**1. Introduction
**

With the first hedge fund
said to be dating back to 1949, hedge funds
have been around for quite some time. Academic
research into hedge funds, however, only
took off towards the end of the 1990s when
sufficient data became available. Since
then, and inspired by the strong growth
of the hedge fund industry worldwide, a
respectable number of research papers and
articles have provided insight in many different
aspects of hedge funds. One question largely
remains unanswered though. Do hedge funds
provide their investors with superior returns?
In other words, do hedge funds provide their
investors with returns, which they could
not have obtained otherwise?

According to the hedge fund industry itself,
the answer to the above question is of course
affirmative, although with the recent disappointing
performance of hedge funds, this point is
put forward less often and less forcefully
than it used to. Nowadays, most emphasis
is on the diversification properties of
hedge funds. Various academic studies have
attempted to shed light on the issue of
hedge fund return superiority as well. Most
of these apply traditional performance measures,
such as the Sharpe ratio or factor model
based alphas, to hedge fund returns obtained
from one or more of the main hedge fund
databases. The conclusion is typically that
hedge fund returns are indeed superior.
From other studies, however, it is now well
understood that raw hedge fund return data
may suffer from various biases, which, when
not corrected for, will produce artificially
high Sharpe ratios and alphas. In addition,
hedge fund returns are typically not normally
distributed and may derive from exposure
to very unusual risk factors. This makes
traditional performance measures unsuitable
for hedge funds, as deviations from normality
as well as every risk factor that is incorrectly
specified or left out altogether, will tend
to show up as alpha, thereby suggesting
superior performance where there actually
may be none.

In theory, once the relevant risk factors
have been identified, factor model based
performance evaluation of hedge fund returns
should work well. In practice, however,
we don't know enough about hedge fund return
generation to be certain that all the relevant
risk factors are included and correctly
specified. As a result, factor models typically
explain only 25-30% of the variation in
individual hedge fund returns, which compares
very unfavourably with the 90-95% that is
typical for mutual funds.

Although the procedure
works better for portfolios of hedge funds,
funds of funds and hedge fund indices, where
most of the idiosyncratic risk is diversified
away, the low determination coefficients
of these models make it impossible to arrive
at a firm conclusion with respect to the
superiority of hedge fund returns.

It is quite surprising that so many people,
on the buy-side as well as in academia,
are so eager to believe that the, sometimes
huge, alphas reported for hedge funds are
truly there. Anyone who is well calibrated
to the world we live in and the global capital
markets in particular, knows how difficult
it is to consistently beat the market, ie,
systematically obtain a better return than
what would be fair given the risks taken.
Over time, hundreds, if not thousands, of
studies have confirmed this. Is it therefore
likely that suddenly we are facing a whole
new breed of super-managers; not one or
two, but literally thousands of them? Of
course not! And if anything, the rise of
the hedge fund industry has made markets
more efficient, not less.

Although by far the most popular, factor
models are not the only way to evaluate
hedge fund performance. Based on previous
work by Amin and Kat (2003), Kat and Palaro
(2005), or KP for short, recently developed
a technique that allows the derivation of
dynamic trading strategies, trading cash,
stocks, bonds, etc, which generate returns
with predefined statistical properties.
The technique is not only capable of replicating
(the statistical properties of) fund of
funds returns, but works equally well for
individual hedge fund returns. Since the
KP replicating strategies are explicitly
constructed to replicate the complete risk
and dependence profile of a fund, the average
return on these strategies can be used as
a performance measure. When the average
fund return is significantly higher than
the average return on the replication strategy,
the fund is the most efficient alternative
and vice versa.

The KP replication technique is similar
to that used in Amin and Kat (2003). The
important difference, however, is that the
latter only replicate the marginal distribution
of the fund return, while KP also replicate
its dependence structure with an investor's
existing portfolio. This is a very significant
step forward as most investors nowadays
are attracted to hedge funds because of
their relatively weak relationship with
traditional asset classes, ie, their diversification
potential. Only replicating the marginal
distribution without giving any consideration
to the dependence structure between the
fund and the investor's existing portfolio
would therefore be insufficient.

From a performance evaluation perspective,
replication of a fund's dependence pattern
with other asset classes is a necessity.
According to theory as well as casual empirical
observation, expected return and systematic
co-variance, co-skewness and co-kurtosis
are directly related. In other words, it
is not so much the marginal distribution,
but its dependence structure with other
assets that determines an asset's expected
return. An asset, which is highly correlated
with stocks and bonds, offers investors
very little in terms of diversification
potential. As a consequence, there will
be little demand for this asset. Its price
will be low and its expected return therefore
relatively high. On the other hand, an asset
that offers substantial diversification
potential will be in high demand. Its price
will be high and its expected return relatively
low. Although hedge funds are not priced
by market forces in the same way as primitive
assets are, they do operate in the latter
markets. It therefore seems plausible that
a similar phenomenon is present in hedge
fund returns as well .

**2. The KP Efficiency
Measure **

Applying the KP replication technique to hedge funds, the goal is to create a dynamic trading strategy, which generates returns with the same statistical properties as a given hedge fund or fund of funds, ie, returns that are drawings from the same distribution as the distribution from which the actual fund returns are drawn. The basic idea behind the procedure is straightforward. From the theory of dynamic trading it is well known that in the standard theoretical model with complete markets any payoff function can be hedged perfectly. This observation forms the foundation of arbitrage-based option pricing theory. If it is possible to find a payoff function which, given the distribution of the underlying assets, implies the same distribution as the one from which the fund returns are drawn, then the accompanying dynamic trading strategy will generate (returns that are drawings from) that distribution.

Given the KP replication technique and following the same reasoning as in Amin and Kat (2003), we derived the following evaluation procedure, which consists of five distinct steps.- Monthly return data
are collected on the fund to be evaluated,
the representative investor's portfolio,
and a so-called reserve asset. The latter
is the main source of uncertainty in the
replication strategy. As we want to know
whether the returns that investors obtain
from hedge funds are superior, fund returns
should be net of all fees.

- From the available
return data, the bivariate distribution
of the fund return and the representative
investor's portfolio return is inferred
(KP refer to this as the 'desired distribution').
The same is done for the bivariate distribution
of the investor's portfolio return and
the return on the reserve asset (the 'building
block distribution'). In line with KP,
we allow for 54 different joint distributions,
choosing between them using the Akaike
Information Criterion (AIC) .

- Assuming an initial
investment in the fund of 100, we determine
the cheapest payoff function, which is
able to turn the building block distribution
into the desired distribution. This payoff
function is known as the 'desired payoff
function' and lies at the basis of the
KP replication strategies.

- The desired payoff
function is priced using the multivariate
option pricing model of Boyle and Lin
(1997), which explicitly allows for transaction
costs. For the pricing of the payoff function,
we estimate the required volatility and
correlation inputs over the period covered
by the track record of the fund being
evaluated. We use the average 1-month
interest rate over the same period for
the interest rate input. We will refer
to the price thus obtained as 'the KP
efficiency measure'.

- Finally, we compare the KP efficiency measure with the 100 initially invested in the fund. If the efficiency measure is 100 as well, then the replication strategy and the fund are equivalent. If the efficiency measure is less (more) than 100, the strategy is cheaper (more expensive) than the fund and the fund therefore inefficient (efficient).

Our procedure is not different. We just use a different characterisation. Where others use volatility or factor loadings, we use the desired payoff function. Where others use the average return on the index or the chosen risk factors, we use the average interest rate, building block volatilities and correlation over a fund's track record to set a benchmark. What is different, however, is that we do not need to make any unrealistically strong assumptions concerning the exact nature of a fund's risk exposure or the behaviour of markets in general. As shown by KP, a fairly limited set of returns will often be enough to obtain a sufficiently good estimate of the desired distribution and the efficiency measure. As such, our procedure is quite robust.

Another point worth noting about the above evaluation procedure is the fact that it explicitly takes transaction costs into account by, instead of a Black-Scholes type option pricing model, using the Boyle and Lin (1997) model. In factor model based evaluations, transaction costs are typically ignored, despite the fact that maintaining the replicating portfolio's factor loadings at their desired levels is likely to require periodic rebalancing. In addition, when dealing with hedge funds the risk factors used may be quite unusual and may therefore be accompanied by significant levels of transaction costs.

In the evaluations, we
do not use hedge funds' raw returns. The
reason is that, as shown in Brooks and Kat
(2002) and Lo et al. (2004) for example,
monthly hedge fund returns may exhibit high
levels of autocorrelation. This primarily
results from the fact that many hedge funds
invest in illiquid securities, which are
hard to mark to market. When confronted
with this problem, hedge fund administrators
will either use the last reported transaction
price or a conservative estimate of the
current market price. This creates artificial
lags in the evolution of hedge funds' net
asset values, ie, artificial smoothing of
the reported returns. As a result, estimates
of volatility, for example, will be biased
downwards.

One possible method to correct for this
bias is found in the real estate finance
literature. Due to smoothing in appraisals
and infrequent valuations of properties,
the returns of direct property investment
indices suffer from similar problems as
hedge fund returns. The approach employed
in this literature has been to "unsmooth"
the observed returns to create a new set
of returns which are more volatile and whose
characteristics are believed to more accurately
capture the characteristics of the underlying
property values. Nowadays, there are several
unsmoothing methodologies available. In
this study we use the method originally
proposed by Geltner (1991).

**3. An Example **

To clarify the above, let's
look at a worked-out example. XYZ is a well-known
fund of hedge funds, which started in 1985.
Given XYZ's monthly, net-of-fee returns
since 1985, the first step is to model the
joint distribution of XYZ and the investor's
portfolio, as well as the joint distribution
of the investor's portfolio and the reserve
asset. Before we can do so we need to decide
what exactly the investor's portfolio and
the reserve asset are, as well as unsmooth
the raw fund return data.

Let's assume that the representative investor's
portfolio consists of 50% S&P 500 and
50% long-dated US Treasury bonds. Let's
also assume that all exposure management
is done in the futures markets. So instead
of investing in the cash market, we will
hold fully collateralised (nearby) futures
contracts. We use nearby Eurodollar futures
as the reserve asset. Futures have several
advantages over cash, in particular high
liquidity and low transaction costs, which
is extremely important given the dynamic
nature of the KP replication strategies.

**Table 1: Risk Statistics XYZ**

Standard Deviation | Skewness | Excess Kurtosis | 1M Auto Correlation | |
---|---|---|---|---|

XYZ smooth | 0.0370 | -1.726 | 11.505 | 0.138 |

XYZ unsmooth | 0.0424 | -1.746 | 11.581 | 0.008 |

Table 1 shows the marginal
risk characteristics of the raw and unsmoothed
XYZ returns. From the table, we see that
XYZ's raw returns exhibit negative skewness
and positive autocorrelation. Application
of the unsmoothing procedure eliminates
the autocorrelation and produces returns
with the same degree of skewness, but with
a substantially higher volatility (annualised
14.7% vs 12.8% for the raw returns).

We are now ready to infer the desired and
the building block distribution. Using the
same methodology as KP, we find that the
best fit (according to the AIC) is provided
by the following set of marginals and copulas
:

**XYZ:** Student-t (µ = 0.0101,
s = 0.0406, df = 4.0544)

**Portfolio:** Normal (µ = 0.0101,
s = 0.0282)

**Reserve:** Johnson (? = 0.0031, ? =
0.0046, ? = -0.60, d = 1.599)

**Copula **(XYZ, portfolio): Normal (?
= 0.754)

**Copula **(portfolio, reserve): Gumbel
(a = 1.3349)

Given the above distributions, we can derive
the desired payoff function following the
methodology developed in KP. The result
is depicted in Figure 1 and shows that the
desired payoff is an increasing function
of both the investor's portfolio and the
reserve asset, implying that the replication
strategy will take long positions in both
assets. Subsequently, we price this payoff
function using the Boyle and Lin (1997)
model, assuming transaction costs in the
futures markets are 1bp one-way. This produces
a value for the KP efficiency measure of
99.53, meaning that, seen over the whole
life of the fund, XYZ's returns are not
as miraculous as many investors may have
thought. Trading S&P 500, T-bond and
Eurodollar futures, investors could have
generated the same risk profile as XYZ and
obtained a higher average return at the
same time.

**Figure 1: Desired Payoff Function for Replication XYZ Returns**

Figure 2: Scatter Plot Investor's Portfolio Returns vs XYZ Returns (left) and

Replicated Returns (right)

Figure 2: Scatter Plot Investor's Portfolio Returns vs XYZ Returns (left) and

Replicated Returns (right)

To see how well the derived
payoff function succeeds in replicating
the desired distribution, Figure 2 shows
a scatter plot of the investor's portfolio
return versus the XYZ return (left) as well
as a plot of the portfolio return versus
the replicated return (right). The two plots
are very similar, suggesting that the replication
has indeed been successful. We see that
the replication strategy is unable to replicate
the three large losses that XYZ reported
during the sample period. This is not surprising
as these are clearly outliers, which simply
cannot be captured by a parametric model
like ours.

A further indication of the accuracy of
the replication strategy comes from comparing
the mean, standard deviation, skewness and
kurtosis of XYZ's returns with those of
the replicated returns. The latter statistics
can be found in Table 2, together with the
correlation and Kendall's Tau with the investor's
portfolio. Since the XYZ returns exhibit
a few negative outliers, apart from the
standard skewness and kurtosis measures,
we also report a more robust skewness and
kurtosis measure . To test whether the marginal
distribution of the replicated returns and
the joint distribution of the replicated
returns and the investor's portfolio are
significantly different from the original
distributions, we use the univariate and
bivariate Kolmogorov-Smirnov (K-S) tests
.

**Table 2: Statistics XYZ and Replicated Returns**

Mean | St. Dev | Skewness | Skewness (robust) | Excess Kurtosis | Ex. Kurt. (robust) | Corr. with Portfolio | Kendall's Tau | |
---|---|---|---|---|---|---|---|---|

XYZ | 0.0102 | 0.0424 | -1.7463 | -0.1600 | 11.5812 | 0.4366 | 0.714 | 0.540 |

Replica | 0.0150 | 0.0388 | 0.1184 | -0.1269 | 1.2691 | 0.6889 | 0.721 | 0.548 |

Univariate K-S Statistic = 0.054, (approximated) p-value = 0.862 | ||||||||

Bivariate K-S Statistic = 0.056, (approximated) p-value 0.924 |

Comparing the entries in
Table 2, it is clear that the statistical
properties of XYZ's returns have been quite
successfully replicated. The replication
strategy has not only replicated the marginal
distribution of XYZ's returns but also its
relationship with the investor's portfolio.
The same conclusion follows from both the
K-S tests.

**4. Distributional Analysis
**

A crucial stage in the evaluation procedure is the proper modelling of the distributional characteristics of the fund, the investor's portfolio and the reserve asset. This means that, although not explicitly designed to do so, the evaluations provide a wealth of information on the distributional properties of fund of funds returns. Table 3 summarises how often (out of a total of 485 funds) a given marginal or copula was used in the evaluations for modelling the fund return marginal and the joint distribution of the fund and the investor's portfolio return.

**Table 3: Distributional Characteristics Fund of Funds Returns**

Marginals | No. | Copulas | No. |
---|---|---|---|

Normal | 145 | Normal | 88 |

Student-t | 257 | Student | 49 |

Johnson | 83 | Gumbel | 36 |

SJC | 40 | ||

Cook-Johnson | 128 | ||

Frank | 144 |

Table 3 confirms that, despite an often substantial degree of diversification in the larger funds, the majority of fund of funds returns are far from normally distributed. Out of 485 funds, 340 funds' marginal return is better modelled by a Student-t or Johnson distribution than a normal distribution. In addition, for only 88 of the 485 funds is the relationship with the investor's portfolio (consisting of 50% S&P 500 and 50% T-bonds) best modelled by the normal copula. This emphasises once more how important it is to evaluate hedge fund and fund of funds performance using a method, which does not rely on the assumption of normally distributed returns.

**5. Evaluation Results
**

Having introduced the evaluation procedure, we now present the evaluation results. Our total sample consists of 485 funds of funds with a minimum of four years of history available. All data were obtained from TASS as of November 2004. Note that this implies that the again disappointing results of 2005 were not taken into account in the evaluation . Funds denominated in another currency than USD were converted to USD, ie, the perspective taken is that of a USD-based investor. Table 4 provides some information on the starting and end dates of the track records of the funds in our sample.

**Table 4: Fund of Funds Starting Date and End Date Details**

Jan 1985 | Jan 1988 | Jan 1991 | Jan 1994 | Jan 1997 | Jan 2000 | Jan 2003 | Oct 2004 | |
---|---|---|---|---|---|---|---|---|

Start after | 479 | 463 | 419 | 329 | 201 | 43 | 0 | 0 |

End before | 0 | 0 | 0 | 0 | 12 | 53 | 133 | 208 |

Table 4 shows that, reflecting the increasing popularity of hedge funds in the second half of the 1990s, the majority of funds started after 1994. Most hedge fund databases, including TASS, first started collecting data around 1994. As a result, our sample contains no funds that stopped reporting before that date. We also see that out of 485, 208 funds stopped reporting before October 2004. This confirms that, although lower than for individual hedge funds, the attrition rate in funds of funds is still quite high.

**Table 5: Length Fund of Funds Track Records**

4-5Y | 5-6Y | 6-7Y | 7-8Y | 8-9Y | 9-10Y | 10-12Y | 12-14Y | 14+ | |
---|---|---|---|---|---|---|---|---|---|

No. funds | 89 | 81 | 62 | 52 | 43 | 40 | 53 | 31 | 34 |

Table 5 provides details
on the length of the available fund of funds
track records. Out of the 485 funds in the
sample, only 118 have more than ten years
of history. This again reflects the fact
that most funds of funds are still relatively
young and attrition can be significant.

As in the example in section 3, in the evaluations
we assume that the representative investor's
portfolio consists of 50% S&P 500 and
50% long-dated US Treasury bonds, with all
exposure management done through fully collateralised
(nearby) futures contracts . Since it is
one of the most traded futures contracts
in the world, we use nearby Eurodollar futures
(trading on the CME) as the reserve asset.
Transaction costs on all futures contracts
are assumed to be 1bp one-way. For the pricing
of the payoff functions, we use 1-month
USD Libor as the relevant interest rate,
while estimating the required volatilities
and correlations over the period covered
by the track record of the fund that is
being evaluated. The interest rate data
was obtained from Datastream, while the
futures data was obtained from Commodity
Systems Inc (CSI).

**Figure
3: Scatter Plot Fund vs Replicated Standard
Deviation**

**Figure
4: Scatter Plot Fund vs Replicated Skewness**

**Figure
5: Scatter Plot Fund vs Replicated Correlation
with Investor's Portfolio**

To get an idea of the typical
accuracy of the replication procedure, Figure
3-5 show scatter plots of the fund standard
deviation (Fig. 3), standard skewness (Fig.
4) and correlation with the investor's portfolio
(Fig. 5) versus the replicated values for
all 485 funds. As is clear from these graphs,
on average the replication of these parameters
is unbiased and quite accurate. Not surprisingly,
the replication of skewness can be difficult
at times as fund returns may contain one
or more outliers, which will have a major
impact on the standard skewness statistic,
but which cannot be replicated. We encountered
this problem before in the example in section
3.

Figures 3-5 also provide additional information
on the risk-return profile of the funds
in our sample. From Figure 4 for example,
we see that for most funds of funds estimated
skewness lies somewhere between -1 and +1.
Likewise, from Figure 5 we see that the
majority of funds are positively correlated
a portfolio of 50% stocks and 50% bonds.
Most correlation coefficients lie between
0 and 0.6, indicating that many funds of
funds' returns are a lot less 'market neutral'
than the term 'absolute returns'suggests
.

**Figure
6: Histogram KP Efficiency Measure 485 Funds
of Funds**

Figure 6 shows a histogram
of the values of the KP efficiency measure
obtained for the 485 funds of funds in our
sample. From the graph we see that the majority
of funds produce a value for the efficiency
measure that is below 100. The average value
for the KP efficiency measure over all 485
funds is 99.36. We tested the statistical
significance of the above efficiency measure
results by calculating bootstrapped confidence
intervals. We distinguished between three
cases and obtained the following results:

- The confidence interval
is entirely lower than 100 -
**389 funds** - The confidence interval
contains 100 -
**41 funds** - The confidence interval
is entirely higher than 100 -
**55 funds**

This confirms the results
in the histogram in Figure 6. *The majority
of funds of hedge funds have not provided
their investors with returns, which they
could not have generated themselves in the
futures market. *

We sorted the funds in our sample in various
ways depending on starting date and/or end
date to see if there was any indication
of old funds doing better than new funds,
live funds doing better than funds that
closed down, etc. However, none of these
subdivisions produced significant results.

**Figure
7: Percentage of Funds that Stopped Reporting
Before October 2004
as Function KP Efficiency Measure**

The histogram in Figure 6 is negatively skewed, implying that some of the funds in our sample have shown extremely bad performance relative to what could have been achieved trading S&P 500, T-bond and Eurodollar futures. Since lack of performance is one of the main reasons for funds to close down, Figure 7 shows the percentage of funds that stopped reporting to the database before October 2004, as a function of their KP measure. From the graph we see that there is a strong relationship. Out of the 93 funds with a KP measure below 99, no less than 71 (76%) stopped reporting. Out of the 70 funds with a KP measure higher than 100, only 16 (23%) did so. A similar relationship is observed in the average KP measures of live and dead funds. The average KP measure over the 208 dead funds is 98.97, while over the 277 funds still alive the average is 99.65.

**6. Conclusion **

In this paper we have used
the hedge fund return replication technique
recently introduced in Kat and Palaro (2005)
to evaluate the net-of-fee performance of
485 funds of hedge funds. The results indicate
that the majority of funds of funds have
not provided their investors with returns,
which they could not have generated themselves
by trading S&P 500, T-bond and Eurodollar
futures. Purely in terms of returns therefore,
most funds of funds have failed to add value.

Compared with the various hedge fund performance
evaluation studies that have been carried
out over the last couple of years, our results
are quite unusual. Often, the conclusion
from hedge fund performance studies is that
funds of funds generate superior returns,
not inferior. This emphasises how tricky
factor model based performance evaluation
really is. As long as one can't be sure
that all relevant risk factors are accounted
for, it is impossible to know whether unexplained
returns are indeed true alpha or just unexplained
because one or more risk factors were left
out or specified incorrectly. Our methodology
is a lot more robust, as it relies on only
one simple principle: "if it can be
replicated, it can't be superior".
Of course, we need to make assumptions as
well, but these are a lot less crucial for
the final outcome of the evaluation than
the kind of assumptions required to make
factor model based alphas work.

Should investors rush out to buy into the
funds with the highest KP measures? Although
tempting, the answer is no. By definition,
extreme events only occur infrequently.
With more than 75% of the funds in our sample
having a track record of less than 120 months,
it is therefore hard to identify the presence
of any catastrophic (but compensated) risks
from the available data. A fund may be taking
the most terrible risks, but if so far it
has been lucky, the premium collected for
taking on those risks will show from the
fund's track record, but the risk itself
won't. A high KP measure should therefore
first and foremost be interpreted as an
indication that further due diligence is
required. One can only speak of truly superior
performance if such follow-up research shows
that the manager in question has generated
the observed excess return without taking
any extreme risks.

Finally, it has to be noted
that although in terms of the returns delivered
to investors, funds of funds do not seem
to add value, this does not mean there is
no economic reason for funds of funds to
exist. Most private and smaller institutional
investors do not have the skills and/or
resources required to perform the necessary
due diligence that comes with hedge fund
investment. In addition, given typical minimum
investment requirements, small private investors
will often lack sufficient funds to build
up a well-diversified hedge fund portfolio.
They therefore have no choice. If they want
hedge funds, they will have to go through
a fund of funds.

Large institutions do have a choice. Most
of them, however, still prefer to go the
fund of funds route. This is quite surprising
given the amount of fees that could be saved
by skipping the middlemen. Apart from believing
that fund of funds managers add enough value
to justify their fees (which research has
shown to be unlikely), part of the reason
that many large institutions go for funds
of funds lies in the fact that the interests
of institutional asset managers are typically
not correctly lined up with the interests
of those whose money they manage. As a result,
job protection becomes an important consideration.
By investing in a fund of funds, instead
of picking hedge funds themselves, institutions
avoid having to take responsibility for
the bottom-line fund selection. In the end,
all they can be held responsible for is
the decision to invest in hedge funds and
the selection of the fund of funds that
they invested in; risks, which can easily
be hedged by not making a move until others
do, hiring a big name consultant and a big
name fund manager, as most institutions
do.

**Reference**

*The authors like to
thank CSI and Rudi Cabral for allowing them
to access the CSI futures database*.

*Akaike, H., Information Theory and an Extension of the Maximum Likelihood Principle, in: B. Petrov and F. Csaki (eds.), Second International Symposium on Information Theory, Academiae Kiado, Budapest, 1973, pp. 267-281.*

*Amin, G. and H. Kat (2003). Hedge Fund Performance
1990-2000: Do the Money Machines Really
Add Value? Journal of Financial and Quantitative
Analysis, Vol. 38, pp. 1-24,*

*
Boyle, P. and X. Lin (1997). Valuation of
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Pennacchi and P. Ritchken (eds.), Advances
in Futures and Options Research, Vol. 9,
Jai Press, pp. 111-127.*

*
Brooks, C. and H. Kat (2002). The Statistical
Properties of Hedge Fund Index Returns and
Their Implications for Investors. Journal
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*

*
Crow, E. and M. Siddiqui (1967). Robust
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Fasano, G. and A. Franceschini (1987). Monthly
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Geltner, D. (1991). Smoothing in Appraisal-Based
Returns. Journal of Real Estate Finance
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*
Hinkley, D. (1975). On Power Transformations
to Symmetry. Biometrika, Vol. 62, pp. 101-111.
*

*Amin, G. and H. Kat (2003). Hedge Fund Performance
1990-2000: Do the Money Machines Really
Add Value? Journal of Financial and Quantitative
Analysis, Vol. 38, pp. 1-24,*

*Kat, H.
and J. Miffre (2005). Hedge Fund Performance:
The Role of Non-Normality Risks and Conditional
Asset Allocation, Working Paper, Alternative
Investment Research Centre, Cass Business
School, City University London, (downloadable
from www.cass.city.ac.uk/airc).*

*
Kat, H. and H. Palaro (2005). Who Needs
Hedge Funds? A Copula-Based Approach to
Hedge Fund Return Replication, Working paper,
Alternative Investment Research Centre,
Cass Business School, City University London,
(downloadable from www.cass.city.ac.uk/airc).
*

*
Lo, A., M. Getmansky and I. Makarov (2004).
An Econometric Analysis of Serial Correlation
and Illiquidity in Hedge Fund Returns. Journal
of Financial Economics, Vol. 74, pp. 529-609.
*

**Footnote**

^{1}
This is confirmed by the results in Kat and Miffre (2005).

^{2}
See Akaike (1973) for details.

^{3}
Distributions and copulas as defined in Kat and Palaro (2005).

^{4}
See Hinkley (1975) and Crow and Siddiqui (1967) for details.

^{5}
See Fasano and Franceschini (1987) for details.

^{6}
The CISDM Fund of Funds Index recorded a return of 4.72% over the first 11 months of 2005. Over the same period, the Barclay/Global HedgeSource Fund of Funds Index registered 4.81%.

^{7}
More in particular, we traded S&P 500 futures on the CME and T-bond futures on the CBOT. Both contracts are in the top 10 of most traded futures contracts in the US.

^{8}
In this context it is important to note that at least for some of the more complex distributions encountered (see Table 3), the correlation coefficient will not be a particularly good measure of dependence and may underestimate the true level of dependence.