Dr
Gérard Gennotte
Quantmetrics Capital Management and
London School of Economics
April 2006
In this article, we try to show that the
horizon of a fund's trades has profound
implications on the difficulties encountered
in assessing performance, on the characteristics
of performance itself, especially in times
of crisis, and on the diversification achieved
by forming portfolios of funds.
Statistical Analysis of Performance
Statistical analysis of the performance
of an investment requires a representative
history of returns. In the best case of
a stationary process, accurate measurement
of expected returns requires a very long
time series. The debate on the appropriate
equity risk premium intensifies periodically,
frequently as a consequence of large moves.
To put things in perspective, a century's
worth of data is only an indicator of future
returns. The graph shows the remarkable
volatility of the excess return on a welldiversified
portfolio: the 10year rolling average of
US equity market returns from 1871 to today.
Historians would argue that the 20th century
was quite positive economically and financially,
hence it is not a guarantee for the future.
Or alternatively an acre of land in central
Rome was a very good investment until the
barbarian invasion unfolded. Hence we should
be wary of a hedge fund's ability to generate
alpha even if it has a good 10year track
record.
10 Year Rolling Average
of US Equity Market Returns
Source: R. Shiller "From Efficient
Markets Theory to Behavioral Finance,"
J. Econ. Pers. 2003
While statistical inference of expected
returns has very stringent data requirements,
other characteristics of the distribution
can be easier to study. In terms of measuring
higher moments of the distribution, eg the
volatility of returns, skewness or the frequency
of tail events, the length of the time series
is less important than the number of observations
it encompasses. For example, the 1year
history of a relative value fund focusing
on trades with horizons of six months to
one year may actually contain only a couple
of sets of nonoverlapping trades. Conversely,
if the trades have a 1day horizon, one
year of data covers at least 250 trading
periods. In the latter case, the realised
performance can be accurately measured statistically,
and the remaining question faced by investors
is whether future performance is likely
to differ from the year of observed returns
history.
In the case of longer horizon trades, statistics
such as Sharpe, Omega or Sortino ratios
are obviously of little help. The shortterm
horizon fund not only has a better statistical
history but going forward the evolution
of returns is more informative in the sense
that it is easier to determine that conditions
have changed over a month (20 trades completed),
than it is for the longer horizon fund.
Indeed, in the latter case it is difficult
for the manager himself to assess what the
distribution of returns will be on the basis
of so few observations, let alone for the
investor. Investors face the additional
difficulty of distinguishing between skill
and luck and are faced with a form of survivorship
bias. In the simplest case, the 1year performance
is based on two bets. If enough different
managers make such bets, some will necessarily
be on the right side of the bets and generate
superior performance. The bias is that managers
with mediocre performance will not receive
much publicity and fall by the wayside.
The smaller the number of bets, the stronger
is this form of survivorship bias. In order
to evaluate past performance and/or predict
future returns, there is no substitute to
the conceptual understanding of the actual
trades.
Trade Horizons, Liquidity and Stoplosses
A strategy which relies on longterm trends
does not require frequent trading and can
afford to be implemented over time. Consequently,
it is compatible with low liquidity and
can be done in sizes such that the liquidity
of the positions becomes limited and the
transactions costs to exit large. The longer
horizon fund will therefore most likely
be always invested and will not be able
to cut losses cheaply or quickly. Furthermore,
it is likely that an adverse move in a longer
term trend actually increases the expected
return of the strategy from that point on.
Hence not only is the fund like an oil tanker,
ie very slow at changing course, it also
may be optimal, from an expected return
standpoint, to accelerate on the same course.
These characteristics – low frequency,
illiquidity and costly exiting of large
positions – apply better to some strategies
such as fixed income relative value, distress
or credit trades. Macro bets and trendfollowing
strategies, by contrast, can sometimes be
implemented in size with highly liquid securities.
Conversely, a shortterm horizon strategy
requires low transaction costs and highly
liquid positions. If it relies on meanreversion
such trend is necessarily shortlived and,
by definition, liquidation of the strategy
on the grounds of expected return becomes
a matter of indifference after a short period
of time. A precommitted stoploss constraint
is therefore much cheaper and also more
likely to be adhered to by a fund using
shortterm strategies. This truncation of
the returns leads to fund return volatility
increasing less with market volatility than
in the other case. The table below summarises
the characteristics generally associated
with long and shortterm horizon strategies.
Longterm horizon
strategy correlates with:

Shortterm horizon
strategy implies:
Always invested
Not always invested
Large size relative
to market
Small size relative
to market
Low liquidity
High liquidity
High transaction
costs
Low transaction
cost
Some degree of
mean reversion
Cheap to stop
loss
Costly to stop
loss
Benefits from
crises
Exposed to crises
Crises
In the hedge fund arena, a key concern
is the impact of crises on returns. By definition
they are rare, hence past returns may not
encompass such occurrences. Some crises
are caused or at least substantially magnified
by hedge fund and proprietary trading strategies
themselves. Such endogeneity has always
been present but it has become more acute
recently with the increase in the amounts
invested and the widespread adoption of
VaR risk management systems. Indiscriminate
liquidations in large portfolios which may
be similar induce increased correlations
among otherwise uncorrelated strategies.
Hence when the crisis hits a part of the
portfolio, the other strategy compartments
may be affected by liquidations creating
a selfreinforcing mechanism. This mechanism
does not depend on the size of a single
actor relative to the size of the market;
it simply requires that their aggregate
size is large relative to market liquidity.
Here again, our two types of funds are
likely to react very differently to crises.
For the longer horizon fund, the issue is
how long the fund is able to withstand a
worsening of the crisis before liquidity
returns, other investors identify the opportunity
and the underlying bets pay off.
Once a crisis hits, the short horizon fund
has a strong incentive to cut losses to
reduce risk and faces low costs of doing
so. Such a fund is not necessarily always
invested, in fact it should selectively
choose the times it enters the market so
as to maximise the probability of gain.
Hence, the fund may not be invested at the
time the crisis hits either because of luck
or because the increase in risk had been
anticipated. By the same token, the fund
is able to swiftly take advantage of the
opportunities the crisis created in a way
a fullyinvested low liquidity fund is unable
to match.
Conclusions: Implications for Hedge
Fund Portfolios
The pitfalls of using statistics based
on data containing a small number of actual
observations compound when constructing
portfolios of hedge funds. The statistics
for some individual funds have little significance,
but estimates of historical correlations
are even less significant. Contagion leads
to a decrease or disappearance of diversification
in times of crises. What is there to do?
Common sense suggests a return to square
one: formulate simple return scenarios and
make assumptions on correlations, especially
in more volatile times. A good starting
point may be to think of maximum losses
for individual trades in states of nature
where correlations are high. To that end,
a careful analysis of stated stoploss constraints
and of the costs and incentives faced by
managers to abide by them deserves special
intention. An implication of the above discussion
is that varying the trade horizon across
the components of the portfolio and mixing
mean reverting and trend following strategies
can substantially enhance diversification
effects across the whole spectrum of market
conditions.
The relevance of these simple points is
reinforced by the recent trend towards investments
in less liquid instruments (ie credit derivatives,
catastrophe bonds, private equity, etc)
and the associated lengthening of trade
horizons.
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