Constrained mean-variance optimization produced a Sharpe ratio of 1.22 on 33 large-cap US stocks over 2005–2025 — outperforming the S&P 500 Total Return Index (0.76) and the naïve equal-weight portfolio (1.18) on a risk-adjusted basis, while limiting the maximum drawdown to –21%.
Shaded regions: GFC (Jan 2008 – Dec 2009) and COVID-19 shock (Jan–Mar 2020). Hover for monthly values.
Both frontiers are estimated in-sample on the same 252 monthly observations. The unconstrained frontier extends above the constrained one because it allows short positions. Hover any point for details.
The optimizer concentrated heavily in low-beta, defensive sectors — consistent with the portfolio's low volatility (10.4% annualised).
The thesis tests whether a constrained mean-variance portfolio beats a naïve equal-weight benchmark and the S&P 500 on risk-adjusted return. The research question is in-sample: does the optimizer produce superior Sharpe ratios by exploiting the full covariance structure of returns?
Four portfolios are compared across a full period (2005–2025) and four sub-periods defined by NBER business cycle dates. The constrained formulation imposes non-negativity and a 30% single-stock cap, following Jagannathan & Ma (2003). The unconstrained variant allows unrestricted short positions.
Excel Solver (GRG Nonlinear method) is used for optimization. Covariance matrices are estimated on the full sample for each period. Unconstrained MVO is excluded from Pre-Crisis and Crisis sub-periods due to near-singular and rank-deficient matrices respectively.