Currency Factor Combination and Cross-Sectional Pricing: Shrinkage Convergence, Alternative Methods, and the Identification of Volatility Risk

Abstract

This paper examines ex-ante combination of currency factor strategies and the cross-sectional pricing of currency risk. We implement seven baseline combination methods from the literature and document a convergence problem: under Ledoit-Wolf shrinkage with average intensity δ = 0.89, five of seven methods collapse to two distinct portfolios. We propose three alternatives that break this convergence-a shrinkage-to-equal-weight blend, a Bayesian predictive-likelihood combination, and a volatility-regime-switching method-and evaluate them on certainty equivalent returns, transaction costs, and bootstrap inference. All combined strategies deliver Sharpe ratios between 1.00 and 1.05 at a 10% volatility target. In the cross-section, Fama-MacBeth regressions on 30 currency-sorted portfolios show that the carry factor commands a risk premium of 0.52% per month (t = 4.76, Shanken-corrected), explaining 76% of return variation. Global realised volatility innovations are statistically insignificant under all corrections (t = 0.59, KRS), reflecting an identification failure at monthly frequency rather than the absence of volatility risk compensation. Progressive improvements using AR(1) innovations and VIX suggest recovery of the negative volatility price at higher measurement frequencies.

Keywords: Currency factors, carry trade, factor combination, shrinkage estimation, Fama-MacBeth, volatility risk, cross-sectional asset pricing JEL Classification: F31, G11, G12, G15