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Economic News, Data and Analysis

Interest Rates and the Stock Market

One of the most common questions that I am asked via email is why Alan
Greenspan’s remarks are so important for the behavior of the stock market.
The initial answer I give is that people interpret Greenspan’s remarks
as an indication as to the future direction of monetary policy as reflected
in interest rates. Of course, that leads to the obvious next question:
why do interest rates matter for the price of stocks?

Here are the basics.

Arbitrage

The fundamental question about the relation between interest rates and
asset prices hinges on the relation between money tomorrow and money today.
A stock share (or some other asset) represents a claim to receive some
amount of money tomorrow (either through dividends or through what you
can sell the stock for tomorrow).

For example, if I buy a share of Amazon.com stock today, I expect to
be able to get some money for that share tomorrow. For example, I might
buy a share of stock for 80$ today hoping to get something like 100$ next
year.

Now, if I happen to have some cash lying around, I could do a couple
of things with it. Either I could put the money in the bank or some other
safe asset (like government bonds) and earn some interest on the money,
or, I could buy that share of Amazon.com and get $100 in a year.

Since I have the choice, this gives us a way to value the share of the
stock. If the price of the stock were “low,” I would choose to buy the
stock. If it were “high,” I would choose to keep the money in bonds. But
how high is “high”?

Present Discounted Value

What we need to do is to compare the return on the two investments.
If the money I get from the bonds is less than the money I get from the
stock ($100), then I should buy the stock, and vice versa.

Lets say that the interest rate is 6%, and the price of the Amazon.com
stock is $P. If I invest in bonds I get $P * (1.06) in one year. If take
the $P and invest in the stock I get 100$.

This means that I will invest in Amazon.com if $100 > $P * (1.06). Or,
via quick algebra, if $P < 100 / (1.06).

If the price is above this value (100/1.06), I will sell the stock (and
so will everyone else), thus driving down the price. And if the price is
below, I will buy the stock (and so will everyone else), thus driving up
the price.

In equilibrium, this means that the price of the stock will be equal
to 100/1.06. In general, this means that the price will be given by 100/(1
+ i) where i is the interest rate expressed as a decimal
(e.g. 6% = 0.06).

So, the higher the interest rate, the lower will be the value (and
hence the price) of a payment in the future – a rise in the interest rate
thus causes stock prices to fall.

In general we can expand the above analysis to find what is called the
“Present Discounted Value” of any stream of future payments.

The formula for a stream {x1, x2, …} of payments in future
years is given by

PDV = (x1 / (1+i)) + (x2 / (1+i)(1+i)) + … .

(Of course, I am ignoring a range of issues involving expectations of
future interest rates, the value of the future payment, and risk. But the
simple case illustrates the interest rate effect.)

Internet Stocks

In addition to the conclusion that higher interest rates imply lower
stock prices, an obvious point from above is that the farther in the future
a payment is received, the less we will value the payment: $100 tomorrow
is worth more that $100 in 10 years. A second, less obvious, point is that
the value of an asset that involves a payment far in the future will be
more sensitive to a change in the interest rate than an asset with
more timely payments.

This second point becomes important when we are talking about internet
stocks. For most of the hot stocks, significant profits from the company
are, in many cases, not expected to materialize for years. So we can expect
that these stocks will be even more sensitive to interest rates
than the more traditional “old economy” stocks.

Example:

Try it for yourself – see how much of a difference a rise in interest
rates will make for the current value of a payment in the future.

The table below shows the value of 100$, payable either in its entirety
in 2 years, or $50 next year and 50$ the year after. Enter a value for
the interest rate and for a cahnge in the interest rate to see how much
the present value of the $100 in the future will fall.

function process() {
document.form1.irate2.value = parseFloat(document.form1.irate.value) + parseFloat(document.form1.dirate.value);
document.form1.pdv1a.value = Math.round(100* ((parseFloat(document.form1.val.value)/2) / (1+(parseFloat(document.form1.irate.value))/100) +
(parseFloat(document.form1.val.value)/2) / ((1+(parseFloat(document.form1.irate.value))/100) * (1+(parseFloat(document.form1.irate.value))/100)) )) / 100;
document.form1.pdv1b.value = Math.round(100* ((parseFloat(document.form1.val.value)/2) / (1+(parseFloat(document.form1.irate2.value))/100) +
(parseFloat(document.form1.val.value)/2) / ((1+(parseFloat(document.form1.irate2.value))/100) * (1+(parseFloat(document.form1.irate2.value))/100)) )) /100;
document.form1.pdv2a.value = Math.round(100* parseFloat(document.form1.val.value) / ((1+(parseFloat(document.form1.irate.value))/100)*(1+(parseFloat(document.form1.irate.value))/100))) /100 ;
document.form1.pdv2b.value = Math.round(100* parseFloat(document.form1.val.value) / ((1+(parseFloat(document.form1.irate2.value))/100)*(1+(parseFloat(document.form1.irate2.value))/100))) / 100 ;
document.form1.pdv1c.value = Math.round(100* ((parseFloat(document.form1.pdv1a.value)-parseFloat(document.form1.pdv1b.value)) / parseFloat(document.form1.pdv1a.value)) *100) /100 + “%”;
document.form1.pdv2c.value = Math.round(100* ((parseFloat(document.form1.pdv2a.value)-parseFloat(document.form1.pdv2b.value)) / parseFloat(document.form1.pdv2a.value)) *100) /100 + “%”;
}

Enter Interest Rate:

Enter Increase: 

Today’s Value (PDV) Today’s Value at the new interest rate % Change in Value 
Payable 50$ + 50$
Payable 100$ (year 2)

More Economics Features

Disagree? Post
in the Forum.

Links From the Web

Federal Reserve
Board


Greenspan’s
bio.


Cnnfn
on the Briefcase Indicator

Filed under: Finance

Greenspan Briefcase Indicator

Another reason why economics is hard

When the Federal Reserve changes interest rates, the stock market often
reacts drastically in one direction or another. An accurate prediction
of the Fed’s actions can thus be a huge advantage for investors – and so
all eyes are on Alan Greenspan and the economy prior to FOMC meetings.
(It turns out that the recent move  – a 25 basis
point
increase – was pretty much anticipated and hence there was little
movement in the stock market).

One of the more bizarre methods of interest rate forecasting focuses
on the size of Greenspan’s briefcase – a thick briefcase on the morning
of the FOMC signals a change in interest rates. The logic is that the additional
evidence is needed to present to the committee a change in policy is necessary.

I think it was CNBC, the cable TV channel with financial news during
the day, that first popularized this indicator. (My favorite quote about
CNBC is from a friend who, the first time she saw the pre-market broadcast,
said “Do they know they’re on TV?”)

What does the briefcase really tell us?

So let’s say that CNBC was right and they found that a thicker briefcase
did indeed signal a change in interest rates. The first thing that would
happen is that you would find an even bigger horde of cameras and reporters
analyzing the briefcase when Greenspan walked to the office in the morning.
The next thing you would find is that there would be a stock market reaction,
which would take place as soon as Greenspan got into camera range and the
markets learned of the size of the briefcase.

If this were all that happened, then economics would be easy – we would
have a good way to predict an economic even based on a nice, easily observed
signal. However, there is an obvious problem with this: Greenspan almost
certainly knows that he is being watched. I’m sure that by now Greenspan
has been told that cameras are zooming in on his briefcase.

So, if Greenspan want to signal higher rates, he may throw a coupe of
magazines in the case to bulk it up a bit. But of course we’re no dummies
– we know that Greenspan may be trying to trick us…, and Greenspan knows
that we know…

 

Given all of this game playing, what does, or, better yet, what will
the briefcase really tell us? If you can figure it out let me know.

Why Economics is hard…

So here’s why economic is hard – we are trying to study people, and
people tend to react in intelligent ways: they may change behavior if they
are being watched, and they tend to act and think strategically.

The Greenspan example is very simplistic, but illustrative of a wider
range of economic phenomenon: as soon as we learn something about the economy,
and try to use that knowledge to our advantage, what we have learned may
no longer be true.

Another example – what would happen if we learn that every third Tuesday
stock prices rose by 20%? Everyone would then try to by on every third
Wednesday and sell on the Thursday – which would then cause prices on Thursday
to no longer rise by 20%.

…but not impossible.

Fortunately people are sometimes predictable, and we can indeed learn
something about the economy. We might have to be clever to find out how
things work, but there do seem to be some regularities that persist over
time (Okun’s
law
for example).

However, I wouldn’t put too much stock in the briefcase indicator in
the future. Pun intended.

Links From the Web

Federal Reserve
Board


Greenspan’s
bio.


Cnnfn
on the Briefcase Indicator

More Features

Nonsense! Economics
is easy! Post in the Forum.


 



Fed Glossary:

Basis point

1 basic point is 0.01%. So a 50 basic point rise is the same as a 0.5%
rise in interest rates. (e.g. from 5.5% to 6.0%).

Central Bank

The institution that is charged with enacting monetary policy and/or
regulating/facilitating the operation of the banking system. Sometimes
called a “bank’s bank”. The Federal Reserve is the central bank of the
US.

Discount rate

The rate of interest that private banks pay for loans from the Federal
Reserve.

The Fed

Short for Federal Reserve. To be more precise, monetary policy decisions
are made at the “Board of Governors of the Federal Reserve System” located
in Washington D.C.

Federal Open Market Committee (FOMC)

The committee that decides on the course of monetary policy. Composed
of the 7 members of the Board of Governors and 5 of the 12 presidents of
the member banks.

Fiscal Policy

Decisions by the government about the level of government spending
and taxation.

Greenspan, Alan

The current Chairman of the Board of Governors of the Fed and the FOMC

Member Banks

The branches of the Federal Reserve System, which are located in each
of the 12 Federal Reserve Districts.

Monetary Policy

Decisions by the government (usually the central bank) about the supply
of money (and hence interest rates).

Filed under: Economics

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