c10 JWBK337-Duc September 6, 2008 15:6 Printer: Yet to come
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
To try to interpret the principal components of the BCIM, we conduct
(on the last 36 months) for each of the 35 implicit
) 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.