On shrinkage covariance estimators: how inefficient is 1/N strategy of covariance estimation for portfolio selection in foreign exchange market?

Abstract

We investigate portfolio selection performance as in Markowitz by evaluating variance matrix estimation criteria in the currency market. This study challenges theoretically rigorous shrinkage covariance estimators using multiple evaluation metrics: systematic loss function, risk profile of minimum variance portfolios, Herfindahl index, financial efficiency, and concentration level. We assess out-of-sample performance across conventional models, factor models, linear shrinkage estimators, and equally weighted portfolios by applying mean-variance criteria and minimum variance framework to the 10 most traded currencies. Our findings reveal that mean-variance optimal portfolios are concentrated, counterintuitive, and highly sensitive to optimizer input choices in currency markets. We discovered that shrinkage estimators do not provide additional benefits to investors and fund managers regarding systematic loss function and minimum variance portfolio risk profiles. The research highlights critical limitations in traditional portfolio construction approaches, demonstrating that portfolios built using mean-variance criteria are prone to significant input data sensitivity and tend to create overly concentrated investments. Consequently, the study suggests that investors and fund managers should exercise caution when selecting covariance estimators and consider exploring more diversified strategies to optimize portfolio performance in foreign exchange markets.