Chapter Six - The Risk and Term Structure of Income Rates

What is the risk structure of interest rates, and what determines it?

The relationship between interest rates on bonds with different characteristics but the same maturity. It is primarily determined by default risk, liquidity, and taxation.

what is default risk (credit risk)?

The possibility that a bond issuer will fail to make interest or principal payments.

what is default risk premium?

The difference between the yield on a risky bond and the yield on a Treasury bond of the same maturity. It compensates investors for accepting additional default risk.

how does an increase in default risk affect corporate bond prices, yields, and the default risk premium?

Investors demand greater compensation for risk. Demand for corporate bonds falls, their prices decrease, and their yields rise. The default risk premium increases.

how does an increase in corporate default risk affect Treasury bonds?

Investors shift toward safer Treasury bonds. Treasury demand increases, prices rise, and yields fall. The spread between risky corporate bonds and Treasury bonds widens.

what are credit ratings?

A rating agency's assessment of an issuer's ability to make required bond payments.

what is creditworthiness?

An issuer's ability to repay debt.

what is credit rating agencies?

Organizations that assess and publish credit ratings update them as an issuer's financial position changes.

why can credit rating agencies face a conflict of interest?

When agencies charge the corporations and governments whose bonds they rate, they may face incentives that compromise the objectivity of their ratings. The U.S. Dodd-Frank Act of 2010 introduced regulatory changes and created an SEC office to oversee credit rating agencies.

what are investment-grade bonds?

Bonds rated BBB or above in the lecture's classification, considered relatively low risk.

what are junk or speculative grade bonds?

Bonds rated below BBB, generally offering higher yields because of greater default risk. Also called high-yield bonds.

what are fallen angels?

Bonds that were investment grade but have been downgraded to junk status.

wha is credit spread?

the difference between yields on bonds with different credit risks, commonly corporate and government bonds of the same maturity

what happened to the BBB-Treasury spread during the financial crisis?

perceived corporate default risk increased, corporate yields rose, and Treasury yields fell, causing the spread to widen.

what is liquidity?

the relative ease with which an asset can be converted into cash

how does liquidity affect bond prices and yields?

It depends partly on selling costs and the number of buyers and sellers. Investors accept lower yields on more liquid bonds.

Greater liquidity → greater demand → higher prices → lower yields.

how do taxes affect bond demand and the risk structure of interest rates?

Investors consider after-tax returns. Coupon interest on Canadian fixed-income securities is taxed as ordinary income in the year received, while the slides describe capital gains as taxed at a lower rate and upon realization. An increase in federal income tax rates makes tax-exempt municipal bonds relatively more attractive than taxable Treasury bonds, shifting demand toward municipal bonds and away from Treasury bonds.

what are the axes and curves in a standard bond-market graph?

Vertical axis: Bond price.

Horizontal axis: Quantity of bonds.

Demand curve: Downward-sloping.

Supply curve: Upward-sloping.

The intersection determines the equilibrium bond price and quantity. Bond yields move inversely to bond prices.

what happens when the demand curve for a bond shifts right or left?

Rightward shift: Demand increases, equilibrium price rises, and yield falls.

Leftward shift: Demand decreases, equilibrium price falls, and yield rises.

how does a graph show an increase in corporate default risk?

In the corporate bond market, demand shifts left, lowering prices and raising yields. In the Treasury bond market, demand shifts right, raising prices and lowering yields. The difference between their yields widens.

how does a graph show an increase in federal income tax rates?

Demand for tax-exempt municipal bonds shifts right, increasing their prices and lowering their yields. Demand for taxable Treasury bonds shifts left, decreasing their prices and increasing their yields.

what is the term structure if interest rates?

The relationship between interest rates on otherwise similar bonds with different maturities. Differences in maturity can produce different yields even when risk, liquidity, and tax characteristics are identical.

what is a yield curve?

A graph of yields against maturities for bonds with the same risk, liquidity, and tax characteristics

what are the three shapes of yield curves?

Upward-sloping: Long-term yields exceed short-term yields.

Flat: Short-term and long-term yields are approximately equal.

Inverted: Long-term yields are below short-term yields.

what are the three facts a theory of the term structure must explain?

1. Interest rates at different maturities move together over time.

2. Yield curves are more likely to slope upward when short-term rates are low and downward or become inverted when short-term rates are high.

3. Yield curves almost always slope upward.

how do you interpret the slope of a yield curve graphically?

Maturity is on the horizontal axis, and yield is on the vertical axis. A rising curve indicates higher long-term yields; a horizontal curve indicates similar yields across maturities; a falling curve indicates lower long-term yields. Under expectations theory, the slope also signals the market's implied expectations for future short-term rates.

what is expectancy theory?

The theory is that the interest rate on a long-term bond equals the average of the short-term interest rates investors expect over the bond's lifetime.

what are the two main assumptions of expectations theory?

1. Investors have the same investment objectives.

2. Bonds with different maturities are perfect substitutes when compared over the same holding period.

what does it mean for bonds of different maturities to be perfect substitutes?

Investors are willing to hold bonds of different maturities interchangeably if the expected returns over the same holding period are equal.

how does expectations theory explain an upward-sloping yield curve?

Investors expect future short-term interest rates to rise. Their average expected future short-term rate exceeds the current short-term rate, so long-term yields are higher.

how does expectations theory explain a downward-sloping yield curve?

Investors expect future short-term rates to fall. Their average expected future short-term rate is below the current short-term rate, so long-term yields are lower.

how does expectations theory explain a flat yield curve?

Investors expect short-term interest rates to remain approximately constant. The average expected future short-term rate is therefore similar to the current short-term rate.

how does expectations theory explain why interest rates at different maturities move together?

A rise in current short-term rates can raise expectations of future short-term rates. Since long-term yields reflect the average of expected future short-term rates, long-term yields also rise.

why does expectations theory predict upward-sloping curves when short-term rates are low?

Investors generally expect low short-term rates to rise toward a more normal level. The average of future expected rates becomes higher than the current short-term rate.

why does expectations theory predict downward-sloping curves when short-term rates are high?

Investors may expect high short-term rates to fall toward a more normal level, lowering the average expected future short-term rate relative to the current rate.

which of the three term structure facts does expectations theory explain, and which does it fail to explain?

Fact 1: Explains why interest rates at different maturities move together.

Fact 2: Explains how yield curve slopes relate to the level of short-term rates.

Fact 3: Cannot explain why yield curves almost always slope upward.

Why can expectations theory not explain the usual upward slope of yeild curves?

It would require investors to expect short-term interest rates to rise most of the time. The slides argue that short-term rates are about as likely to rise as to fall at any given time.

how does the slope of the yield curve predict future short-term interest rates under expectations theory?

Upward slope: Future short-term rates are expected to average above the current rate.

Flat slope: Future short-term rates are expected to average approximately the current rate.

Inverted slope: Future short-term rates are expected to average below the current rate.

what is segmented markets theory?

The theory that the interest rate on a bond of a particular maturity is determined only by the supply and demand for bonds of that maturity.

what are the two main assumptions or observations behind segmented markets theory?

Investors have different investment objectives, and they do not view bonds of different maturities as perfect substitutes.

what does it mean for bond markets to be segmented?

Investors in one maturity's bond market do not participate in markets for bonds of other maturities. Each maturity's market is treated as separate.

how does segmented markets theory explain upward-sloping yield curves?

Investors often prefer short-term bonds because they have less interest-rate risk. Demand for long-term bonds is therefore relatively lower, resulting in lower prices and higher yields on long-term bonds.

why might investors prefer short-term bonds over long-term bonds?

Short-term bonds generally have less interest-rate risk. Their prices are typically less sensitive to interest-rate changes than those of otherwise comparable long-term bonds.

Which term structure fact does segmented markets theory explain?

Yield curves usually slope upward because investors tend to prefer short-term bonds.

why can segmented markets theory not explain why interest rates at different maturities move together?

Since markets are treated as completely separate, a change in the interest rate on bonds of one maturity has no necessary effect on rates for other maturities.

why can segmented markets theory not explain how yield curve slopes relate to short-term rates?

The theory does not establish how the supply and demand for short- and long-term bonds change as short-term interest rates rise or fall. It therefore cannot explain Fact 2.

what is liquidity premium theory?

The theory that a long-term bond's interest rate equals the average of expected future short-term interest rates plus a liquidity premium, also called the term premium.

what is a liquidity premium or term premium?

The additional interest investors require to hold a long-term bond rather than a comparable sequence of short-term bonds.

what are the key assumptions of liquidity premium theory?

Bonds of different maturities are substitutes, meaning expected returns influence each other, but they are not perfect substitutes. Investors can prefer particular maturities.

why is the liquidity premium positive, and how does it change with maturity?

Investors generally prefer short-term bonds because they have less interest-rate risk. They require extra compensation to hold longer-term bonds. In the lecture model, the premium is positive and increases with maturity.

what is the relationship between long-term interest rates, expectations, and the liquidity premium?

Long-Term Rate = Average Expected Future Short-Term Rates + Liquidity Premium

The first component reflects expectations; the second compensates investors for holding longer-term bonds.

what is preferred habitat theory?

A theory in which investors prefer bonds of particular maturities but will purchase bonds outside their preferred maturity if offered a sufficiently higher expected return.

what is an investor's preferred habitat?

The maturity range of bonds that best matches the investor's objectives and preferences.

how does preferred habitat theory differ from expectations theory?

Expectations theory assumes perfect substitution between maturities. Preferred habitat theory allows for maturity preferences and requires a higher expected return to encourage investors to move outside their preferred maturity.

How does liquidity premium theory explain Fact 1: Interest Rates move together?

Long-term rates share a component based on expected future short-term rates. When those expectations change, yields across different maturities tend to move together.

How does liquidity premium theory explain Fact 2: yield curve slopes depend on short-term rates?

When short-term rates are low, expectations of rising future rates and the positive liquidity premium reinforce an upward slope. When short-term rates are high, expected declines can produce an inverted curve if they outweigh the premium.

how does liquidity premium theory explain Fact 3: yield curves usually slope upward?

The liquidity premium increases with maturity, tending to push long-term yields above short-term yields even when expected future short-term rates do not rise.

how do the three major theories differ in what determines interest rates?

Expectations theory: Average expected future short-term interest rates.

Segmented markets theory: Supply and demand within each maturity-specific market.

Liquidity premium theory: Average expected future short-term rates plus a positive liquidity premium.

which theory best explains all three facts, and why?

Liquidity premium theory, because it combines expectations about future short-term rates with a positive premium that increases with maturity.

what is the most important difference between expectations theory and liquidity premium theory?

Liquidity premium theory includes extra compensation for holding long-term bonds; expectations theory does not.

can the yield curve be inverted under liquidity premium theory?

Yes. If expected future short-term rates fall sufficiently, their average can be low enough to outweigh the positive liquidity premium, leaving long-term yields below short-term yields.

what is a forward rate?

A future interest rate implied by current yields on bonds with different maturities, under a specified term-structure model.

what does a forward rate represent under expectations theory?

it represents the future short-term interest rate implied by current bond yields, assuming the expectations theory relationship holds.

what is an adjusted forward-rate forecast?

A forward-rate estimate that accounts for liquidity premiums embedded in bond yields, aiming to isolate expected future short-term interest rates.

why must liquidity premiums be considered when forecasting future interest rates?

Long-term yields include both expected future short-term rates and a liquidity premium. Treating the full long-term yield as a forecast of future rates can overstate the expected future short-term rate.

how does the yield curve help financial institutions forecast interest rates?

Its slope provides information about the market's implied expectations for the future path of interest rates, helping institutions assess future borrowing and lending conditions.

why are interest-rate forecasts important for financial institutions?

Future interest-rate changes affect profitability. Forecasts also help managers set rates on loans they commit to making in the future.

how can a bank use forward rates when considering a future loan commitment?

The bank estimates the future interest rate using current bond yields, adjusts for the liquidity premium, and compares the expected rate with the rate needed to cover its costs and earn a profit.

what determines whether a bank should accept a future loan commitment?

Whether the expected interest rate it can earn on the loan is sufficient to cover lending costs and achieve its required return.

what is the key distinction between a forward rate and an actual future interest rate?

A forward rate is an estimate implied by current bond yields under a model. The actual future interest rate may differ because market expectations, economic conditions, and other factors can change.