Mean-Reversion Risk, Autocorrelation APT and the Autocovariance CAPM

Abstract

I derive a single period, inter-temporal, static APT that values asset time-interval risks. Uncorrelated mean-reversion risk factors form an exact factor structure APT. An equilibrium multi-beta CAPM with long-term mean-reversion betas is developed. I define mean-reversion risk by using digital signal processing to decompose risk into orthogonal time horizon risks. Risks are measured relative to factor portfolios, or the market. Mean-reversion betas give a linear relationship between expected return and multiple horizon risk premiums. Calendar and non-calendar length risks have unique prices. Auto-correlation, arbitrage-pricing theory (A-APT), and the auto-covariance, capital asset pricing model (A-CAPM) determine the prices of long-horizon risks.

Keywords: APT, CAPM, Mean-Reversion Risk, Long-Horizon Asset Pricing, Digital Signal Processing, Hedging and Speculative Demand, Digital Portfolio Theory, Capital Market Efficiency, Frequency Domain

JEL Classification: G10, G11, G12, G14, C61