Time-varying Minimum Variance Portfolio

This paper proposes a new time-varying minimum variance portfolio (TV-MVP) in a large investment universe of assets. Our method extends the existing literature of minimum variance portfolio by allowing for time-varying factor loadings, which is the facilitator to capture the dynamics of asset returns' covariance structure (hence the optimal investment strategy in a dynamic setting). We also use a shrinkage estimation method based on a quasi-likelihood function to regularize the residual covariances further. We establish the desired theoretical properties of proposed time-varying covariance and the optimal portfolio estimators under a more realistic heavy-tailed distribution. Specifically, we provide consistency of the optimal Sharpe ratio of the TV-MVP and the sharp risk consistency. Moreover, we offer a test of constant covariance structure and show the asymptotic distribution of the test statistic. Simulations and empirical analysis suggest that the proposed TV-MVP has superior performance in estimation accuracy and out-of-sample Sharpe ratio, among other popular contemporary methods