My point above is that if you, as most textbooks do, assume that asset
prices *at a given point in time* are a continuous random
variable...the probability that X (upper case) will take any
specific value x (lower case) is zero...The area of a straight line
is zero.
At a "given point point in time" asset prices are what they are, and
so the probability of their being anything else is zero *by
definition*. But asset prices only mean something to market
participants *over a period of time* (in the limit case one as short
as the elapsed time between the placing of an order and its execution,
even a period so short as to be measured in microseconds). Thus the
area under the "probability density curve" is never zero.
And any function of a *random* variable is itself a *dependent*
variable.
And if "correct" price is taken to mean "value", that itself is always
almost perfectly determinate ex post (determined by the summation,
discounted at the present risk-free interest rate, of all future cash
returns from that asset plus the discounted cash value of that asset,
if any, when that ex post determination is being made). Of course this
means that the EMH is nonsense because most of the relevant--value
determining--information is totally unavailable to the market and, as
Stiglitz got his Nobel for recognizing, not even those bits of
relevant information that exist are *generally* available to the market.
Shane Mage
This cosmos did none of gods or men make, but it
always was and is and shall be: an everlasting fire,
kindling in measures and going out in measures."
Herakleitos of Ephesos
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