Measuring the Degree of Efficiency of Financial Market

This essay discusses first two competing hypotheses of market efficiency: the classical Efficient Market Hypothesis (EMH) of Samuelson and Fama, and the Fractal Market Hypothesis (FMH) of Mandelbrot and Peters and their weaknesses. The EMH depends on the empirically uncorroborated i.i.d. (= independence & stationarity) assumption of market innovations. The time - invariant FMH risk depends on the lengths of time horizons, as measured by the Hurst exponent. By way of empirical examples in the cash, bond and options an futures markets, it is demonstrated that scientifically a much broader concept of financial market risk is needed. This new risk concept should allow for the measurement of the degree of market efficiency, which is time and horizon dependent. The proposed definition of financial market risk is a time - frequency distribution function P, where the shape of the function is determined not only by the second-order moments σ, differentiated by the investment asset return categorizations ω, but also of the length investment horizons, or maturities of the investment securities τ, and of the time period t. In other words, the new concept of financial risk P(ω,τ,t) should be able to account for both LT and ST nonlinear time dependence and for strict non- stationarity to be empirically compatible and thus scientifically acceptable. Such a time - frequency distribution P(ω,τ,t) can be measured and identified by modern forms of time - frequency signal processing analysis, like windowed Fourier and wavelet multiresolution analysis.