Time horizon dimensions are added to asset pricing theory. Single period, static, arbitrage pricing theory (APT) describes single period risk with long horizon contributions in the frequency domain. Mean-reversion risks correspond to horizon variances. Mean-reversion risk is measured using the...

The nature of risk and long-term returns is not fully understood. There is a need for a measure of long-term risk at multiple horizons. Digital signal processing and an additive noise model are used to test the white noise hypothesis for total and idiosyncratic risk of individual firms at...

I examine capabilities of Digital Portfolio Theory (DPT) and extend it to control portfolio size. DPT is a static, single period mean-variance-autocovariance portfolio optimization paradigm that allows returns to be mean-reverting. The optimal dynamic single period solutions depend on the...

The paper compares three portfolio optimization models. Modern portfolio theory (MPT) is a short-horizon volatility model. The relevant time horizon is the sampling interval. MPT is myopic and implies that investors are not concerned with long-term variance or mean-reversion. Intertemporal...

A model of risk with multiple independent unconditional calendar and non-calendar variance components is used to explain time-varying returns. Digital signals represent finite stock return series. The random walk hypothesis is tested using digital signal processing methods. A stochastic additive...