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FINS5513 Term Structure
创建日期：2024-05-04 16:06:22
所属分类：金融Finance
标签： FINS5513
Term Structure

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FINS5513 Lecture 8A

Term Structure and
Bond Risk
2❑ 8.1 Bond Risk: Default Spread and Term Spread
➢ Default spread
➢ Term Spread
❑ 8.2 Theories of Term Structure
➢ Expectations Hypothesis
➢ Liquidity Preference Theory
• Liquidity risk and reinvestment risk
➢ Interpretation of Yield Curve Theories
• Interpreting the term structure
• Inverted yield curves
❑ 8.3 Interest Rate Risk
➢ Bond Price Sensitivity to Changes in Interest Rates
• Maturity, coupon and YTM impacts on interest rate risk
Lecture Outline
8.1 Bond Risk: Default
Spread and Term
Spread
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4Default Spread
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5❑ The main reason that two bonds with the same term, coupon and face value may have
different yields to maturity is due to the relative likelihood of issuer default
❑ Default premiums and default spreads on risky bonds are often referred to as the risk
structure of interest rates
❑ There is a difference between the yield based on expected cash flows (which prices in the risk
of default) and the yield based on promised cash flows (with no default risk)
➢ The difference between the (default risk weighted) expected yield and the promised yield
(i.e. the yield of an otherwise identical riskless government bond) is the default risk
premium
• The yield to maturity is higher for bonds with higher default risk
• That is, bonds with greater default risk have a higher default risk premium
Default Risk
6❑ Determination of the default risk premium on a bond is mainly driven by its credit rating
❑ Rating companies
➢ Moody’s Investor Service, Standard & Poor’s, Fitch
❑ Rating Categories
➢ Highest rating is AAA or Aaa
➢ Investment grade bonds (BBB- or Baa3 and above)
➢ Speculative grade/junk bonds (below BBB- or Baa3)
❑ Determinants of bond safety and credit rating
➢ Coverage ratios; Leverage ratios; Liquidity ratios; Profitability ratios; Cash flow-to-debt ratios
Bond Credit Ratings
Further Reading 8AR1: “S&P Credit Rating Essentials”
7❑ The default spread is often derived by showing the difference between yields on AAA bonds
and yields on either low-level investment grade bonds (BBB-) or speculative grade high
yielding bonds
Default Premiums and Spreads
Further Reading
8AR2: “S&P Credit
Markets Update Asia
Pacific - Q3 2021”
8Term Spread
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9❑ How yields change based on maturity is the term structure of interest rates (or yield curve)
Term Premiums and Spreads
❑ The term spread is often a
proxy for the yield curve
➢ The term spread is the yield
on 10-year bonds less the
yield on 90-day bills over
time
➢ We have seen the yield
curve is upward sloping –
which means a positive term
spread
➢ Allows the yield curve to be
graphed over time (rather
than at one point in time) and
inversions easily identified
Further Reading 8AR3: “Predicting Recessions Using the Term Spread”
8.2 Theories of Term
Structure
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11
Expectations Hypothesis
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12
❑ We showed previously that under certainty, we can exactly replicate cash flows of long-term
bonds by reinvesting cash flows from short-term bonds:
1 + 2
2 = (1 + 1)(1 + 12)
➢ However, in reality 12 is not known with certainty at = 0
➢ The final realized cash flow of the 2-year zero (the LHS) is known at time 0. But the final
realized cash flow of the 1 year rollover strategy (the RHS) is not known with certainty at
time 0
❑ However it may be that the market has an expectation that the (certain) cash flow from the
2-year zero will equal the expected cash flow from the 1-year rollover. That is:
1 + 2
2 = (1 + 1)(1 + E(12))
❑ This is known as the Expectations Hypothesis
Expectations Hypothesis
13
❑ Since forward rates are inferred from the term structure, a common way to denote the
Expectations Hypothesis (EH) is:
= ()
❑ We know from the earlier generalised forward rate equation that:
1 +
= (1 + )
× (1 + )
(−)
Therefore under EH: 1 +
= (1 + )
× (1 + ())
(−)
❑ However, the yield curve is typically upward sloping
➢ If Expectations Hypothesis were to hold, this means the market expects actual interest rates
in the future to be higher than today almost all the time
➢ Perhaps there is some other explanation for the typically upward sloping yield curve?
Expectations Hypothesis
14
Liquidity Preference Theory
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15
❑ Example 8A1: You are an investor with a 1-year horizon to save $1000. You have a choice
of buying either:
A) a 1-year zero coupon bond and hold it to maturity; or
B) a 2-year zero coupon bond and selling after 1 year
a) Price a 1-year and a 2-year $1,000 zero (use the pure yield curve from 7B3)
b) How many 2-year bonds would you buy (include fractions) to outlay the same amount as
strategy A
c) Show that strategy A is riskless (excluding default risk) while strategy B contains risk.
What type of risk is this called?
➢ 1 year zero: 1 =
1000
(1.05)
= $952.38 2 year zero: 2 =
1000
(1.06)2
= $890.00
➢ Number of 2-year zeros bought to outlay the same $’s as the 1-year strategy:
952.38
890.00
= 1.0701 2-year zeros for every 1-year zero
Example: Liquidity Risk
16
➢ If the 1-year interest rate in 1 year 12 = 12 = 7.01% as predicted by the yield curve, the two
strategies are equivalent:
Strategy A = $1000 = Strategy B =
1,000
1.0701
× 1.0701
➢ But what if 1-year interest rate in 1 year’s time is more (or less) than 7%?
If actual rate is 6%:
1,000
1.06
× 1.0701 = $1009 > $1000
If actual rate is 8%:
1,000
1.08
x 1.0701 = $991 < $1000
➢ The actual realised return on Strategy A is certain but the actual return on the 2-year bond is
uncertain! Therefore Strategy B is uncertain - it is exposed to interest rate risk (namely
liquidity or price risk)
❑ When an investor’s time horizon is shorter than the term of the bond they are holding, they
are exposed to interest rate risk known as liquidity risk
❑ When an investor’s time horizon is longer than the term of the bond they are holding, they
are exposed to interest rate risk known as reinvestment risk
Example: Liquidity Risk
17
❑ Strategy B has uncertainty and is more risky. Strategy A is certain and therefore less risky
❑ The Liquidity preference theory refers to the case where most investors in the market have
shorter horizons and therefore prefer short-term investments to avoid the liquidity risk of
holding long-term bonds
➢ Therefore, investors with shorter term horizons will require a risk premium – called the
liquidity risk premium - to hold a longer-term bond (eg the 2 year bond). That is:
> ()
OR = +
❑ This LRP or liquidity risk premium compensates short-term investors for the uncertainty about
future interest rates (interest rate risk)
Liquidity Preference Theory
Further Reading 8AR4: “The Bond Market Term Premium”
18
Interpretation of Yield Curve
Theories
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19
Summary of Theories of Term Structure
Expectations Hypothesis Liquidity Preference Theory
❑ = () ❑ = + (LRP > 0)
❑ Forward rates are market expectations of
future spot rates
❑ Forward rates are market expectations of
future spot rates plus a liquidity premium
❑ The liquidity premium reflects the fact that
long term bonds are more risky
❑ Investors with long-term horizons offset
those with short-term horizons – therefore
no net liquidity premium in the market (the
liquidity risk premium is zero)
❑ Investors with short-term horizons dominate
the market requiring a liquidity premium to
avert liquidity risk
❑ Does not explain the typically upwards
sloping yield curve
❑ Explains the typically upward sloping yield
curve
❑ The yield curve has an upward bias built
into the long-term rates because of the
liquidity premium
20
❑ If there is a liquidity
premium the yield
curve is biased
upward, particularly
if the premium
increases with
maturity
Liquidity Premium Impact on the Yield Curve
21
❑ The yield curve reflects expectations of future interest rates
➢ But the forecasts of future rates are clouded by other factors, such as liquidity premiums
❑ Therefore, an upward sloping curve could indicate:
➢ Rates are expected to rise
and/or
➢ Investors require large liquidity premiums to hold long term bonds
❑ The yield curve is a good predictor of the business cycle
➢ Long term rates tend to rise in anticipation of economic expansion
➢ An inverted yield curve may indicate that interest rates are expected to fall and therefore
may signal a recession
• Read the lecture topic 7 case study carefully to understand exactly why
Interpreting the Term Structure
Mini Case Study Lecture Topic 7: “Dark Clouds of Yield Inversion”
Further Reading 8AR5: “Analysing the Effect of an Inverted Yield Curve on Investors”
8.3 Interest Rate Risk
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23
Bond Price Sensitivity to
Changes in Interest Rates
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24
❑ Interest rate sensitivity
① Bond prices and yields are inversely related YTM  P 
② Bond prices move up in response to an interest rate fall more than they move down in
response to the same size interest rate increase (convexity)
③ Long-term bond prices are more interest rate sensitive than short-term bond prices
T  ΔP 
④ As maturity increases, price sensitivity to interest rate changes increases at a decreasing
rate
⑤ High coupon bond prices are less interest rate sensitive than low coupon bond prices
C  ΔP 
⑥ Higher YTM bond prices are less interest rate sensitive than lower YTM bond prices
YTM  ΔP 
Bond Price Sensitivity to ∆ Interest Rates
25
Bond Price Sensitivity to ∆ Interest Rates
①Downward sloping left to
right
②Convex
③ B more sensitive than A
④ Slide 28
⑤C more sensitive than B
⑥D more sensitive than C
26
❑ Example 8A2: Rank these bonds in order of interest rate risk:
a) A 10 year bond with a 6% coupon and 8% yield to maturity
b) A 3 year bond with a 6% coupon and a 8% yield to maturity
c) A 10 year bond with a 4% coupon and a 5% yield to maturity
d) A 10 year bond with a 4% coupon and 8% yield to maturity
➢ c) 10 year 4% coupon YTM = 5% bond price is: more interest rate sensitive than
➢ d) 10 year 4% coupon YTM = 8% bond price (higher YTM) is: more interest rate sensitive
than
➢ a) 10 year 6% coupon YTM = 8% bond price (higher coupon) is: more interest rate sensitive
than
➢ b) 3 year 6% coupon YTM = 8% bond price (shorter maturity)
Example: Interest Rate Risk
27
❑ Example 8A3: Consider the following $1000 6% annual coupon bonds with maturities of 1
year, 10 years and 20 years, all trading at a yield to maturity of 6%.
a) Price each of the bonds at YTM = 6%. Price each bond assuming YTM changes to 7%.
b) What can you say about the relationship between maturity and interest rate risk (i.e. the
bond price sensitivity to changes in interest rates)? As the interest rate increases, does
the interest rate sensitivity for bonds of different tenor increase/decrease at an increasing
or decreasing rate?
➢ Long-term bonds prices are more interest rate sensitive than short-term bond prices
T  ΔP . That is, longer term bonds have more interest rate risk (principle 3, slide 25)
➢ As maturity increases, price sensitivity to interest rate changes increases at a decreasing
rate (principle 4, slide 25)
Example: Maturity Impact on Interest Rate Risk
YTM 1 year (CR = 6%) 10 year (CR = 6%) 20 year (CR = 6%)
6% $1,000.00 $1,000.00 $1,000.00
7% $990.65 $929.76 $894.06
Change in Price -0.9% -7.0% -10.6%
28
❑ Example 8A4: Now price $1000 1 year, 10-year and 20-year zero-coupon bonds at a 6%
and 7% yield to maturity. Are they more or less sensitive to a change in interest rates than
the coupon bonds? Can you explain why?
➢ Zero coupon bond prices are more interest rate sensitive than coupon bonds
➢ Why? More of the return on zeros is “back-ended” so higher interest rates erode present
values on zeros proportionately more
➢ If the return is back-ended, does this indicate zero-coupon bonds have longer effective
maturity than coupon bonds?
➢ We will discuss the concept of duration next lecture
Example: Coupon Impact on Interest Rate Risk
YTM 1 year (Zero) 10 year (Zero) 20 year (Zero)
6% $943.40 $558.39 $311.80
7% $934.58 $508.35 $258.42
Change in Price -0.9% -9.0% -17.1
29
❑ BKM Chapter 16
❑ 8.4 Measuring Interest Rate Risk: Duration
❑ 8.5 Managing Interest Rate Risk: Immunisation
Next Lecture
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