Com 4FJ3

Fixed Income Analysis

Week 3

Determinants of Interest Rates

2

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

3

Sample On the Run Rates

Maturity Yield3 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%

April 4, 2003

4

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

5

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

6

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

7

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, & CanadianAAA, A++ C, D

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Rating Categories

Dominion(DBRS)

Canadian(CBRS)

Quality Grade

AAA A++

AA A+High

A A

BBB B++

Investment

Medium

BB B+

B BLow

CCC C

CC D

C

Speculative

Very Low

NR NR Not RatedBonds rated CC, C or D are actually in default.

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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

10

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

11

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

12

After-Tax Yield

• To compare yields, express all on an after-tax 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

rate tax maginal 1

yieldexempt tax yield taxableEquivalent

13

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

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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

15

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

16

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

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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

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Yield Curve; September 1982

U.S. Yield Curve Dynamics

0%

2%

4%

6%

8%

10%

12%

14%

16%

0 5 10 15 20 25 30

Time to Maturity

Yie

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Yield Curve; March 1980

U.S. Yield Curve Dynamics

0%

2%

4%

6%

8%

10%

12%

14%

16%

0 5 10 15 20 25 30

Time to Maturity

Yie

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Yield Curve; January 1970

U.S. Yield Curve Dynamics

0%

2%

4%

6%

8%

10%

12%

14%

16%

0 5 10 15 20 25 30

Time to Maturity

Yie

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rity

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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

22

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

23

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

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21

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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

25

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

26

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

27

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.

28

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.

29

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?

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Forward Rates

• The investment effectively pays 7.76% in years 6 and 7.

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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.

32

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

33

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

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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.

35

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

36

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

37

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

38

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

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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

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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

41

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