Tracking Problems, Hedge Fund Replication and Alternative Beta

Abstract

As hedge fund replication based on factor models has encountered growing interest among professionals and academics, and despite the launch of numerous products (indexes and mutual funds) in the past year, it faced many critics. In this paper, we consider three of the main critiques, namely the lack of reactivity of hedge fund replication and its deciency in capturing tactical allocations; its failure to apprehend non-linear positions of the underlying hedge fund industry and higher moments of hedge fund returns; and, nally, the lack of access to the alpha of hedge funds. To address these problems, we consider hedge fund replication as a general tracking problem which may be solved by means of Bayesian lters. Using the linear Gaussian model as a basis for discussion, we provide the reader with an intuition for the inner tenets of the Kalman lter and illustrate the results' sensitivity to the algorithm specication choices. This part of the paper includes considerations on the type of strategies which can be replicated, as well as the problem of selecting factors. We then apply more advanced Bayesian lters' algorithms, known as particle lters, to capture the non-normality and non-linearities documented on hedge fund returns. Finally, we address the problem of accessing the pure alpha by proposing a core/satellite approach of alternative investments between high-liquid alternative beta and less liquid investments.

Hedge Funds: A Dynamic Industry in Transition

“…Bondarenko (2004) and Buraschi, Kosowski and Trojani (2015) introduce and analyze variance and correlation risk factors for hedge funds. Roncalli and Weisang (2010) apply advanced Bayesian filters' algorithms, known as particle filters, to capture nonlinearities documented in hedge fund returns (see Section 6.6 for a more detailed discussion in the context of hedge-fund beta replication). And introduce a new econometric methodology to capture nonlinearities and time-series variation in hedge funds' exposures to risk factors using highfrequency data, and find that these exposures vary significantly across months.…”

Hedge fund replication

“…Our simulations could incorporate this information through making the standard deviation of the Gaussian distribution of factor returns a variable noise factor; perhaps this factor would be shocked in months where the change in a volatility index such as VIX was large. 38 5 gives a review of some problems found in these replicators; in particular slow reactivity, problems modelling non-linear returns, capturing tactical allocations, capturing alpha and matching higher moments of returns.…”

“…Hedge funds are a class of investment vehicle aiming for absolute return -making a profit regardless of the market 1-3 conditions. They 4,5 often have a very loose mandate which means they are unconstrained in terms of the strategies they may employ and the markets they may enter. They may use over-the-counter derivatives tailored to a particular exposure profile, highly leveraged positions and short selling.…”

On the Tracking and Replication of Hedge Fund Optimal Investment Portfolio Strategies in Global Capital Markets in Presence of Nonlinearities, Applying Bayesian Filters: 1. Stratanovich Kalman Bucy Filters for Gaussian Linear Investment Returns Distribution and 2. Particle Filters for Non-Gaussian Non-Linear Investment Returns Distribution

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