Aggregate hedge funds’ flows and returns

Abstract

In this article, a multivariate unobserved components model for returns and net inflows into hedge funds is employed to assess whether the flows of funds into the industry are dynamically related to returns. The econometric model is used to estimate expected flows and expected returns as unobserved components. The results point to strong autocorrelation in both flows and returns and to positive correlation between past returns and future flows, while the evidence concerning the linkage between past flows and future returns is mixed.

Acknowledgement

The authors are grateful to two anonymous referees for constructive comments.

Notes

¹ Our model is similar to the latent VAR used by Brandt and Kang (2004) to study the relationship between the conditional mean and the volatility of stock returns, albeit in our case the state space model is linear and Gaussian.

² The contemporaneous interrelation between flows and returns can be evaluated as follows. By projecting ε_{1 t} onto ε_{2 t} , i.e. ε_{1 t} = β₁ ε_{2 t} + η_{1 t} with β₁ = cov(ε_{1 t} , ε_{2 t} )/var(ε_{2 t} ), and noting that from Equation 2, , it follows . By substituting into Equation 1, the reduced form for the return equation is obtained. Similarly, the reduced form for the flows equation can be written as  From the reduced form equations, it can be noted that if the error terms in the measurement equations are correlated, i.e. cov(ε_{1 t} , ε_{2 t} ) ≠ 0, flows not only have a lagged impact on returns, but also a contemporaneous impact, with sign determined by the sign of the covariance between the error terms. Similarly, returns may contemporaneously affect flows, with the sign of the impact still depending on the sign of the covariance. In both cases, it is however the size of the ratios β₁ = cov(ε_{1 t} , ε_{2 t} )/var(ε_{2 t} ) and β₂ = cov(ε_{1 t} , ε_{2 t} )/var(ε_{1 t} ) which allows to determine whether such contemporaneous linkage is negligible or not.

³ The weak rejection of normality may seem puzzling given the evidence of nonnormality usually associated with hedge funds returns, see, e.g. Eling and Schuhmacher (2006). However, our dataset is based on quarterly observations, for which there are less deviations from normality. Moreover, Eling and Schuhmacher (2006) themselves find that even with monthly data the economic implications from standard financial indicators like the Sharpe ratio are similar to those obtained from more general performance measures, which are robust to nonnormality. Moreover, even if the data were not Gaussian, using a Gaussian model would still lead to consistent estimation of the parameters, as a quasi-maximum likelihood interpretation could be provided to the estimator.

⁴ See also Harri and Brorsen (2004) on performance persistence.