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Chapter 6. The Term Structure & Risk Structure Of Interest Rates. The Term Structure Of Interest Rates. It is the relationship at any given time between the length of time to maturity and the yield on a debt security.

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Chapter 6 l.jpg

Chapter 6

The Term Structure &

Risk Structure Of Interest Rates


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The Term Structure Of Interest Rates

  • It is the relationship at any given time between the length of time to maturity and the yield on a debt security.

  • The yield curve graphically depicts the term structure of interest rates.

    • The length of time to maturity is on the horizontal axis and the yield on the vertical axis.

    • Each point on a curve corresponds to the yield on a given day of a particular type of bond for a particular maturity date.

    • Other factors constant; default risk, liquidity, …


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The Term Structure Of Interest Rates (2)

  • Term structure exists for different types of debt instruments—usually bonds

    • US Treasuries

    • Corporate Bonds

    • State and Local Bonds

  • The yield curve is typically ascending, but can be flat, descending, or humped.


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Figure 6-1

High Interest rate

Downward Slope

Low Interest rate

Upward slope


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The Term Structure Of Interest Rates

  • The shape of yield curve (Figure 6-2)

    • Flat yield curve

    • Ascending (Upward sloping) yield curve

    • Descending (Downward sloping, inverted) yield curve

    • Humped yield curve

  • These shape can be explained by

    4 Theories of Term Structure


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4 Theories Of Term Structure

  • The pure expectations theory

  • The liquidity premium theory

  • The segmented markets theory

  • The preferred habitat theory


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1. Pure Expectations Theory

  • Current expectations of financial market participants toward future interest rates is the determinant of the current term structure rates.

  • Market forces produce a yield curve or term structure that equalizes expected returns among alternative maturities for any planning period or investment horizon.


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Assumptions of the Pure Expectations Theory

  • Investors seek to maximize holding period returns

  • Investors have no institutional preference for particular maturities. They regard various maturities as perfect substitutes for each other.

  • There are no transactions costs associated with buying and selling securities.

  • Large numbers of investors form expectations about the future course of interest rates, & act aggressively on those expectations.


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Assumptions of the Pure Expectations Theory (2)

“If these assumptions are valid, the term structure of interest rates reflects only expectations about future interest rates.”


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1. Pure Expectations Theory (2)

  • Yield on a long-term bond equals the geometric mean (or average) of the current short-term yield and successive future short-term yields.

  • If transactions costs are zero, the investor would expect to earn the same average return over the long run if they:

    • purchase a short-term bond & "roll it over" every time it matures.

    • purchase a long-term bond & hold it to maturity


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1. Pure Expectations Theory

Option 1: Invest in 1-year bond and roll-over

0i1 = 4%

1i2 = 8%

0

1

2

0i1 = 4%

1i2 = 8%

Option 2: Invest in 2-year bond

0i2 = 6%

0

1

2

0i2 = 6%


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Pure Expectations Theory: Implications

  • If investors believe that short-term interest rates will be higher in the future, the yield curve today slopes upward.

Interest rate (%)

Maturity (Years)


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Pure Expectations Theory: Implications

  • If investors think interest rates will decline in the future, the yield curve is downward.

Interest rate (%)

Maturity (Years)


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Pure Expectations Theory: Implications

  • In the pure expectations theory:

    • an ascending yield curveis evidence of market that interest rates are rising

    • a downward-slopingor inverted yield curve implies that market expects that interest rates are falling

    • a flat yield curve implies a consensus that future yields will remain the same as current yields

  • In the pure expectations theory, nothing except the outlook for interest rates affects the shape of the yield curve.


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2. Liquidity Premium Theory

  • The pure expectations theory of term structure is correct, except for this issue: long-term bonds entail greater market risk than short-term securities do

    • Market risk is the risk of fluctuation in the price of the security due to interest rate changes.

    • Investors may have to sell their assets prior to maturity, exposing themselves to the possibility of losses as interest rates & thus market prices change.


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2. Liquidity Premium Theory

  • If bond buyers are risk averse, they must be compensated with a term premium for the greater market risk inherent in long-term bonds.

    • tRL = tRL-1 + TP

    • The Liquidity Premium Theory states that the term premium (TP) is positive & increases with the length of term, so the normal yield structure is ascending (Upward sloping).

    • Bond with longer maturity provides higher yield


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3. Segmented Markets Theory

Interest rates depend on supply and demand in each market

Long term interest rates depend on

1. Long-term supply for fund

(Long-term lenders)

2. Long-term demand for fund

(Long-term borrowers)

Short term interest rates depend on

1. Short-term supply for fund

(Short-term lenders)

2. Short-term demand for fund

(Short-term borrowers)


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3. Segmented Markets Theory

  • Securities of different maturities are very poor substitutes for one another.

  • This theory disagrees with the second assumption underlying the pure expectation theory.

  • Various lenders and borrowers have a strong preferences for particular maturities.


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3. Segmented Markets Theory

For Lenders (Supply):

Short term securities provide liquidity & stability of principal (price stability)

Lenders who prefer protection of principal will prefer to invest in Short term securities (T-Bills)

Long term securities provide stability of income (i.e. coupon bond)

Lenders who prefer income stability over principal stability will prefer to invest in Long term securities (T-Bonds)


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3. Segmented Markets Theory

For borrowers: Individuals & firms are strongly motivated to match the maturities of their assets with the maturities of their liabilities

Families buying homes prefer long-term fixed rate mortgages

Municipalities & corporations investing in long-term capital projects  borrow long-term

Firms borrowing to finance inventories prefer short-term loans

Banks need liquidity  prefer to invest short-term


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3. Segmented Markets Theory

  • Securities of different maturities cannot be substituted for one another in response to perceived yield advantages.

  • Each maturity sector of the market is viewed as almost totally separated from other maturity sectors.


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Segmented Markets Theory: Implications

  • Yields in any maturity sector are determined strictly by supply & demand in that sector.

  • Corporate & U.S. Treasury debt management decisions significantly influence the shape of the yield curve.

    • If firms & the government are currently issuing predominantly long-term debt  the yield curve will be relatively steep.

    • If they are issuing short-term debt  short-term yields will be high relative to long-term yields.


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Segmented Markets Theory: Implications

  • Treasury debt management is a potential tool of economic policy because it can influence the yield curve.

Gov. wants to raise Short term yield & reduce Long term yield

Gov. will issue only Short term debt

 higher demand

 higher Short term yield

 Twisting the yield curve


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4. Preferred Habitat Theory

  • This hybrid theory combines elements of the other three.

  • Borrowers & lenders do hold strong preferences for particular maturities.

  • The yield curve will not conform strictly to the predictions of the other three theories.

    • If expected additional returns to be gained by deviating from their preferred maturities become large enough, institutions will deviate from their preferred maturities.


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4. Preferred Habitat Theory

  • Institutions will accept additional risk in return for additional expected returns.

  • Institutions change from their preferred maturities or habitats if expected additional returns from other maturities are large enough.

  • Example (p. 133): banks shift to invest in L-T securities if L-T securities provide large additional return (yield)


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4. Preferred Habitat Theory

In accepting those theories yet rejecting their extreme polar positions, this theory moves closer to explaining real world phenomena.


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The Risk Structure Of Interest Rates

  • A security issuerdefaults if it fails to meet the terms of the contractual agreement (indenture) in full.

    • For a bond, default is either the borrower's failure to make full interest payments or to redeem at face value

  • Embedded in the yields of risky securities is a premiumto compensate lenders for default risk


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Risk Premiums

Moody's and Standard and Poor's, provide ratings of the quality of bonds in the United States

(ranging from investment grade bonds to junk bonds)


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Risk Premiums

Risk premium = risky yield – risk free yield

  • Risk premiums increases during recessions & other times when firms experience financial distress.

  • It decreased modestly during the economic boom.


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Figure 6-7

Default-Free Market

Risky Market

Sr2

Interest rate

Interest rate

Sr1

Sd1

ir2

Sd2

ir1

id1

Dr1

id2

Dd1

Loanable Funds (Q)

Loanable Funds (Q)