Com 4FJ3
Fixed Income Analysis
Week 3
Determinants of Interest Rates
Base Interest Rate
• Defined as the minimum interest rate that
investors would require for an investment of
a particular maturity
• Often referred to as a benchmark rate
• Typically the “on the run” treasury notes
– on the run; issued during the most recent
treasury auction
– not all maturities represented
2
Sample On the Run Rates
April 4, 2003
Maturity
Yield
3 months
1.10%
6 months
1.10%
1 year
1.15%
2 years
1.54%
5 years
2.84%
10 years
3.95%
30 years
4.96%
3
Yield Spread
• The difference between the base rate and
the YTM of an issue
• Often called the risk premium
– Verizon (A1), 10 year bond yields 4.93%
– US Treasury, 10 year bond yields 3.95%
– Yield spread = 4.93 - 3.95 = 0.98%
= 98 basis points
4
Yield Ratio
• Sometimes you want to present spreads as a
relative measure
– Verizon (A1), 10 year bond yields 4.93%
– US Treasury, 10 year bond yields 3.95%
– Yield ratio = 4.93/3.95 = 1.248
• May be more useful if interest rates are
highly volatile
5
Type of Issuer
• Different market sectors in bond market
have different characteristics; US Gov’t,
foreign Gov’t, credit, municipal, etc.
• Subsectors in credit market; industrial,
utility, finance, and noncorporate
• Intermarket sector spread; the difference
between the average rates in a sector and
the corresponding treasury
6
Credit Rating
• Usually credit quality is not calculated by
individuals but left up to major credit rating
companies.
• USA; Moody’s, S&P, Fitch
Aaa, AAA, AAA  C, D, D
• Canada; Dominion, & Canadian
AAA, A++  C, D
7
Rating Categories
Dominion
(DBRS)
Canadian
Quality
Grade
(CBRS)
AAA
AA
A
BBB
BB
B
CCC
CC
C
A++
A+
A
B++
B+
B
C
D
NR
NR
High
Investment
Medium
Low
Speculative
Very Low
Not Rated
Bonds rated CC, C or D are actually in default.
8
Quality Spread
• Also known as credit spread
• That part of the spread that is explained by
the difference in credit rating
• Should compare bonds that are “identical in
all respects except for quality”
• Often awkward to set up in practice
9
Embedded Options
• Call options and others that are beneficial to
the issuer will cause the risk premium to be
larger than bonds without those options
• Put, conversion, extendible, etc. options that
benefit the buyer will reduce the spread
– Can drive YTM below treasury bill yields
– Can even drive YTM negative
10
Taxation in USA
• Municipal bonds not taxed federally
• Treasury bond interest not taxed by
municipalities, so part of the spread
between treasuries and corporate bonds is
actually not a credit spread
• Some states tax both, neither, or some
combination
11
After-Tax Yield
• To compare yields, express all on an aftertax basis, multiply by (1 - marginal rate)
– Complication, not all investors have same rate
– Given a bond with a 5% pre-tax yield
• 40% tax rate investor: (5%)(1 - .4) = 3.0%
• 30% tax rate investor: (5%)(1 - .3) = 3.5%
• Can also calculate equivalent taxable yield
tax exempt yield
Equivalent taxable yield 
1  maginal tax rate
12
More Taxation
• Tax rates on interest and capital gains are
different; high marginal tax rate investors
have an incentive to buy discount bonds
• RRSP holdings are tax deferred, all income
is treated the same… so, an incentive to buy
premium bonds
13
Liquidity
• The more frequently a bond is traded, the
lower the bid/ask spread
• Therefore issues with high liquidity have
lower required yields
• Part of yield spread over treasury is due to
lower liquidity since treasuries are usually
the most liquid bonds
14
Financeability
• If a bond can easily be used as collateral for
short term borrowing, it can have a lower
yield spread
• Repo market can see a high demand for
some issues as security dealers need access
to those issues to “cover their shorts,” this
can increase the value of the issue and drive
down the yield spread
15
Term to Maturity
• Value of bond changes over time as the
term to maturity changes
• Three main maturity sectors in bond market
– Short-term; 1 - 5 years
– Intermediate term; 5 - 12 years
– Long-term; greater than 12 years
• Less than 1 year = money market
16
Yield Curve
• Different maturities have different required
yields
• A plot of the required yields vs. time to
maturity is call a yield curve
• Not all bonds will fall on the yield curve
– Consider 2, 5-year treasury bonds with coupons
of 12% and 3%, YTM is likely to be different
17
Yield Curve; September 1982
U.S. Yield Curve Dynamics
16%
Yield to Maturity
14%
12%
10%
8%
6%
4%
2%
0%
0
5
10
15
20
25
30
Time to Maturity
18
Yield Curve; March 1980
U.S. Yield Curve Dynamics
16%
Yield to Maturity
14%
12%
10%
8%
6%
4%
2%
0%
0
5
10
15
20
25
30
Time to Maturity
19
Yield Curve; January 1970
U.S. Yield Curve Dynamics
16%
Yield to Maturity
14%
12%
10%
8%
6%
4%
2%
0%
0
5
10
15
20
25
30
Time to Maturity
20
Yield Curve Concerns
• Using YTM as single discount rates does
not consider information in yield curve
• Bonds can be considered as a package of
zero coupon bonds
• Each cashflow could have an appropriate
discount rate based on the term structure of
interest rates or theoretical spot rate
21
Term Structure of Interest Rates
• The theoretical spot rate for zero coupon
bonds for each maturity in the market
• Can be calculated by bootstrapping
• Often done with on the run treasury bonds
assuming that they should trade at par
22
Bootstrapping Example
• A six month bond has a YTM of 5.25%
• A one-year par bond has a YTM of 5.5%
– Present value the cash received at end of 6
months and 1 year, calculate the pure discount
1 year rate
P  100 
2.875
102.875
102.875


2
.
8014

2
 0.0525   x  2
x


1 
 1  
1 

2   2

 2
x  5.757%
23
Bootstrapping
• See the text for an enhanced example
• Calculate each six month rate over the 30
year maturity of the long treasury bond
• For missing maturities, use linear
interpolation of the required YTM
– can cause problems due to the fact that there are
many maturities with no on the run treasuries to
use… particularly between 10 and 30 years
24
Other Methods
• Other source groups of bonds can be used
– On the run and select off the run
– All treasury bonds; but sophisticated techniques
needed as not all bonds of a particular maturity
have the same yield, e.g. exponential spline
– Treasury coupon strips: created by securities
dealers, already pure discount, but include some
liquidity and taxation issues
25
Using Theoretical Spot Rates
• Instead of discounting all spot rates at YTM
discount each cashflow at the appropriate
rate and sum the present values (p. 108)
– Note: the price in this example is not what you
get from YTM due to rounding and missing
data for term structure
• Since securities dealers can split up those
coupons we should expect to see that price
26
Implicit Forward Contracts
• A contract that commits both parties to a
specific transaction in the future is a
forward contract.
• A bank offering to pay you 10% interest on
a $1,100 deposit that you agree to make one
year from today, is offering a forward
contract.
27
Implicit Forward Contracts
• If the bank is currently offering a one year rate of
10% and a 10% two year rate.
• Accepting that two year rate would be equivalent
to accepting the one year rate with a $1,000
investment now and also entering into the forward
contract detailed above.
• With the rates that the bank is offering, the bank
implies that they would be willing to enter into
that forward contract.
28
Forward Rates
• How can we find the forward rate?
• The basic tactic is to find the future value of the
two investments and then future value the shorter
investment to find the rate that would set the two
investments equal.
• Consider a 5-year GIC at 6% e. a. r. and a 7-year
GIC at 6.5% e. a. r.
• What is the effective annual rate that you are
implicitly being offered for the final 2 years of the
investment?
29
Forward Rates
1  r5   1  f   1  r7 
7


1

r
2
7
1  f  
5
1  r5 
5
2
7
f  7.76%
• The investment effectively pays 7.76% in
years 6 and 7.
30
Which is Better?
• It depends on you expect interest rates to be in 6 years.
• If you expect interest rates to be greater than 7.76% six
years from now, you should choose the 5-year GIC and
reinvest the proceeds in a two-year GIC.
• If you think that interest rates are unlikely to be that high,
the 7-year investment will be a better option.
• Of course if you need to have the money available in five
years and you are not allowed to sell or cancel the GIC
before maturity, you'd want the five-year investment.
• The term structure can therefore be used to gauge what the
market believes interest rates will be in the future.
31
Market Consensus Rates
• Forward rates calculated from bond market
yields are often called market consensus
rates
• Some don’t like the implication of the
above and refer to the forward rate as a
hedgeable rate, since you can hedge the 6
month rate six months from now using 6
month and one year t-bills
32
Term Structure Theory
• What do the calculated forward rates tell us
about the market participant’s forecast of
future interest rates
• 2 main theories;
– expectations theory
• pure expectation vs. biased expectation
– market segmentation
33
Unbiased Expectations Theory
• Also know as pure expectations theory
• UET says that the forward rates calculated
by examining the bond market is the market
estimate of the future rate of interest.
• If the forward rate is too high, speculators
will want to lock in lending, causing high
supply, driving the rate down.
34
Subsets of Pure Expectations
• Local Expectations Theory
– The expected return on holding the bond is the
same for all maturities for short holing periods
• Return-to-maturity expectations theory
– The expected return on a 5 year pure discount
bond is the same as the expected return of a
series of 6 month bonds
35
Biased Expectations Theory
• Investing in bonds with maturities other
than what your planning horizon increases
the level of risk an investor faces
• Investors will add a risk premium to bonds
in addition to their forecast level of future
interest rates
36
Liquidity (Preference) Theory
• LPT says that longer maturities have more
risk (interest and reinvestment) and
therefore long rates are higher than the
market participants actual expectations to
compensate for the added risk.
• This liquidity premium is positively related
to the time to maturity
37
Preferred Habitat
• Which is riskier, a 2-year zero or a 1-year zero
reinvested for a second year?
• Depending on an investor’s needs, longer bonds
could be less risky than short bonds
• This theory says that market participants have
preferences and can only be lured to other
maturities by better rates
• The risk premium in bonds is not necessarily
directly related to the time to maturity
38
Market Segmentation Theory
• MST says that the markets for different maturities
are virtually independent and the forward rates
calculated are meaningless
• Money market participants will not look at long
bonds or even medium bonds, long bond buyers
are unconcerned with money market rates
• There are not enough speculators to balance the
markets
39
PH vs. MST
• The strong version of market segmentation
says market participants will not be swayed,
even by 1 year in time to maturity, by price
differences
• In the weak version, market participants
will consider other maturities, depending on
prices, is virtually indistinguishable from
the preferred habitat expectations theory
40
Summary
• There is not just 1 interest rate
• Yield spread over treasury is common, for
credit, liquidity, options, etc.
• Yield curve for treasuries can be converted
to term structure of interest rates
• Exactly how the market forecast of interest
rates affect the term structure is debatable
41