On the ‘Steady State’ Properties of Financial Ratios

This paper uses the methods of continuous time stochastic calculus to investigate the ‘steady state’ properties of financial ratios. Basing our analysis on previous work in the area, we show that, if a financial ratio can be characterised as a diffusion process which possesses an asymptotic equilibrium, then the Fokker-Kolmogorov-Planck forward equation may be used to ‘retrieve’ its probability density. The approach is ‘flexible’ enough to incorporate a wide variety of density functions, many of which have not been investigated in the literature. We demonstrate the procedures which may be used to derive both the cross-sectional and time series tests implied by these distributions. The paper also includes a section dealing with the methods which may be used for parameter estimation, once the underlying distribution has been determined.