11

The Risk and Term Structure of Interest Rates

Chapter 6

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Why Do Bonds With Same Why Do Bonds With Same Maturity Have Different Prices?Maturity Have Different Prices?

Some might be riskier than others.Some might be riskier than others.Some might be more liquid than others.Some might be more liquid than others.Some might have lower taxes than others.Some might have lower taxes than others.Collectively, these influences are called Collectively, these influences are called

““risk structure of interest ratesrisk structure of interest rates.”.”Of course, if prices of various bonds differ Of course, if prices of various bonds differ

so do their yield to maturity.so do their yield to maturity.

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Risk Structure of Interest RatesRisk Structure of Interest Rates

Default riskDefault risk - inability of the bond issuer - inability of the bond issuer to pay interest or face value.to pay interest or face value.

Liquidity riskLiquidity risk - inability to find a buyer - inability to find a buyer when one decides to sell her bond when one decides to sell her bond before it matures.before it matures.

Income taxIncome tax - interest earnings on - interest earnings on municipal bonds are free from federal municipal bonds are free from federal income tax.income tax.

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Default RiskDefault RiskUS Treasury bonds are risk free.US Treasury bonds are risk free.

Congress can raise taxes.Congress can raise taxes.Federal government can print money.Federal government can print money.

The interest difference between a default-The interest difference between a default-free bond and one with default risk is called free bond and one with default risk is called ““risk premiumrisk premium.”.”

Buyers of bonds have to get higher interest Buyers of bonds have to get higher interest bonds (lower price bonds) to persuade bonds (lower price bonds) to persuade them to buy the riskier bonds.them to buy the riskier bonds.

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Long-Term Bond Yields, 1919–2008Long-Term Bond Yields, 1919–2008

Sources:Sources: Board of Governors of the Federal Reserve System, Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970Banking and Monetary Statistics, 1941–1970 ; Federal Reserve: ; Federal Reserve: www.federalreserve.gov/releases/h15/data.htmwww.federalreserve.gov/releases/h15/data.htm

..

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Why Do Similar Bonds With Different Why Do Similar Bonds With Different Maturities Have Different Prices?Maturities Have Different Prices?

Two bonds could be identical in their risk Two bonds could be identical in their risk structure but they may have different yield structure but they may have different yield to maturity if their maturities differ.to maturity if their maturities differ.

This is called “This is called “term structure of interest term structure of interest ratesrates.”.”

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Interest Rates on U.S. Government Interest Rates on U.S. Government Bonds with Different MaturitiesBonds with Different Maturities

Sources:Sources: Federal Reserve: Federal Reserve: www.federalreserve.gov/releases/h15/data.htmwww.federalreserve.gov/releases/h15/data.htm

..

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Increase in Default Risk on Increase in Default Risk on Corporate BondsCorporate Bonds

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Application: The Subprime Application: The Subprime Collapse and the Baa-Treasury Collapse and the Baa-Treasury

SpreadSpreadCorporate Bond Risk Premium and Flight to

Quality

0

2

4

6

8

10

Corporate bonds, monthly data Aaa-RateCorporate bonds, monthly data Baa-Rate10-year maturity Treasury bonds, monthly data

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Interest Rate Differentials During Recession

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1990 1990.5 1991 1991.5 1992Months

Inte

rest

Rat

es Series1Series2Series3

Series 1 is Moody’s Baa Corporate Bond Yield. Series 2 is 1-yr Treasury Constant Maturity Rate. Series 3 is the difference between the two. Source: http://www.stls.frb.org/fred/data/irates.html (Discontinued).

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http://research.stlouisfed.org/fred2/categories/22/1

During the 2001 recession, Baa yields fell from 8.5% to 8%; treasuries fell from 6% to below 4%, adding 3.5% to the risk premium.

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Decline in Corporate Bond RiskDecline in Corporate Bond Risk

P1

P1

Q of US bonds Q of corporate bonds

P2P2

White arrow shows the risk premium initially. Red arrow isthe new risk premium.

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Risk PremiumRisk Premium

During recessions default risk generally During recessions default risk generally rises.rises.

Rating agencies evaluate single Rating agencies evaluate single companies and issue a rating indicating companies and issue a rating indicating the default risk of the company’s bonds.the default risk of the company’s bonds.

Rating agencies also evaluate the Rating agencies also evaluate the default risk of foreign bonds.default risk of foreign bonds.

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http://www.economist.com/finance/displaystory.cfm?story_id=8628827

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LiquidityLiquidity

The more liquid an asset is, the quicker The more liquid an asset is, the quicker and cheaper it can be converted to and cheaper it can be converted to cash.cash.Cheaper means lower transaction cost.Cheaper means lower transaction cost.

The more liquid an asset is the higher The more liquid an asset is the higher the demand for it.the demand for it.

What happens to the risk premium if What happens to the risk premium if corporate bonds become less liquid?corporate bonds become less liquid?

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Corporate Bonds Become Less LiquidCorporate Bonds Become Less Liquid

Q of Corporate Bonds Q of T-bonds

i

ii

i

PP

Initially, corporate bond market and T-bond market are at equilibrium at the intersection of white S and D. Corporate bonds have lower P and higher I. Less liquidity increases the D for T-bonds and reduces the D for corporate bonds. Interest rates on corporate bonds rise, on T-bonds fall.

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Municipal BondsMunicipal Bonds

Municipal bonds have lower interest Municipal bonds have lower interest rates than T-bonds.rates than T-bonds.

Municipal bonds are not risk-free.Municipal bonds are not risk-free.Cleveland defaulted in early 1970s.Cleveland defaulted in early 1970s.New York defaulted in late 1970s.New York defaulted in late 1970s.Orange County, California defaulted in Orange County, California defaulted in

1994.1994. Is there a contradiction?Is there a contradiction?

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Tax Advantage of Municipal BondsTax Advantage of Municipal Bonds Earnings from municipal bonds are exempt from Earnings from municipal bonds are exempt from

federal income tax.federal income tax. A person at 33% income tax bracket can earn a A person at 33% income tax bracket can earn a

higher after-tax return from a riskier municipal higher after-tax return from a riskier municipal bond than a risk-free T-bond.bond than a risk-free T-bond.

$1000 face-value T-bond with 10% coupon rate $1000 face-value T-bond with 10% coupon rate selling for $1000 would yield $67 after-tax selling for $1000 would yield $67 after-tax income to this person.income to this person.

$1000 face-value muni-bond with 8% coupon $1000 face-value muni-bond with 8% coupon rate selling for $1000 would yield $80 after-tax rate selling for $1000 would yield $80 after-tax income to this person.income to this person.

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The Effect of Tax Elimination on The Effect of Tax Elimination on Municipal BondsMunicipal Bonds

Q of Muni Bonds Q of T-bonds

PP

ii

Assuming similar risk and liquidity we start with same P and i.Eliminating taxes for munis would increase the demand for them,While reducing the demand for T-bonds.

i

P

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What Would Happen If the Top What Would Happen If the Top Tax Rate Were Increased?Tax Rate Were Increased?

D for munis will increase.D for munis will increase.D for T-bonds will decrease.D for T-bonds will decrease.P of munis will rise.P of munis will rise.P of T-bonds will drop.P of T-bonds will drop. Interest rates on munis will fall.Interest rates on munis will fall. Interest rates on T-bonds will rise.Interest rates on T-bonds will rise.

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Term Structure of Interest RatesTerm Structure of Interest Rates

Bonds with identical risk, liquidity and Bonds with identical risk, liquidity and tax considerations may have different tax considerations may have different interest rates because of their maturity.interest rates because of their maturity.Typically, bonds with maturity far into the Typically, bonds with maturity far into the

future have higher interest rates than future have higher interest rates than bonds that will mature soon.bonds that will mature soon.

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Yield CurvesYield CurvesYields of different maturity but identical risk, Yields of different maturity but identical risk,

liquidity, tax characteristics are plotted. liquidity, tax characteristics are plotted. Yield curves typically move upwards, but Yield curves typically move upwards, but

sometimes they are flat or downward sometimes they are flat or downward sloping.sloping.When short term interest rates are high yield When short term interest rates are high yield

curves may be inverted.curves may be inverted.Yield curves at different dates usually show Yield curves at different dates usually show

that short and long term interest rates move that short and long term interest rates move up and down together.up and down together.

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Term-structure of Interest RatesTerm-structure of Interest Rates

Source: http://www.stls.frb.org/docs/publications/mt/2000/cover4.pdf

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Term Structure of Term Structure of Interest RatesInterest Rates

Bonds with identical risk, liquidity, and tax Bonds with identical risk, liquidity, and tax characteristics may have different interest rates characteristics may have different interest rates because the time remaining to maturity is differentbecause the time remaining to maturity is different

Yield curve—a plot of the yield on bonds with differing Yield curve—a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax terms to maturity but the same risk, liquidity and tax considerationsconsiderations Upward-sloping Upward-sloping long-term rates are above long-term rates are above

short-term ratesshort-term rates

Flat Flat short- and long-term rates are the same short- and long-term rates are the same

Inverted Inverted long-term rates are below short-term rates long-term rates are below short-term rates

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FactsFacts1.1. Interest rates on bonds of different Interest rates on bonds of different

maturities move together over timematurities move together over time

2.2. When short-term interest rates are low, When short-term interest rates are low, yield curves are more likely to have an yield curves are more likely to have an upward slope; when short-term rates are upward slope; when short-term rates are high, yield curves are more likely to slope high, yield curves are more likely to slope downward and be inverteddownward and be inverted

3.3. Yield curves almost always slope upwardYield curves almost always slope upward

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Explaining Yield CurvesExplaining Yield Curves

The expectations theoryThe expectations theoryThe segmented markets theoryThe segmented markets theoryThe liquidity premium theoryThe liquidity premium theory

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Expectations TheoryExpectations TheoryExplains why interest rates move together.Explains why interest rates move together.Explains why when short-term interest Explains why when short-term interest

rates are low, yield curves are more likely rates are low, yield curves are more likely to be upward sloping.to be upward sloping.

Explains why when short-term interest Explains why when short-term interest rates are high, yield curves are more likely rates are high, yield curves are more likely to be downward sloping.to be downward sloping.

Doesn’t explain why yield curves are Doesn’t explain why yield curves are usually upward sloping.usually upward sloping.

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Expectations TheoryExpectations Theory

Assume bonds with different maturities are Assume bonds with different maturities are perfect substitutes.perfect substitutes.

Demand for bonds with higher yield will be Demand for bonds with higher yield will be higher.higher. Their prices will go up and their yields will decline.Their prices will go up and their yields will decline. Yields on different maturity bonds will be equal.Yields on different maturity bonds will be equal.

How can you have an upward (or downward) How can you have an upward (or downward) sloping yield curve if the expected yields on sloping yield curve if the expected yields on different maturity bonds is the same?different maturity bonds is the same?

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An ExampleAn Example

Suppose you consider to save your funds for a Suppose you consider to save your funds for a period of four years.period of four years.

You can put these funds in a four-year bond or you You can put these funds in a four-year bond or you can put them in four successive one-year bonds.can put them in four successive one-year bonds.

Expectations theory says the returns from these Expectations theory says the returns from these two choices should be the same.two choices should be the same.

If the expected yearly returns for the next four If the expected yearly returns for the next four years are 6%, 7%, 8%, and 9%, then the return on years are 6%, 7%, 8%, and 9%, then the return on the four-year bond should be 7.5%.the four-year bond should be 7.5%.

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Expectations TheoryExpectations Theory If short term interest rates have been inching up If short term interest rates have been inching up

(down), people will expect them to increase (down), people will expect them to increase (decrease) in the future, too.(decrease) in the future, too. Short and long-term rates will move together.Short and long-term rates will move together.

If short-term rates are unusually high (low), people If short-term rates are unusually high (low), people will expect them to move down (up) in the future.will expect them to move down (up) in the future. Inverted (regular) yield curve.Inverted (regular) yield curve.

Chances of interest rates moving in either direction Chances of interest rates moving in either direction are equal. We shouldn’t see primarily upward are equal. We shouldn’t see primarily upward sloping yield curves.sloping yield curves.

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Segmented Markets TheorySegmented Markets TheoryAssumption: different maturity bonds are not Assumption: different maturity bonds are not

substitutes.substitutes.People with a short holding period will buy People with a short holding period will buy

short-term bonds, people with a long holding short-term bonds, people with a long holding period will buy long-term bonds.period will buy long-term bonds.

Interest rates on these bonds will be Interest rates on these bonds will be determined by the specific supply and determined by the specific supply and demand of the short and long bond markets.demand of the short and long bond markets.

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Segmented Markets TheorySegmented Markets TheoryWhy do yield curves usually have an Why do yield curves usually have an

upward slope?upward slope?Typically, long-term bonds will carry higher Typically, long-term bonds will carry higher

interest rate risk so will have a lower demand, interest rate risk so will have a lower demand, lower price and higher interest rate.lower price and higher interest rate.

Why do interest rates move together?Why do interest rates move together?Segmented Markets Theory cannot explain this.Segmented Markets Theory cannot explain this.

Why when short-term interest rates are Why when short-term interest rates are high, yield curves are inverted?high, yield curves are inverted?Segmented Markets Theory cannot explain this.Segmented Markets Theory cannot explain this.

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Liquidity Premium TheoryLiquidity Premium Theory

Interest rate on a long-term bond will be equal Interest rate on a long-term bond will be equal to the average of expected short term returns to the average of expected short term returns plus a liquidity premium that reflects the lower plus a liquidity premium that reflects the lower demand for long-term (high interest rate risk) demand for long-term (high interest rate risk) bonds.bonds.

Liquidity premium on a five-year bond will be Liquidity premium on a five-year bond will be lower than a ten-year bond.lower than a ten-year bond. Bonds of different maturities are partial (not Bonds of different maturities are partial (not

perfect) substitutesperfect) substitutes

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Liquidity Premium TheoryLiquidity Premium Theory

Even if the expected future interest Even if the expected future interest rates were to remain constant, liquidity rates were to remain constant, liquidity premium will show an upward sloping premium will show an upward sloping yield curve.yield curve.

Yield curve will be mildly rising if future Yield curve will be mildly rising if future short term rates were expected to fall.short term rates were expected to fall.

An inverted curve indicates a sharp fall An inverted curve indicates a sharp fall in the expected future short term rates.in the expected future short term rates.

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Preferred Habitat TheoryPreferred Habitat Theory

Investors have a preference for bonds of Investors have a preference for bonds of one maturity over anotherone maturity over another

They will be willing to buy bonds of They will be willing to buy bonds of different maturities only if they earn a different maturities only if they earn a somewhat higher expected returnsomewhat higher expected return

Investors are likely to prefer short-term Investors are likely to prefer short-term bonds over longer-term bondsbonds over longer-term bonds

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Liquidity Premium (Preferred Liquidity Premium (Preferred Habitat) and Expectations TheoryHabitat) and Expectations Theory

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Why the Yield Curve Became Why the Yield Curve Became Inverted in 2000?Inverted in 2000?

Do we expect a lower inflation 10, 30 years in the Do we expect a lower inflation 10, 30 years in the future?future? Perhaps; but a current inflation rate of 3-3.5% is already Perhaps; but a current inflation rate of 3-3.5% is already

low.low.

Do we have a lower liquidity premium than before?Do we have a lower liquidity premium than before? Unlikely. Unlikely.

Is there an unusual supply-demand condition in the Is there an unusual supply-demand condition in the long-term bond market?long-term bond market? Yes. The federal government announced retirement of Yes. The federal government announced retirement of

debt.debt. Read the one-page explanation of St. Louis Fed at Read the one-page explanation of St. Louis Fed at

http://research.stlouisfed.org/publications/mt/20000401/cover.pdfhttp://research.stlouisfed.org/publications/mt/20000401/cover.pdf

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Yield Curves for U.S. Government BondsYield Curves for U.S. Government Bonds

Sources:Sources: Federal Reserve Bank of St. Louis; Federal Reserve Bank of St. Louis; U.S. Financial DataU.S. Financial Data, various issues; , various issues; Wall Street JournalWall Street Journal, , various dates.various dates.

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