Hedge fund replication is driven by the investor’s desire for liquidity, transparency, low fees, and the need to arrive at a meaningful benchmark for products that managed to escape benchmarking for a (too) long time.
Broadly we can distinguish factorbased models based on mean–variance portfolio theory as proposed by Lo and Hasanhodzic (2007) and models based on no arbitrage capital market equilibrium and stochastic discount factors as suggested by Kat (2007).
Factor-based models attempt to find the best tracking portfolios out of a set of prespecified macro risk factors (value, size, credit, commodities, ...), option strategies (short put, look-back, ...), and naive active strategies (forward rate bias, momentum, equal weighting, ...). Typically linear regressions (equivalent to finding the combination of factors that minimize the tracking error between fund and replicating portfolio) or Kalman filter techniques (to allow for time varying exposures) are used.
The resulting combination of factors that tracks a hedge fund (index) best is said to be a clone of this index. The intercept from this regression (alpha) measures the amount of real skill that is neither subsumed in risk taking or in engineering bets on infrequent events nor inherent in naïve strategies widely known to the market.
In essence it is what is worth paying for and what makes a hedge fund unique. In spirit this is identical to the so-called mean–variance spanning tests. Though intuitively appealing, the shortcomings of this approach are manifold.
Potentially missing factors, limited account of dynamic trading, the assumption of normality, and most of all the very limited out of sample explanation of individual as well as hedge fund indices put a dent into its practical importance.
Models based on stochastic discount factors attempt at generating the same distributional characteristics as the targeted hedge fund. Dybvig (1988) has shown how arbitrary dynamic trading strategies can be priced in capital market equilibrium.
This has two immediate consequences. Kat first arrives at a performance measure that is deeply rooted in economic theory and independent from distributional assumptions.
As such it is preferable to mean–variancebased factor models that do not provide this generality. Second, once we can price a given return stream, we can also derive its dynamic hedging policy. This directly leads to the implementation of a replication program.
While cloning hedge funds is the correct way to evaluate the alpha generating abilities of a hedge fund manager and therefore it allows a much better discussion about the level of fees justified by a particular product offering, it is not clear investors want to invest in clones.
After all, hedge fund replicating portfolios are complex beta bundles and the real question is whether investors need that bundle in the first place. In other words, investors would be better off to decide first which betas they need (in a corporate risk management or pure asset allocation context) and then where to source them from.