2. The Risk and Term Structure of Interest Rates
Chapter Five
The Risk and Term Structure of Interest Rates

3. Term Structure of Interest Rates
The Term structure is a plot of interest rates of equal risk but different maturities
Three term structure theories
Unbiased expectations theory
Liquidity preference theory
Segmented markets theory
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4. Term Structure Facts to Be Explained
Interest rates for different maturities move together
Yield curves tend to have steep upward slope when short rates are low and downward slope when short rates are high
Yield curve is typically upward sloping
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5. Interest Rates on Different Maturity Bonds Move Together
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6. Yield Curves
Dynamic yield curve that can show the curve at any time in history
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7. Canada’s Term Structure: 1988 - 1994
Rates used are:
3 month T bills
6 month T bills
1-3 year bonds
3-5 year bonds
5-10 year bonds
10+ year bonds
Data source: Bank of Canada Review (Table F1)
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8. Canada’s Changing Term Structure
Important concepts
what is the relationship between the general level of interest rates and the phase of the business cycle?
Rates tend to be low during economic contractions & rise during economic expansions
what is the relationship between the slope of the term structure and the phase of the business cycle?
The term structure tends to slope upward during economic expansions. An inverted yield curve often foreshadows an economic downturn.
Excellent article - “The term structure of interest rates as a leading economic indicator: A technical note” Bank of Canada Review, Winter
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9. Unbiased Expectations Theory of the Term Structure
Assumption: In an efficient market, investors should be indifferent between holding one long bond or a series of short bonds
The Theory: Unbiased expectations theory states that long interest rates are the geometric average of expected future short interest rates
Result: if term structure slopes up, future short interest rates are expected to rise. If term structure slopes down, future short interest rates are expected to fall
Predicting future short interest rates - the implied forward rate.
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10. The Implied Forward Rate
One year spot rates are currently 5%
Two year spot rates are currently 6%
What is the market predicting for one year rates, one year from today? 1 2 5% ?% 6%
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11. Calculating the Implied Forward Rate
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12. Pure Expectations Theory and Term Structure Facts
Explains why yield curve has different slopes
When short rates are expected to rise in future, average of future short rates is above today's short rate; therefore yield curve is upward sloping
When short rates expected to stay same in future, average of future short rates same as today's, and yield curve is flat
Only when short rates expected to fall will yield curve be downward sloping
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13. Pure Expectations Theory and Term Structure Facts
Explains fact 2—that yield curves tend to have steep slope when short rates are low and downward slope when short rates are high
When short rates are low, they are expected to rise to normal level, and long rate = average of future short rates will be well above today's short rate; yield curve will have steep upward slope
When short rates are high, they will be expected to fall in future, and long rate will be below current short rate; yield curve will have downward slope
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14. Pure Expectations Theory and Term Structure Facts
Doesn't explain fact 3—that yield curve usually has upward slope
Short rates as likely to fall in future as rise, so average of expected future short rates will not usually be higher than current short rate: therefore, yield curve will not usually slope upward
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15. Segmented Markets Theory
assumes that both lenders & borrowers confine themselves to certain maturity sectors of the term structure due to:
high search & information costs leading to specialization
legal restrictions
matching of asset & liability maturities
given market segmentation, rates on different maturities will vary with the supply & demand within each maturity bucket
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16. Market Segmentation Theory
Key Assumption: Bonds of different maturities are not substitutes at all
Implication: Markets are completely segmented; interest rate at each maturity determined separately
Explains fact 3—that yield curve is usually upward sloping
People typically prefer short holding periods and thus have higher demand for short-term bonds, which have higher prices and lower interest rates than long bonds
Does not explain fact 1 or fact 2 because it assumes long and short rates are determined independently
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17. Liquidity Preference Theory
Liquid instrument defined as:
one which is quickly & easily converted to cash
at or near face value
Investors prefer more liquid to less liquid instruments
short term instruments are more liquid than long term ones (why)
borrowers are willing to pay a liquidity premium to reduce refunding costs
result is a term structure which is a product of both expected future short rates plus a liquidity premium
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18. Liquidity Premium Theory
Key Assumption: Bonds of different maturities are substitutes, but are not perfect substitutes
Implication: Modifies Pure Expectations Theory with features of Market Segmentation Theory
Investors prefer short rather than long bonds  must be paid positive liquidity premium to hold long term bonds
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19. Figure 6: Relationship Between the Liquidity Premium and Pure Expectations Theory
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20. Liquidity Premium Theory: Term Structure Facts
Explains All 3 Facts
Explains fact 3—that usual upward sloped yield curve by liquidity premium for long-term bonds
Explains fact 1 and fact 2 using same explanations as pure expectations theory because it has average of future short rates as determinant of long rate
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21. Some Observations
for a given change in interest rates, the price of long securities will fluctuate more than the price of short securities
for a given change in price, the yield on short securities will fluctuate more than the yield on long securities
short interest rates are more volatile than long interest rates
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22. Term Structure & the Business Cycle
During the recessionary trough, interest rates are low but expected to rise - term structure slopes up
At the expansionary peak, interest rates are high but expected to fall - term structure slopes down
But these results do NOT happen in a vacuum
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23. Factors Which Influence Slope of Term Structure
Recession: rates low but expected to rise
lenders - increase the supply of short dated loanable funds; demand for short bonds rises; short bond price rises, short bond yield falls
borrowers - increase demand for long dated funds; supply of long bonds up; price of long bonds fall; yield on long bonds up
inventories & A/R - demand for short term financing is low; supply of short bonds down; price up; yield down
demand deposits - quantity up, loan demand down; demand for short bonds up; price rises; yield falls
Bank of Canada - stimulate the economy; demand for short bonds up; price rises, yield falls
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24. Term Structure & the Banking Industry
Given an upward sloping term structure, temptation is to borrow short and lend long
Risk is that short rates will move higher before the long asset matures, creating a negative spread
Management of the mismatch is called GAP management, where GAP is defined as: GAP = Rate Sensitive Assets - Rate Sensitive Liabilities
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25. Pure Intermediation Spread
Banks & Term Structure
Interest Rates
Lend
Borrow
11%
Spread with risk
9.75%
Pure Intermediation Spread 9%
Overnight Rate
One year rate
Maturity
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26. Coupon Rates & Bond Yields
The coupon is the periodic interest paid by a bond. However, the relationship between a bond’s yield to maturity and the relative size of its coupon is not always clear. Three possibilities are:
1. Low coupon bonds have greater price volatility than high coupon bonds. This should cause low coupon bonds to trade at a lower price & a higher yield.
2. If the term structure of interest rates is upward sloping, the realized yield is greater for a low coupon bond. This should cause low coupon bonds to trade at a higher price and a lower yield to maturity.
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27. Coupon Rates & Bond Yields
Procedure for solving #2 on previous page:
1. Calculate the total future cash flows available at the bond’s maturity date (reinvest the coupons)
2. Calculate the realized yield by setting:
FV = PV(1+r)t and solving for r
3. Calculate the price required to equate the realized yields by dividing the total cash flows from the high coupon bond by (1 + r)t where r is realized yield on the low coupon bond.
4. Calculate the yield to maturity for the high coupon bond based on the new price calculated in step #3.
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28. Coupon Rates & Bond Yields
3. Tax effects - high tax bracket investors prefer capital gains to interest income. Since low coupon bonds have greater capital gains potential, they should trade at a lower pre-tax yield to maturity (if most bond investing is done by high tax bracket investors).
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29. Market Predictions of Future Short Rates
Figure 7: Yield Curves and the Market’s Expectations of Future Short-Term Interest Rates

30. Risk Structure of Long Bonds
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31. Yield Spreads
Yield spreads are the spreads between high-risk and low-risk securities of equal maturity
Yield spread narrows during expansions and widens during contractions
Expansions - confidence is high, investors chase high yields. Drives price of risky up and yield down
Contractions - safety of principal is paramount. Flight to quality. Price of safe security rises, yield falls.
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32. Increase in Default Risk on Corporate Bonds
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33. Analysis of Figure 2: Increase in Default on Corporate Bonds
Corporate Bond Market
Re on corporate bonds , Dc , Dc shifts left
Risk of corporate bonds , Dc , Dc shifts left
Pc , ic 
Canada Bond Market
Relative Re on Canada bonds , DT , DT shifts right
Relative risk of Canada bonds , DT , DT shifts right
PT , iT 
Outcome
Risk premium, ic - iT, rises
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34. Bond Ratings
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35. Copyright © 2004 Pearson Education Canada Inc.

36. Decrease in Liquidity of Corporate Bonds
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37. Analysis of Figure 4: Corporate Bond Becomes Less Liquid
Corporate Bond Market
Liquidity of corporate bonds , Dc , Dc shifts left
Pc , ic 
Canada Bond Market
Relatively more liquid Canada bonds, DT , DT shifts right
PT , iT 
Outcome
Risk premium, ic - iT, rises
Risk premium reflects not only corporate bonds' default risk but also lower liquidity
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38. The CPI & Inflation
The CPI (consumer price index) is often used as a measure of historic inflation. However, there is significant research to indicate that the CPI overstates true inflation by a significant amount due to :
quality improvements
substitution effects
basket adjusted only infrequently (misses price reductions as new products are introduced & then fall in price)
On June 26, 1995 the US Senate Finance Committee appointed an expert panel chaired by Michael Boskin, chief economic adviser in the Bush Administration, to study the CPI. Their interim report , released on Sept. 15, 1995, concluded that the US CPI overstated inflation by about 1%. If this is true, by restating the CPI to its true level would slash about $634 billion from the US deficit over the next ten years, or about a third of all savings needed to balance the budget. In addition, people who thought their wages were stagnant would now be told that their real wages were in fact rising.
What might be missed?
1. Health care costs are not included in the CPI basket. In the US, these are one of the most dramatic sources of consumer inflation.
2. Quality declines (such as no airline meals, overcrowded flights, poor medical care) are not included.
3. Quality of life deterioration's that entail new costs, such as having to install alarm systems in home and cars or spend more money in legal fees to protect yourself against being sued, are not included.
Source: Business Week, Nov.. 27, 1995, p. 26.
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