仅用三个矩阵就能战胜市场？投资组合优化的可观测矩阵动态
Are Three Matrices All You Need To Beat the Market? Observable Matrix Dynamics for Portfolio Optimization
AI总结：
该研究提出仅用三个基于标普500数据的矩阵构建动态投资组合，其策略在两个样本外测试集战胜市场及经典投资组合，残差距离多元化与凸性叠加层可进一步提升表现。
AI中文摘要：
我们提出了一种仅使用每日价格、交易量和市值的动态投资组合管理简单框架。其状态由价格历史构建的三个固定大小矩阵组成：收益率相关性的距离矩阵，以及两个马尔可夫链的转移矩阵，这两个马尔可夫链按月对标普500成分股的滞后收益率和滞后波动率进行排名。这三个矩阵仅基于价格历史，与马科维茨均值-方差优化所依赖的信息相同，但它们取代了其预期收益率向量和协方差矩阵。我们的方法无需矩阵求逆，适用于对异常值具有鲁棒性的横截面排名，且是动态的而非单期的。实证研究表明，波动率排名可提前一步预测，而收益率排名几乎不可预测。基于这些预测构建的投资组合，即市场中性动量多空策略结合机会型多头部分，在两个不重叠的样本外测试集（2022年1月至2024年12月、2025年1月至2026年7月）中战胜了市场，在扣除5个基点的交易成本并按每日盯市后，夏普比率分别为1.06和1.32，而市场的夏普比率分别为0.78和1.14。它还优于经典的最小方差和最大多元化投资组合。通过残差距离对多头部分进行多元化，进一步提升了两个时期的表现，将夏普比率分别提升至1.08和1.44，年化收益率分别从18%提升至20%、从44%提升至56%。一个凸性信息领导者叠加层单独为市场中性部分提供保障，以小幅牺牲收益率为代价买入凸性并降低回撤，且夏普比率保持不变。
英文摘要：
We present a simple framework for dynamic portfolio management that uses nothing but daily prices, trading volumes, and market capitalizations. Its state is three fixed-size matrices built from the price history: the distance matrix of the return correlations and the transition matrices of two Markov chains that rank the S\&P 500 names monthly by trailing return and by trailing volatility. These three matrices rest on the price history alone, the same information Markowitz mean-variance optimization draws on, but they replace its expected-return vector and covariance matrix. Our method requires no matrix inversion, works on outlier-robust cross-sectional ranks, and is dynamic rather than single-period. Empirically the volatility rank is forecastable one step ahead while the return rank stays close to unforecastable. A portfolio built on the forecasts, a market-neutral momentum long-short blended with an opportunistic long-only sleeve, beats the market on two non-overlapping out-of-sample test sets, January 2022 to December 2024 and January 2025 to July 2026, at Sharpes of $1.06$ and $1.32$ against the market's $0.78$ and $1.14$, respectively, net of a five-basis-point trading cost and marked to market daily. It also outperforms the classical minimum-variance and maximum-diversification portfolios. Diversifying the long sleeve by residual distance adds a further edge on both periods, lifting the Sharpe to $1.08$ and $1.44$ and the annualized return from $18\%$ to $20\%$ and from $44\%$ to $56\%$, respectively. A convex information-leader overlay separately insures the market-neutral sleeve, buying convexity and a shallower drawdown at a small cost in return, the Sharpe unchanged.
