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 $\theta_{tm}$ ?

  • 2
    $\begingroup$ 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 $\endgroup$ – Henry Jul 22 '19 at 6:36

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