Alpha Estimation and Risk-Adjusted Performance: Performance Evaluation of U.S based Active and Passive Investment Vehicles using Multi-factor Asset Pricing Models

Abstract

This study contributes to the active versus passive investment debate by empirically examining whether active investment vehicles generate superior risk-adjusted performance relative to passive counterparts after controlling for systematic risk exposures. To estimate abnormal performance (alpha), we employ the Fama–French three-factor model, the Carhart four-factor model, and the Fama–French five-factor model. These multifactor asset pricing specifications allow for a comprehensive decomposition of returns into market, size, value, momentum, profitability, and investment risk premia. In addition to alpha estimation, total risk–adjusted performance is evaluated using the Sharpe ratio, thereby incorporating both systematic and idiosyncratic volatility. The sample consists of 15 U.S.-based mutual funds, 7 exchange-traded funds (ETFs), and one fund of funds, enabling an assessment of diversification effects within actively managed portfolios. The dependent variable is the monthly excess return of each investment vehicle, while the independent variables include the market risk premium (MKT), size factor (SMB: small minus big), value factor (HML: high minus low), momentum factor (WML: winners minus losers), operating profitability factor (RMW: robust minus weak), and investment factor (CMA: conservative minus aggressive). The empirical findings yield three principal results. First, all sampled mutual funds exhibit statistically significant negative alphas across model specifications, indicating persistent underperformance relative to benchmark-adjusted expectations. Second, passive investment vehicles (ETFs) consistently outperform active mutual funds across the return distribution. Third, the fund of funds demonstrates relatively stronger performance than mutual funds within the lower alpha quartile, suggesting partial diversification benefits. The evidence indicates that passive investment strategies deliver superior long-term risk-adjusted performance compared to active strategies. These findings reinforce the argument that passive investment vehicles represent a cost-efficient and performance-consistent alternative for investors in the U.S. equity market.