The Law of Large Numbers: An Analysis of the Renaissance Fund

A case study in hedge fund replication and risk management

September 04, 2007

The Law of Large Numbers, one of the last great gifts of the Renaissance, was first described by Jacob Bernoulli as so simple that “even the stupidest man instinctively knows it is true.” It then took him over twenty years to derive a rigorous proof of his famous theorem. Some three hundred years later, the same law under a new name “diversification” has found its proof in financial markets. Our analysis of the Renaissance Institutional Equities Fund shows that thousands of trades, based on fundamental signals generated by computer models, can average to a simple combination of factors that mimic the performance of this large and well-known hedge fund.


In the beginning of August 2007, quantitatively managed funds had been making headlines for higherthan-anticipated losses in increasingly volatile markets. One of these high-profile funds receiving much attention is also one of the largest: the $26B Renaissance Institutional Equities Fund (RIEF), managed by Renaissance Technologies of East Setauket, New York. Renaissance Technologies, started in early 1980’s by former mathematics professor James Simons and employing a team that includes over seventy PhDs, is also home to the famous Medallion fund, which has an exemplary track record dating back to the 1980’s. The Medallion fund’s 5% management fee and 44% performance fee are head and shoulders above the industry’s standard 2/20. Unlike Medallion, RIEF has lower fees, higher capacity of $100B and targets institutional investors.

On August 10, Reuters reported that Simons had sent a letter to the funds’ investors stating its July loss to be between -4.0% and -4.5%, and August-to-date losses “in the order of 7%.” The refrain from most articles appears to be that either the models broke or, perhaps more likely, that different models in many other quant shops appear to have been advocating similar positions. The need to liquidate these positions while waiting for their models to recover from the markets’ paradigm shift could have caused increased systematic exposure at the worst possible time. However, this may only be a part of the story.

Using Dynamic Style Analysis, (referred to as “DSA” from this point forward), MPI’s proprietary returns-based factor model, and the fund’s historical performance data (NAV returns), we performed our own quantitative due diligence analysis on the fund in an attempt to see if some of the losses could (or should) have been anticipated.

Please note, at no time in this analysis are we claiming to know or insinuate what the actual strategy, positions or holdings of this fund were; nor are we commenting on the quality or merits of Renaissance’s strategy or that of any other manager. Instead, we are seeking to demonstrate how advanced returns-based analysis can be used to better understand fund behavior, anticipate performance, identify risks and, possibly, replicate fund performance in certain cases.

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