A Hedge Extension of the CAPM Model: An Empirical Investigation

Abstract

Extending the CAPM with practical hedging strategies presents an innovative approach to managing portfolios. This study extends CAPM through incorporation of a Hedge Extension that utilizes cointegration-based pairs trading within a core satellite portfolio framework. While CAPM remains foundational in asset pricing and portfolio optimization, its reliance on market efficiency assumptions and the exclusion of idiosyncratic risk undermines its efficacy in volatile markets. This paper bridges these gaps by constructing a core satellite portfolio where the JALSH functions as the passive core, while a dynamically managed satellite component employs cointegration-based pairs trading that provides an uncorrelated source of returns due to relative mispricing. Using daily closing prices of Financial and Basic Material sector stocks listed on the JSE between 2nd January 2015 and 31st December 2024, this study tests the Hedge Extension’s efficacy. The pairs were selected using the Engle-Granger two-step approach, where positions were traded when normalized cointegration spreads exceeded ±2 standard deviations, and unwound upon mean reversion. The hedge portfolio was constrained to a gross exposure limit of 200% and 2.5% net exposure cap per pair on entry. In terms of risk-adjusted returns, the hedge portfolio notably outperformed the market portfolio. The performance yielded a Jensen’s alpha of 4.28%, a Sharpe ratio of 0.1582 (in contrast to -0.1754), along with a Modigliani Squared ratio of 11.39% (compared to the markets return of 5.49%). Cumulative returns for the hedge portfolio reached 111.15%, substantially exceeding the 68.50% achieved by the market. The hedge portfolio’s systematic risk decreased significantly due to the hedging effect of cointegrated pairs, while idiosyncratic risk increased marginally due to higher gross exposure and residual pair volatility. These findings validate the hedge extension of CAPM’s efficacy and reveal how cointegration-based pairs trading is used as a mechanism to enhance CAPM’s practical utility. Thus, the strategy offers a comprehensive framework for portfolio construction, equipping portfolio managers with practical insights into how this hedging strategy can serve as an effective alpha generator within a diversified portfolio. This study advances portfolio management theory by demonstrating that integrating a dynamic hedging strategy with equilibrium models can reconcile theoretical frameworks with real world market complexities