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**

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**Links From the Web**

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Greenspan’s

bio.

Cnnfn

on the Briefcase Indicator

Filed under: Finance