in the principle and interest payments of a credit instrument. Say you decided to buy
a GE bond and wanted to insure yourself against any losses that might occur should
GE have problems. You could buy a CDS from a variety of sources that would provide
removed derivative securities, such as CDSs, from regulatory oversight. Additionally,
it preempted states from enforcing gaming laws on these types of securities. The
affect of this regulation was to make it possible for investors to speculate on the
possibility of default on securities they did not own. Consider the idea that you could
buy life insurance on anyone you felt looked unhealthy. Insurance laws prevent this
type of speculation by requiring that you must be in a position to suffer a loss before
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you can purchase insurance. The Commodity Futures Modernization Act removed
this requirement for derivative securities. Thus, speculators could, in essence, legally
bet on whether a firm or security would fail in the future.
During the period between 2000 and 2008 major CDS players included AIG,
Lehman Brothers, and Bear Stearns. The amount of CDSs outstanding mushroomed
to over $62 trillion by its peak in 2008. To put that figure in context, the Gross
National Product of the entire world is around $50 trillion. In 2008, Lehman Brothers
failed, Bear Stearns was acquired by J.P. Morgan for pennies on the dollar, and AIG
required a $182 billion government bailout. This topic is discussed in greater detail
in Chapter 21 “Insurance and Pension Funds.”
Current Yield Calculation
Chapter 3 introduced interest rates and described the concept of yield to maturity.
If you buy a bond and hold it until it matures, you will earn the yield to maturity.
This represents the most accurate measure of the yield from holding a bond.
Current Yield
The current yield is an approximation of the yield to maturity on coupon bonds that
is often reported because it is easily calculated. It is defined as the yearly coupon pay-
ment divided by the price of the security,
(1)
where
i
c
= current yield
P = price of the coupon bond
C = yearly coupon payment
This formula is identical to the formula in Equation 5 of Chapter 3, which describes
the calculation of the yield to maturity for a perpetuity. Hence for a perpetuity, the
current yield is an exact measure of the yield to maturity. When a coupon bond has
a long term to maturity (say, 20 years or more), it is very much like a perpetuity, which
pays coupon payments forever. Thus, you would expect the current yield to be a rather
close approximation of the yield to maturity for a long-term coupon bond, and you can
safely use the current yield calculation instead of looking up the yield to maturity in
a bond table. However, as the time to maturity of the coupon bond shortens (say, it
becomes less than five years), it behaves less and less like a perpetuity and so the
approximation afforded by the current yield becomes worse and worse.
We have also seen that when the bond price equals the par value of the bond, the
yield to maturity is equal to the coupon rate (the coupon payment divided by the
par value of the bond). Because the current yield equals the coupon payment divided
by the bond price, the current yield is also equal to the coupon rate when the bond
price is at par. This logic leads us to the conclusion that when the bond price is at par,
the current yield equals the yield to maturity. This means that the nearer the bond
price is to the bond’s par value, the better the current yield will approximate the yield
to maturity.
The current yield is negatively related to the price of the bond. In the case of
our 10% coupon rate bond, when the price rises from $1,000 to $1,100, the cur-
rent yield falls from 10% (
) to 9.09% (
). As Table 3.1
⫽ $100>$1,100
⫽ $100>$1,000
i
c
⫽
C
P
Chapter 12 The Bond Market
295
in Chapter 3 indicates, the yield to maturity is also negatively related to the price
of the bond; when the price rises from $1,000 to $1,100, the yield to maturity falls
from 10% to 8.48%. In this we see an important fact: The current yield and the
yield to maturity always move together; a rise in the current yield always signals that
the yield to maturity has also risen.
What is the current yield for a bond that has a par value of $1,000 and a coupon inter-
est rate of 10.95%? The current market price for the bond is $921.01.
Solution
The current yield is 11.89%.
where
C =
yearly payment
=
P =
price of the bond
= $921.01
Thus,
i
c
⫽
$109.50
$921.01
⫽ 0.1189 ⫽ 11.89%
0.1095
⫻ $1,000 ⫽ $109.50
i
c
⫽
C
P
E X A M P L E 1 2 . 2 Current Yield
The general characteristics of the current yield (the yearly coupon payment
divided by the bond price) can be summarized as follows: The current yield better
approximates the yield to maturity when the bond’s price is nearer to the bond’s
par value and the maturity of the bond is longer. It becomes a worse approximation
when the bond’s price is further from the bond’s par value and the bond’s maturity
is shorter. Regardless of whether the current yield is a good approximation of the
yield to maturity, a change in the current yield always signals a change in the same
direction of the yield to maturity.
Finding the Value of Coupon Bonds
Before we look specifically at how to price bonds, let us first look at the general
theory behind computing the price of any business asset. Luckily, the value of all
financial assets is found the same way. The current price is the present value of all
future cash flows. Recall the discussion of present value from Chapter 3. If you have
the present value of a future cash flow, you can exactly reproduce that future cash
flow by investing the present value amount at the discount rate. For example, the
present value of $100 that will be received in one year is $90.90 if the discount rate
is 10%. An investor is completely indifferent between having the $90.90 today or hav-
ing the $100 in one year. This is because the $90.90 can be invested at 10% to pro-
vide $100.00 in the future (
). This represents the essence of
value. The current price must be such that the seller is indifferent between contin-
uing to receive the cash flow stream provided by the asset or receiving the offer price.
$90.90
⫻ 1.10 ⫽ $100
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One question we might ask is why prices fluctuate if everyone knows how value
is established. It is because not everyone agrees about what the future cash flows are
going to be. Let us summarize how to find the value of a security:
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