Transcript ch05_final.ppt

Chapter Five
The Risk and Term Structure
of Interest Rates
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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Slide 5–3
Term Structure Facts to Be Explained
1. Interest rates for different maturities move together
2. Yield curves tend to have steep upward slope when
short rates are low and downward slope when short
rates are high
3. Yield curve is typically upward sloping
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Slide 5–4
Interest Rates on Different Maturity Bonds
Move Together
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Slide 5–5
Yield Curves
Dynamic yield curve that can show the curve
at any time in history
http://stockcharts.com/charts/YieldCurve.html
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Slide 5–6
Canada’s Term Structure:
1988 - 1994
14
1988
1989
1990
1991
1992
1993
1994
12
10
8
6
4
2
0
3 Month 6 Month
1-3
Year
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3-5
Year
5 - 10
Year
10+ Year
Slide 5–7
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.
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Slide 5–8
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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Slide 5–9
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?
0
1
5%
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6%
2
?%
Slide 5–10
Calculating the Implied Forward Rate
1  R   1  R 1  R 
1.06   1.05  1  R 
2
0,2
0,1
1,2
2
1,2
1.06 

R1,2 
1.05 
2
 7.01%
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Slide 5–11
Pure Expectations Theory
and Term Structure Facts
• Explains why yield curve has different slopes
1. 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
2. When short rates expected to stay same in future,
average of future short rates same as today's, and yield
curve is flat
3. Only when short rates expected to fall will yield curve be
downward sloping
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Slide 5–12
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
1. 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
2. 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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Slide 5–13
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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Slide 5–14
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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Slide 5–15
Market Segmentation Theory
• Key Assumption:
• Implication:
Bonds of different maturities are not
substitutes at all
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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Slide 5–16
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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Slide 5–17
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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Slide 5–18
Figure 6: Relationship Between the Liquidity
Premium and Pure Expectations Theory
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Slide 5–19
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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Slide 5–20
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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Slide 5–21
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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Slide 5–22
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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Slide 5–23
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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Slide 5–24
Banks & Term Structure
Interest
Rates
Lend
Borrow
11%
Spread
with risk 9.75%
9%
Pure
Intermediation
Spread
Overnight
Rate
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One year
rate
Maturity
Slide 5–25
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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Slide 5–26
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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Slide 5–27
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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Slide 5–28
Market
Predictions
of Future
Short Rates
Figure 7: Yield Curves
and the Market’s
Expectations of Future
Short-Term Interest Rates
Risk Structure of Long Bonds
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Slide 5–30
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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Slide 5–31
Increase in Default Risk on Corporate Bonds
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Slide 5–32
Analysis of Figure 2:
Increase in Default on Corporate Bonds
• Corporate Bond Market
1. Re on corporate bonds , Dc , Dc shifts left
2. Risk of corporate bonds , Dc , Dc shifts left
3. Pc , ic 
• Canada Bond Market
4. Relative Re on Canada bonds , DT , DT shifts right
5. Relative risk of Canada bonds , DT , DT shifts right
6. PT , iT 
• Outcome
– Risk premium, ic - iT, rises
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Slide 5–33
Bond Ratings
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Slide 5–34
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Slide 5–35
Decrease in Liquidity of Corporate Bonds
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Slide 5–36
Analysis of Figure 4:
Corporate Bond Becomes Less Liquid
• Corporate Bond Market
1. Liquidity of corporate bonds , Dc , Dc shifts left
2. Pc , ic 
• Canada Bond Market
1. Relatively more liquid Canada bonds, DT , DT shifts right
2. 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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Slide 5–37
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)
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Slide 5–38