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

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. First, we modify the Fung and Hsieh (2004) model by combining the lookback option return variables included in their factorial model into one principal component. Second, in an augmented version of the market model, we relate hedge fund returns to increasingly important determinants of stock returns, i.e., the term structure spread and the VIX, an indicator of the implicit volatility of stock returns. Third, it is obvious that hedge fund models, regardless of their precision, contain specification errors. These errors may be due to omitted variables or inherent to the measurement of their risk factors (Fama and McBeth, 1973; Chen et al., 1986; Shanken, 1992; Campbell et al., 1997; Lettau and Ludvigson, 2001; Cochrane, 2005). They can also be attributable to biases related to the report of hedge fund returns, like the survivorship bias. We run these models with an innovative Hausman procedure tackling the measurement errors embedded in the models factor loadings.   We design instruments which are appropriate when the distribution of the variables under study is not Gaussian, i.e. when it is asymmetric or leptokurtic. More precisely, we propose a new weighting of two well-known cumulant instruments originally designed to tackle errors-in-variables, which are the Durbin (1954) and Pal (1980) estimators, and use it as an input to the two-stage least squares (TSLS) and the generalized method of moments (GMM) estimations. Our new optimal instruments are in line with the works of Fuller (1987), Racicot (1993), Dagenais and Dagenais (1997), Cragg (1997), Lewbel (1997), Coën and Racicot (2007), Meng et al. (2011) and Racicot and Théoret (2012). Our empirical method also allows confronting the drawbacks of the instruments used to estimate hedge fund asset pricing models.