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Econ 251a
Fall 2006
Price Dynamics of LongLived Assets
The "zero" prices
π
t
are known to all serious market participants. These enable
participants to calculate forward rates
1+
i
F
t
.
In the last lecture we assumed that
these were stationary:
1+
i
F
t
=1+
i.
In this lecture we drop stationarity.
If there is no uncertainty in the world, then the forward rates will be completely
reliable predictors of the future interest rates;
1+
i
F
t
=1+
i
t
. Since the present values
of securities with purely nominal (money) payo
f
s are determined entirely by interest
rates and those cash
f
ows, it follows that if we can predict future interest rates and
future cash
f
ows, then we can also predict the future present values of the securities.
Without uncertainty, present values and prices will be the same. Hence the whole
evolution of security prices can be foreseen from the zero prices
π
t
.
Putting this another way, an economist who does not know much about the world
but who can see the the zero prices
π
t
can deduce what the traders think the future
will be, provided the traders themselves see no uncertainty in the world.
In this chapter we examine the evolution of prices for some simple securities,
assuming various simple scenarios of forward interest rates and security payo
f
s. The
easiest and most important scenario is when the forward rate
i
F
t
=0
(implying that
traders expect a zero interest rate between time
t
and time
t
+1)
and the security
payo
f
is
0
at time
t
+1
.
This scenario is not farfetched at all. If the length of time
between period
t
and
t
+1
is very short, the interest rate will indeed usually be very
low, and the security might well not pay any dividends. The implication, if traders
face no uncertainty about the future, is that they must be expecting the security
pr
iceatt
ime
t
+1
tobethesameasatt
ime
t.
Thus we could not be in a rational
world if every trader was sure the price of some asset (like housing or oil) was going
to go up over a very short time interval.
On the other hand, over longer periods, if the interest rate is nonzero or if
dividends are not zero (and even
f
uctuate), we should often expect prices to change.
We give examples including discount and premium bonds for which the price must
change over time, which for some reason surprises many people.
1P
r
e
s
e
n
t
V
a
l
u
e
We denote the price today (at time 0) of $1 at time t by
π
t
=
price today for $1 at time
t
π
t
=
1
1+
R
t
1
π
t
=1+
R
t
=
price at time
t
of $1 today
We say that the present value of a dollar at time
t
is
π
t
.
Sometimes
π
t
is called
the
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View Full Document1.1 Interest Rate
Since people are impatient (and since money is storable) it is always the case that
π
t
≤
1
Anybody who gives up $1 today can expect to get more than $1 tomorrow,
1
π
t
≥
1
.
Many people
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 '09
 GEANAKOPLOS,JOHN

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