Shrinkage Estimators

Covariance Matrix Analysis for Optimal Portfolio Selection ArXiv ID: 2407.08748 “View on arXiv” Authors: Unknown Abstract In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. This inverse covariance matrix also prescribes the hedge trades in which a stock is hedged by all the other stocks in the portfolio. In practice with finite samples, however, multicollinearity gives rise to considerable estimation errors, making the hedge trades too unstable and unreliable for use. By adopting ideas from current methodologies in the existing literature, we propose 2 new estimators of the inverse covariance matrix, one which relies only on the l2 norm while the other utilizes both the l1 and l2 norms. These 2 new estimators are classified as shrinkage estimators in the literature. Comparing favorably with other methods (sample-based estimation, equal-weighting, estimation based on Principal Component Analysis), a portfolio formed on the proposed estimators achieves substantial out-of-sample risk reduction and improves the out-of-sample risk-adjusted returns of the portfolio, particularly in high-dimensional settings. Furthermore, the proposed estimators can still be computed even in instances where the sample covariance matrix is ill-conditioned or singular ...

Black-Litterman, Bayesian Shrinkage, and Factor Models in Portfolio Selection: You Can Have It All ArXiv ID: 2308.09264 “View on arXiv” Authors: Unknown Abstract Mean-variance analysis is widely used in portfolio management to identify the best portfolio that makes an optimal trade-off between expected return and volatility. Yet, this method has its limitations, notably its vulnerability to estimation errors and its reliance on historical data. While shrinkage estimators and factor models have been introduced to improve estimation accuracy through bias-variance trade-offs, and the Black-Litterman model has been developed to integrate investor opinions, a unified framework combining three approaches has been lacking. Our study debuts a Bayesian blueprint that fuses shrinkage estimation with view inclusion, conceptualizing both as Bayesian updates. This model is then applied within the context of the Fama-French approach factor models, thereby integrating the advantages of each methodology. Finally, through a comprehensive empirical study in the US equity market spanning a decade, we show that the model outperforms both the simple $1/N$ portfolio and the optimal portfolios based on sample estimators. ...