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A quantitative comparison of modern and post-modern portfolio theory optimal portfolios
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School of Business |
Master's thesis
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en
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41
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Abstract
Standard Modern Portfolio Theory (MPT) relies on the assumption that risk is symmetric, penalizing upside volatility equally to downside losses. Motivated by the behavioral reality of loss aversion (Kahneman & Tversky, 1979), this thesis challenges that paradigm by strictly minimizing Lower Partial Moments. While Post-Modern Portfolio Theory (PMPT) is theoretically superior, its adoption has been hindered by computational complexity and estimation bias.
This study leverages convex optimization to solve the Global Minimum Semivariance problem as a Second-Order Cone Program (SOCP), ensuring convergence to true global minima without heuristic approximation. Using a Point-in-Time rolling window of US equities (2008–2024), we apply the Shumway (1997) correction to mitigate delisting bias across two distinct universes: stable large-caps (“Giants”) and high-tail-risk assets (“Skewed”).
The findings reveal a stark trade-off between capital protection and diversification. PMPT successfully hedged market crashes, reducing Maximum Drawdown in the large-cap universe by approximately 16 percentage points (-23.72% vs. -39.62%) compared to MPT. In the universe of negatively skewed assets, the semi-variance framework generated superior risk-adjusted returns (Sortino Ratio 1.30 vs. 0.96) and higher absolute wealth accumulation (11.48% CAGR).
Contrary to theoretical expectations, the unconstrained semi-variance optimizer rarely converged to extreme “corner solutions.” While PMPT portfolios were significantly more concentrated than MPT (median max single-asset weight ≈23% vs. 5%), they generally maintained a diversified basket. Extreme allocations (> 70%) were observed only as rare outliers in the high-skewness universe. The study concludes that while PMPT effectively isolates the “Low Downside Anomaly,” the elevated concentration and turnover (up to 85.90%) necessitate practical constraints to manage idiosyncratic risk.