Regularizing Mean–Variance Portfolios with an ℓ₁ Total-Exposure Constraint: Evidence From S&P 100 (OEX) Monthly Data

This study shows that a total exposure cap can improve the implementability of a mean–variance portfolio. The dataset contains monthly S&P 100 (OEX) returns and a matching nominal risk-free rate from the same workbook. The analysis compares four strategies: an unconstrained portfolio, portfolios with exposure caps of 2.0 and 1.8, and an equal-weighted portfolio. All strategies use the same inputs and the same rebalancing frequency, only the exposure budget changes. The results show that both constrained strategies outperform the unconstrained one in Sharpe ratio and drawdown control. The 1.8 cap performs best in most sub-periods in the later years. For the constrained portfolios, the gross exposure hits the cap each month. For the unconstrained portfolio, the average gross exposure is about 1.4. A normalized HHI based on absolute weights indicates lower concentration under caps, while the relative ranking across strategies remains unchanged. These findings suggest that exposure caps enhance portfolio stability and improve risk-adjusted returns. In practice, a 1.8 cap is a reasonable starting point, with later adjustments guided by edge-hitting behavior and concentration changes.