This paper compares, first, two competing hypotheses of market efficiency: the classical Efficient Market Hypothesis (EMH) of Samuelson (1965) and Fama (1970), and the Fractal Market Hypothesis (FMH) of Mandelbrot (1968) and Peters (1994). The market-neutral EMH risk depends on the empirically uncorroborated i.i.d. (= independence amp; stationarity) assumption of market innovations. The non-neutral FMH risk depends on the length of the investment time horizon: its degree of horizon dependence, or Long Memory (LM), is measured by the Hurst exponent. Next, it is demonstrated that an empirically better measurable definition of financial market risk is needed by all market participants. This new definition of market risk should allow for a measurement of the degree of market efficiency, which is both horizon and time dependent. The proposed definition of market risk is the time - frequency distribution P, where the shape of the P function is determined not only by second-order moments, differentiated by investment asset return categorization, but also by the length of the investment horizon, and by time t. In other words, the new definition of financial market risk embodied by the function P(s,w,t) should be able to account for the empirically observable strict non-stationarity to be scientifically acceptable. Such a categorized, horizon-dependent, time-varying, time - frequency distribution P(s,w,t) can be measured and identified by modern forms of time - frequency signal processing analysis, like wavelet multiresolution analysis. Two possible consistent diffusion models to generate such empirical time-frequency distributions P(s,w,t) are the non-arbitrage-neutral Fractional Brownian Motion and the, theoretically more acceptable) arbitrage-neutral Multifractional Model of Asset Returns
