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 on minimum variance portfolios by allowing for time-varying factor loadings, which facilitates the capture of the dynamics of the covariance structure of asset returns (and 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. Simulation and empirical studies suggest that the performance of the proposed TV-MVP is superior, in terms of estimation accuracy and out-of-sample Sharpe ratio, compared with that of other popular contemporary methods.