it by 5 minutes. Rational expectations theory implies that this is exactly what Joe
will do because he will want his forecast to be the best guess possible. When
Joe has revised his forecast upward by 5 minutes, on average, the forecast error
will equal zero so that it cannot be predicted ahead of time. Rational expecta-
tions theory implies that forecast errors of expectations cannot be predicted.
T H E E F F I C I E N T M A R K E T H Y P OT H E S I S : R AT I O N A L
E X P E C TAT I O N S I N F I N A N C I A L M A R K E T S
While the theory of rational expectations was being developed by monetary econ-
omists, financial economists were developing a parallel theory of expectation for-
mation in financial markets. It led them to the same conclusion as that of the
rational expectations theorists: expectations in financial markets are equal to opti-
mal forecasts using all available information.
3
Although financial economists gave
their theory another name, calling it the
efficient market hypothesis
, in fact their
theory is just an application of rational expectations to the pricing of not only
stocks but other securities.
The efficient market hypothesis is based on the assumption that prices of secu-
rities in financial markets fully reflect all available information. You may recall from
Chapter 4 that the rate of return from holding a security equals the sum of the cap-
ital gain on the security (the change in the price), plus any cash payments, divided
by the initial purchase price of the security:
(9)
where
R
rate of return on the security held from time
t
to
t
1 (say, the
end of 2010 to the end of 2011)
P
t
1
price of the security at time
t
1, the end of the holding period
P
t
price of the security at time
t
, the beginning of the holding
period
C
cash payment (coupon or dividend payments) made in the
period
t
to
t
1
Let s look at the expectation of this return at time
t
, the beginning of the hold-
ing period. Because the current price
P
t
and the cash payment
C
are known at the
beginning, the only variable in the definition of the return that is uncertain is the
price next period,
P
t
1
.
4
Denoting the expectation of the security s price at the end
of the holding period as
P
e
t
1
, the expected return
R
e
is:
R
e
P
t
1
e
P
t
C
P
t
R
P
t
+1
P
t
C
P
t
C H A P T E R 7
Stocks, Rational Expectations, and the Efficient Market Hypothesis
151
3
The development of the efficient market hypothesis was not wholly independent of the development
of rational expectations theory, in that financial economists were aware of Muth s work.
4
There are cases where
C
might not be known at the beginning of the period, but that does not make
a substantial difference to the analysis. We would in that case assume that not only price expectations
but also the expectations of
C
are optimal forecasts using all available information.
152
PA R T I I
Financial Markets
The efficient market hypothesis also views expectations of future prices as
equal to optimal forecasts using all currently available information. In other words,
the market s expectations of future securities prices are rational, so that:
which in turn implies that the expected return on the security will equal the optimal
forecast of the return:
(10)
Unfortunately, we cannot observe either
R
e
or
P
e
t
+
1
, so the rational expectations
equations by themselves do not tell us much about how the financial market behaves.
However, if we can devise some way to measure the value of
R
e
, these equations will
have important implications for how prices of securities change in financial markets.
The supply and demand analysis of the bond market developed in Chapter 5
shows us that the expected return on a security (the interest rate, in the case of
the bond examined) will have a tendency to head toward the equilibrium return
that equates the quantity demanded to the quantity supplied. Supply and demand
analysis enables us to determine the expected return on a security with the follow-
ing equilibrium condition: The expected return on a security
R
e
equals the equi-
librium return
R
*, which equates the quantity of the security demanded to the
quantity supplied; that is,
(11)
The academic field of finance explores the factors (risk and liquidity, for example)
that influence the equilibrium returns on securities. For our purposes, it is suffi-
cient to know that we can determine the equilibrium return and thus determine
the expected return with the equilibrium condition.
We can derive an equation to describe pricing behaviour in an efficient market
by using the equilibrium condition to replace
R
e
with
R
* in the rational expecta-
tions equation (Equation 10). In this way, we obtain:
(12)
This equation tells us that
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