Cumulant instrument estimators for hedge fund return models with errors in variables

Abstract

We revisit the factors incorporated in asset pricing models following the recent developments in financial markets – i.e., the rise of shadow banking and the change in the transmission channel of monetary policy. We propose two versions of the Fung and Hsieh (2004) hedge fund return model, especially an augmented market model which accounts for the new dynamics of financial markets and the procyclicality of hedge fund returns. We run these models with an innovative Hausman procedure, tackling the measurement errors embedded in the models factor loadings. Our empirical method also allows for confronting the drawbacks of the instruments used to estimate hedge fund asset pricing models.

Keywords:

• asset pricing models
• hedge funds
• cumulant instruments
• Hausman tests
• GMM

JEL Classification:

• C13
• C19
• C58
• G12
• G23

Notes

¹ The term ‘haircut’ refers to the percentage of equity required in market funding. It is the inverse of the leverage associated with a funding operation.

² Note that the market model is the empirical counterpart of the CAPM model, which includes only one explanatory variable: the market risk premium.

³ Other well-known biases in the reporting of hedge fund data are the backfill, incubation and smoothing biases.

⁴ In the following discussion, for the sake of simplicity, we refer to 10Y as the 10-year interest rate.

⁵ According to the risk-taking channel, monetary policy impacts business conditions by changing the perception of risk in the financial system. It focuses on financial frictions in the lending sector.

⁶ Indeed, it is well known that the Durbin and Pal’s instruments lack robustness (Cheng and Van Ness, 1999).

⁷ Note that we use as weighting matrix in the GLS estimator (Equation 10). This matrix can be replaced by the White’s (1980) asymptotically consistent variance–covariance matrix. The properties of this estimator, named β_E, are discussed in the aforementioned reference. Actually, we implicitly use an augmented version of this estimator in this article.

⁸ Note that we do not report the results associated with the methods using the z instruments because of their low performance in our estimations. The results related to the d instruments, which are a smoothed version of the z ones, are much better.

⁹ We previously compared the results obtained with the GAI and Hedge Fund Research (HFR) databases for a similar time period and the results are essentially the same. These results are available on demand.

¹⁰ The address of the French’s website is http://mba.tuck.darmouth.edu/pages/faculty/ken.french/data_library.html

¹¹ The website of the Hsieh’s database is http://faculty.fuqua.duke.edu/~dah7/DataLibrary/TF-FAC.xls

¹² This fact may be explained by the option-like trading strategies followed by hedge funds (Heuson and Hutchinson, 2012).

¹³ According to Pagan (1984, 1986), generated variables are endogenous variables which must be estimated by IV methods.

¹⁴ Note that we must be prudent here regarding the interpretation of the alpha as a risk-adjusted return in Model 3, since the term structure spread and the VIX are not portfolio returns.

¹⁵ In this respect, see Heuson and Hutchinson (2012). As noted before, the positive asymmetry of the return distribution of many hedge fund strategies is due to their option-like trading strategies.