31 May 2007
For nearly a year now, the hedge fund industry has been poked and prodded by ”hedge fund replicators”. Wave after wave of academic research seemed to show that hedge funds weren’t that special after all. When it looked like factor modeling might face some limitations, a new technique known as “distributional replication” was heralded by some as the proverbial nail in the coffin of the hedge fund industry.
The truth about hedge fund replication likely lies somewhere between the mythical “pure alpha” hedge fund manager and the black box hedge fund “clone”. But, sometimes the hedge fund industry seemed to be caught off-balance by the replicators - unable to produce the “counter-research” that cogently makes their side of the argument (perhaps because the industry was doing just fine and had no economic reason to respond).
Now one company has released a comprehensive analysis of both replication techniques (factor modeling and distributional replication). Toronto-based fund of funds manager Northwater Capital Management has just completed a rather extensive report that may give the hedge fund industry what it’s looking for - quantitative research giving another side of the replication story. Northwater’s thesis is that both underlying approaches to hedge fund replication are “limited in their ability to access the performance of hedge funds”.
Northwater has traditionally held its cards close to its chest, but has broken with tradition and allowed us to exclusively provide the report at AllAboutAlpha.com (here).
The firm argues that linear factor replication has reasonable success when applied to broad-based hedge fund indices that already possess significant linear dependence on market factors. However, they say linear replication is not successful where market factors are unable to explain a large proportion of the return series. This is not dissimilar to Professor Harry Kat’s recently published view that factor replication works well for the entire HFRI, but not so well for its individual sub-indices.
But Northwater departs from Kat’s view of the world when it comes to the critical issue of distributional replication models. As regular readers know, Professor Kat of the Cass Business School at City University (London) has developed a method of replicating - not the monthly returns - but the statistical characteristics of return distributions (e.g. standard deviation, skew, correlation to any selected portfolio). It turns out, argues Kat, that the return generated by synthetically-created distributions with similar characteristics to real hedge funds is remarkably close to the return actually generated by those real hedge funds. In fact, the returns from the “clone” portfolio actually beat the returns of the original funds up to 80% of the time.
Northwater tests Kat’s theory (the “Kat-Palaro” or “KP” approach) in this paper and draws several interesting conclusions…
Choice of “Reserve Asset” is Critical
As students of replication know, Kat’s replicated portfolios are created by applying complex dynamic trading strategies to a small number of very straightforward futures contracts - called the “reserve asset” in aggregate (S&P, commodities, fixed income etc.). Kat describes the reserve asset this way:
“…The next step is the selection of the “reserve asset” (which is) the main source of uncertainty in the fund. Although allocations to the reserve asset will change over time, the strategy will never sell the reserve asset short. As such, it can be interpreted as the core portfolio of the fund.”
Northwater wondered if the resulting mean returns from these new distributions are actually just a result of the specific futures contracts selected for the “reserve asset”. After creating a model that it says closely approximates Kat’s, Northwater concludes that the choice of “reserve asset” is actually critical to the very success of the enterprise:
“The risk-adjusted returns achieved from distributional replication are dependent upon the selection of market factors utilized within the replication process. Alteration of the market factors results in large differences in risk-adjusted performance.”
The firm runs their distributional replication model on 11 hedge fund sub-indices. As they illustrate using the following chart, the model produces a fund of the same volatility and correlation (to a predefined “target portfolio”) as the 11 sub-indices (not shown) and also generates very similar mean return as Kat’s approach (shown). So far, so good.
But when Northwater removed the Russell 2000 and the GSCI from the “reserve asset” and added in the poorly performing S&P Information Technology and Telecommunications Services Index, look what happened to the mean return (in blue):
(Note they leave the original KP results on the chart for comparison purposes.)
As you can see, the reader is left to conclude that either a) Northwater’s distributional replication approach is materially different that Kat’s or b) that the hedge fund-beating returns generated by the KP approach are primarily the result of astute asset class selection, not the approach itself.
Replicas’ Correlations Matched vis a vis Investor’s Portfolio
Professor Kat’s methodology creates synthetic funds that not only match the target fund’s volatility and skew, but also its correlation to a pre-defined portfolio owned by the investor.
Northwater’s research shows that the correlation similarities end there, however. While the replicated funds may indeed possess the same correlation to one pre-defined portfolio, they rarely also posses the same correlation to other assets. Thus the synthetic fund’s correlation to gold, for example, might be very different from the target fund’s own correlation to gold. Says the report:
“The return series of the replica may possess a large correlation to market factors included within the replication process but excluded from the correlation specifications, and a factor analysis would indicate a large R-squared.”
The paper includes the following illustrative example related to a dedicated short-selling index. Note that the replica’s correlation to a “50/50 portfolio” is very similar to that of the index, yet its correlation to other assets is quite different. This makes intuitive sense when you consider that the actual monthly returns of the distributional replica are not meant to actually match those of the hedge fund index.
Bottom-Line: Distributional Replicas Fundamentally Same as Plain Vanilla Mean-Variance
Finally, Northwater argues that the addition of dynamically-traded reserve assets such as S&P futures, commodities, etc. only serves to increase an investor’s exposure to these assets. Thus, the resulting portfolio is very analogous to an actively managed and optimized portfolio.
In the report’s words:
“Construction of optimal portfolios using replicas leads to the same solution that can be achieved using traditional mean-variance portfolio design, indicating a redundancy associated with correlation targeting.”
The Value of Distributional Replication
But while Northwater says distributional replication may have led us back to square one, they say it does serve a useful purpose. It provides a framework that can be used to compare the returns from different distributions. An example of this can be found on the Fund Creator website where Kat provides the mean return from several distributions including a normal distribution, a positively skewed distribution, and a distribution with a monthly return floor of -5%. It turns out the effect of the -5% floor and a skew of 2.0 have the same effect on mean return - shaving off approximately 3% per annum each.
Ergo, says Northwater, one can represent the returns from a synthetically-generated fund in terms of the volatility of the replica vs. the “reserve asset” (a la CAPM), the cost of the positive skewness (”P dist”), the cost to give the distribution a certain correlation (”P corr”) and transaction costs (”C trans“).
Northwater explains it this way:
“Separation of the two components of distributional replication and various numerical experiments has led us to develop a comparative framework for benchmarking the performance of distributional replication. The results of the following sections demonstrate that the performance of replication is dependent upon the selection of the market factors utilized within the reserve portfolio and therefore dependent on the excess return of the reserve portfolio. Distributional adjustments alter the distributional characteristics of an underlying portfolio of market factors. A daily trading process equivalent to delta hedging is required to achieve the desired distributional characteristics. An implicit net option premium and payoff, P-dist will result from distributional adjustments. Targeting a negative correlation to an investor’s portfolio will have a cost associated with paying away risk premium, referred to as a correlation premium, P-corr.”
According to Northwater, distributional replication can be a useful analytical framework and they continue to pursue it as an analytical instrument. However, they say, claims of out-performance seem to be predicted on picking the right inputs.
So it appears the old adage “garbage in garbage out” might apply here.
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