Improving Index Funds via Idiosyncratic Returns

The rising concentration of major market indices has increasingly undermined the diversification benefits and increased the market risk of index investing. To address this issue, we propose a portfolio strategy designed to minimize variance relative to a given index fund. We decompose each stock’s return into an index return and an idiosyncratic return, defined as the excess return over the index. By exploiting the resulting covariance structure—either between the index return and idiosyncratic returns or among the idiosyncratic returns themselves—we construct portfolios that enhance index efficiency by reducing portfolio variance. Using U.S. monthly stock data, we show that incorporating idiosyncratic returns into portfolio construction through this covariance structure consistently reduces out-of-sample variance relative to multiple basis index portfolios, including the S&P 500 index, the Equal-weighted S&P 500 index, and the CRSP value-weighted market portfolio. Crucially, portfolio returns remain comparable to those of the basis portfolios, leading to overall improvements in Sharpe ratios. These findings demonstrate that effective variance reduction can be achieved without sacrificing return performance.