We theoretically show that ranking risk factors based on their ability to explain common variation in asset returns, e.g., principal component analysis (PCA), is ambiguous because PC volatilities can be arbitrarily scaled without changing the underlying fundamental asset pricing model.
As a consequence, market-based stochastic discount factors (SDFs) constructed from such PCs suffer from overfitting issues. In contrast, ranking risk factors based on their prices of risks instead (i.e., Sharpe ratios) is not subject to such spurious scaling. We therefore argue that empirical SDF estimation should center around inference about Sharpe ratios. To this end, we propose a novel statistical method for factor analysis using Bayesian learning that shrinks more aggressively risk factors with lower prices of risk giving rise to sparse SDFs. Since our SDFs do not suffer from overfitting, we show using a large cross-section of asset returns that SDFs based on Sharpe ratios significantly outperform SDFs based on PCA, increasing out-of-sample maximum Sharpe ratios up to a factor of two.
Erasmus University Rotterdam, E building, room ET-18
- Andrea Vedolin (Boston University)
LocatieBurgemeester Oudlaan 50,
3062 PA Rotterdam