Can Hedge-Fund Returns Be Replicated?: The Linear Case

By: Jasmina Hasanhodzic & Andrew Lo, MIT
Published: August 16, 2006
This is a much-cited paper that aims to explain the returns of hedge funds, in aggregate, using several risk factors.  The conclusion:

“This raises the possibility of creating passive replicating portfolios or clones using liquid exchange-traded instruments that provide similar risk exposures at lower cost and with greater transparency...the performance of linear clones is often inferior to their hedge-fund counterparts, they perform well enough to warrant serious consideration.”

To their credit, the authors point out to questionable practicality of using highly complex risk factors to replicate hedge funds:

“…some of the derivatives-based replication strategies may be more complex than the hedge-fund strategies they intend to replicate, defeating the very purpose of replication…”

As a result, they stick with easy-to-buy factors: “the stock market”, “the bond market”, “currencies”, “commodities”, “credit”, and “volatility.” 

The media has cited this study as evidence that: 

  1. Clone funds often have a higher return than hedge funds themselves, and,
  2. Clone funds have a comparable risk/reward ratio to the hedge funds themselves

A Higher Return?

The paper says:

“The results are striking for several categories, the average mean return of the clones is only slightly lower than that of their fund counterparts, and in some categories, the clones do better. For example, the average mean return of the Convertible Arbitrage fixed-weight clones is 7.40%, and the corresponding figure for the funds is 8.41%. For Long/Short Equity Hedge funds, the average mean return for fixed-weight clones and funds is 13.12% and 14.59%, respectively. And in the Multi-Strategy category, the average mean return for fixed-weight clones and funds is 10.32% and 10.79%, respectively.

“In five cases, the average mean return of the fixed-weight clones is higher than that of the funds: Dedicated Short Bias (6.70% vs. 5.98%), Equity Market Neutral (10.00% vs. 8.09%), Global Macro (15.54% vs. 11.38%), Managed Futures (27.97% vs. 13.64%), and Fund of Funds (9.29% vs. 8.25%).”

The “clones do better”?  This is bad news indeed for hedge fund managers. 

But is this really a surprise?  Imagine if your mutual fund had a 0.70 beta to the price of oil at the beginning of 2004.  Let’s further assume that the rest of your fund’s return was totally inexplicable (i.e. that it was all alpha) and it was approximately 3% – good, but not as good as black gold.  The “clone fund” would essentially be an oil & gas ETF.     

As you sit here today, you’d be kicking yourself for not just investing in the clone fund back in 2004 – even though your manager was producing solid alpha along the way. 

You would have no reason to cry foul at your manager for “underperforming” the clone since A) your manager produced positive alpha B) you neglected to time the bull market for energy.   

When the authors regress hedge fund returns against their six factors, they show that the proportion of returns explained by the factors is actually quite small, and the proportion of returns resulting from manager skill is actually quite large:            


Fixed Weights vs. Rolling Windows 

This leads us to the second inaccurate conclusion that can be drawn from this paper by the media: that the hedge fund clones have a comparable risk/reward ratio to the funds themselves.

At first blush the results are striking.  The Sharpe ratios of the synthetic clones are nearly as high as those of the hedge funds themselves.


But before you fire your hedge fund manager, take note: Hasanhodzic & Lo say there is a major caveat to this analysis.  They calculate the factor weights in the clone portfolio from all of the data in their sample (i.e. 1986-2005).  Then each month, they rebalance back to those weights so they remain “fixed”.  Sharpe used the same approach in his seminal work on manager style analysis in 1992.

A casual observation of this technique suggests that these fixed weights ought to be a good fit with the actual hedge fund data.  After all, the weightings benefit from “knowing” all of the data in the sample.  Hasanhodzic & Lo call the resulting bias, “look ahead bias”.  They are basically saying “of course our weightings lead to a low tracking error, the weightings know what the data will do in future periods”.

To mitigate this look ahead bias, the authors also use a “rolling window” technique where the factor weightings are derived only from recent history, not from the full sample.  They argue this is more realistic since it is the technique you would use going forward into the (unknown) future.  Not knowing what’s coming in the future, you would conduct your regression based only on recent history (e.g. the past 24 months).  Aside from being more realistic and practical, this approach also captures short-term changes in factor correlations.    

Of course, the “rolling window” method isn’t perfect either.  You need to rebalance monthly as your window shifts and the sample size is much smaller (n=24 for a 24 month rolling window) so your factor-weights will be less accurate.

Ultimately, the authors say that the choice between fixed-weight and rolling-window techniques depends on the extent to which the investor is able to recalculate and rebalance the portfolio.

But (and this is a big “but”), check out the results of their analysis when the rolling-window is used:



Ouch!  The Sharpe ratios of the clones are even further below those of the funds themselves.  Although they’re actually not that bad, a little of the sheen has come off the clones. 

The weaker results of the rolling-window approach can be blamed on one simple inalienable fact: ****-happens…Things change…Correlations from the past 24 months can easily morph going forward. 

So before we proclaim that hedge funds can be replicated synthetically, we need to understand the statistical techniques being used.  This paper illustrates that you can replicate aggregate hedge funds returns closely as long as you know the returns of both the factors and the hedge funds over the next 20 years.  If you do not happen to own a crystal ball, then you can take stab at it based on recent history.  But your results will not be quite as enticing for headline writers.

A Brave New World 

Even if hedge funds could be cloned in a laboratory, the authors are cautious about the current state of human kind’s technology (not to mention the profound ethical questions..;)

“Of course, a number of implementation issues remain to be resolved before hedge-fund clones become a reality, e.g., the estimation methods for computing clone portfolio weights, the implications of the implied leverage required by our renormalization process, the optimal rebalancing interval, the types of strategies to be cloned, and the best method for combining clones into a single portfolio.”

Read Full Paper


Post Script: Portable Alpha

Hasanhodzic & Lo also make an observation in this paper that we have seen more and more of recently: that the much-maligned “hedge fund beta” is still better than a kick in the face: 

“While portable alpha strategies have become fashionable lately among institutions, our research suggests that for certain classes of hedge-fund strategies, portable beta may be an even more important source of untapped expected returns and diversification.”

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