Principal Component Analysis of Time Variations in the Mean-Variance Efficient Frontier

Abstract

We explain the variability of the mean-variance efficient frontier over time with a statistical three factor model. For an asset universe consisting of 22 stocks listed in Switzerland, the model explains more than 99% of the time variations in the efficient frontier.

The three factors can be interpreted as level, slope and curvature effects. This result is similar to statistical factors that have been identified in the analysis of yield curve dynamics.

We also show that the first factor which explains about 95% of the variability in the efficient frontier is highly correlated with average stock returns. This can be interpreted as evidence that the efficient frontier is mainly driven by time-variation in returns. Risk, on the other hand, measured by both asset volatilities and asset correlations, seems to be a second-order effect.

Keywords: mean-variance, efficient frontier, PCA, Principal Component Analysis, dynamic time-varying return, volatility, risk

JEL Classification: C10, G11