MarketRank: ranking stocks by the stationary probabilities of a Markov chain over estimated money flows, with a topological landscape view

B. Kaan Karamete

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arXiv · 2610.08946

MarketRank: ranking stocks by the stationary probabilities of a Markov chain over estimated money flows, with a topological landscape view

B. Kaan Karamete

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Abstract

Every trading day, money leaves some stocks and moves into others. MarketRank asks where that money concentrates and how the concentration shifts over time. It treats the market as a Markov chain whose states are stocks. The chance of moving from one stock to another is the share of the first stock's outgoing dollars that goes to the second, and a stock's MarketRank score is its long run (stationary) probability in that chain, computed by damped power iteration on a sparse transition matrix. PageRank ranks web pages with the same idea, using links instead of dollars. Who sold what to buy what is not public, so the flows are estimated from daily prices and volumes with a correlation tilted gravity model, in a deterministic parallel C++ engine. On a universe of 10K US stocks and ETFs, the ranking is led by the large semiconductor and technology names, and estimated flows stay within a sector more often than chance. The level of the score, however, does not predict next day returns: it shows where money sits, not where prices go next. A 3D landscape view, Fluxscape, turns the ranking into terrain: Louvain communities of the recent flow graph, reclustered on every bar, become territories, ordered by recursive spectral bisection along a generalized Hilbert curve, interpolated by inverse distance weighting, smoothed by a centroidal Voronoi style relaxation with portfolio holdings pinned to their exact values, and rendered as a Gouraud shaded mesh. The surface is for reading trends; the exact ranked table remains the reference. The practical question is whether MarketRank can improve real portfolio moves, and we answer it with tests fixed in this study.

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B. Kaan Karamete. 2026-10-06. MarketRank: ranking stocks by the stationary probabilities of a Markov chain over estimated money flows, with a topological landscape view. https://arxiv.org/abs/2610.08946

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