By Peter Urbani
So what is a perfect hedge and how do you create one anyway? A perfectly “hedged” fund is one which has no downside risk. Its payoff relative to the market or some other benchmark is the same as that of the fund plus a put option that provides protection against the downside.
In the real world, however, this tail protection is not costless and the costs of implementing your “hedge” tend to come either out of your upside in the form of lower upside return capture or in terms of not providing a perfect hedge or full downside protection. The art of hedge fund management is thus largely managing these competing forces and trying to generate sufficient excess returns or “alpha” to offset the costs of implementing whatever downside protection, if any, is put in place whilst at the same time performing as well or at least partly as well as the market or benchmark when it is up. Ideally the hedge fund manager will need to add alpha in both up and down market regimes in order to be able to achieve this. The manager who is able to do so will have the aforementioned option like payoff and a positively skewed probability distribution (since the left tail of the distribution is truncated at or around zero) . It is these differential sensitivities to upside and downside movements that are largely responsible for the non-linearity inherent in hedge fund payoffs. Using traditional linear methods to measure these sensitivities thus makes little sense for hedge funds that do any hedging because of their implied embedded optionality. How then to measure this?
Fortunately there are pre-existing models which enable us to do so. For example, the Henriksson Merton (HM) model, which has been around since the 1980’s, seeks to separate the ability of a portfolio manager into “selection” and “timing” abilities by introducing a dual alpha and beta formulation of the familiar CAPM – Alpha and Beta model. The model essentially posits that an ability to have a low or zero downside beta is evidence of the managers ability to exit (time) the market ahead of downside moves. Similarly a higher upside Beta and Alpha are taken as evidence of superior stock picking or selection skills.
In a recent paper on , Andreas Steiner approached this dual alpha and beta model and how it can be used to examine the sensitivities to different market regimes after the fact. The efficacy of this method in an out-of-sample subsequent period forecast sense has yet to be examined fully, but the mere fact that it is capturing the non-linear attributes and providing a deeper insight into the manager’s ability to protect the downside makes it a more useful metric than the single index model.
The straitjacketed restrictions of the long-only paradigm of the original CAPM – Alpha and Beta models do not apply to the hedge fund manager due to his/her ability to short or otherwise hedge out the risks of his long positions rather than by having to follow the risky ( and unwise ) practice of physically exiting and entering or ‘timing’ the market. In contrast the hedge fund manager will in general seek to maintain a permanent hedge.
There are probably no more used ( and abused ) words in finance than Alpha and Beta and their meanings and intended definitions are not always consistent. For Hedge funds the generally understood ( by the public ) meaning of Beta as being your sensitivity to movements in the broad equity market ( typically the S&P500, MSCI World or some other suitable Equity Index ) only really applies in the context of Long Short Equity, Dedicated Short and Market Neutral strategies and obviously has no direct relationship to Credit Strategies and the like which require that alternative benchmarks be used. In those cases some or other multi-factor model can be used. These typically take the form of the models suggested by Fung and Hsieh etc.
Portfolio managers in general, and active ones especially, generally dislike the whole concept of benchmarking but by comparing the performance of a hedge fund against an idealised primitive trading strategy or other suitable benchmark consistent with what the manager says he does additional insights can be gained in particular into the managers ability to hedge.