Chapter 7

Risk Structure and Term Structure of Interest

Rates

Risk Structure of Interest Rates

• A bond is a promise to make a future payment. However, the promise might not be kept.

• An issuer of a bond might be said to be in default if they miss a payment of interest or principal.

• Though all bonds involve some risk, for all practical purposes, are default-free. In the $US bond market, U.S. Treasury bonds are the benchmark default free bond. In HK, Exchange Fund bonds play this role. (Be careful, not all government debt is risk-free).

• A bond with a significant probability of default must pay a higher yield to compensate purchasers for the risk. This is called a Default risk premium.

• Bond rating agencies (Moody’s and Standard & Poors assess default risk for bonds).

• Default-risk premium = bond yield - yield on a comparable default-risk-free bond.

Basis Points

• Yields are typically not integers in percentage points e.g. i=5.78% or 3.37%

• One one-hundredth of an interest rate is referred to as a basis point. Risk premium are often measured in basis points.

• If an Exchange fund bond is yielding at 2.4% and a Hutchison bond is selling at 2.84%, the risk premium is .44% or 44 basis points.

Market Segments

• Divide the Bond Market into two sub-markets:. The first is a market for low-default-risk debt, the second is a market for

• There is a supply and demand for bonds of each type.

• High default risk debt has a lower equilibrium price and the difference expresses the risk premium.

Flight to Quality

• An increase in risk reduces portfolio demand for high-risk debt and increases portfolio demand for low-risk debt (at every price).

• An increase in risk shifts demand curve for high-risk debt in and shifts demand curve for low risk debt out.

• The price of high-risk debt will fall and the price of low-risk debt will rise. Yields on high-risk debt will rise and yield on low-risk debt will fall.

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Liquidity Premium

• Liquid vs. Illiquid Bonds – Markets for some bonds are thick, I.e. at any point in time there are many buyers and sellers.

• Easy to find a buyer for a government bond. Less easy to find buyer for corporate debt, especially small corporations. Government bonds very liquid.

• An increase in liquidity in illiquid markets will reduce the liquidity spread.

• Example: Michael Milken, Drexel Burnham Lambert, and Junk Bonds.

Term Structure of Interest Rates

• The same borrower often issues debt of different maturities at the same time.

• For example there are Exchange Fund bonds of different maturity yields.

1. A bond with an initial maturity date 1 year or less is referred to as a bill.

2. A bond with an initial maturity date between 1 year and 10 years is a note.

3. A bond with an initial maturity date of greater than 10 years is a bond.

History of Exchange Fund Notes

• On average, yields on later maturing bonds are larger than average on short bonds.

• Bond yields tend to move together. – Correlation 1-Year with 2-Year = 98%– Correlation 1-Year with 5-Year= 90%– Correlation 1-Year with 10-Year = 85%

Mean Yield Curve

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8

1 Year 2 Year 3 Year 5 Year 10Year

Yield

Matu

rity Series1

Segmented Market Theory

• Long-term bonds have different (liquidity, risk, information) characteristics than short-term bonds.

• If portfolio holders of short-term bills and notes are fundamentally different than holders of long-term bonds, the two markets may be essentially independent.

• Prices and yields of long-term bonds have essentially no relationship.

• Long-term bonds have greater interest rate risk and less liquidity. This explains why long-term bonds have greater yields on average.

Expectations Theory

• Portfolio holders are indifferent between long and short-term bonds.

• Yield to maturity over the life of a long-term bond must be equal to average yields on repeated rollovers of short-term bond holdings during the same period.

• Consider two strategies which should have the same expected pay-off. Starting with $1.

1. Buy a two year discount bond and hold it for two years. Payoff:

2. Buy a 1 year bond. After 1 year, invest pay-off in another 1 year bond. Payoff:

• Equal pay-offs imply that yield on a two year bond is equal to the expected average yield of 1 year bonds over the next two years.

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• In general, if the pay-off for investing in an n period bond should be the same as the pay-off from rolling over 1 year bonds for n periods:

• Then a n period bond yield is (approximately) equal to the average expected yield on 1 period bonds between today and date n.

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Preferred Habitat Theory• Segmented Market Theory explains why long-

term bond yields are far more often than not larger than short-term bond yields but not why bond yields are correlated .

• Expectations Theory explains why bond yields are correlated but not why there are differences in yield on average.

• Combination is preferred habitat theory. PH theory acknowledges bonds have some differences in risk and liquidity characteristics. Regardless, they are close substitutes and the expectation theory well describes the connection between bonds of different yields.

Modified Expectations Theory

• Yields of bonds of period T are represented as the

• The maturity premium hn tends to be increasing in n.

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Forecasting with the Term Structure

• If the expectations theory holds, long-term interest rates can be used to infer market expectations of future interest rates.

• Steep yield curve indicates low short-term rates and high future interest rates.

• Inverted yield curve indicates high short-term rates and low future interest rates.

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Term Structure and Business Cycles

• Many economists use the yield curve in forecasting future real activity.

• Inverted yield curves are associated with impending recessions or slowdown.

• Steep yield curves are associated with impending expansions.

Money and the Yield Curve

• Yield curve is indicative of monetary policy of central banks in countries which conduct monetary policy by setting short-term interest rates.

• Rise in short-term interest rates indicates a monetary policy tightening which in the long run will reduce inflation. The Fisher effect indicates this will reduce long-term interest rates.

• Fall in short-term interest rates indicates a monetary policy loosening, increasing long-term inflation and long-term interest rates.