Chapter 10
Interest Rates
Chapter outline
•
•
•
•
•
•
•
Interest rate history and money
market rate
Money market prices and rates
Rates and yields on fixed-income
securities
The term structure of interest rates
Nominal versus real interest rates
Traditional theories of the term
structure
Determinants of nominal interest
rates
Chapter Objective
Our goal in this chapter is to
discuss the many different
interest rates that are commonly
reported in the financial press.
We will also:
Find out how different
interest rates are calculated
and quoted, and
Discuss theories of what
determines interest rates.
11- 1
Ayşe Yüce Copyright © 2012 McGraw-Hill Ryerson
%0
2001/01
2001/06
2001/11
2002/04
2002/09
2003/02
2003/07
2003/12
2004/05
2004/10
2005/03
2005/08
2006/01
2006/06
2006/11
2007/04
2007/09
2008/02
2008/07
2008/12
2009/05
2009/10
2010/03
2010/08
2011/01
Canadian Interest Rate History
7
I
n 6
t
e
5
r
e
4
s
t
3
r
2
a
t
e 1
Tbill
Bonds
Date
10- 2
U.S. Interest Rate History
3
Money Market Rates





Prime rate - The basic interest rate on short-term loans that
the largest commercial banks charge to their most
creditworthy corporate customers.
Prime rate is well known as a bellwether rate –Interest rate
that serves as a leading indicator of overall market’s
condition or future trends, e.g. inflation.
Bank rate-Interest rate that the Bank of Canada offers to
commercial banks for overnight reserve loans.
Discount rate - The interest rate that the Fed offers to
commercial banks for overnight reserve loans.
Federal funds rate - Interest rate that U.S. banks charge
each other for overnight loans of $1 million or more.
10- 4
Money Market Rates







Commercial paper - Short-term, unsecured debt issued by the largest
corporations.
Certificate of deposit (CD) - Large-denomination deposits of
$100,000 or more at commercial banks for a specified term.
Banker’s acceptance - A postdated check on which a bank has
guaranteed payment. Commonly used to finance international trade
transactions.
Call money rate - The interest rate brokerage firms pay for call money
loans from banks. This rate is used as the basis for customer rates on
margin loans.
Eurodollars - Certificates of deposit denominated in U.S. dollars at
commercial banks outside the USA.
London Interbank Offered Rate (LIBOR) - Interest rate that
international banks charge one another for overnight Eurodollar loans.
10- 5
.
Money Market Interest Rates
6
Money Market Prices and Rates
A Pure Discount Security is an interest-bearing asset:



It makes a single payment of face value at maturity.
It makes no payments before maturity.
There are several different ways market participants
quote interest rates.




Bank Discount Basis
Bond Equivalent Yields (BEY)
Annual Percentage Rates (APR)
Effective Annual Rates (EAR)
10- 7
The Bank Discount Basis


The Bank Discount Basis is a method of quoting interest rates on
money market instruments.
 It is commonly used for T-bills and banker’s acceptances.
The formula is:
Days to Maturity


Current Price  Face Value x 1
x Discount Yield 
360



Note that we use 360 days in a year in this (and many
other) money market formula.

The term “discount yield” here simply refers to the quoted
interest rate.
10- 8
Calculating a Price Using a Bank Discount Rate


Suppose a banker’s acceptance that will be paid in 60
days has a face value of $1,000,000.
If the discount yield is 3%, what is the current price of
the banker’s acceptance?
 Days to maturity

Current Price  Face Value  1
 Discount yield 
360


60


 $1,000,000  1
 0.03 
 360

 $1,000,000  1 - 0.005

Remember to
multiply before
you subtract.
 $995,000.
10- 9
Treasury Bill Quotes in The Wall Street Journal
Figure 10.3
10- 10
Bond Equivalent Yields

Canadian T-bill rates are quoted using Bond Equivalent
Yields (BEY) instead of bank discount yield

You can convert a bank discount yield to a bond
equivalent yield using this formula:
10- 11
Treasury Bill Prices


For T-bills the bid and ask price can be calculated using bank
discount rate formula
If bond equivalent yield is given, Treasury Bill prices can be
calculated using the formula:
FaceValue
BillPrice 
1  ( Bond Eq.Yield X Days to Maturity) / 365

If the bond equivalent rate is given as 3.315% on a T-bill with
170 days to maturity and $1,000,000 face value then the price is
$1,000,000
$984,795 
1  0.03315 X 170 / 365
10- 12
More Ways to Quote Interest Rates

“Simple” interest basis - Another method to quote
money market interest rates.




Calculated just like annual percentage rates (APRs).
Used for CDs.
The bond equivalent yield on a T-bill with less than six
months to maturity is also an APR.
An APR understates the true interest rate, which is
usually called the effective annual rate (EAR).
10- 13
Converting APRs to EARs

In general, if we let m be the number of periods in a
year, an APR can be converted to an EAR as follows:
APR 

1 EAR   1

m 


m
EARs are sometimes called effective annual yields,
effective yields, or annualized yields.
10- 14
Converting Credit Card APRs to EARs

Some Credit Cards quote an APR of 18%.



18% is used because 18 = 12 times 1.50
That is, the monthly rate is really 1.50%.
What is the EAR?
1  EAR 

1 


1  EAR 

1


APR m
m 
0.18 12
12
 1.01512



 1.1956
so, the EAR 19.56%.
Ouch.
10- 15
Rates and Yields on Fixed-Income Securities

Fixed-income securities include long-term debt contracts from a
wide variety of issuers:
 Federal governments,
 Real estate purchases (mortgage debt),
 Corporations, and
 Provincial and municipal governments

When issued, fixed-income securities have a maturity of
greater than one year.
When issued, money market securities have a maturity
of less than one year.

10- 16
The Treasury Yield Curve

The Treasury yield curve is a plot of Treasury
yields against maturities.

It is fundamental to bond market analysis,
because it represents the interest rates for
default-free lending across the maturity
spectrum.
© 2009 McGraw-Hill Ryerson
Limited
10- 17
The Treasury Yield Curve
10- 18
Canadian Yield Curve
19
The Term Structure of Interest Rates





The term structure of interest rates is the relationship between
time to maturity and the interest rates for default-free, pure
discount instruments.
The term structure is sometimes called the “zero coupon yield
curve” to distinguish it from the Treasury yield curve, which is
based on coupon bonds.
The term structure can be seen by examining yields on STRIPS.
STRIPS are pure discount instruments created by “stripping”
bonds into separate parts, which are then sold separately.
The term STRIPS stands for Separate Trading of Registered
Interest and Principal of Securities.
© 2009 McGraw-Hill Ryerson
Limited
10- 20
STRIPS


An asked yield for a STRIP is an APR,
calculated as two times the true semiannual rate.
Recall:
Present value 

Future value
1  r N
Therefore, for STRIPS:
STRIPS Price 
Face Value

1  YTM
2

2M
M is the number of years to maturity.
10- 21
US TREASURY STRIPS
Ayşe Yüce Copyright © 2012
McGraw-Hill Ryerson
22
Example: Pricing US Treasury STRIPS

Let’s find the price of the following Strip.


The ask YTM is 6.40%.
Matures in 13.5 years from the time of the quote
Face Value
100
100
STRIPS Price 


 $42.72.
2
M
2

13.5
27
0.0640
0.0640
1  YTM
1

1

2
2
2







Let’s calculate the YTM from the quoted price of 42.72
1
 Face Value 2M1

 100 213.5





YTM  2  
 1  0.0640 or 6.40%.
  1  2  

 42.72 

 42.72 





10- 23
Nominal versus Real Interest Rates


Nominal interest rates are interest rates as they are
observed and quoted, with no adjustment for inflation.
Real interest rates are adjusted for inflation effects.
Real interest rate = nominal interest rate – inflation rate


The Fisher Hypothesis asserts that the general level of
nominal interest rates follows the general level of
inflation.
According to the Fisher hypothesis, interest rates are,
on average, higher than the rate of inflation.
10- 24
Real T-bill Rates
10- 25
Inflation Rates and T-bill Rates
Figure 10.6
10- 26
Traditional Theories of the
Term Structure



Expectations Theory: The term structure of interest
rates reflects financial market beliefs about future
interest rates.
Maturity Preference Theory: Long-term interest
rates contain a maturity premium necessary to
induce lenders into making longer term loans.
Market Segmentation Theory: Debt markets are
segmented by maturity, so interest rates for various
maturities are determined separately in each segment.
10- 27
Problems with Traditional Theories

Expectations Theory



Maturity Preference Theory



The term structure is almost always upward sloping, but interest rates have
not always risen.
It is often the case that the term structure turns down at very long maturities.
The government borrows much more heavily short-term than long-term.
Many of the biggest buyers of fixed-income securities, such as pension
funds, have a strong preference for long maturities.
Market Segmentation Theory



The government borrows at all maturities.
Many institutional investors, such as mutual funds, are more than willing to
move maturities to obtain more favorable rates.
There are bond trading operations that exist just to exploit perceived
premiums, even very small ones.
10- 28
Modern Term Structure Theory


Long-term bond prices are much more sensitive to interest rate
changes than short-term bonds. This is called interest rate risk.
So, the modern view of the term structure suggests that:
NI = RI + IP + RP

In this equation:
NI = Nominal interest rate
RI = Real interest rate
IP = Inflation premium
RP = Interest rate risk premium

The previous equation shows the component of interest rates on
default-free bonds that trade in a liquid market. Not all bonds do.
Therefore, a liquidity premium (LP) and a default premium (DP)
must be added to the previous equation:
NI = RI + IP + RP + LP + DP
10- 29

Modern Term Structure Theory
30
Useful Internet Sites








www.money-rates.com (latest money market rates)
www.bba.org.uk (learn more about LIBOR)
www.bankofcanada.ca (price and yield data for Canadian government
securities)
www.govpx.com (price and yield data for U.S. Treasuries)
www.bloomberg.com (current U.S. Treasury rates)
www.fin.gc.ca (current Canadian Treasury securities)
www.smartmoney.com/bonds (view a “living yield curve” *exceptional*)
www.publicdebt.treas.gov (information on STRIPS, and other U.S. debt)
© 2009 McGraw-Hill Ryerson
Limited
10- 31