Summary study book The Economics of Money, Banking, and Financial Markets of Mishkin, Matthews and Giuliodori - ISBN: 9781782730552, Edition: European Edition, Year of publication: 2013
Book: “The Economics of Money, Banking, and Financial Markets”,
European Edition
Week1
A security (also called a financial instrument) is a claim on the issuer’s future income or
assets (any financial claim or piece of property that is subject to ownership). A bond
is a debt security that promises to make payments periodically for a specified period of
time
Both 10-year bond rates and consol rates fluctuate less than the Treasury bill rate (TBR) but
are higher,
C4: Understanding Interest Rates
Let’s look at the simplest kind of debt instrument, which we will call a simple loan. In
this loan, the lender provides the borrower with an amount of funds (called the principal)
that must be repaid to the lender at the maturity date, along with an additional payment
for the interest. For example, if you made your friend, Jane, a simple loan of €100 for one
year, you would require her to repay the principal of €100 in one year’s time along with
an additional payment for interest – say, €10. In the case of a simple loan like this one, the
interest payment divided by the amount of the loan is a natural and sensible way to measure
the interest rate. This measure of the so-called simple interest rate,i, is
This timeline immediately tells you that you
are just as happy having :100 today as having :110 a year from now
2 A fixed-payment loan (which is also called a fully amortized loan) in which the lender
provides the borrower with an amount of funds, which must be repaid by making the
same payment every period (such as a month), consisting of part of the principal and
interest for a set number of years. For example, if you borrowed €1,000, a fixed-payment
loan might require you to pay €126 every year for 25 years. Instalment loans (such as car
loans) and mortgages are frequently of the fixed-payment type.
3 A coupon bond pays the owner of the bond a fixed-interest payment (coupon payment)
every year until the maturity date, when a specified final amount (face value or par
value) is repaid. (The coupon payment is so named because the bondholder used to
obtain payment by clipping a coupon off the bond and sending it to the bond issuer,
who then sent the payment to the holder. Nowadays, it is no longer necessary to send
in coupons to receive these payments.) A coupon bond with €1,000 face value, for
example, might pay you a coupon payment of €100 per year for ten years, and at the
maturity date, repay you the face value amount of €1,000. (The face value of a bond is
usually in €1,000 increments.)
A coupon bond is identified by three pieces of information. First is the corporation or
government agency that issues the bond. Second is the maturity date of the bond. Third
is the bond’s coupon rate, the money amount of the yearly coupon payment expressed
as a percentage of the face value of the bond. In our example, the coupon bond has a
yearly coupon payment of €100 and a face value of €1,000. The coupon rate is then
:100/:1,000 = 0.10, or 10%. Capital market instruments such as UK government
bonds (known as consols) and corporate bonds are examples of coupon bonds.
4 A discount bond (also called a zero-coupon bond) is bought at a price below its face
value (at a discount), and the face value is repaid at the maturity date. Unlike a coupon
bond, a discount bond does not make any interest payments; it just pays off the face
value. For example, a one-year discount bond with a face value of €1,000 might be
bought for €900; in a year’s time the owner would be repaid the face value of €1,000.
UK Treasury bills, US savings bonds and long-term zero-coupon bonds are examples of
,discount bonds.
These four types of instruments require payments at different times: simple loans and
discount bonds make payment only at their maturity dates, whereas fixed-payment loans
and coupon bonds have payments periodically until maturity.
Of the several common ways of calculating interest rates, the most important is
the yield
to maturity, the interest rate that equates the present value of cash flow
payments received
from a debt instrument with its value today. Most accurate way to measure
interest rate.
is, it equals the simple interest rate on the loan. An important point to recognize is that for simple
loans, the simple interest rate equals the yield to maturity.
Table 4.1 shows the yields to maturity calculated for several bond prices. Three interesting
facts emerge:
1 When the coupon bond is priced at its face value, the yield to maturity equals the
coupon rate.
2 The price of a coupon bond and the yield to maturity are negatively related; that is, as the
yield to maturity rises, the price of the bond falls. As the yield to maturity falls, the price
of the bond rises.
3 The yield to maturity is greater than the coupon rate when the bond price is below its
face value.
There is one special case of a coupon bond that is worth discussing because its yield to
maturity is particularly easy to calculate. This bond is called a consol or a perpetuity; it is
a perpetual bond with no maturity date and no repayment of principal that makes fixed
coupon payments of €C for ever. When a coupon bond has a long term to maturity
(say, twenty years or more), it is
very much like a perpetuity, which pays coupon payments for ever. This is because the cash
flows more than twenty years in the future have such small present discounted values that
the value of a long-term coupon bond is very close to the value of a perpetuity with the
same coupon rate. Thus ic in Equation 4.5 will be very close to the yield to maturity for any
long-term bond. For this reason, ic, the yearly coupon payment divided by the price of the
security, has been given the name current yield and is frequently used as an approximation
to describe interest rates on long-term bonds.
Summary
The concept of present value tells you that a euro in the future is not as valuable to you
as a euro today because you can earn interest on this euro. Specifically, a euro received n
years from now is worth only :1/(1 + i)n today. The present value of a set of future cash
flow payments on a debt instrument equals the sum of the present values of each of the
future payments. The yield to maturity for an instrument is the interest rate that equates
the present value of the future payments on that instrument to its value today. Because the
procedure for calculating the yield to maturity is based on sound economic principles, this
is the measure that economists think most accurately describes the interest rate.
Our calculations of the yield to maturity for a variety of bonds reveal the important fact
, that current bond prices and interest rates are negatively related: when the interest rate
rises (or falls), the price of the bond falls (or rises).
The distinction between interest rates and returns
For any security, the rate of return is defined as the payments to the owner plus the
change in its value, expressed as a fraction of its purchase price. To make this definition
clearer, let us see what the return would look like for a €1,000-face-value coupon bond
with a coupon rate of 10% that is bought for €1,000, held for one year, and then sold for
€1,200. The payments to the owner are the yearly coupon payments of €100, and the
change in its value is :1,200 - :1,000 = :200. Adding these together and expressing
them as a fraction of the purchase price of €1,000 gives us the one-year holding-period
return for this bond:
You may have noticed something quite surprising about the return that we have just
calculated: it equals 30%, yet as Table 4.1 indicates, initially the yield to maturity was only
10%. This demonstrates that the return on a bond will not necessarily equal the yield to
maturity on that bond. We now see that the distinction between interest rate and return
can be important, although for many securities the two may be closely related.
This
rewritten formula illustrates the point we just discovered: even for a bond for which the
current
yield ic is an accurate measure of the yield to maturity, the return can differ substantially from
the interest rate. Returns will differ from the interest rate, especially if there are sizeable
fluctuations in the price of the bond that produce substantial capital gains or losses.
when interest rates
on all these bonds rise from 10% to 20%. Several key findings in this table are generally true
of
all bonds:
■ The only bond whose return equals the initial yield to maturity is one whose time to
maturity is the same as the holding period (see the last bond in Table 4.2).
■ A rise in interest rates is associated with a fall in bond prices, resulting in capital losses
on bonds whose terms to maturity are longer than the holding period.
■ The more distant a bond’s maturity, the greater the size of the percentage price change
associated with an interest-rate change.
■ The more distant a bond’s maturity, the lower the rate of return that occurs as a result of
the increase in the interest rate.
■ Even though a bond has a substantial initial interest rate, its return can turn out to be
negative if interest rates rise.
At first it frequently puzzles students (as it puzzles poor Irving the Investor) that a rise in
interest rates can mean that a bond has been a poor investment. The trick to understanding
this is to recognize that a rise in the interest rate means that the price of a bond has fallen.
A rise in interest rates therefore means that a capital loss has occurred. If this loss is large
enough, the bond can be a poor investment indeed. For example, we see in Table 4.2 that
the bond that has 30 years to maturity when purchased has a capital loss of 49.7% when
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