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BCI Model and Hedge
Fund Clones
The objective of the Best Choice Implicit Model is to represent infor-
mation in a space defined by a set of orthogonal implicit variables called
principal components. For hedge funds, these principal components can
be seen as projections or as an average of alternative investment strate-
gies active indices. Obviously, the drawback of this approach lies in its
lack of legibility. The hedge funds making up the constituencies of each
index are not directly known (one would need to know all components
of all underlying indices). Moreover, as hedge funds indices may be
difficult to interpret with respect to traditional risk factors, the interpre-
tation of the principal components is even harder: the implicit approach
applied to the risk measure may b e particularly exposed to hidden risk.
If the next chapter provides some tools to reduce this risk for large in-
vestors in hedge funds through homogeneity analysis, this chapter aims
to provide an explicit understanding of these principal components with
regard to the traditional risk factors. The idea is to apply two different
methodologies that are clearly connected with the model used for hedge
funds clones. As we will see, if some factors can be easily explained by
these approaches, some cannot. In other words, the level of heterogene-
ity and complexity of hedge funds requires the Best Choice Implicit
Model to be a good model at the individual investment vehicle level.
The fact that the clones model can duplicate only a small part of the set
of alternative risk factors simply illustrates that these methodologies are
too restrictive for the hedge funds universe.
Fung and Hsieh (2004) proposed to model the excess return (in excess
of the risk-free rate) of a diversified hedge fund with seven fac-
tors representing four traditional buy-and-hold and four primitive
trend-following (PTS) strategies. The Fung and Hsieh (2004) factors
are S&P 500 excess return (S&P rf ), Wilshire small cap minus
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200 Market Risk Management for Hedge Funds
large cap return (SC LC), change in the constant maturity yield of the
10-year Treasury (BD10RET), change in the spread of Moody’s Baa
minus the 10-year Treasury (BAAMTSY) and the return of primitive
trend-following strategies on bonds (PTFSBD), currencies (PTFSFX),
and commodities (PTFSCOM). Fung and Hsieh (2001) modelled Prim-
itive Trend-Following as a portfolio of lookback straddles. More re-
cently, the primitive trend-following strategy on short-term interest
(PTFSST) as well as the buy-and-hold strategy on emerging mar-
kets have been added. All data are available on http://faculty.fuqua
.duke.edu/dah7/DataLibrary/TF-FAC.xls. Finally, following Agarwal
and Naik (2000a), the Fama–French’s book-to-market (HML) factor
was added.
To try to interpret the principal components of the BCIM, we conduct
1023 regressions
(on the last 36 months) for each of the 35 implicit
factors (C
) as of December 2005 in order to reflect all possible combi-
nations of the 10 factors. Then the model with the highest R-square and
with all slope coefficients significatively different from zero is selected.
Table 10.1 shows, for each of the 35 principal components, the results
of this process as well as the percentage of hedge funds significantly
exposed to the implicit factors.
Out of the 35 factors, 12 cannot be explained by the model (no signifi-
cant coefficient), while the average adjusted coefficient of determination
rises to 0.17 for the model with at least one significant slope. The ad-
justed R-square is larger than 0.30 for only two components. Remember
that the implicit factors consists of an average of indices, and as s uch
the idiosyncratic risk is diversified away. The low quality of fit cannot
be explained by specific exposures. As the system defined by the prin-
cipal components enables us to explain a large universe of hedge funds,
the average low R-square value of the 10 factors model is implied by
the omission of important risk factors that drive the performance of the
alternative investment strategies.
Not surprisingly, at the individual hedge fund level, the quality of
fit of the 10-factor model is also disappointing. Indeed, the average
adjusted coefficient of determination
for 2238 hedge funds with at
least a 36-month track record as of December 2005 is 0.33, i.e. half of
the quality of fit of the Best Choice Implicit Model. Table 10.2 exhibits
the distribution of adjusted R-square for the 10-factor model and for the
The all possible regression process has the advantage of being not path dependent.
For regressions with significant slope coefficient computed with backward regressions.

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