Discussing the article: "Online Portfolio Selection: A Provable Regret Bound, and the Cost That Eats It"
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Check out the new article: Online Portfolio Selection: A Provable Regret Bound, and the Cost That Eats It.
Most portfolio methods published for this platform start the same way. You collect returns, you build a covariance matrix, you feed it to an optimizer, and you get weights. The weakness is not the optimizer. It is that the matrix you built from the last 500 bars is not the matrix that governs the next 500, and the optimizer has no way of knowing that. Estimation error is the quiet tax on the whole family.
Online Portfolio Selection answers that differently. It estimates no statistical model: no covariance matrix, no return forecast, no distributional assumption. That is not the same as assuming nothing, and the mean reversion algorithms later in this article carry an explicit hypothesis about market structure along with a window, a threshold and a chosen basket. Each period you choose a portfolio, the market reveals what the prices did, your wealth multiplies by the dot product of the two, and you update. What replaces the model is a guarantee about regret: how far behind you finish against the best fixed portfolio somebody could have chosen if they had known the whole future in advance. Cover proved in 1991 that a specific algorithm keeps that gap growing slower than time itself, on any sequence of prices that meets the model's own technical conditions: price relatives strictly positive and bounded, so log wealth stays finite.
Author: Hammad Dilber