When Cover Universal Portfolios Can Beat Fixed Rebalancing Benchmarks

Summary

The document asks how Cover’s universal portfolio algorithm compares with two simple allocations: a constant-relative-proportions portfolio that rebalances to equal weights, and a buy-and-hold allocation that initially divides wealth equally across assets. It seeks benchmark sequences where the universal portfolio outperforms both, ideally examples that are established in the literature or drawn from market data.

The author reports that in tested cases, including examples associated with early universal-portfolio papers, equal-weight rebalancing performed better. In a cited two-asset sequence with alternating price relatives for one asset and a constant second asset, the reported ordering is buy-and-hold as weakest, Cover’s method next, and equal-weight rebalancing strongest. These are the author’s observations, not a systematic benchmark study; the document provides no broader results or explanation of conditions under which Cover’s method wins. Its central lesson is that the choice of comparison strategy can materially affect assessments of universal-portfolio performance.

Key ideas

• Cover’s universal portfolio is compared with equal-weight rebalancing and equal-weight buy-and-hold allocations.
• The author seeks examples where Cover’s method outperforms both simple benchmarks.
• In the reported two-asset sequence, equal-weight rebalancing performs better than Cover’s method.
• The document offers observations from selected examples rather than a comprehensive performance analysis.

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# Are there known benchmark examples where Cover universal portfolio performs better than naive uniform CRP and Split-and-Forget?












I am investigating the performance of Cover universal portfolios cf. https://en.wikipedia.org/wiki/Universal_portfolio_algorithm (and references therein).

I would like to know if there are any benchmarks to test such algorithms. In particular are any 'classical' examples where the Cover U.P. is better than the simple naive CRP (Constant Relative Proportions with 1/n of wealth in each asset, rebalanced thereafter keeping the proportions) and also better than the "Split-and-Forget" allocation (that only trades at t=0 buying 1/n of initial wealth worth of each asset, with no rebalancing) ?

Maybe I'm wrong but in many cases I tested the "naive" CRP(1/n,...,1/n) has better results than Cover's U.P., for instance the examples in Cover's initial paper.

For the example of 2 assets (one constant and another with price relatives 2,0.5,2,0.5 from the Helmbold et al, 1998 link, Ordentlich and Cover, 1996 link) Split-and-Forget is worse than Cover which is worse than CRP(1/2,1/2).

I'm sure one can came up with artificial examples where Cover U.P. is better than CRP(1/n,1/,...,1/n) and Split-and-Forget but I wonder if some of them are known and "classical" (and possibly from market data)...

best, G.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.