Posted by John Irons at February 18, 2000 02:25 PM

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.

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Links From the Web

Federal Reserve Board
Greenspan’s bio.
Cnnfn on the Briefcase Indicator

Posted by John Irons at February 18, 2000 02:25 PM