The First Book of Arbitrage
208
face value bond paying 10% annually. The issuer of the bond will therefore pay you $10
per year in interest and will continue doing so no matter what the market rate is. If bonds
being issued today are paying 15% and you try to sell your 10% bond, a buyer will pay
you only about $67 for it. At that price, the $10 interest payment the buyer will receive
will equal approximately 15% of the amount paid for the bond. On the other hand, if
bonds being issued today are paying 8%, you can skip off to McDonald's and treat the
family because investors will pay you $125 for your 10% bond.
So your bond that looks so solidly dependable paying $10 year after year is really a
capricious negotiable instrument whose value varies depending on the market. You don't
care, you say, because you have no plans to sell your bond and you will ride the market
out. But, if the market goes up to 15% you have lost money even if you don't sell your
bond because you have lost the opportunity to take back your $100 and reinvest it at 15%.
We have been talking around the concept of yield. It is now time to hit it straight on.
All calculations of yield, including those involving calculations of rebate, are
based on certain assumptions about economic behavior. The most basic of these
assumptions is that available funds are always invested. That means that if someone gives
you $1000, you do not spend it on rent or a new camcorder. Instead, you invest it at the
best rate you can find consistent with the degree of risk you are willing to accept.
Another basic assumption is that the actual value of an amount of money depends
upon when you receive it. This assumption actually flows from the first one. If you
receive $1000 today, you will invest that $1000 and one year from today you will have the
$1000 plus whatever it earned during the year. A good way to remember this rule is that
"money now is worth more than money later."
Suppose you borrow $100 from your mother. You agree to pay back your mom in
two years, with interest at 8 percent. (She's tough but fair.) How much do you owe at the
end of two years? At first blush, the answer would seem to be $116 ($100 of principal
plus $16 of interest for two years). This answer, however, ignores earnings of "interest on
interest." This "interest on interest" is called compounding. The actual worth of a
particular interest rate depends upon how often the compounding is done. The more
frequent the compounding, the more interest upon which interest is earned. Thus, an
interest rate of 5% compounded quarterly is worth more than one compounded annually.
For example, $1000 invested at 5% compounded annually will yield $50 in one year. But
the same amount and the same interest rate, compounded quarterly, will yield
approximately $51 in one year. The dollar amount of the difference in this example is
very small. But if you consider larger sums of money and more frequent compounding,
the differences will be quite significant.
For example, suppose that you agreed to pay your mom interest at the end of the
first year, but that if you did not make that payment, you would pay interest on interest for