GAIM recently had an all-day conference in New York City on hedge fund replication. There are three approaches, and I’m a little sceptical/skeptical about them all.

Hedge fund returns display all sorts of nonlinearities — some because the underlying instruments are noninear, others because they modify their exposure to linear securities as markets move, inducing a nonlinearity.

The first method is linear factor replication — a sort of least squares regression of observed hf returns to market factors, an APT model.

The second is nonlinear factor replication — a similar statistical analysis using nonlinear factors or nonlinear trading strategies.

The third is distribution replication — an attempt to build a payoff distribution, out of any underlying security (copper, electricity, the S&P, the price of sugar — pick one) that will have the same shape as the hedge fund returns your trying to replicate. Value the distribution as an option, compare its value to the value of the actual hedge fund you’re interested in, and then, if it looks cheaper, replicate it by dynamic delta hedging. The idea is that since you have the same distribution of returns, you should earn the same expected return. Same (expected) risk, same (expected) return.

There’s a funny cartoon in Grant’s Interest Rate Observer that has a picture of a road sign saying “Entering Greenwich CT: 2 and 20.” Getting hedge fund returns on the cheap is what this activity of replication is all about.

Does it work well enough to use reliably? I’m a little scepticalskeptical.

The main problem is that you don’t really know the payoff function for hedge funds, whereas you do for options. Probably this stuff is more useful for creating synthetic beta-driven hedge funds, with betas to anything you like, that can run algorithmically for cheap and may expose you to synthetic merger arb funds or vol trading funds.

The distribution approach is in the true spirit of finance, driven by the idea of equal risk equal return even when lognormality doesn’t hold. But it requires so much statistics on such poor data that it’s hard to swallow. And furthermore, since you replicate the eventual return distribution (if there is a stable one and if the method works) but not the month by month exposure, you don’t know how long it’ll take to generate the same return you expect from the hedge fund.

Necessity is the mother of invention. Invention often requires desperate measures.