Index-mixed optimal portfolio selection under borrowing restrictions

Given a set of risky assets, we consider mean-variance (MV) optimal portfolio selection under exogenous borrowing restrictions to achieve increased target returns. We show that MV-efficiency can be improved significantly by mixing the risky assets with a market fund (such as a benchmark index asset) rather than infusing with additional capital. We derive theoretical conditions related to asset and market parameters that lead to enhancing portfolio efficiency without external borrowing. This contrasts with the usual practice under unconstrained borrowing, where it is optimal to proportionately-leverage the tangency portfolio on the securities market line to achieve higher targets at lower volatility risk. We conduct an empirical study with select-sector ETF assets underlying the S&P 500 index to evaluate the out-of-sample performance of our optimal mixed-fund approach. The resulting risk-adjusted returns are shown to generate positive excess returns, relative to the usual MV model, without incurring additional margin risk or trading intensity. The proposed approach has the potential to narrow the gap in performance enjoyed by borrowing-unconstrained investors who employ the concept of low-beta anomaly.