Assessing and Valuing the Non-Linear Structure of Hedge Fund Returns

Tracking Problems, Hedge Fund Replication and Alternative Beta

“…One may wonder however why there is apparently no need to take into account a high frequency factor. Beside the fact that it is rather good news from a practitioner point-of-view, one must point out that in our example, we replicated the HFRI Fund Weighted Composite Index, which is the most general industry aggregate provided by Hedge Fund Researh, Inc. As such, in light of the results presented by Diez de los Rios and Garcia [11], we surmise that the eect of high frequency trading which would in part appear as nonlinear is negligible. In this paper, we presented a formal framework for hedge fund replication by introducing the notion of tracking problems which may be solved using Bayesian lters.…”

“…As noticed in [5], this methodology has so far not been implemented as a direct replication process, but rather as an assessment tool for HF investors. As such, the results in [11] are interesting. For the global index, they cannot reject the null hypothesis of linear returns, while at the category index level, they reject the hypothesis of linearity of returns only for the event-driven and managed futures categories at the 5% level, and for xed-income arbitrage at the 10% level.…”

“…Diez de los Rios and Garcia [11] further nd that there is statistical support for rejecting linearity only for a few categories (emerging markets, short bias and managed futures). If we consider the HFRI Macro and Relative Value indices, considering the results and the improvement in the proportion of HF returns explained, one may consider, in a rst approach, that they exhibit this non-linear structure.…”

“…Recently, factor models including an option factor have been used to assess the nature and the extent of the presence of nonlinearities in hedge fund returns [11]:…”

“…From the point of view of investors, however, the complexity of these algorithms certainly does not alleviate the lack of understanding in the replication procedure. Furthermore, despite superior dynamic procedures and an ever expanding set of explanatory factors, some nonlinear features of HF returns [11] as well as a substantial part of their performance remain unexplainable, unless surmising ultrahigh frequency trading and investments in illiquid assets or in derivative instruments by HF managers. To our knowledge, while commonly accepted by most authors, because of practical diculties, these explanations have not led to a systematic assessment nor have been subject to systematic replication procedures.…”