In his paper, Eugene Fama gives the definition of a "fair game" as given below. I disagree. AFAIK, a martingale has the following property: $E[X_{t+\tau} | X_t] = X_t$. What am I missing?
Footnote 9 says:
And again, in a previous statement:
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1$\begingroup$ What does Footnote 9 say? $\endgroup$– nbbo2Jul 15, 2020 at 17:47
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$\begingroup$ @noob2 Nothing that would justify the zero in my opinion. I've updated. $\endgroup$– s5sJul 15, 2020 at 18:00
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$\begingroup$ What does it mean for martingales to be "incorrect"? $\endgroup$– AcccumulationJul 16, 2020 at 5:46
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The way I understand it is:
In equation 2 $x_{j, t + 1}$ is defined as the change in of $p_j$ over the period $t$ to $t + 1$. The formula says that the expectation of the change is zero which is the same as saying that the expectation of the original variable at $t+1$ is equal to its current value.
answered Jul 15, 2020 at 18:13