Hedge Fund Returns

Why not make them yourself?

Harry M. Kat, Professor of Risk Management, Cass Business School
Originally published in the May 2005 issue

Over the last 10 years hedge funds have become extremely popular with high net worth investors and are currently well on their way to acquiring a significant allocation from many institutions as well. The growing popularity of hedge funds and the availability of various hedge fund databases have spawned several hundred of academic research papers on various aspects of the hedge fund industry and especially the return performance of hedge funds and fund of funds. Many of these papers apply methods, like standard mean-variance and Sharpe ratio analysis for example, which are ill-suited for the analysis of hedge funds returns and have, as a result, produced incorrect conclusions. Fortunately, some studies have taken a more sophisticated approach and havemade it clear that hedge fund returns are not really superior to the returns on traditional asset classes, but primarily just different.

With hedge fund performance getting worse every year, the hedge fund industry has come to more or less the same conclusion. Unlike in the early days, hedge funds are no longer sold on the promise of superior performance, but more and more on the back of a diversification argument: due to their low correlation with stocks and bonds, hedge funds can significantly reduce the risk of a traditional investment portfolio without giving up expected return.

Given that more and more people are accepting that hedge fund returns are not better, but just different, the obvious next question is: is it possible to generate hedge fund-like returns ourselves by mechanically trading stocks and bonds (either in the cash or futures markets)? Although hedge fund managers typically put a lot of effort into generating their returns, maybe it is possible to generate very similar returns in a much more mechanical way and with a lot less effort?

At the Alternative Investment Research Centre at Cass Business School we have done quite some research in this area, which has led to the development of a general procedure that allows investors to design simple trading strategies in stock index and bond futures that generate returns with statistical properties that are very similar to those of hedge funds. In what follows I will briefly describe this procedure as well as provide an example of its amazing results.

The General Idea

In theory at least, there are several ways to replicate hedge fund returns. One popular approach is to estimate a so-called factor model, i.e. a model which explains fund returns from a number of "risk factors", such as changes in the S&P 500, interest rates, credit spreads, volatility, etc. Once these factors have been identified and the fund's sensitivity to these factors has been estimated, one can construct a portfolio of stocks, bonds, and other securities with the same factor sensitivities as the fund in question. Since it has the same factor sensitivities, the resulting portfolio will generate returns that are similar to those of the fund. The problem with this approach is that in practice we have little idea how hedge fund returns are actually generated. In other words, we don't really know which risk factors to use. As a result, factor models for hedge funds typically explain only a small portion (15-20%) of a hedge fund's total return. Obviously, this is not enough to refer to this as proper "replication".

Given the failure of the factor model approach, one could say that by trying to replicate hedge funds' month-to-month returns we are aiming too high. Fortunately, this is not a real problem.

When investors like a hedge fund it is (hopefully) not because of the fund manager's smooth sales rap, his expensive Armani suit or his big Rolex. It is because of the manager's track record. In fact, it is (or should be) because of the statistical properties of that track record, i.e. the average, standard deviation, etc. of the fund return and the correlation with the investor's existing portfolio. This implies that we do not necessarily have to replicate a fund's month-to-month returns. It is enough if we can generate returns with the same statistical properties as the returns generated by the fund. This is exactly what the replication procedure that we have developed does.

The Procedure

Designing trading strategies that generate returns with the same statistical properties as managed fund returns sounds easy, but of course it is not. The first step consists of a thorough analysis of the available data and the selection of a statistical model that best describes this data. Since hedge fund returns often have very challenging statistical properties, the set of models to choose from needs to be sufficiently flexible to allow for a good fit, whatever the actual fund strategy. Once the statistical model is chosen, an optimal trading strategy is derived. This is done in very much the same way as investment banks derive hedging strategies for their OTC option positions. In essence, this means our strategies date back to the famous Black-Scholes option pricing model, which is well-tested in practice and which forms the foundation of today's trillion dollar derivatives industry.

A Real-Life Example

Since the proof is always in the eating, let's see how our replication procedure does in reality. George Soros is generally considered one of our time's great investors so if we can replicate (the statistical properties of) his returns we may really be on to something. Let's therefore take Soros' Quantum Emerging Growth Fund as the fund to replicate. This fund is included in the well-known TASS database where it is classified as "global macro", with monthly return data starting in January 1992 and ending in June 2000. Assuming we trade S&P 500 and T-Bond futures to replicate Quantum's returns, Figure 1 shows one of the output screens of our replication system, which allows us to easily evaluate the accuracy of the replication.

The system looks at a whole array of goodness-of-fit measures but the easiest way to evaluate the quality of the replication is to simply look at the four figures in the bottom left corner of the screen. These four figures compare the average, standard deviation, skewness and kurtosis of the monthly fund return (in blue) with the same statistics calculated from the replicated returns.From these figures it is clear that (the statistical properties of) Quantum's returns can indeed be successfully replicated by trading S&P 500 and T-bond futures. All statistics are very similar and the mean of the replicated returns is in fact 20bps per month higher than that of the Quantum fund itself (but (part of) this difference might well be the result of sampling error, so we should be careful not give too much weight to it).

What about the correlation with other asset classes? Maybe the replicated returns have a much higher correlation with the stock market than Quantum, which would explain the higher mean. This is definitely not the case, however. Quantum has a correlation with the S&P 500 of 0.430, while the replicated returns have a correlation with the S&P 500 of only 0.278. The replicated returns therefore provide even more diversification benefit than the actual fund returns. This is not the only benefit that the replicated returns offer over the real thing though. Since they are generated in a completely different way, the replicated returns do not suffer from the typical drawbacks that hedge funds and other alternative investments tend to suffer from.

  1. Since we trade two of the most liquid futures markets in the world, we are not confronted with liquidity or capacity problems. Want to add or take out a couple of hundred million? It typically won't be a problem.
  2. We don't have any transparency problems either. All we do is trade futures and anyone who wants to see what the portfolio looks like can do so at any point in time.
  3. Finally, investors do not have to be afraid of style drift. Real-life managers can and do change their strategy over time, which changes the statistical properties of the fund return. Taking a fund's historical track record as our point of departure, we aim to extrapolate the past into the future, i.e. we aim to generate returns with exactly those properties that attracted investors to the fund in question in the first place.

Taking the replication results in combination with the above benefits, any rational investors will prefer the replicated returns over the real thing. Does it require superior skills? Yes, it does, but this time in applied econometrics, not trading and investment.

Tailor-Made Returns Are Now a Reality

It is important to realize that we do not have to wait for a fund with the right returns to come by before we can put our replication skills into practice. We can use the same methodology as before to design trading strategies that generate returns with certain pre-defined characteristics, without there being a fund generating similar returns. Since in that case we do not have a historical track record to go by, we can use stochastic simulation methods to generate a "synthetic track record" with all the desired properties. Given this self-made track record, we can then apply the exact same procedure as before.

Being able to design trading strategies that generate returns with pre-defined statistical properties opens up a whole new range of possibilities. Basically, it means that investors no longer have to go through the usual process of finding and combining individual assets and funds into portfolios in a costly and often unsuccessful attempt to construct an overall investment portfolio with the exact characteristics they require. Investors can simply tell us what it is they are after and the replication system will design the strategy to match. No more do-it-yourself portfolio building, no more beauty parades, no more ALM hassle. Buy directly what you need and relax.


By dynamically trading stocks and bonds in very much the same way as investment banks hedge their OTC option positions it is possible to generate returns that are statistically very similar to the returns generated by hedge funds without any of the usual drawbacks surrounding alternative investments, i.e. without liquidity, capacity, transparency or style drift problems and without paying over-the-top management fees. Hedge fund returns may be different, but they are certainly not unique. There is more than one road leading to Rome!

Harry M. Kat is Professor of Risk Management and Director Alternative Investment Research Centre at Cass Business School, City University, London