetzmann (2003) have identified between five and eight investment styles,
whereas, Bianchi Drew, Veeraraghavan, and Whelan (2005) have found the presence of only
three different Hedge Fund styles. In contrast, Hedge Fund database providers classify Hedge
Funds into between 11 and 31 investment styles. Therefore choosing a number of strategies is
not an easy task, especially because we are not persuaded by the precedent results.13. Thus,
it seems better for this study to follow the 23 strategies defined by the provider plus the CTA
as another strategy as well as Fund of Funds.
{please insert Table I here}
HedgeFund.net uses 31 strategies that we have grouped in order to obtain the same 23 strate-
gies from the CISDM.
12
This database combines four main group, Hedge Funds, Funds of Funds, CTA, and CPO.13it will be the topic we are going to turn to next.
7
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 8/49
{please insert Table II here}
The main analyzes consider the merge database14 due to the specificity of these products that
they tend to avoid direct regulation (by the SEC or any regulatory authorities).
4 Factors
Hedge Funds can be divided into four main groups, market directional, corporate restructuring
fund, convergence trading fund and opportunistic funds. We can add to each of them a major
risk factor. The exposure to the stock market is the major risk affecting market directional
funds 15. The major risk affecting corporate restructuring funds 16 is exposure to the event
risk17 which is the same for the convergence trading fund 18. Into every group, each strategy
can also have a specific exposure to another risk factors and therefore risk exposure can change
drastically in regards to the strategy.
Consequently, defining factors is not an easy task. Precedent articles have shown that the
relation between Hedge Fund returns and market returns are nonlinear. Moreover, Hedge
Funds have a systematic risk but it is not possible to capture this risk with standard asset
benchmarks. Therefore many researchers have suggested factors in order to explain Hedge
Fund returns (Fung and Hsieh (1999, 2000, 2001, 2004), Mitchell and Pulvino (2001) and
Agarwal and Naik (2004)). Nevertheless, it is not the only problem that we have with factors.
Indeed, knowing the right number of factors is major in order to capture risk correctly. If
some risk factors are missing, the model is misspecified and we can question whether alpha
corresponds to the manager skill. If there are too many factor, we can have a problem of
multicollinearity.
To the best of our knowledge, the most accomplished article about Hedge Fund factors was
written by Fung and Hsieh (2004). They showed that their seven factor model strongly explains
variation in Hedge Fund returns and at the same time avoid multicollinearity19. Moreover,
they managed to obtain similar results using the Agarwal and Naik (2004) option-based factor
14We merged the HedgeFund.Net database to the CISDM and found that they are 925 funds in common.15equity Long/Short, Short selling and equity market timing.16distressed securities, merger arbitrage and event driven.17failure of the proposed transaction.18fixed income arbitrage, convertible bond arbitrage, equity market neutral, statistical arbitrage, and relative value
arbitrage.19We use the diagnostic technique presented in chap 3 of Regression Diagnostic by Belsley, Kuh, and Welsh (1980).
The diagnostic is capable of determining the number of near linear dependencies in a given data matrix X, and thediagnostic identifies which variable are involved in each linear dependency. We do not detect any multicollinearitywith these eight factors.
8
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 9/49
model.
Their paper included seven factors and they added an eighth factor on their website 20 that we
have also added.
Therefore we will follow the eight Hedge Fund risk factors defined in Fung and Hsieh’s paper(2004)21.
These factors are :
Three Trend-Following Factors: Bond, Currency and Commodity22 which capture a non linear
exposure.
•• 2 Equity-oriented Risk Factors: S&P500 minus risk free rate23 and Size Spread Factors defined
by the Russell 2000 index monthly total return less S&P500 monthly total return.
• 2 Bond-oriented Risk Factors: a Bond Market Factor represented by the monthly change in the
10-year treasury constant maturity yield, and a Credit Spread Factor formed by the monthly
change in the Moody’s Baa yield less 10-year treasury constant maturity yield.
• One Emerging Market Risk Factor, the MSCI Emerging market minus the risk free rate.
5 Structural Change
Few researchers have tested if there has been a structural change. The tests used considered
only one structural change and most of them needed to know when the break point should
happened. Indeed, the classical test for structural change is typically attributed to Chow
(1960) with the weakness that the breakdate must be known a priori. Quandt (1960) treated
the breakdate as unknown but, in this case, the chi-square critical values are inappropriate.
The problem of critical values was solved simultaneously in the early 1990s by several sets of
authors. Nevertheless, the best known solution was provided by Andrews (1993), and Andrews
and Plobergers (1994). Andrews, Lee and Ploberger (1996) developed the precedent results
into a class of optimal tests for linear models with known variance. This class of optimal
tests allows an arbitrary number of changepoints. However, Bolley and Whaley implemented
this test using just one changepoint. The problem with these tests in the case of multiple
structural change is practical implementation. According to Perron, the Avg-W and Exp-W
20
http://faculty.fuqua.duke.edu/ dah7/.21For more details about the construction of these factors see Fung and Hsieh, 1997, 2001, 2004a.22These factors are downloadable on http://faculty.fuqua.duke.edu/ dah7/DataLibrary/TF-FAC.xls .233-month USD LIBOR
9
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 10/49
tests require the computation of the W-test over all permissible partitions of the sample. Bai
and Perron (1998, 2004) solved this problem with a very efficient algorithm which is available
on their website24. Although Bai and Perron (1998, 2004) proposed three different tests25, we
have applied just one of them which is, in our opinion, the most significant for this analysis.This is the second test provided by Bai and Perron, called Double Maximum Test. It is a
test of no structural breaks against an unknown number of breaks given some upper bound
(M = 5 in our application). In this category, there are two tests, the UDmax and the WDmax
which differ by their weight methodology26.
The results are conclusive.
{please insert Table III here}
The majority of Hedge Funds present structural breaks. By strategy, the minimum percentage
of Hedge Funds with breaks is 31 percent (Other Relative Value) and the maximum is 70
percent for Event Driven Multi Strategy. If we consider the most representative strategy
(Equity Long/Short, 2142 Hedge Funds), 62 percent present some structural changes. All
these precedent results took into consideration track records with more than 30 months. Bai
and Perron’s tests also give the break’s date. Therefore another interesting view is to look at
the frequency of break’s dates in the Hedge Fund’s universe by considering the number of the
breaks at time t; relative to one fund. Indeed, the increase in the amount of Hedge Funds is
considerable and we must take this huge growth into consideration within our analysis. For
this reason, we have suggested to create a ratio called Rbreaks, which is defined as the number
of breaks at time t divided by the number of funds at time t.
{please insert Graph I,II,III,IV here}
Once again, the results are conclusive. Whatever the strategy, we have noted an increase in
the ratio over the period 2002-2007 as well as an increase in the frequency of breaks.
There are two interesting things to say about the two crisis. In August 1998, the Russian gov-
ernment defaulted on the payment of its outstanding bonds. This default caused a worldwide
liquidity crisis with credit spreads expanding rapidly all around the globe. The Russian debt
24http://people.bu.edu/perron/. This code is a companion to the paper: Estimating and testing structural changesin multivariate regressions (Econometrica, 2007) (developed by Zhongjun Qu).
25The primer test considers no break versus fixed number of breaks (up to 5 breaks)This test considers the sup Ftype test of no structural break (m = 0) versus the alternative hypothesis that there are m = 1,..., 5 breaks. It is ageneralization of the sup F test considered by Andrews (1993). The latter is a test of the null hypothesis of l breaksagainst the alternative that an additional break exists. This sequential procedure estimates each break one at a time.
It stops when the sup F (l + 1|l) test is not significant.26See Bai and Perron (1998) for a full explanation on the different weights.
10
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 11/49
crisis (LTCM) was a crisis that materially affected Hedge Fund returns that was confirmed by
the results from Rbreaks. Furthermore, the precedent results for a majority of strategies were
confirmed.
Surprisingly, we noticed the opposite for the equity bubble crisis which corroborated the con-
clusions of Brunnermeier and Nagel (2002).
The conditions for financial markets in 1999 were very good, especially for riskier assets.
During this period a bubble developed. According to Brunnermeier and Nagel (2002) most
Hedge Funds, despite irrational levels of valuation, decided to ride the bubble rather than
clear their positions. They explained that Hedge Funds heavily tilted their portfolios towards
technology stocks without offsetting this long exposure by short or derivatives. They concluded
that Hedge Funds deliberately held technology stocks and were able to exploit this opportunity.
These arguments are confirmed by the fact that Rbreaks is very low, for the majority of the
strategies, showing fewer structural changes.
This section has shown that it is not enough to purely take into consideration different dis-
tributions but also that alpha and beta could be dynamic and consequently depend on time.
Furthermore, we showed that the risk in Hedge Funds increased over the last few years es-
sentially due to the use of leverage in order to reach the investors desired return target. The
next section presents an answer to the problem of dynamic for alpha and beta. We suggest a
time-varying coefficient model with the Fung and Hsieh factors which are, in this way, better
suited for Hedge Funds.
6 Our Model
Stone (1977) introduced local linear least squares kernel estimators as a regression estimator
which has been generalized by Cleveland (1979)27.
Stone (1980, 1982) used local linear least squares kernel and its generalization to higher-order
polynomials to show the achievement of his bounds on rates of convergence of estimators of a
function m and its derivatives. Fan (1992, 1993) showed in the univariate case that another
important advantage of local linear least squares kernel estimators is that the asymptotic bias
and variance expressions are particularly interesting and appear to be superior to those of
the Nadaraya-Watson or Gasser-Muller kernel estimators. Furthermore, Kernel estimators27The robust local regression estimators.
11
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 12/49
have the advantage of being simple to understand and globally used by researchers. The
mathematical analyze and the implement into a computer is easy, and they are consistent for
any smooth m, provided the density f of X is satisfies certain assumptions.
The varying coefficient model assumes the following conditional linear structure:
Y t =
p j=1
β j(t)X jt + εt = α(t) + Xβ (t) + εt
for a given covariates (t, X 1,...,X p) and variable Y . See appendix for more details on the
Time-Varying Coefficient Model.
Thus β i(t) depend on t, this hypothesis can significantly reduce the modeling bias and espe-
cially avoid the “curse”of dimensionality28.
To practice statistical inferences such as the construction of confidence interval for β i(t) dif-
ferent methods have been suggested. Coling and Chiang (2000)29 suggest a naive bootstrap
procedure that we have applied in this article.
The main advantage of this naive bootstrap procedure is that it does not rely on the asymp-
totic distributions of β i(t). Coling and Chiang (2000) recommend another alternative boot-
strap procedure suggested by Hoover et al. (1998), which relies on normal approximations
of the critical values30. According to the authors, both bootstrap procedures may lead to
good approximations of the actual (1 − α) confidence intervals when the biases of β i(t) are
negligible31.
It is well-known in kernel regression that the selection of bandwidths is more important than
the selection of kernel function. In practice, bandwidth may be selected by examining the plots
of the fitted curves. Moreover, for this study we need an automatic bandwidth selection. Colin,
Wu and Chiang (2000) suggest that we apply the choice of bandwidth “leave-one-subject-
out”cross-validation32. We illustrated the performance of our estimator by a simulation study.
We used the bandwidth defined above and a number of data equal to 50 in order to respect
28Kernel depends, in this context, only on t.29Another paper of Galindo, Kauermann, and Carroll (2000) suggest another bootstrap method based on the wild-
bootstrap of Hardle and Marron (1991)30Construct pointwise intervals of the form
β i(t) ± z(1−α/2) se∗B(t),
where se∗B(t) is the estimated standard error of β i(t) from the B bootstrap estimators and z(1−α/2) is the (1− α/2th)
percentile of the standard Gaussian distribution.31They point out that theoretical properties of these bootstrap procedures have not yet been developed.32Appendix I gives a summary to the algorithm.
12
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 13/49
the average size of Hedge Fund tracks (see appendix).
We regress the net-of-fee monthly excess return (in excess of the risk-free rate) of a Hedge
Fund on the excess returns earned by traditional buy and hold and primitive trend following
strategies defined above33. We have grouped the estimates together into the 23 strategies
defined by the CISDM. In each group obtained, we have formed 2 groups. The first is composed
by all tracks record which is superior to 30 months. The second has the first requirement (more
than 30 months) but only has funds which were available during the 2 crisis.
{please insert Table I here}
Indeed, we are concerned with the 2 different aspects. The first focusses on the security
selection ability ( α(t)). The second aspect treats the ability to anticipate market events or
to cope with them (i.e. robust ability). In order to capture anticipation in alpha, we are
going to look at 2 strong market events: the LTCM crisis and the Equity Bubble crisis. To
properly cover these periods, we have selected 3 consecutive months. For the LTCM period we
will focus on July, August, and September 1998, and for the Equity Bubble period, February,
March and April 200035. Using these 3 months’ data, we have built 2 indicators for α36 and
2 indicators for β i, (i = 1, ..., 8). The 2 primers are the difference between the second month
and the first month and the difference between the last month and the second month.37 The 2
indicators for beta38 have the same differences but are augmented by 10 percent39. By doing
this, we were able to determine whether or not managers were able to react quickly and also
if we can capture change exposure superior to 10%. In each case, we have used the t-statistic, ti,α = αi/ σ αi and ti,β = β i/ σ β ifor every α j(t) and β ij(t), i = 1, ..., 8. For every indicator
33Kat and Lu (2002), Brooks and Kat (2002) show that the net-of-fees monthly returns of the average individualHedge Funds exhibit positive first-order serial correlation which is due, according to the authors, to marking-to-marketproblems. We have removed serial correlation by applying the same methodology as used in Brooks and Kat’s paper(2001), called the simple Blundell-ward filter34.
The observed (or smoothed) value V ∗t of a Hedge Fund at time t could be expressed as a weighted average of the true
value at time t, V t and the smoothed value at time t − 1, V ∗t−1:
V ∗t = αV t + (1 − α)V ∗t−1,
rt =r∗t − αr∗t−1
1− α.
35End of month of July, Auguste, and September and end of month of February, March, and April.36αt − αt−137These two indicators were created in order to show a new methodology that this model bring to the analysis of
Hedge Funds. Nevertheless, some others indicators could be more appropriate for a specific analysis of these marketevents.
38β t − (1.1) × β t−139
This methodology is simply a linear relation between 2 independent variables which, under the condition of normality for β jt j = 1,...N j ; N j being the number of funds, assure that the linear relation follows also a normaldistribution.
13
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 14/49
covering the 2 periods i.e. 4 indicators by fund for α j(t) and 32 indicators by fund for β ij(t).
Once it was done, we calculated the p-value for every indicator and the precedent means.40
If we examine just 1 fund, we only have to test a null hypothesis H 0 versus an alternative H 1
based on a statistic (let’s say X ). We have 2 possibilities for a given rejection region Γ. Either
we reject H 0 when X ∈ Γ or we accept H 0 when X ∈ Γ. Nevertheless, there is the possibility
that there is an error in the test. On the one hand, the test can reject H 0 whereas H 0 is true,
called type I error. On the other hand, the test can accept H 0 whereas it is H 1 which is true.
This error is called a type II error. Now, if we want to test for numerous Hedge Funds this
problem becomes much more complicated. Testing numerous Hedge Funds is to do, in fact, a
multiple-hypothesis testing.
A first approach was suggested by Kosowski, Naik and Teo (2005), using a bootstrap proce-
dure; They analyzed whether or not Hedge Fund performance can be explained by luck and if
Hedge Fund performance persists at annual horizons. Their methodology tested the skills of
a single fund that was chosen from the universe of alpha-ranked funds. Barras, Scaillet, and
Wermers (2008) suggested another approach which is notably informative with regards to the
prevalence of outstanding managers in the whole fund population. Their approach simultane-
ously estimated the prevalence and location of multiple outperforming fund within a group;
examining fund performance, in this manner, from a more general perspective. Therefore we
have used their methodology called False Discovery Rate (FDR hereafter) in our multiple-
hypothesis test.
Step 1, for each strategy, we have applied the FDR on α (security selection ability) in order to
determine the proportion of zero-alpha funds and skilled and unskilled funds; but also for the
indicator defined above αt − αt−1 (timing ability) for the 2 crisis. In this way, we were able
to determine, for each strategy, the proportion of the security selection ability as well as theproportion of the timing ability.
Step 2, we applied the FDR on the “beta” indicators defined above during the 2 crisis in order
to determine if we could observe a common increasing trend for change in market exposure i.e.
a common increase in beta value of more than 10%. Moreover, we calculated the median of the
percentage change for each beta of each strategy in order to give an “I.D.” of the possibility
change in market exposure.
40
The t-statistic distributions for individual Hedge Funds are generally non-normal. In order to overcome the non-normality, we use the same approach as Barras, Scaillet, and Wermers (2008), consisting of the use of a bootstrap tomore accurately estimate the distribution of t-statistics for each Hedge Funds (and their associated p-values).
14
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 15/49
With these results, we brought 2 different views about exposure change. Firstly, a view about
common trend change and secondly about what are the highest impacted beta.
7 Results
Generally speaking, Mutual Fund managers use a buy and hold strategy consisting of buying
a range of financial products according to their investment strategy and then they hold them
according to the time horizon (or investment horizon)41. Therefore Mutual Funds are often
associated with Funds that have a relative performance. Unsurprisingly, Barras, Scaillet and
Wermers (2008) have shown that only 0.6 percent of Mutual Funds generate positive alpha
and a majority of them can also be considered as zero-alpha funds. So the legitimate question
is: Are the results relatively the same for Hedge Funds or are they completely different?
On the one hand, if we apply a static linear factor model such as the Newey-West (1987)
heteroscedasticity and autocorrelation consistent estimator, we determine a “static”alpha that
does not capture the particularities of Hedge Fund Strategies. And therefore we have showed
that, whatever the strategies, the majority of Hedge Funds are zero-alpha funds.
On the other hand, when we applied our time-varying coefficient model, we were able to
capture other skills from Hedge Fund managers, resulting in obtaining us a non negligible
increase of positive alpha funds.
{please insert Table V here}
Concerning the risk behavior, we showed that the majority of Hedge Funds have a tendency
to get an increase in credit spread as well as bond market risk factors. We are going to look
into the results for seven out of the twenty four strategies in the following part of this paper 42.
Results for the CTA
We observed a strong difference for estimated alpha between the static factors model (SFM
hereafter) and our time-varying coefficient model (TVCM hereafter). The SFM gave a very
small percentage of positive and negative alpha funds with two percent and one percent respec-
tively. Whereas the TVCM roughly gave nineteen and twenty eight percent. The estimated
alpha from the two different crisis are interesting to point out. Although The CTA coped
41refer to the time between making an investment and needing the funds.42The results and the graphs for the seventeen remaining strategies are available upon request.
15
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 16/49
during the two crisis it obtained a strong percentage of positive alpha funds during the Equity
Bubble Crisis where approximately twenty seven percent were positive alpha funds.
During the Summer of 1998, CTAs had one of its best performances43 while all other Hedge
Fund strategies were struggling.Unsurprisingly, during the two events, the CTA had a tendency to show a slight increase in
the credit spread risk factor and the emerging market risk factor. Nevertheless this sensitivity
concerned only a small percentage of our population. The majority of CTAs had a relatively
stable exposure.
{please insert Graph XI here}
Emerging Markets
The emerging market strategy showed a good proportion of stock-picker skilled funds where
approximately twelve percent generated positive-alpha which pointed out that the majority of
managers were fundamental bottom-up stock-pickers. We obtained the same results using the
SFM. It indicated that the estimated alpha was more “static”than with other strategies. The
proportion of dynamic skilled funds was very good during the two crisis with a huge number of
roughly forty percent, of positive alpha funds. These results confirmed that emerging market
equity hedge fund managers perceived the high volatility of emerging markets as an asset.
During the Equity Bubble and LTCM we noticed a greater dynamic strategy than previously
seen where approximately twenty-five and fifty percent of our population showed an increase
in two risk factors: the credit spread risk factor and the bond market risk factor. The credit
spread risk factor was the most sensitive factor during LTCM, whereas, four out of the eight
factors showed a sensitivity during the Equity Bubble crisis.
{please insert Graph V here}
Equity Long/Short
Equity Long/Short obtained approximately the same results as the CTA apart from the Equity
Bubble crisis. It obtained a better percentage with twenty four percent using the TVCM. The
SFM gave a small four percent and three percent of negative alpha funds. Certain Equity
Long/Short specialize in a specific sector like technology, and, unsurprisingly, the timer ability
had been more impact during the Equity Bubble than during LTCM. Generally speaking, the
43Approximately 10 percent in August and 7.5 percent in September according to CSFB/Tremont Managed Futures
16
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 17/49
proportion stayed relatively consistent pointing-out their ability to switch from the short to
the long position and visa versa.
A small percentage of the population showed an increase or a decrease in exposure during the
two crisis. We still noticed a sensitivity to the credit spread risk factor and to the commoditiesfactors during LTCM. Whereas emerging risk factor was the most sensitive during the Equity
Bubble crisis.
{please insert Graph VI here}
Equity Market Neutral
This strategy produced a very interesting result where the proportion of stock-picker skilled
funds was three percent higher than the estimated proportion using the SFM. Therefore the
two results were relatively closer than with the other strategies. Furthermore this result was
confirmed by the obtained percentage of estimated alpha during LTCM with zero percent. It
didn’t cope as well during the equity bubble. We noticed a tiny four percent during the first
period which reached a strong sixteen percent in the second period.
{please insert Graph VII here}
It was the most robust strategy in terms of change in exposure. Nevertheless, for a minorityof the population we noticed that the credit spread and the commodity showed the biggest
sensitivity during LTCM and the emerging market factor during the Equity Bubble.
Event Driven Multi Strategy
Event Driven Multi Strategy obtained the worst percentage of skilled-funds with zero percent
for the SFM and a small two point five percent for the TVCM. The result was confirmed
during the two crisis with zero percent during LTCM. This was surprising because the two
crisis created several opportunities44, and only the second crisis was more profitable. On the
other hand it was the strategy which obtained the smallest proportion of unskilled funds.
Therefore we can define it as a zero-alpha fund strategy.
{please insert Graph VIII here}
Another strength, for this strategy, concerned the percentage of the population to show a
variation in factor exposure. A negligible part showed an instability during the crisis. The44Invests in mergers, spin-offs, reorganizations, and other announced events.
17
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 18/49
factors concerned were the credit spread the emerging market factor and the commodity factor
for LTCM and the emerging risk factor for the equity bubble.
Global Macro
Global Macro showed a proportion of stock-picker skilled funds equal to five percent using
TVCM and one percent using the SFM. It obtained one of the bigger groups of unskilled
funds with roughly twenty eight percent. Unsurprisingly, the percentage of positive alpha
during LTCM increased up to twenty six percent. These results confirmed that global macro
managers have the most extensive investment universe and that they were able to find some
arbitrages. The Equity Bubble crisis also gave a good percentage of positive alpha funds with
eighteen percent.
Less than ten percent of our population showed an increase or decrease in our general expo-
sure. Credit Spread risk factor stayed the most sensitive during LTCM. Whereas, the size
spread factor, the emerging market risk factor and the credit spread risk factor (slightly) were
concerned about the change in exposure.
{please insert Graph IX here}
Short Bias
Step one, it is important to say that the number of Hedge Funds following this strategy was
relatively small, so the result, in our opinion, could be debatable.
The SFM gave five percent of skilled funds whereas the TVCM gave thirty five percent.
Furthermore, this strong percentage was less than the seventy one percent of positive alpha
funds found during LTCM. The Equity Bubble obtained a tiny twenty seven percent: This
impressive result confirmed the strong dynamic within the strategy.
Moreover, the short bias produced the best percentage of variation exposure in. More than
sixty percent of our population showed an increase in different market risk factors. Credit
spread was still present during LTCM while Size-spread risk factor had an non negligible
sensitivity to bond, commodity and emerging market risk factors during the Equity Bubble.
{please insert Graph X here}
18
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 19/49
Robustness
The goal of this section is to demonstrate that our model is robust to structural change and
that we succeeded to capture a jump in estimated alpha or beta. For this, we created a track
of return where the two betas had a structural change. We allowed for three different sizes:
fifty, one hundred and one hundred and fifty months which akin the size of Hedge Funds that
we can find in different databases.
The main problem with structural change concerns some technical conditions. Mainly that the
second derivative is required to be continuous in a neighborhood of t. As showed in appendix
I, we managed to obtain some very good results; even in the short sample.
Furthermore, in order to show that our results were independent to our model we created
another time-varying coefficient model which was also based on the work of Fan and Zhang
(1999). Nevertheless in second step to our estimator we used a B-spline smoothing instead of
a local regression. We retested the ability to capture a structural break (see appendix I). The
results were also very good.
We used one of the same example as in Zhang, Lee and Song (2002). Our result are less
accurate than Zhang, Lee and Song due to three reasons.
Firstly, our sample contains between 50 and 150 values in opposite to the range in 250-1000.Secondly, we did not apply a monte carlo study in order to find the optimal bandwidth (or
knot for the second model). Because of the size of our database, the use of a second bootstrap
algorithm for each fund (the first algorithm calculates the p-value) would have made the
estimation process too costly.
Thirdly, we used the S&P500 and the monthly change in the 10-year treasury constant maturity
yield as factors which are not a perfect factors set. And therefore these differences slightly
alter the performance of our estimator. For these reasons the different graphics truly represent
the obtained result for each fund.
In a second step, we applied the false discovery rate to the estimated alpha and betas obtained
by B-spline. The results gave approximately the same percentage of unskilled, zero and skilled
funds for our population.
19
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 20/49
8 Conclusion
Hedge Funds cover many different strategies which radically vary in terms of market exposure
and risk. However there are some common characteristics. Hedge Fund managers try to focus
on positive return (whatever the market conditions), the use of leverage and their structural
fees. If we want to model Hedge Funds, these characteristics imply a model which takes
some new assumptions into consideration. No assumption about statistical distribution, the
dynamic in beta as well as non linearity exposure to the market.
In order to overcome these drawbacks, we used a time-varying coefficient model as well as
the whole factors; defined in Fung and Hsieh’s paper (1997, 2001, 2004). The model allowed
us to postulate that alpha and beta are a function which depended on time and avoided
parametric distribution. The use of the factors from Fung and Hsieh allowed us to capture
the non-linearity in beta and therefore gave the best overall risk factors.
This model allowed us to separate manager skill into two components pointed-out by the (stock
or bond or funds)-picking and the ability to anticipate market events. It also allowed us to see
what were the changes in beta exposure or the managers’ reactions according to the market’s
conditions.
Whereas Barras, Scaillet and Wermers (2008) showed us that only 0.6 percent of Mutual
Funds generated positive alpha and therefore a majority of them can be considered as zero-
alpha funds. We found a different result for Hedge Funds. Hedge Fund managers seek absolute
returns and try to outperform the market whatever the market conditions are. We showed
that this dynamic was not well-captured by a static factor model where the results considered
Hedge Funds as zero-alpha funds. Whereas our model found a better proportion of positive
alpha funds but also, unfortunately, a proportion of negative alpha funds.
Another advantage of this model was its capacity to analyze change in factorial exposure. We
saw three main results. Firstly, that a majority of Hedge Funds with a track record superior
to 30 months had a minimum of one structural break. Furthermore we noticed that the
frequency of breaks has increased over the last few years. Secondly, by strategy, we examined
the percentage change between our eight factors and saw if there was a persistent for beta
parameters. Our results suggest that the common increasing percentage change of different
Hedge Funds in the down-state of the market is strongly represented by one exposure. it
was the credit spread risk factor. Last but not least, we applied the FDR to determine the
20
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 21/49
proportion of the fund’s population which had an increase, a decrease, or stayed constant
in the market’s exposure during the two crisis (LTCM and the Equity Bubble). We show
that within a strategy, Hedge funds have a tendency to have an increase in market exposure.
The changes in factorial exposure and the proportion of funds give us a strong tool for riskmanagers and specifically for stress-testing.
21
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 22/49
References
[1] Ackermann C., McEnally R., and Ravenscraft D. The Performance of Hedge Funds:Risk, Return, and Incentives. The journal of finance, 54:833–874, 1999.
[2] Agarwal V., Bakshi G., and Huij J. Dynamic Investment Opportunities and the Cross-
Section of Hedge-Fund Returns: Implications of Higher-Moment Risks for Performance. Work-ing Paper , May 2008.
[3] Agarwal V., Boyson N. M., and Naik N. Y. Poor Man’s Hedge Funds?, Performance andRisk-taking of Hedged Mutual Funds. Working paper , 2006.
[4] Agarwal V., Daniel N., and Naik N. Y. Do Hedge Funds Manage their Reported Returns.Working Paper , 2007.
[5] Agarwal V. and Daniel N. D.and Naik N. Y. Flows, Performance, and Managerial Incen-tives in Hedge Funds. Working paper , 2004.
[6] Agarwal V. and Fung W. H.and Loon Y. C. Risk and Return in Convertible Arbitrage:Evidence from the Convertible Bond Market. Working paper , 2006.
[7] Agarwal V. and Naik N. Y. Multi-Period Performance Persistence Analysis of Hedge Funds.The Journal of Financial and Quantitative Analysis, 35:327–342, 2000.
[8] Agarwal V. and Naik N. Y. Performance Evaluation of Hedge Funds with Option-basedand Buy-and-Hold Strategies. Working Paper , 2000.
[9] Agarwal V. and Naik N. Y. Risks and Portfolio Decisions Involving Hedge Funds. Working Parer , 2002.
[10]Agarwal
V.,Naik
N. Y., andDaniel
N. D. Role of Managerial Incentives and Discretionin Hedge Fund Performance. Working Paper , 2003.
[11] Ahmad I., Leelahanon S., and li Q. Efficient Estimation of a Semiparametric PartiallyLinear Varying Coefficient Model. The annals of Statistics, 33(1):258–283, 2005.
[12] Amenc N., El Bied S., and Martellini L. Evidence of Predictability in Hedge Fund Returnsand Multi-Style Multi-Class Tactical Style Allocation Decisions. Working paper , 2002.
[13] Amenc N. and Martellini L. Portfolio Optimization and Hedge Fund Style AllocationDecisions. Working paper , March 2002.
[14] Amin G. S. and Kat H. M. Portfolio of Hedge Funds. Working Paper , 2002.
[15] Amin G. S. and Kat H. M. Hedge Fund Performance 1990-2000. Working Paper , January 4,2002.
[16] Ang A. and Bollen N. P.B. Locked Up by a Lockup: Valuing Liquidity as a Real Option.Working Paper , November 2008.
[17] Avramov D., Kosowski R., Naik N. Y., and Teo M. investing in Hedge Funds whenReturns are Predictable. Working Paper , 2008.
[18] Bacmann J.-F. and Jeanneret A. Funds of Funds Are Still Providing Alpha. Hedgequest ,1(1):22–26, 2005.
[19] Bailey W., Li H., and Zhang X. Hedge Fund Performance Evaluation: A Stochastic Dis-count Approach. Working Paper , December 2004.
22
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 23/49
[20] Bansal R. and Viswanathan S. No arbitrage and arbitrage pricing: A new approach. TheJournal of Finance, 48:1231–1262, 1993.
[21] Bartholdy J. and Peare P. Estimation of Expected Return: Capm vs Fama and French.Working Paper , 2004.
[22] Beran R. and Hall P. estimating Coefficient Distributions in Random Coefficient Regres-sions. The annals of Statistics, 20(4):1970–1984, Dec., 1992.
[23] Billio M., Getmansky M., and Pelizzon L. Non-Parametric Analysis of Hedge FundReturns: New Insights from High Frequency Data. Working Paper , 2008.
[24] Bollen N. P.B. and Whaley R. E. Hedge Fund Risk Dynamics: Implications for Perfor-mance Appraisal. Working Paper , 2008.
[25] Brealey R.A. and Kaplanis E. Hedge Funds and Financial Stability: an Analysis of FactorExposures. International Finance, 4(2):161–187, 2001.
[26] Brooks C. and Kat H. M. The Statistical Properties of Hedge Fund Index Returns and theirImplications for Investors. Journal of Alternative investments, 2002.
[27] brown S., Goetzmann W.and Liang B., and Schwarz C. estimating Operational Risk forHedge Funds the ω-Score. Working Paper , May 2008.
[28] Brown S. J. and Goetzmann W. N. Hegde Funds and Style. Journal of Portfolio Manage-ment , 29(2):101–112, 2003.
[29] Brown S. J., Goetzmann W. N., and Ibbotson R. G. Offshore Hedge Funds: Survival andPerformance, 1989-95. The Journal of Business, 72:91–117, 1999.
[30] Brown S. J., Goetzmann W. N., and Park J. Careers and Survival: Competition and Riskin the Hedge Fund and CTA Industry. The journal of Finance, 56:1869–1886, 2001.
[31] Brown S. J.and Goetzmann W. N.and Liang B. Fees on Fees in Funds of Funds. Working paper , 2004.
[32] Brunnermeier M. K.and Nagel S. Arbitrage at its Limits: Hedge Funds and the TechnologyBubble. Working Paper , 2002.
[33] Carol A. and Dimitriu A. A Comparison of Cointegration and Tracking Error Models forMutual Funds and Hedge Funds. Working paper , 2004.
[34] Chambers J. M. and Hastie T. J. Statistical Models in S . Wadsworth, Pacific Grove, 1992.
[35] Chan K. S. Consistency and Limiting Distribution of the Least Squares Estimator of aTreshold Autoregressive Model. The annals of Statistics, 21(1):520–533, 1993.
[36] Chan N., Getmansky M., Haas S. M., and Lo A. W. Systemic Risk and Hedge Funds.Working paper , 2005.
[37] Christiansen C. B., Madsen P. B., and Christensen M. A Quantitative Analysis of HedgeFund Style and Performance. Working paper , 2004.
[38] Colin O. and Chin-Tsang C. Kernel Smoothing on Varying Coefficient Models with Longi-tudinal Dependent Variable. Statistica Sinica , 10:433–456, 2000.
[39] Darolles S. and Florens J. P.and Simon G. Hedge Fund Duration: Endogeneity of Per-formance and Assets Under Management. Working Paper , 2009.
23
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 24/49
[40] Darolles S., Gourieroux C., and Jasiak J. L-Performance with an Application to HedgeFunds. Working Paper , July 2008.
[41] Davies R. J., Kat H. M., and Lu S. Fund of Hedge Funds Portfolio Selection: A Multiple-Objective Approach. Working Paper , August,2005.
[42] Detemple J.B., Garcia R., and Rindisbacher M. A Monte Carlo Method for OptimalPortfolios. The journal of Finance, 58:401–446, 2003.
[43] Eberlein E. and Madan D. B. Hedge Fund Performance: Sources and Measures. Working Paper , 2008.
[44] Fan J. Design-Adaptive Nonparametric Regression. J. Amer. Statist. Assoc., 87:998–1004,1992.
[45] Fan J. Local Linear Regression Smoothers and their Minimax Efficiencies. Ann. Statist ,21:196–216, 1993.
[46]Fan
J. andGijbels
I. Variable Bandwidth and Local Linear Regression Smoothers. Ann.Statist , 20:2008–2036, 1992.
[47] Fan J. and Huang T. Profile Likelihood Inferences on Semiparametric Varying-CoefficientPartially Linear Models. Bernoulli , 11(6):1031–1057, 2005.
[48] Fan J. and Zhang W. Statistical Estimation in Varying Coefficient Models. The annals of Statistics, 27(5):1491, Oct., 1999.
[49] Favre L. and Galeano J.A. Mean-Modified Value-at-Risk Optimization with Hedge Funds.The Journal of Alternative Investments, 5:21–25, 2002.
[50] Favre L. and Signer A. The Difficulties of Measuring the benefits of Hedge Funds. Journal of alternative investments, 2002.
[51] Fung W. and Hsieh D. A. Empirical Characteristics of Dynamic Trading Strategies: Thecase of Hedge Funds. The Review of Financial Studies, 10:275–302, 1997.
[52] Fung W. and Hsieh D. A. Is Mean-Variance Analysis Applicable to Hedge Funds. EconomicsLetters, 62:53–58, 1999.
[53] Fung W. and Hsieh D. A. A Primer of Hedge Funds. Working paper , 1999.
[54] Fung W. and Hsieh D. A. Performance Characteristics of Hedge Funds and CommodityFunds: Natural vs. Spurious Biases. The Journal of Financial and Quantitative Analysis,
35:291–307, 2000.
[55] Fung W. and Hsieh D. A. The Risk in Hedge Fund Strategies: Theory and Evidence fromTrend Followers. The Review of Financial Studies, 14:313–341, 2001.
[56] Fung W. and Hsieh D. A. Asset-Based Style Factors for Hedge Funds. Analyst Journal ,58(5):16–27, 2002.
[57] Fung W. and Hsieh D. A. The Risk in Fixed Income Hedge Fund Styles. Journal of Fixed Income, 2002.
[58] Fung W. and Hsieh D. A. Extracting Portable Alphas from Equity Long/Short Hedge Funds.
Journal of Investment Management , 2:1–19, 2004.[59] Fung W. and Hsieh D. A. Hedge Fund Benchmarks: A Risk Approach. Financial Analyst
Journal , pages 65–80, 2004.
24
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 25/49
[60] Fung W. and Hsieh D. A. Hedge Funds: An Industry in its Adolescence. Economic Review ,Fourth Quarter 2006.
[61] Fung W., Hsieh D. A., Naik N. Y., and Ramadorai T. Hedge Funds: Performance, Riskand Capital Formation. Working paper , 2006.
[62] Galindo C. D., liang H. andKauermann G., and Carroll R. J. Bootstrap ConfidenceIntervals for Local Likelihood, Local Estimating Equations and Varying Coefficient Models.working paper , sept, 2000.
[63] Gayer G., Gilboa I., and Lieberman O. Rule-Based and Case-Based Reasoning in HousingPrices. Working Paper , 2004.
[64] Geltner D. Smoothing in Appraisal-Based Returns. journal of Real Estate Finance and Economics, 4:327–345, 1991.
[65] Geltner D. Estimating Market Values from Appraisal Values without Assuming an EfficientMarket. Journal of Real Estate Research , 8:325–345, 1993.
[66] Getmansky M., Lo A. W., and Makarov I. An Econometric Model of Serial Correlationand Illiquidity in Hedge Fund Returns. Working paper , 2003.
[67] Glosten L.R.and Jagannathan R. A Contingent Claim Approach to Performance Evalua-tion. Journal of Empirical Finance, 1:133–160, 1994.
[68] Goodworth T. R. and Jones C. M. Factor-Based, Non-parametric Risk MeasurementFramework for Hedge Funds and Funds-of-Funds. The European Journal of Finance, 13:7:645–655, October 2007.
[69] Hardle W. and Marron J. S. Bootstrap Simultaneous Error Bars for Nonparametric Re-
gression. The annals of Statistics, 19:778–796, 1991.
[70] Hastie T. and Tibshirani R. Varying-Coefficient Models. Journal of the Royal Statistical Society. Series B(methodological), 55(4):757–796, 1993.
[71] Hildreth C. and houck J. P. Some Estimators for a Linear Model with Random Coefficients.Journal of the american Statistical Association , 63(322):584–595, Jun., 1968.
[72] Hodder J. E. and Jackwerth J. C. Incentive Contracts and Hedge Fund Management.Working paper , 2005.
[73] Hsiao C. Some Estimation Methods for a Random Coefficient Model. Econometrica ,43(2):305–325, Mar., 1975.
[74] Jaeger L. and Wagner C. Factor Modelling and Benchmarking of Hedge Funds: CanPassive Investments in Hedge Fund Strategies Deliver. Working Paper , 2005.
[75] Kat H. Integrating Hedge Funds into the Traditional Portfolio. Working paper 0022 , 2005 january.
[76] Kat H. and Palaro H. Replication Evaluation of Fund of Hedge Funds Returns. Working Paper n28 , January 2006.
[77] Kat H. M. Managed Futures and Hedge Funds: A Match Made in Heaven. Working Paper ,November,2002.
[78] Kat H. M. The Dangers of Mechanical Investment Decision-Making: The Case of HedgeFunds. Working Paper , November,2003.
25
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 26/49
[79] Kat H. M. In Search of the Optimal Fund of Hedge Funds. Working Paper , October,2002.
[80] Kat H. M. Taking the Sting Out of Hedge Funds. Working Paper , October,2002.
[81] Kat H. M. and Lu S. An Excursion into the Statistical Properties of Hedge Funds. Working paper , 2002.
[82] Kat H. M. and Miffre J. Performance Evaluation and Conditioning Information: The Caseof Hedge Funds. Working paper , 2002.
[83] Kat H. M. and Miffre J. The Impact of Non-Normality Risks and Tactical Trading onHedge Fund Alphas. Working paper , May 2006.
[84] Kat H. M. and Palaro H. P. Who Needs Hedge Funds ? Working Paper 0027 , 2005.
[85] Kosowski R., Naik N. Y., and Teo M. Do Hedge Fund Deliver Alpha ? A Bayesian andBootstrap Analysis. Journal of Financial Economics, 2005.
[86] Li S. and Patton A. J. Time-Varying liquidity in Hedge Fund Returns. Working Paper,
London school of Economics, 2006.
[87] Li S. and Patton A. J. Time-Varying Liquidity in Hedge Fund Returns. Working Paper ,May 2007.
[88] Liang B. Hedge Funds: The Living and the Dead. Journal of Financial and QuantitativeAnalysis, 35:309–336, 2000.
[89] Linton O. and Li S. Evaluating Hedge Fund Performance: a Stochastic Dominance Approach.Working paper , 2007.
[90] Malkiel B. G. and Saha A. Hedge Funds: Risk and Return. Working Paper , 2004.
[91] McFall Lamm R. Asymmetric Returns and Optimal Hedge Fund Portfolios. The journal of Alternative Investments, 2003.
[92] Mitchell M. and Pulvino T. characteristics of Risk and Return in Risk Arbitrage. The journal of Finance, 56:2135–2175, 2001.
[93] Pezier J. and White A. The Relative Merits of Investable Hedge Fund Indices and of Fundsof Hedge Funds in Optimal Passsive Portfolios. Working Paper , 2006.
[94] Popova I., Morton D., Popova E., and Yau J. Optimal Hedge Fund Allocation withAsymmetric Preferences and Distributions. Working paper .
[95] Ruppert D. and Wand M. P. Multivariate Locally Weighted Least Squares Regression. Theannals of Statistics, 22(3):1346–1370, 1994.
[96] Schneeweis T. and Spurgin R. Multifactor Analysis of Hedge Fund and Managed Futures,Return and Risk Characteristics. Journal of Alternative Investments, 1:1–24, 1998.
[97] Severini Thomas A. and H. W. Wong. Profile Likelihood and Conditionally ParametricModels. The Annals of Statistics, 20(4):1768–1802, Dec., 1992.
[98] Stone C. J. optimal Global Rates of Convergence for Nonparametric Regression. Ann. Statist ,10:1040–1053.
[99]Stone
C. J. Consistent Nonparametric Regression. Ann. Statist , 5:595–620, 1977.[100] Stone C. J. Optimal Rates of Convergence for Nonparametric Estimator. Ann. Statist ,
8:1348–1360, 1980.
26
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 27/49
[101] Swamy P. A. V. and Mehta J. S. Estimation of Linear Models with Time and Cross-Sectionally Varying Coefficients. Journal of the American Statistical Association , 72(360):890–898, Dec., 1977.
[102] zhang W., Lee S.-Y., and Song X. Local Polynomial Fitting in Semivarying CoefficentModel. journal of Multivariate Analysis, 82:166–188, jan. 2002.
27
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 28/49
Table I
See Appendix I for definitions of fund types. The funds used at minimum cover the LTCM and bubble period which
represent a track record of a minimum of 30 months. Certain of the funds used are considered as dead funds i.e. they
stopped their activities. The database marked by a asterisk give the number of funds covering the 2 specific periods
i.e, LTCM period (July, Auguste, and September 1998) and the Equity Bubble years (February, March, and April 2000)
Strategies Number of Hedge Funds
CISDM merge CISDM* merge*
Equity Long/Short 2141 3519 1561 2525
Multi Strategy 251 734 142 462
Emerging Markets 445 635 331 461
Sector 387 630 296 468
Equity Market Neutral 322 698 227 519
Event Driven Multi Strategy 224 384 168 293Global Macro 303 534 205 377
Equity Long Only 148 276 99 174
Single Strategy 114 112 50 50
Fixed Income 153 326 109 260
Distressed Securities 162 268 131 232
Fixed Income Arbitrage 190 314 143 237
Convertible Arbitrage 207 271 181 227
Relative Value Multi Strategy 89 179 74 137
Fixed Income - MBS 74 98 59 69Option Arbitrage 29 126 17 76
Merger Arbitrage 126 139 111 122
Other relative Value 16 32 7 17
Short bias 51 74 32 56
Regulation D 16 56 13 44
Capital Structure Arbitrage 21 30 13 21
Market Timing 2 3 1 1
Unclassified 58 521 37 369
CTAs (systematic) 1003 759
CTAs (discretionary) 283 1915 202 1394
FoHFs (multi strategy) 1837 1390
28
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 29/49
Table II
See Appendix I for definitions of fund types. This table shows how we have grouped the 31 strategies from Hedge-
Fund.Net and the 23 strategies from CISDM .
CISDM database HedgeFund.Net database23 Strategies 31 Strategies
Multi StrategyMulti Strategy
Statistical Arbitrage
Equity Long/Short Equity Long/Short
Short bias Short bias
Event Driven Multi Strategy Event Driven
Emerging Markets Emerging Markets
Merger Arbitrage Merger (risk) Arbitrage
Fixed Income Fixed Income (non arbitrage)
Equity Market Neutral Market Neutral Equity
Global Macro Macro
Relative Value Multi Strategy Value
Sector
Small/Micro Cap
Finance Sector
Technology Sector
Energy Sector
Healthare Sector
Equity Long Only Long Only
Distressed Securities Distressed
Single Strategy FoF Market Neutral
Unclassified
Asset Based Lending
country specific
Special situations
short-term trading
Fixed Income - MBS Mortgage
Convertible Arbitrage Convertible Arbitrage
Fixed Income Arbitrage Fixed Income Arbitrage
Other relative Value Other Arbitrage
Market Timing Market Timer
Option Arbitrage Option Strategies
Regulation D Regulation D
Capital Structure Arbitrage Capital Structure Arbitrage
29
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 30/49
Table III: Test of Multiple Structural Changes
See Appendix I for definitions of fund types. The funds used at minimum cover the LTCM and bubble period which
represent a track record a minimum of 30 months. Listed is a test provided by Bai and Perron (1998) to analyze
whether Hedge Funds have some structural. We note the percentage of Hedge Funds significant to the test after
applying the False Discovery Rate methodology . The test considers tests of no structural break against an unknownnumber of breaks given some upper bound (m = 5).
Strategy Double Maximum test
UDmax WDmax
Equity Long/Short 38% 38%
Multi Strategy 46% 46%
Emerging Markets 34% 34%
Sector 41% 41%
Equity Market Neutral 49% 49%
Event Driven Multi Strategy 35% 35%
Global Macro 42% 42%
Equity Long Only 53% 53%
Single Strategy 71% 71%
Fixed Income 40% 40%
Distressed Securities 20% 20%
Fixed Income Arbitrage 41% 41%
Convertible Arbitrage 41% 41%
Relative Value Multi Strategy 30% 30%
Fixed Income - MBS 58% 58%
Option Arbitrage 57% 57%
Merger Arbitrage 27% 27%
Other relative Value 75% 75%
Short bias 51% 51%
Regulation D 29% 29%
Capital Structure Arbitrage 53% 53%
Market Timing 100% 100%
Unclassified 38% 38%
Fund of Hedge Funds 65% 66%
CTA Systematic 70% 70%
CTA Discretionary 66% 66%
30
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 31/49
T a b l e V : e s t i m a t e d p r o p
o r t i o n s o f z e r o - a l p h a , u n s k i l l e d , a n d s k i l l e
d f u n d s f r o m
m e r g e d a t a b a s e
S e e A p p e
n d i x I f o r d e fi n i t i o n s o f f u n d t y p e s .
T h i s t a b l e d i s p l a y s t h e e s t i m a t e d p r o p o r t i o n s o f z e r o - a l p h a , u n s k i l l e d , a n
d s k i l l e d f u n d f o r e a c h s t r a t e g y a f t e r
a p p l y i n g t h e f a l s e
D i s c o v e r y
r a t e m e t h o d o l o g y d e v e l o p e d b y B a r r a s , S c a i l l e t a n d W e r m e r s ( 2 0 0 8 ) . T h e s e r e s u l t s c o m e f r o m t h e m e r g e b e t w
e e n t h e C I S D M a n d t h e H e g d e F u n d . n e t d a t a b a s e s . T h e
f u n d s u s e
d a t m i n i m u m c o v e r t h e L T C M a n d b u b b l e p e r i o d w h i c h r e p r e s e n t a t r a c k
r e c o r d a m i n i m u m o f 3 0 m o n t h s . W e e s t i m a t e a l p h a w i t h t h e t i m e - v a r y i n
g c o e ffi c i e n t m o d e l
d e fi n e d i n
s e c t i o n 6 . W i t h t h e e s t i m a t e s , w e c r e a t e t h e m e a n ( α ) w h i c h r e p r e s e n t s t
h e s t o c k - p i c k e r a b i l i t y a n d t h e i n d i c a
t o r s d e fi n e d i n s e c t i o n 7 d u r i n g t h e 2
c r i s i s : α L 1
a n d α L 2
f o r L T C M
a n d α B 1
a n d α B 2
f o r t h e E q u i t y B
u b b l e w h i c h r e p r e s e n t s t h e d i ff e r e n t m a r k e t t i m e r a b i l i t i e s . W e a l s o g a v e
t h e r e s u l t u s i n g a l i n e a r f a c t o r m o d e
l : t h e N e w e y - W e s t
( 1 9 8 7 ) h e
t e r o s c e d a s t i c i t y a n d a u t o c o r r e l a t i o n c o n s i s t e n t e s t i m a t o r . W e d o n o t g i v e
s o m e r e s u l t s f o r S i n g l e S t r a t e g y b e c a u s e o f t o o f e w d a t a . F u r t h e r m o r e t h
e r e s u l t s a b o u t t h e
o t h e r s t r a t e g i e s a r e a v a i l a b l e u p o n r e q u e s t .
S t r a t e
g y
M o
d e
l
α
α L 1
α L 2
α B 1
α B 2
u s e
d
π + A
π 0
π − A
π + A
π 0
π − A
π + A
π 0
π − A
π + A
π 0
π − A
π + A
π 0
π − A
E q .
L o
n g
/ S h o r t
T V C M
1 8 . 6 %
5 8 . 8
%
2 2 . 6
%
1 6 . 0
%
6 1 . 9
%
2 2 . 1
%
2 2 . 8
%
6 2 . 2
%
1 5 . 0
%
1 7
. 0 %
5 8 . 8
%
2 4 . 2 %
1 7
. 0 %
5 8 . 8
%
2 4
. 2 %
N w e s t
3 . 8
% %
9 3 . 5
%
2 . 7
% %
E m e r g
i n g
M a r k e t s
T V C M
1 2 . 6 %
4 1 . 5
%
4 5 . 9
%
4 4
. 2 %
4 2 . 6
%
1 3 . 2
%
3 8 . 9
%
4 3 . 8
%
1 7
. 3 %
4 4
. 4 %
3 9 . 2
%
1 6 . 4 %
4 3 . 6
%
3 9 . 2
%
1 7
. 3 %
N w e s t
1 2 . 3 %
8 7
. 5 %
0 . 2
%
E q .
M
a r k e t N e u t r a l
T V C M
1 1 . 6 %
7 4
. 1 %
1 4
. 2 %
0 . 0
%
9 0 . 4
%
9 . 6
%
0 . 0
%
9 2 . 2
%
7 . 8
%
4 . 3
%
8 3 . 2
%
1 2 . 5 %
1 6 . 4
%
8 3 . 2
%
0 . 5
%
N w e s t
8 . 6 %
8 9 %
2 . 4
%
E v e n t
D r i v e n
M .
S .
T V C M
2 . 5 %
9 7
. 5 %
0 . 0
%
0 . 0
%
9 7
. 5 %
2 . 5
%
0 . 0
%
9 9 . 8
%
0 . 2
%
0 . 9
%
9 0 . 7
%
8 . 4 %
0 . 9
%
9 0 . 7
%
8 . 4
%
N w e s t
0 %
1 0 0 %
0 %
G l o b a l M a c r o
T V C M
5 . 2 %
6 7
. 0 %
2 7
. 8 %
2 6 . 1
%
6 9 . 1
%
4 . 8
%
2 6 . 2
%
6 6 . 8
%
7 . 0
%
1 8 . 5
%
5 9 . 9
%
2 1 . 6 %
1 8 . 5
%
5 9 . 9
%
2 1 . 6
%
N w e s t
1 %
9 6 %
3 %
S h o r t
b i a s
T V C M
3 5 . 2 %
9 . 5
%
5 5 . 2
%
7 1 . 4
%
0
. 0 %
2 8 . 6
%
7 1 . 4
%
0 . 0
%
2 8 . 6
%
4 9 . 0
%
1 9 . 0
%
3 1 . 9 %
4 9 . 0
%
1 9 . 0
%
3 1 . 9
%
N w e s t
5 . 3 %
6 3 . 6
%
3 1 . 2
%
C T A
T V C M
1 8 . 8 %
5 3 . 1
%
2 8 . 1
%
1 7
. 0 %
6 0 . 2
%
2 2 . 8
%
1 7
. 0 %
6 0 . 2
%
2 2 . 8
%
2 7
. 2 %
5 5 . 3
%
1 7 . 5 %
2 7
. 2 %
5 5 . 3
%
1 7
. 5 %
N w e s t
2 %
9 7 %
1 %
31
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 32/49
Figure I:
3 1− Ma r− 19 97 3 0− No v− 19 98 3 1− Ju l− 20 00 3 1− Ma r− 20 02 3 0− No v− 20 03 3 1− Ju l− 20 05 3 1− Ma r− 20 070
0.2
0.4
0.6
0.8
1LTCM Equity Bubble
Rbreaks
Capital Structure Arbitrage
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2LTCM Equity Bubble
Rbreaks
Convertible Arbitrage
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2LTCM Equity Bubble
Rbreaks
CTA
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2LTCM Equity Bubble
Rbreaks
Distressed Securities
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2
0.25LTCM Equity Bubble
Rbreaks
Emerging Markets
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.1
0.2
0.3
0.4LTCM Equity Bubble
Rbreaks
Equity Long Only
See Appendix I for definitions of fund types. The number of hedge Funds has increased drastically since 2000 thereforethe number of breaks in 1995, for instance, has not the same significance as the number of breaks in 2002. In orderto overcome this problem and to study correctly the dynamic in beta we define a ratio: Rbreaks which is equal to
the number of funds at time t divided by the number of break at time t. In this way, we are able to study how thedynamic in hedge Funds behaves during a long period.
The bar figures illustrate the number of breakdates relative to one fund.
32
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 33/49
Figure II:
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2LTCM Equity Bubble
Rbreaks
Equity Long/Short
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2LTCM Equity Bubble
Rbreaks
Equity Market Neutral
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2
0.25LTCM Equity Bubble
Rbreaks
Event Driven Multi Strategy
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.1
0.2
0.3
0.4
0.5LTCM Equity Bubble
Rbreaks
Fixed Income − MBS
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.1
0.2
0.3
0.4LTCM Equity Bubble
Rbreaks
Fixed Income Arbitrage
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2
0.25LTCM Equity Bubble
Rbreaks
Fixed Income
See Appendix I for definitions of fund types. The number of hedge Funds has increased drastically since 2000 thereforethe number of breaks in 1995, for instance, has not the same significance as the number of breaks in 2002. In orderto overcome this problem and to study correctly the dynamic in beta we define a ratio: Rbreaks which is equal to
the number of funds at time t divided by the number of break at time t. In this way, we are able to study how thedynamic in hedge Funds behaves during a long period.
The bar figures illustrate the number of breakdates relative to one fund.
33
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 34/49
Figure III:
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2LTCM Equity Bubble
Rbreaks
Global Macro
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.1
0.2
0.3
0.4LTCM Equity Bubble
Rbreaks
Merger Arbitrage
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.1
0.2
0.3
0.4
0.5LTCM Equity Bubble
Rbreaks
Multi Strategy
− −1993 30−Nov−1995 30−Sep−1997 31−Aug−1999 30−Jun−2001 31−May−2003 31−Mar−2005 28−Feb−2007 31−Dec−1993
LTCM Equity Bubble
Option Arbitrage
− −1993 30−Nov−1995 30−Sep−1997 31−Aug−1999 30−Jun−2001 31−May−2003 31−Mar−2005 28−Feb−2007 31−Dec−1993
LTCM Equity Bubble
Other Relative Value
− −1993 30−Nov−1995 30−Sep−1997 31−Aug−1999 30−Jun−2001 31−May−2003 31−Mar−2005 28−Feb−2007 31−Dec−1993
LTCM Equity Bubble
Regulation D
See Appendix I for definitions of fund types. The number of hedge Funds has increased drastically since 2000 thereforethe number of breaks in 1995, for instance, has not the same significance as the number of breaks in 2002. In orderto overcome this problem and to study correctly the dynamic in beta we define a ratio: Rbreaks which is equal to
the number of funds at time t divided by the number of break at time t. In this way, we are able to study how thedynamic in hedge Funds behaves during a long period.
The bar figures illustrate the number of breakdates relative to one fund.
34
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 35/49
Figure IV:
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2
0.25LTCM Equity Bubble
Rbreaks
Relative Value Multi Strategy
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2
0.25LTCM Equity Bubble
Rbreaks
Sector
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.1
0.2
0.3
0.4
0.5LTCM Equity Bubble
Rbreaks
Short Bias
28−Feb−1994 31−Jan−1996 31−Dec−1997 30−Nov−1999 30−Sep−2001 31−Aug−2003 31−Jul−2005 30−Jun−2007 28−Feb−0
0.2
0.4
0.6
0.8
1LTCM Equity Bubble
Rbreaks
Single Strategy
31−Dec−1993 31−Aug−1995 30−Apr−1997 31−Dec−1998 31−Aug−2000 30−Apr−2002 31−Dec−2003 31−Aug−2005 30−Apr−20070
0.05
0.1
0.15
0.2LTCM Equity Bubble
Rbreaks
unclassified
See Appendix I for definitions of fund types. The number of hedge Funds has increased drastically since 2000 thereforethe number of breaks in 1995, for instance, has not the same significance as the number of breaks in 2002. In orderto overcome this problem and to study correctly the dynamic in beta we define a ratio: Rbreaks which is equal to
the number of funds at time t divided by the number of break at time t. In this way, we are able to study how thedynamic in hedge Funds behaves during a long period.
The bar figures illustrate the number of breakdates relative to one fund.
35
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 36/49
F i g u r
e V :
L T C M
f i r s t P e r i o
d
0 . 0
0 9 6
0 . 0
1 9
0 . 0
2 9
0 . 0
3 8
0 . 0
4 8
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
S e c o n d P e r i o d
0 . 0
0 9 9
0 . 0
2
0 . 0
3
0 . 0
4
0 . 0
4 9
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e F i r s t P e r i o d
0 . 0
0 5
0 . 0
1
0 . 0
1 5
0 . 0
2
0 . 0
2 5
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e S e c o n d P e r i o d
0 . 0
0 4 1
0 . 0
0 8 2
0 . 0
1 2
0 . 0
1 6
0 . 0
2
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
f i r s t p e r i o
d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
s e c o n d p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S
P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e f i r s t p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M E
q u i t y B u b b l e s e c o n d p e r i o d
f a c t o r
π A −
π 0
π A +
E m e r g i n g M a r k e t s
L e g e n d :
1 ) T F B
: B o n d T r e n d − F o l l o w i n g f a c t o r
2 ) B T C o
: C o m m o d i t y T r e n d − F o l l o w i n g f a c t o r
3 ) T F C u
: C u r r e n c y T r e n d − F o l l o w i n g f a c t o r
4 ) S P 5 0 0 : S & P 5 0 0
5 )
S S d
: S i z e S p r e a d f a c t o r
6 )
B M
: B o n d m a r k e t f a c t o r
7 )
C S
: C r e d i t S p r e a d f a c t o r
8 )
E M
: E m e r g i n g M a r k e t f a c t o r
S e e A p p e
n d i x I f o r d e fi n i t i o n s o f f u n d t y p e s . T h e n u m b e r o f f u n d s c o v e r i n g t h e p e
r i o d i s e q u a l t o 4 6 1 . T h e b a r fi g u r e s
i l l u s t r a t e t h e p r o p o r t i o n o f f u n d s h a
v i n g m o r e t h a n 1 0
p e r c e n t d
e c r e a s e ( b l u e o r π − A ) , c o n s t a n t ( w h i t e
o r π 0 ) , a n d i n c r e a s e ( r e d o r π
+ A ) m a r k
e t e x p o s u r e d u r i n g t h e 2 c r i s i s . E a c h c r i s i s i s d i v i d e d i n 2 p e r i o d ( s e e s e c t i o n 7 : m e t h o d o l o g y ) .
. T h e s e c
o n d fi g u r e s ( F a c t o r R a d a r C h a r t ) i n d
i c a t e s t h e s t r a t e g y ’ s s e n s i t i v i t i e s ( p e r c e n t a g e c h a n g e ) t o v a r i o u s f a c t o r s i n
r e g a r d s t o t h e 2 c r i s i s .
36
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 37/49
F i g u r
e V I :
L T C M
f i r s t P e r i o
d
0 . 0
0 4 3
0 . 0
0 8 7
0 . 0
1 3
0 . 0
1 7
0 . 0
2 2
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
S e c o n d P e r i o d
0 . 0
0 4 1
0 . 0
0 8 2
0 . 0
1 2
0 . 0
1 6
0 . 0
2 1
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e F i r s t P e r i o d
0 . 0
0 5 7
0 . 0
1 1
0 . 0
1 7
0 . 0
2 3
0 . 0
2 8
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e S e c o n d P e r i o d
0 . 0
0 5 8
0 . 0
1 2
0 . 0
1 7
0 . 0
2 3
0 . 0
2 9
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
f i r s t p e r i o
d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
s e c o n d p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S
P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e f i r s t p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M E
q u i t y B u b b l e s e c o n d p e r i o d
f a c t o r
π A −
π 0
π A +
E q u i t y L o n g / S h o r t
L e g e n d :
1 ) T F B
: B o n d T r e n d − F o l l o w i n g f a c t o r
2 ) B T C o
: C o m m o d i t y T r e n d − F o l l o w i n g f a c t o r
3 ) T F C u
: C u r r e n c y T r e n d − F o l l o w i n g f a c t o r
4 ) S P 5 0 0 : S & P 5 0 0
5 )
S S d
: S i z e S p r e a d f a c t o r
6 )
B M
: B o n d m a r k e t f a c t o r
7 )
C S
: C r e d i t S p r e a d f a c t o r
8 )
E M
: E m e r g i n g M a r k e t f a c t o r
S e e A p p e
n d i x I f o r d e fi n i t i o n s o f f u n d t y p e s .
T h e n u m b e r o f f u n d s c o v e r i n g t h e p
e r i o d i s e q u a l t o 2 5 2 5 . T h e b a r fi g u r e s i l l u s t r a t e t h e p r o p o r t i o n o f f u n d s
h a v i n g m o r e t h a n
1 0 p e r c e n t d e c r e a s e ( b l u e o r π − A ) , c o n s t a n t ( w h i t e o r π 0 ) , a n d i n c r e a s e ( r e d o r π
+ A ) m a r k e t e x p o s u r e d u r i n g t h e 2 c r i s i s . E a c h c r i s i s i s d i v i d e d i n 2 p e r
i o d ( s e e s e c t i o n 7 :
m e t h o d o l o g y ) . . T h e s e c o n d fi g u r e s ( F a c t o r R
a d a r C h a r t ) i n d i c a t e s t h e s t r a t e g y ’ s s e n s i t i v i t i e s ( p e r c e n t a g e c h a n g e ) t o v a r i o u s f a c t o r s i n r e g a r d s t o t h e 2 c r i s i s .
37
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 38/49
F i g u r
e V I I :
L T C M
f i r s t P e r i o
d
0 . 0
0 9 1
0 . 0
1 8
0 . 0
2 7
0 . 0
3 6
0 . 0
4 5
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
S e c o n d P e r i o d
0 . 0
0 7 9
0 . 0
1 6
0 . 0
2 4
0 . 0
3 2
0 . 0
3 9
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e F i r s t P e r i o d
0 . 0
0 4 1
0 . 0
0 8 1
0 . 0
1 2
0 . 0
1 6
0 . 0
2
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e S e c o n d P e r i o d
0 . 0
0 4 3
0 . 0
0 8 5
0 . 0
1 3
0 . 0
1 7
0 . 0
2 1
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
f i r s t p e r i o
d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
s e c o n d p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S
P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e f i r s t p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M E
q u i t y B u b b l e s e c o n d p e r i o d
f a c t o r
π A −
π 0
π A +
E q u i t
y M a r k e t N e u t r a l
L e g e n d :
1 ) T F B
: B o n d T r e n d − F o l l o w i n g f a c t o r
2 ) B T C o
: C o m m o d i t y T r e n d − F o l l o w i n g f a c t o r
3 ) T F C u
: C u r r e n c y T r e n d − F o l l o w i n g f a c t o r
4 ) S P 5 0 0 : S & P 5 0 0
5 )
S S d
: S i z e S p r e a d f a c t o r
6 )
B M
: B o n d m a r k e t f a c t o r
7 )
C S
: C r e d i t S p r e a d f a c t o r
8 )
E M
: E m e r g i n g M a r k e t f a c t o r
S e e A p p e
n d i x I f o r d e fi n i t i o n s o f f u n d t y p e s . T h e n u m b e r o f f u n d s c o v e r i n g t h e p e
r i o d i s e q u a l t o 5 1 9 . T h e b a r fi g u r e s
i l l u s t r a t e t h e p r o p o r t i o n o f f u n d s h a
v i n g m o r e t h a n 1 0
p e r c e n t d
e c r e a s e ( b l u e o r π − A ) , c o n s t a n t ( w h i t e
o r π 0 ) , a n d i n c r e a s e ( r e d o r π
+ A ) m a r k
e t e x p o s u r e d u r i n g t h e 2 c r i s i s . E a c h c r i s i s i s d i v i d e d i n 2 p e r i o d ( s e e s e c t i o n 7 : m e t h o d o l o g y ) .
. T h e s e c
o n d fi g u r e s ( F a c t o r R a d a r C h a r t ) i n d
i c a t e s t h e s t r a t e g y ’ s s e n s i t i v i t i e s ( p e r c e n t a g e c h a n g e ) t o v a r i o u s f a c t o r s i n
r e g a r d s t o t h e 2 c r i s i s .
38
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 39/49
F i g u r
e V I I I :
L T C M
f i r s t P e r i o
d
0 . 0
0 5 7
0 . 0
1 1
0 . 0
1 7
0 . 0
2 3
0 . 0
2 9
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
S e c o n d P e r i o d
0 . 0
0 4 2
0 . 0
0 8 5
0 . 0
1 3
0 . 0
1 7
0 . 0
2 1
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e F i r s t P e r i o d
0 . 0
0 8 4
0 . 0
1 7
0 . 0
2 5
0 . 0
3 4
0 . 0
4 2
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e S e c o n d P e r i o d
0 . 0
0 8 4
0 . 0
1 7
0 . 0
2 5
0 . 0
3 4
0 . 0
4 2
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
f i r s t p e r i o
d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
s e c o n d p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S
P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e f i r s t p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M E
q u i t y B u b b l e s e c o n d p e r i o d
f a c t o r
π A −
π 0
π A +
E v e n t D r i v e
n M u l t i S t r a t e g y
L e g e n d :
1 ) T F B
: B o n d T r e n d − F o l l o w i n g f a c t o r
2 ) B T C o
: C o m m o d i t y T r e n d − F o l l o w i n g f a c t o r
3 ) T F C u
: C u r r e n c y T r e n d − F o l l o w i n g f a c t o r
4 ) S P 5 0 0 : S & P 5 0 0
5 )
S S d
: S i z e S p r e a d f a c t o r
6 )
B M
: B o n d m a r k e t f a c t o r
7 )
C S
: C r e d i t S p r e a d f a c t o r
8 )
E M
: E m e r g i n g M a r k e t f a c t o r
S e e A p p e
n d i x I f o r d e fi n i t i o n s o f f u n d t y p e s . T h e n u m b e r o f f u n d s c o v e r i n g t h e p e
r i o d i s e q u a l t o 2 9 3 . T h e b a r fi g u r e s
i l l u s t r a t e t h e p r o p o r t i o n o f f u n d s h a
v i n g m o r e t h a n 1 0
p e r c e n t d
e c r e a s e ( b l u e o r π − A ) , c o n s t a n t ( w h i t e
o r π 0 ) , a n d i n c r e a s e ( r e d o r π
+ A ) m a r k
e t e x p o s u r e d u r i n g t h e 2 c r i s i s . E a c h c r i s i s i s d i v i d e d i n 2 p e r i o d ( s e e s e c t i o n 7 : m e t h o d o l o g y ) .
. T h e s e c
o n d fi g u r e s ( F a c t o r R a d a r C h a r t ) i n d
i c a t e s t h e s t r a t e g y ’ s s e n s i t i v i t i e s ( p e r c e n t a g e c h a n g e ) t o v a r i o u s f a c t o r s i n
r e g a r d s t o t h e 2 c r i s i s .
39
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 40/49
F i g u r
e I X :
L T C M
f i r s t P e r i o
d
0 . 0
0 6 7
0 . 0
1 3
0 . 0
2
0 . 0
2 7
0 . 0
3 4
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
S e c o n d P e r i o d
0 . 0
0 6
0 . 0
1 2
0 . 0
1 8
0 . 0
2 4
0 . 0
3
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e F i r s t P e r i o d
0 . 0
0 4 3
0 . 0
0 8 5
0 . 0
1 3
0 . 0
1 7
0 . 0
2 1
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e S e c o n d P e r i o d
0 . 0
0 3 4
0 . 0
0 6 9
0 . 0
1
0 . 0
1 4
0 . 0
1 7
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
f i r s t p e r i o
d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
s e c o n d p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S
P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e f i r s t p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M E
q u i t y B u b b l e s e c o n d p e r i o d
f a c t o r
π A −
π 0
π A +
G l o b a l M a c r o
L e g e n d :
1 ) T F B
: B o n d T r e n d − F o l l o w i n g f a c t o r
2 ) B T C o
: C o m m o d i t y T r e n d − F o l l o w i n g f a c t o r
3 ) T F C u
: C u r r e n c y T r e n d − F o l l o w i n g f a c t o r
4 ) S P 5 0 0 : S & P 5 0 0
5 )
S S d
: S i z e S p r e a d f a c t o r
6 )
B M
: B o n d m a r k e t f a c t o r
7 )
C S
: C r e d i t S p r e a d f a c t o r
8 )
E M
: E m e r g i n g M a r k e t f a c t o r
S e e A p p e
n d i x I f o r d e fi n i t i o n s o f f u n d t y p e s . T h e n u m b e r o f f u n d s c o v e r i n g t h e p e
r i o d i s e q u a l t o 3 7 7 . T h e b a r fi g u r e s
i l l u s t r a t e t h e p r o p o r t i o n o f f u n d s h a
v i n g m o r e t h a n 1 0
p e r c e n t d
e c r e a s e ( b l u e o r π − A ) , c o n s t a n t ( w h i t e
o r π 0 ) , a n d i n c r e a s e ( r e d o r π
+ A ) m a r k
e t e x p o s u r e d u r i n g t h e 2 c r i s i s . E a c h c r i s i s i s d i v i d e d i n 2 p e r i o d ( s e e s e c t i o n 7 : m e t h o d o l o g y ) .
. T h e s e c
o n d fi g u r e s ( F a c t o r R a d a r C h a r t ) i n d
i c a t e s t h e s t r a t e g y ’ s s e n s i t i v i t i e s ( p e r c e n t a g e c h a n g e ) t o v a r i o u s f a c t o r s i n
r e g a r d s t o t h e 2 c r i s i s .
40
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 41/49
F i g u r
e X :
L T C M
f i r s t P e r i o
d
0 . 0
1
0 . 0
2
0 . 0
3
0 . 0
4
0 . 0
5
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
S e c o n d P e r i o d
0 . 0
0 6 7
0 . 0
1 3
0 . 0
2
0 . 0
2 7
0 . 0
3 3
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e F i r s t P e r i o d
0 . 0
0 5 1
0 . 0
1
0 . 0
1 5
0 . 0
2 1
0 . 0
2 6
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e S e c o n d P e r i o d
0 . 0
0 5 4
0 . 0
1 1
0 . 0
1 6
0 . 0
2 2
0 . 0
2 7
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
f i r s t p e r i o
d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
s e c o n d p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S
P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e f i r s t p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M E
q u i t y B u b b l e s e c o n d p e r i o d
f a c t o r
π A −
π 0
π A +
S h o r t B i a s
L e g e n d :
1 ) T F B
: B o n d T r e n d − F o l l o w i n g f a c t o r
2 ) B T C o
: C o m m o d i t y T r e n d − F o l l o w i n g f a c t o r
3 ) T F C u
: C u r r e n c y T r e n d − F o l l o w i n g f a c t o r
4 ) S P 5 0 0 : S & P 5 0 0
5 )
S S d
: S i z e S p r e a d f a c t o r
6 )
B M
: B o n d m a r k e t f a c t o r
7 )
C S
: C r e d i t S p r e a d f a c t o r
8 )
E M
: E m e r g i n g M a r k e t f a c t o r
S e e A p p e
n d i x I f o r d e fi n i t i o n s o f f u n d t y p e s .
T h e n u m b e r o f f u n d s c o v e r i n g t h e p e r i o d i s e q u a l t o 5 6 . T h e b a r fi g u r e s
i l l u s t r a t e t h e p r o p o r t i o n o f f u n d s h a
v i n g m o r e t h a n 1 0
p e r c e n t d
e c r e a s e ( b l u e o r π − A ) , c o n s t a n t ( w h i t e
o r π 0 ) , a n d i n c r e a s e ( r e d o r π
+ A ) m a r k
e t e x p o s u r e d u r i n g t h e 2 c r i s i s . E a c h c r i s i s i s d i v i d e d i n 2 p e r i o d ( s e e s e c t i o n 7 : m e t h o d o l o g y ) .
. T h e s e c
o n d fi g u r e s ( F a c t o r R a d a r C h a r t ) i n d
i c a t e s t h e s t r a t e g y ’ s s e n s i t i v i t i e s ( p e r c e n t a g e c h a n g e ) t o v a r i o u s f a c t o r s i n
r e g a r d s t o t h e 2 c r i s i s .
41
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 42/49
F i g u r
e X I :
L T C M
f i r s t P e r i o
d
0 . 0
0 3 8
0 . 0
0 7 6
0 . 0
1 1
0 . 0
1 5
0 . 0
1 9
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
S e c o n d P e r i o d
0 . 0
0 3 9
0 . 0
0 7 7
0 . 0
1 2
0 . 0
1 5
0 . 0
1 9
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e F i r s t P e r i o d
0 . 0
0 6 4
0 . 0
1 3
0 . 0
1 9
0 . 0
2 6
0 . 0
3 2
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e S e c o n d P e r i o d
0 . 0
0 6 2
0 . 0
1 2
0 . 0
1 8
0 . 0
2 5
0 . 0
3 1
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
f i r s t p e r i o
d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M
L T C M
s e c o n d p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S
P 5 0 0
S S d
B d M t
C S
E M
E q u i t y B u b b l e f i r s t p e r i o d
f a c t o r
0 %
5 0 %
1 0 0 %
T F B
T F C u
T F C o
S P 5 0 0
S S d
B d M t
C S
E M E
q u i t y B u b b l e s e c o n d p e r i o d
f a c t o r
π A −
π 0
π A +
C T A s M e r g e
L e g e n d :
1 ) T F B
: B o n d T r e n d − F o l l o w i n g f a c t o r
2 ) B T C o
: C o m m o d i t y T r e n d − F o l l o w i n g f a c t o r
3 ) T F C u
: C u r r e n c y T r e n d − F o l l o w i n g f a c t o r
4 ) S P 5 0 0 : S & P 5 0 0
5 )
S S d
: S i z e S p r e a d f a c t o r
6 )
B M
: B o n d m a r k e t f a c t o r
7 )
C S
: C r e d i t S p r e a d f a c t o r
8 )
E M
: E m e r g i n g M a r k e t f a c t o r
S e e A p p e
n d i x I f o r d e fi n i t i o n s o f f u n d t y p e s .
T h e n u m b e r o f f u n d s c o v e r i n g t h e p
e r i o d i s e q u a l t o 1 3 9 4 . T h e b a r fi g u r e s i l l u s t r a t e t h e p r o p o r t i o n o f f u n d s
h a v i n g m o r e t h a n
1 0 p e r c e n t d e c r e a s e ( b l u e o r π − A ) , c o n s t a n t ( w h i t e o r π 0 ) , a n d i n c r e a s e ( r e d o r π
+ A ) m a r k e t e x p o s u r e d u r i n g t h e 2 c r i s i s . E a c h c r i s i s i s d i v i d e d i n 2 p e r
i o d ( s e e s e c t i o n 7 :
m e t h o d o l o g y ) . . T h e s e c o n d fi g u r e s ( F a c t o r R
a d a r C h a r t ) i n d i c a t e s t h e s t r a t e g y ’ s s e n s i t i v i t i e s ( p e r c e n t a g e c h a n g e ) t o v a r i o u s f a c t o r s i n r e g a r d s t o t h e 2 c r i s i s .
42
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 43/49
Appendix I
Definition of Strategies
• The emerging markets strategy attempts to capture gains from inefficiencies in emergingmarkets.
• The Equity Long/Short strategy refers to taking both long and short positions in equities.
• The Market Timer focus on securities associated with companies that will soon experiencea significant event.
The Distressed Securities Strategy focuses on asset of distressed companies. Buys equity,debt, or trade claims at deep discounts of companies in or facing bankruptcy or reorganization.
• The Merger Arbitrage Strategy also called risk arbitrage strategy exploit pricing inef-ficiencies associated with a merger or acquisition.
• The event driven multi-strategy can use both the distressed securities style and/or themerger arbitrage style.
• The Relative Value arbitrage style take positions in 2 securities that are mispriced relativeto each other, with the expectation that their prices will converge to appropriate values in thefuture(Arbitrage, Market neutral.
• The arbitrage involves simultaneously purchasing and selling related securities that are mis-priced relative to each other.
• Convertible Arbitrage Strategy can be described by taking a long position in a convertiblebond and sells short the associated stock. Convertible arbitrage - exploit pricing inefficiencies
between convertible securities and the corresponding stocks.
• Fixed Income Arbitrage Strategies encompass a wide range of strategies in both domesticand global fixed-income markets. Fixed income arbitrage - exploit pricing inefficiencies betweenrelated fixed income securities.
• Equity Market Neutral style creates a position that attempts to hedge out most marketrisk by taking offsetting positions. This strategy exploits the mispricing between a stockwhich is overvalued and one that is undervalued such that beta of the combined position iszero. Statistical arbitrage - equity market neutral strategy using statistical models.
• Index arbitrage style generally attempts to exploit mispricing between an index and deriva-
tives on that index.
• Mortgage-backed securities arbitrage style exploit the mispricing of mortgage-backedassets relative to Treasury securities.
• multi-strategy style uses different styles and may change exposures to different styles basedupon changing market conditions.Multi strategy in Macro strategy - combination of discre-tionary and systematic macro. Multi strategy in FoHF - a hedge fund exploiting a combinationof different hedge fund strategies to reduce market risk.
• dedicated short selling style only takes short equity positions.
• Global Macro Discretionary macro - trading is done by investment managers instead of
generated by software.Systematic macro (Systematic diversified) - trading is done mathematically, generated bysoftware without human intervention.
43
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 44/49
• Sector funds - expertise in niche areas such as technology, health care, biotechnology, phar-maceuticals, energy, basic materials.
• Fundamental value - invest in undervalued companies.
• Fundamental growth - invest in companies with more earnings growth than the broad equity
market.
• Quantitative Directional, statistical arbitrage - equity trading using quantitative tech-niques.
• Multi manager - a hedge fund where the investment is spread along separate sub managersinvesting in their own strategy.
• Trend following - long-term or short-term. Non-trend following (Counter trend) - profitfrom trend reversals.
• Regulation D - specialized in private equities.
• Credit arbitrage or fixed income arbitrage strategy - specialized in corporate fixedincome securities.
• Fixed Income asset backed - fixed income arbitrage strategy using asset-backed securities.
• Volatility arbitrage - exploit the change in implied volatility instead of the change in price.
• Yield alternatives - non fixed income arbitrage strategies based on the yield instead of theprice.
• Capital Structure Arbitrage - involves taking long and short positions in different financialinstruments of a company’s capital structure, particularly between a company’s debt and
equity product.
44
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 45/49
Two-step Time-Varying Coefficient Model
The varying coefficient model assumes the following conditional linear structure:
Y t =
p
j=1
β j(t)X jt + εt = α(t) + Xβ (t) + εt
for a given covariates (t, X 1,...,X p) and variable Y with
E [ε|t, X 1,...,X p] = 0,
V ar[ε|t, X 1,...,X p] = σ2(t),
In this study, we took X 1 = 1 as the intercept term and t = time.
if we consider that β i depends on t: (β i(t)), we can approximate the function locally asβ i(t) ≈ ai + bi(t − t0). This leads to the following local least-squares problem:
minimizen
i=1
Y i −
p j=1
{a j + b j(T i − t0)}X ij
2 K h(T i − t0)
for a given kernel function K and bandwidth h, where K h(.) = K (./h)/h.In matrix notation:
Let
X0 = X 11 X 11(T 1 − t0) . . . X 1 p X 1 p(T 1 − t0)
... ... . . . ... ...X n1 X n1(T n − t0) . . . X np X np(T p − t0)
Y = (Y 1,...,Y n) and W 0 = diag(K h0(T 1 − t0),...,K h0(T n − t0))
Then the solution to the least-squares problem can be expressed as:
a j,0 = e2 j−1,2 p(X0W 0X0)−1X
0W 0Y
With these estimates,
a j,0, a local least-square regression is fitted again via substituting the
initial estimate into the local least-squares problem:
ni=1
Y i −
p−1 j=1
a j,0(T i)X ij −
a p + b p(T i − t0) + c p(T i − t0)2 + d p(T i − t0)3
X ip
2
×K h2(T i−t0)
where h2 is the bandwidth in the second step. In this way, a two-step estimator is obtained.Fan and Zhang showed that the bias of the two-step estimator is of O(h4
2) and the varianceO
(nh2)−1
45
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 46/49
Two-step Time-Varying Coefficient Model using B-splines
As mentioned by Fan and Zhang (1999), other techniques such as smoothing splines can alsobe used in the second stage of fitting. Therefore we built the second two-step estimator basedon the same article but we used during the second step a smoothing splines instead of local
regression.From the first step, we obtained the estimates:
a j,0 = e2 j−1,2 p(X0W 0X0)−1X
0W 0Y
In a second step, knowing that we can approximate each β p(t) by a basis function expansion
β p(t) K k=0
γ ∗ pkB pk(t),
We can now minimized in order to estimate γ ∗kp:
ni=1
wi
Y i −
p−1 j=1
a j,0(T i)X ij −
K k=0
γ kpBkp
X ip
2
then it is natural to estimate β p(t) by
β p(t) =K k=1
γ kpBkp(t).
46
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 47/49
Robustness: local and B-spline Time-Varying Coefficient Model
The following example will be used to illustrate the performance of our estimator. We created two “betas”(called β icreated) which represent a possible structural change for a Hedge Fund. We put up a simulated HedgeFund track (RHF ) in this manner:
RHF = β 1createdX1 + β 2createdX2 + ε
where X1, X2 are the S&P500 and the monthly change in the 10-year treasury constant maturity yield respec-tively. The random variable ε follows a normal distribution with mean zero and variance 1.We called the local time-varying coefficient model: L-TVCM and the B-spline time varying coefficient model:B-TVCM.
Short sample: 50 months
0 20 40 60−2
−1
0
1
2
β 1 and true β 1 using L-TVCM
months
0 20 40 60−5
0
5
10
β 2 and true β 2 using L-TVCM
months
0 20 40 60−2
0
2
4
β 2 and true β 2 using B-TVCM
months
0 20 40 60−2
0
2
4
6
β 2 and true β 2 using B-TVCM
months
FIG.: Comparison of the performance between the one-step estimator (long-dashed curve) and the true coeffi-cient function (the solid curve).
47
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 48/49
Medium sample: 100 months
0 50 100−2
−1
0
1
β 1 and true β 1 using L-TVCM
months
0 50 100−2
0
2
4
β 2 and true β 2 using L-TVCM
months
0 50 100−1
−0.5
0
0.5
1
β 2 and true β 2 using B-TVCM
months
0 50 100−2
0
2
4
6
β 2 and true β 2 using B-TVCM
months
FIG.: Comparison of the performance between the one-step estimator (long-dashed curve) and the true coeffi-cient function (the solid curve).
Long sample: 150 months
0 50 100 150−2
−1
0
1
β 1 and true β 1 using L-TVCM
months
0 50 100 150−2
0
2
4
β 2 and true β 2 using L-TVCM
months
0 50 100 150−1
−0.5
0
0.5
1
β 2 and true β 2 using B-TVCM
months
0 50 100 150−2
−1
0
1
2
β 2 and true β 2 using B-TVCM
months
true β
β
FIG.: Comparison of the performance between the one-step estimator (long-dashed curve) and the true coeffi-cient function (the solid curve).
48
8/3/2019 Criton Scallet Time Varying Coefficients HF E4b
http://slidepdf.com/reader/full/criton-scallet-time-varying-coefficients-hf-e4b 49/49
Bootstrap Confidence intervals
We summarize the methodology from Colin and Chiang (2000) in order to create confidenceregions.
According to the author this following naive bootstrap procedure can be used to constructapproximate pointwise percentile confidence intervals for β i(t):
• 1) Randomly sample n subjects with replacement from the original data set, and let{(t∗ij, X∗
i ), Y ∗ij ; 1 = i = n, 1 = j = ni} be the longitudinal bootstrap sample.
• 2) Compute the kernel estimator β booti (t)
• 3) Repeat the above 2 steps B times, so that B bootstrap estimators β booti (t) of β i(t) areobtained.
• 4) Let Lα/2(t) and U (α/2)(t) be the (α/2)th and (1 − α)th i.e. lower and upper (α/2th) per-
centiles, respectively, calculated on the B bootstrap estimators. An approximate (1 − α)bootstrap confidence interval for β i(t) is given by (L(α/2)(t), U (α/2)(t)).
bandwidth ”leave-one-subject-out” cross-validation methodology
The leave-out method is based on regression smoothers in which one, say the jth, observationis left out. So, for N values,
• 1) Compute the leave-out estimate mh,j(X j) = n−1
i= j
W hi(X j)Y i.
• 2) Construct the cross validation function CV (h) = n−1n
j=1(Y j − mh,j(X j))2w(X j). where w
denotes a weight function.
• 3) With this N CV(h), we can, now, define the automatic bandwidth as h = arg minh∈H n
[CV (h)]