VONG vs. SCHG: A Parable of Growth Investor Choices

These twin fund-creatures, born of Vanguard and Schwab, were not mere collections of tickers but living entities, their souls entangled in the fate of U.S. large-cap stocks. One was a maestro of 391 instruments, its fingers stained with the ink of diversification; the other, a sculptor of 198 select stones, each polished to a mirror sheen. Their battle was not for supremacy but for the hearts of investors who, like villagers in a drought, sought rain in the form of returns.




![The optimal transport plan reveals a concentration of probability mass along a diagonal-consistent with the martingale constraint [latex]\mathbb{E}[X\_{1}|X\_{0}]=X\_{0}[/latex]-and highlights a high-probability transition path clustered near the point [latex](5500, 6500)[/latex].](https://arxiv.org/html/2601.05290v1/x5.png)


