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...

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...

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...

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...