The Law of Large Numbers: An Analysis of the Renaissance Fund
MPI Quantitative Research Series
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 true1.” 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.
During the recession of 1989-92, the hypothetical portfolio underperformed the index for four consecutive years–about 65% in total. During the technology
“bubble” of 1999-2000, it underperformed by about 25%, trailing the index in each consecutive year.
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