# Fama's Definition of Market Efficiency

I'm reading Fama's Nobel lecture "Two Pillars in Asset Pricing" and I'm a little confused by his mathematical definition of market efficiency. Here it is below:

Suppose time is discrete, and $$P_{t+1}$$ is the vector of payoffs at time $$t + 1$$ (prices plus dividends and interest payments) on the assets available at $$t$$. Suppose $$f(P_{t+1} |\theta_{tm})$$ is the joint distribution of asset payoffs at $$t + 1$$ implied by the time $$t$$ information set $$\theta_{tm}$$ used in the market to set $$P_t$$, the vector of equilibrium prices for assets at time $$t.$$

Finally, suppose $$f(P_{t+1} |\theta_t)$$ is the distribution of payoffs implied by all information available at $$t$$, $$\theta_t$$; or, more pertinently, $$f(P_{t+1}|\theta_t)$$ is the distribution from which prices at $$t + 1$$ will be drawn.

The market efficiency hypothesis that prices at $$t$$ reflect all available information is $$f(P_{t+1} |\theta_{tm}) = f(P_{t+1} |\theta_t).$$

I think that my confusion stems from the fact that I don't understand the difference between the two information sets $$\theta_{tm}$$ and $$\theta_{t}$$. Is $$\theta_t$$ just a "less updated" information set relative to $$\theta_{tm}$$ ?

• The suggestion seems to be that the information used by the market $\theta_{tm}$ to set prices at time $t$ is a subset of all information $\theta_t$ available at time $t$, and that market efficiency is the suggestion that nothing in $\theta_t$ beyond $\theta_{tm}$ helps understanding the distribution of future payoffs – Henry Jul 22 '19 at 6:36