The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


The highest credit rating belongs to the U.S. federal government, since there is effectively
no risk of the federal government failing to pay its debt obligations.^4 Corporations, state
and local governments, and other issuers carry varying bond ratings depending on the
agencies’ assessments of their financial strength and prospects. Bonds of issuers whose rat-
ings fall within the range that are typically considered low to moderate risk are sometimes
referred to as investment grade. Bonds of issuers whose ratings fall in a range suggesting
that there is a realistic cause for concern are sometimes referred to as junk bonds.
A bond issuer’s credit rating can have a significant impact on the interest rates that it
will have to pay to borrow money, just as consumers with good credit ratings can bor-
row more easily at more attractive rates than consumers with poor ratings. After a bond
has been issued, changes in a company’s credit rating can affect the value of its bonds. If
you own a Zarofire Systems bond and one or more of the major rating agencies upgrades
the company’s bond rating, it is reasonable to expect that the price of your bond will rise.
When a company’s credit risk profile improves, its bonds become more attractive to buy-
ers and hence command higher prices. On the other hand, if an issuer’s ratings drop, it is
equally reasonable to expect that the prices of its bonds will drop, as a poorer credit risk is
obviously less attractive to buyers.
Bonds also carry what is known as interest rate risk. The interest rates that prevail in the
market change over time. In the early 2000s, it was not unusual for a savings account to pay
an interest rate of only 1% or even less, whereas the same type of account 20 years earlier
might have carried a rate of 8% or more. Through the mid 2000s interest rates have been
rising. Rates change over time depending on an enormous number of factors at work in the
economy. These changes in interest rates pose both risks and opportunities for owners of
bonds. The Zarofire Systems 8% coupon rate bond sold for a premium because the 8% rate
was higher than the prevailing market rate for similar bonds, and so the bond commanded a
higher price. If, however, market conditions change so that the prevailing rate for bonds rises
to 9^1 ⁄ 2 %, what do you think will happen to the market value of this bond? Naturally, if the
market rate rises, buyers will no longer be willing to pay such a premium for a bond with an
8% coupon rate. In fact, the bond will go from selling at a premium to selling at a discount.
As interest rates rise, the selling prices of bonds tend to go down; as rates decline, bond
prices tend to rise. When two quantities move in opposite directions as these do, we say
that they are inversely correlated.

Example 6.2.6 Jack has a lot of money invested in government bonds. His fi nancial
advisor tells him that interest rates are rising. Is this good news for Jack?

At fi rst blush, it might sound as though higher interest rates are good news for Jack, but this
is not correct. If interest rates are rising, that means that the value of the bonds that Jack
already owns will go down. Jack will not be pleased to hear this news.

Example 6.2.7 Jill has no bond investments, but she expects to take out a mortgage
loan to buy a new house soon. A report on the morning news says that bond prices are
expected to rise over the next few months. Will she be happy to hear this news?

Since bond prices and interest rates are inversely correlated, rising bond prices mean declin-
ing interest rates. Since Jill has not yet taken out the loan she should be happy to hear this,
because it suggests that she will be able to get her loan at a lower rate.

The astute reader will notice that Jack and Jill are getting contradictory information about
the direction of interest rates. This really isn’t all that surprising. Future interest rates are
quite difficult to predict, and so it really isn’t all that unusual to get contradictory pre-
dictions from two different sources. In the words of the noted philosopher Yogi Berra:
“Predictions are difficult to make. Especially about the future.”

(^4) Even if worst came to worst and the federal government were unable to collect enough in taxes to pay its debts, it
has a printing press. Printing money to pay debts might have disastrous economic consequences, but the bondholders
would still get paid (though the dollars they would get paid with would probably be worth a lot less than the dollars
are worth today). The risks this would pose are enormous, but they are not credit risks.
6.2 Bonds 267

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