@vince.quant: Can a portfolio beat the market without predicting which stocks will win? In 2005 Fernholz, Karatzas and Kardaras proved that it can. If the market stays diverse, meaning no single stock ever dominates, you can build a portfolio from nothing but the current market weights and outperform the index over a long enough horizon, with probability one. The recipe is simple: take each stock's market weight, raise it to a power p between zero and one, and renormalize. That shaves a little off the giants and spreads it across the rest, and it gives the diversity-weighted portfolio. Fernholz's master equation splits your performance over the market into a bounded diversity term plus a cumulative excess-growth term that never decreases, so once that term has had enough time to build up, you are provably ahead. That is what the paper calls relative arbitrage: you outperform the market portfolio, which is not the same as a riskless profit. The engine underneath is the excess growth rate, the return you harvest by holding a diverse basket and letting it rebalance. Worth keeping in mind: this is a theorem and not investment advice, it holds only under its assumptions of market diversity, non-degenerate volatility and continuous rebalancing, and it ignores frictions like transaction costs, taxes and implementation limits, though recent work shows the edge survives realistic costs, just smaller. Paper: "Diversity and Relative Arbitrage in Equity Markets" (2005), Finance and Stochastics. #finance #quant #trading #algotrading #stocks

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Monday 22 June 2026 22:59:49 GMT