Incorporating Forward-Looking Signals into Covariance Matrix Estimation for Portfolio Optimization

The widespread assumption of stationary in financial models is typically unjustified; however, there exist distinct periods during which market returns follow relatively consistent distributions. During these time periods, or regimes, it is reasonable to assume that future returns will behave similarly to those of the past. Effective trading strategies should adjust accordingly to regime changes, since an optimal portfolio during one time period may prove inefficient for a subsequent regime. A traditional approach to diversify holdings at a given time is to perform a Markowitz portfolio optimization, assigning weights to distribute investments under the assumption that asset returns exhibit stationarity. This method entails estimating the covariance matrix of asset returns with an aggregate of past data, thus ignoring the possibility of different regimes.

We adapt Markowitz portfolio optimization to take regime change into account via a method which dynamically estimates the covariance matrix of asset returns. The estimation method first adjusts the sample covariance matrix using the shrinkage transformation as described by Ledoit and Wolf in 2003. The method subsequently readjusts the transformed covariance matrix using a mixing parameter that is derived from forward-looking signals based on implied volatility. We find that our methods typically outperform the standard Markowitz portfolio optimization on stocks from both the Dow Jones Industrial Average and the S&P 500 during time periods since the collapse of the dot-com bubble in 2001.