Cap Weighted Portfolios Are Sub-Optimal Portfolios

Jason Hsu

Volume 4, Number 3, Third Quarter 2006

In this paper, we show that under a fairly innocuous assumption on price inefficiency, market capitalization weighted portfolios are sub-optimal. If market prices are more volatile than is warranted by changes in firm fundamentals, then cap-weighted portfolios do not capture the full premium commensurate their risk. The sub-optimality arises because cap-weighting tends to overweight stocks whose prices are high relative to their fundamentals and underweight stocks whose prices are low relative to their fundamentals. The size of the cap-weighted portfolio underperformance is increasing in the magnitude of price inefficiency and is roughly equal to the variance of the noise in prices. However, portfolios constructed from weights, which do not depend on prices, do not exhibit the same underperformance observed for cap-weighted portfolios. We illustrate this cap-weighting underperformance empirically by comparing returns from cap-weighted portfolio versus non-cap-weighted portfolios with similar characteristics. We also derive testable implications from our model assumption and find empirical support.