On Market Timing And Investment Performance Part I An Equilibrium Theory of Va

Cover On Market Timing And Investment Performance Part I An Equilibrium Theory of Va
On Market Timing And Investment Performance Part I An Equilibrium Theory of Va
Robert C Merton
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By hypothesis, y(t) is distributed independent of Zjj(t) . Therefore, p^(t) = prob{Y(t) = 0|Zj^(t) R(t)} = 1 - p^(t). Hence, p, (t) + p^(t) = 1, and by Proposition III. 2, the forecast has zero value.
So, if forecasts are formed by simply flipping a (not necessarily fair) coin where n is the probability that the forecast will be Y(t) = and 1 - ri is the probability that the forcast will be Y(t) = 1, then p, (t) = r\ and p«(t) = 1 - n, and therefore, such forecasts will have zero value. Include
...d as a special case of this type of forecast is to always forecast that Z (t) _ R(t) (i. E. , Y(t) = 1, p^(t) = n = and p„(t) = 1). Like a stopped clock, such a forecast will sometimes be correct, but it never has any value.
Having established that completely random forecasts have zero value, we now go to the other extreme and show that completely predictable forecasts also have zero value.


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