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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

1

(on the last 36 months) for each of the 35 implicit

factors (C

k

) 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

2

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

1

The all possible regression process has the advantage of being not path dependent.

2

For regressions with signiﬁcant slope coefﬁcient computed with backward regressions.