The Risk and Term Structure The Risk and Term Structure of Interest Ratesof Interest Rates

Chapter 5Chapter 5

The Term Structure of Rates The Term Structure of Rates and the Yield Curveand the Yield Curve

Term StructureTerm Structure– Relationship among yields of different Relationship among yields of different

maturities of the same type of security.maturities of the same type of security.

Yield Curve Yield Curve – Graphical relationship between yield and Graphical relationship between yield and

maturity.maturity.

Empirical FactsEmpirical Facts

Interest rates on bonds of different maturities Interest rates on bonds of different maturities move together over time.move together over time.

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

Yield curves almost always slope upward.Yield curves almost always slope upward.

Different Theories of the Shape Different Theories of the Shape of the Yield Curveof the Yield Curve

Supply and DemandSupply and Demand– Determined by relative supply/demand of Determined by relative supply/demand of

different maturitiesdifferent maturities– Deals with each maturity by itself and ignores Deals with each maturity by itself and ignores

the the interrelationshipsinterrelationships between different between different maturities of the same securitymaturities of the same security

Expectations HypothesisExpectations Hypothesis

The shape of the yield curve is determined by the The shape of the yield curve is determined by the investors’ expectations of future interest rate investors’ expectations of future interest rate movements.movements.

The interest rate on the long-term bond will equal an The interest rate on the long-term bond will equal an average of short-term interest rates that people expect to average of short-term interest rates that people expect to occur over the life of the long-term bond.occur over the life of the long-term bond.

If the one-year interest rate over the next five years is If the one-year interest rate over the next five years is expected to be 5, 6, 7, 8, 9 percent, expected to be 5, 6, 7, 8, 9 percent, – then the interest rate on the two-year bond would be 5.5%.then the interest rate on the two-year bond would be 5.5%.– While for the five-year bond it would be 7%.While for the five-year bond it would be 7%.

Investors are indifferent between short and long-term Investors are indifferent between short and long-term securities.securities.

Liquidity Premium ModificationLiquidity Premium Modification

Investors know from experience that short-term Investors know from experience that short-term securities provide greater marketability and have securities provide greater marketability and have smaller price fluctuations than do long-term smaller price fluctuations than do long-term securities. securities.

The liquidity premium is that premium demanded The liquidity premium is that premium demanded for holding long-term securities.for holding long-term securities.

Therefore, a two-year security would have to Therefore, a two-year security would have to yield more than the average of the two one-year yield more than the average of the two one-year securities as a reward for bearing more risk.securities as a reward for bearing more risk.

The Preferred Habitat ApproachThe Preferred Habitat Approach

The interest rate on a long-term bond will equal an The interest rate on a long-term bond will equal an average of short-term interest rates expected to occur average of short-term interest rates expected to occur over the life of the long-term bond plus a term (liquidity) over the life of the long-term bond plus a term (liquidity) premium that responds to supply and demand conditions premium that responds to supply and demand conditions for that bond.for that bond.

If investors prefer the habitat of short-term bonds over If investors prefer the habitat of short-term bonds over long-term bonds, they might be willing to hold short-term long-term bonds, they might be willing to hold short-term bonds even though they have a lower expected return. bonds even though they have a lower expected return. This means that investors would have to be paid a This means that investors would have to be paid a positive term premium to be willing to hold a long-term positive term premium to be willing to hold a long-term bond.bond.

Real-World ObservationsReal-World Observations

When interest rates are high relative to When interest rates are high relative to past rates, investors past rates, investors expect expect them to them to decline and the price of bonds to rise in decline and the price of bonds to rise in the future resulting in big capital gains the future resulting in big capital gains

Investors would then favor long-term Investors would then favor long-term securities, which drives up price and securities, which drives up price and lowers yield—downward sloping yield lowers yield—downward sloping yield curvecurve

Real-World ObservationsReal-World Observations

If interest rates are low relative to past—If interest rates are low relative to past—results in an upward sloping curveresults in an upward sloping curveHistorically, over the business cycle Historically, over the business cycle short-short-term rates fluctuate more than longer-term rates fluctuate more than longer-term rates term rates Yield curves tend to be upward sloping Yield curves tend to be upward sloping more often, suggesting the more often, suggesting the liquidity liquidity premiumpremium is the dominate theory is the dominate theory

Summary of Term Structure Summary of Term Structure TheoryTheory

Expectations theory forms the foundation Expectations theory forms the foundation of the slope of the curveof the slope of the curveLiquidity premium theory makes a long-Liquidity premium theory makes a long-term permanent modification that suggests term permanent modification that suggests an upward sloping curvean upward sloping curveOver short periods, relative supplies of Over short periods, relative supplies of securities have an impact on yields, securities have an impact on yields, altering the shape of the curvealtering the shape of the curve

Government BondsGovernment Bonds

Reading the WSJ.Reading the WSJ.

Current coupon or on the run issue.Current coupon or on the run issue.

MarketabilityMarketability

Recently issued government bonds Recently issued government bonds (current coupon—“(current coupon—“on the runon the run”) are more ”) are more marketable than older issues (“marketable than older issues (“off the off the runrun”)”)– Because these newly issued bonds are highly Because these newly issued bonds are highly

marketable, they carry somewhat lower yields marketable, they carry somewhat lower yields to maturity as compared to older issues to maturity as compared to older issues 

Default RiskDefault Risk

Other than US Federal government securities, Other than US Federal government securities, bonds carry a risk of bonds carry a risk of defaultdefaultRisk on Risk on municipal bondsmunicipal bonds used to be used to be considered very lowconsidered very low– However, experience of New York City (1975), However, experience of New York City (1975),

Cleveland (1978) and Orange Country, California Cleveland (1978) and Orange Country, California (1995) suggest these bonds are becoming riskier(1995) suggest these bonds are becoming riskier

Corporate bonds generally have a higher Corporate bonds generally have a higher default riskdefault risk than municipal bonds than municipal bondsInvestors will expect higher return to Investors will expect higher return to compensate for increased default risk compensate for increased default risk

Default RiskDefault Risk

Standard and Poor’s and Moody’s Standard and Poor’s and Moody’s Investors Service rate the default risk on Investors Service rate the default risk on bonds which serve as a guide to investorsbonds which serve as a guide to investorsThe introduction of risk in the yield curve The introduction of risk in the yield curve will cause the curve to shift since another will cause the curve to shift since another variable other than “maturity” has changed variable other than “maturity” has changed The higher the perceived risk, the greater The higher the perceived risk, the greater the upward shift of the curve for that the upward shift of the curve for that particular securityparticular security

Risk and Tax Structure of RatesRisk and Tax Structure of Rates

Investors are concerned about the Investors are concerned about the after after tax returntax return on bonds on bonds

Although municipal bonds are riskier than Although municipal bonds are riskier than federal government bonds, federal government bonds, tax exempt tax exempt statusstatus of municipal bonds will generally of municipal bonds will generally result in a lower yield (downward shift of result in a lower yield (downward shift of the curve)the curve)

Duration ExampleDuration Example

Given two bonds A Given two bonds A and B, which has and B, which has more interest rate more interest rate risk?risk?

Bond ABond A Bond BBond B

CouponCoupon 8%8% 10%10%

MaturityMaturity 8 years8 years 10 years10 years

Duration ExampleDuration Example

Given two bonds A Given two bonds A and B, which has and B, which has more interest rate more interest rate risk?risk?

Bond ABond A Bond BBond B

CouponCoupon 8%8% 10%10%

MaturityMaturity 8 years8 years 10 years10 years