Market Risk Management for Hedge Funds: Foundations of the Style and Implicit Value-at-Risk

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10

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.

10.1 THE TEN-FACTOR MODEL

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

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.