An Alternative Approach to Alternative Beta

Abstract

Hedge fund replication based on factor models is encountering growing interest. In this paper, we investigate the implications of substituting standard rolling windows regressions, which appear ad-hoc, with more efficient methodologies like the Kalman filter. We show that the copycats constructed this way offer risk-return profiles which share several characteristics with the ones posted by hedge funds indices: Sharpe ratios above buy-and-hold strategies on standard assets, moderate correlation with standard assets and limited drawdowns during equity downward trends. An interesting result is that the shortfall risk seems less important than with hedge fund indices and regressions based-trackers. We finally propose new breakdowns of hedge fund performance into alpha, traditional beta and alternative beta.Hedge fund replication has become highly fashionable during recent months. Under this generic term, three main approaches can be identified:• Mechanical duplication of strategies. A growing number of investment banks are proposing products which aims to reproduce in a systematic and quantitative manner a strategy followed by hedge funds. For instance, several investable indices have been proposed which mark-tomarket systematic short of put options or variance swaps. Thanks to the positive premia between implied and realized volatilities, this kind of strategy seems able to generate superior Sharpe ratios while exposing to the risk of huge losses when the underlying asset plunges (Lo [2005], Goeztmann et al. [2007] • Replication of distribution. A very different approach has been advocated by Kat and Palaro [2007]. Their postulate is that investors enter into hedge funds for their characteristics in terms of expected returns, volatility and correlation, not for their month-by-month return. While the argument might be generalized to other assets, it is probably all the more meaningful as diversification is a major motivation for investing in hedge funds. In practice, the copycat is based on a passive futures trading strategies 1 . The investor first determines its existing portfolio (for instance, an equally-weighted mix of US Treasuries and S&P 500), the futures he wants to trade and then the statistical properties in terms of correlation with the existing portfolio, shortfall probability, skewness sign, etc. The investor then receives the line-up of the strategy: that is the daily trading volume of each futures contract he has to trade to replicate the fictive option so that in the end the fund has the desired properties. However, there is no indication on how long it will take for this result to materialize and,

On Fund Mapping Regressions Applied to Segregated Funds Hedging Under Regime-Switching Dynamics

“…The usual industry practice to represent basis risk between a segregated fund and its hedging instrument is to use a fund mapping regression, see for instance Roncalli and Teïletche (2007) for such mappings. The fund mapping regression assumes the following relationship between returns of F and S:…”

Tracking Problems, Hedge Fund Replication and Alternative Beta

“…One such method, used extensively [16, 18, inter alia], is to use rolling-windows OLS where the coecients w A common choice for the window length L is 24 months, even though one could consider a longer time-span trading-o the dynamic character of the coecients for more stable and more robust estimates. By means of an example, Roncalli and Teiletche [30] have demonstrated however that such methodology captures poorly the dynamic allocation, in particular in comparison with the Kalman lter (KF). As we extensively expose the use of KF and similar methodologies in the rest of the paper, we will say little for now, except to point out that despite its superiority, the use of KF estimation requires caution in its implementation, making the estimation of the positions w (i) k a non-trivial aair.…”

“…We consider the example of replicating the HFRI index as in [30]. In Appendix B.1, we discuss some of the nontrivial choices which must be taken when specifying the model.…”

“…Yet, for now, the standard rolling-windows OLS regression methodology, used to capture the dynamic exposures of the underlying HF's portfolio has failed to show consistent out-of-sample results, stressing the diculty of capturing the tactical asset allocation (TAA) of HF's managers. More recently, more advanced methodologies, in particular Markov-Switching models and Kalman Filter (KF), have been introduced [5,30] and show superior results to the standard rolling-windows OLS approach. 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.…”

Using hedge funds to enhance asset allocation in life cycle pension funds

“…2,3 This paper develops a framework to assess the potential benefi t of using hedge fund of funds to replace some or all of the equity allocation in life cycle investment funds.…”