Financial markets• Be familiarised with bond features
• Be familiarise with bond valuation
• Be able to use duration to estimate the sensitivity of bond to interest rate changes
• Be aware of the role of credit rating agencies and the use of credit ratings
• Know the term structure of interest rates
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Bond
A debt security where the issuer pays interest and/or principal to the holder.
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Secured vs unsecured
Senior vs subordinate
General obligation bonds
• Foreign corporates
• Foreign governments
Bond maturity
Maturity – the number of years the issuers promise to meet the conditions of the bonds
• Indicates the life of a bond
• Affect the yield of a bond
• Linked to the price volatility of a bond
• Modifiable by provisions
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Coupon – the periodic interest payment made to investors
• Usually fixed for the life of the bonds (e.g. 5% due in 2026)
• Exceptions: zero-coupon bonds (STRIPS); inflation-indexed bonds; floating-rate securities
• Coupon rate influences price volatility of bonds
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Principal of bond
Principal – par or face value when the bonds are retired or mature
• Forms the basis for coupon payment
• Market price as a percentage of the principal
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Bond features
Call provision – entitles the issuer to retire the bond before maturity
• Beneficial to issuers and detrimental to investors
• Callable bonds have higher yields
• Call protection period
Bond features
Put provision –grants the right to investors to sell the bond back to the issuer before maturity
• Beneficial to investors and detrimental to issuers
• Putable bonds have lower yields
• Designated put dates and restricted amounts
Bond initiation and trading
C = coupon payment
R = yield-to-maturity / redemption yield / internal rate of return
n = years to mature
Example 1
Swahili plans to issue a 3-year bond with a coupon rate of 10% and a face value of €100. What’s the price of the bond if the required yield is 11%?
P = 10/1.11 + 10/1.112 + 110/1.113
= 97.56
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Example2
What is the yield-to-maturity of a 3-year bond with a coupon rate of 10% and face value of €100, if the bond is currently traded @ €97?
97 = 10/(1+R) + 10/(1+R)2 + 110/(1+R)3
R = 11.23%
Yield-to-maturity
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Summary
• Investors will not hold a bond which has a yield below the prevailing market required yield
• However, due to demand-supply relationship, it is almost impossible to find a bond which yields more than the market required yield
• Therefore, yield-to-maturity often equals to market required yield. A bond with a coupon yield that is higher than the market required yield will be issued at a premium; conversely the bond will be issued at a discount
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Summary • The prices of a premium bond and a discount
bond converge as the maturity approaches
• Bond prices also change during the life of the bond due to changes in market required yield (e.g. changes in interest rates)
*However, changes in bond prices are not only related to changes in interest rates. Other factors such as the credit quality of the issuers also play an important role
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Pricing a zero-coupon bond
A zero-coupon bond is characterised by a single cash flow at maturity (bullet payment). Due to the simplicity in cash flow pattern, the yield- to-maturity of a zero-coupon bond is easy to calculate.
1)(
)1(
/1 −=
Example 3
What is the price of a zero-coupon bond with a remaining maturity of 30 months if the required yield is 10%?
P = 100/1.12.5 = 78.799
Par Coupon rate = yield-to- maturity
Premium Coupon rate > yield-to- maturity
Discount Coupon rate < yield-to- maturity
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Duration
Where: P = price of the bond
C = coupon payment
R = yield-to-maturity
Example 4
Calculate the duration and modified duration of a 3-year bond with a coupon rate of 10% if the required yield is 11%.
D=[10/1.11+2(10/1.112)+3(110/1.113)]/(10/1.11 +10/1.112+110/1.113)=2.7321
MD=D/1.11=2.4614
Example 5
In example 4, what is the percentage change in bond price given a 50bps increase in interest rate? What is the change in bond price?
(P2 - P1)/P1= - MD*(R2 - R1) = -2.4614*0.005 = - 0.012307 = -1.2307%
(P2 - P1) = -0.012307*97.56=-1.2007
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Issued by rating agencies
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Why credit ratings Price risky (defaultable) bonds
• Credit rating based Markov models (e.g. Jarrow, Lando and Turnbull 1997)
Compute economic & regulatory capital (e.g. Basel II: Pillar I)
• Economic capital is used to offset predicted default on fixed income assets
• Regulatory capital is required by regulators for a number of purposes
• Both need a measure of risk
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Calculate risk weights and calibrate internal ratings of financial institutions
• Basel II: Pillar I
Form guidelines for asset allocation • Plan sponsors and fund managers need to
have a benchmark for bond investment • Credit rating is a relative objective and publicly
available tool
Definition: The relationship between yield and maturity
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The base interest rates
Also referred to as benchmark interest rates Bonds yielding the base interest rates are those
without credit risk Interest rates on (on-the-run) US Treasury securities are
generally viewed by market participants as benchmark interest rates (however not all the Treasury securities can be used to measure the base interest rates)
Base interest rates are benchmarks for pricing all other bonds, and are the minimum interest rates investors would demand on non-Treasury bonds with comparable maturities
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The yield curve
Definition: the graphical depiction of the relationship between the yield on the bonds of the same credit quality but different maturities
The Treasury yield curve serves as a benchmark for pricing bonds and setting yields in other sectors
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Upward-
slopping
Downward-slopping
Flat
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The pure expectation theory The entire term structure at a given time reflects the
market’s current expectations of future short-term rates
Given the relationship between spot rates and forward rates, an upward-slopping yield curve indicates that the market expects short-term rates to rise throughout the future; a flat yield curve reflects an expectation of constant future short-term rates; a downward-slopping yield curve reflects an expectation of declining future short-term rates
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The pure expectation theory Origins of a rising (upward-slopping) term structure –
expectation of rising future short-term rates • Investors will not buy long-term bonds since they
expect a higher short-term rates in the future • Speculators expecting rising rates would anticipate a
fall in long-term bond prices, therefore they may short sell long-term bonds
• Borrowers wish to borrow more now since the cost of funding will be higher in the future
• Higher supply and lower demand for long-term bonds puts downward pressure on prices and in turn upward pressure on yields
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The liquidity theory Due to the reinvestment risk and uncertainty in
price, investors in long-term bond need to be compensated by a premium on top of the interest rate expectation related yield
This premium is usually referred to as the liquidity premium which is proportional to the maturity
This theory explains why yield curves are normally upward-slopping
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Market segmentation theory
The difference between this theory and the preferred habitat theory is that this theory assumes that investors are restricted to certain maturity sector due to asset/liability management (ALM) constraints (either self- imposed or regulatory)
Expectation of interest rate movement plays a marginal role in this theory due to the ALM constraints
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Market segmentation theory
Therefore, the shape of yield curve according to this theory largely depends on the demand and supply for securities within each maturity sector
Market segmentation theory can be used to explain all possible shapes of yield curves
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The Economist (2009)