Chapter 12: Bond Valuation Flashcards
Relationship between yield and price:
Inverse relationship.
- Higher yield => lower price
- Lower yield => higher price
7 Yield measures
Nominal Yield Current Yield Yield to maturity Yield to call Yield to put Realised yield Spot and forward rates
Nominal yield
Coupon rate of an issue.
Current yield
Interest income only.
CY = Annual Coupon payment / bond price
Yield to maturity
An annualised internal rate of return based on a bond’s price, coupon payments and par value.
= single discount rate used to price a bond.
Yield to call calc.
Call price is substituted for the par value.
Number of periods to the call substituted for the time to maturity.
Yield to put calc.
Put price is substituted for the par value.
Number of periods until the put date is substituted for the time to maturity.
Realised yield
Takes account of the expected per-period reinvestment rates during the investment.
Spot rates
derived from Treasury bonds of varying maturities and coupons effectively removing any coupon, reducing each bond to a zero-coupon bond at a particular maturity.
Yield curve
Plot of the yields against their maturities.
4 General shapes to the yield curve
Normal (upward sloping)
Inverted (downward sloping)
Flat
Humped
Normal (upward sloping)
• Longer maturity bonds have higher yields due to investors requiring a higher rate of return for taking the added risk of lending money for a longer period of time.
Inverted (downward sloping)
• Shorter-term yields are greater than longer-term, which can signal an upcoming recession.
Flat
- Equal at every maturity.
- One in which the shorter- and longer-term yields are very close.
- Signifies that investors have no opinion on the movement of interest rates and are unsure about future economic growth and inflation.
Humped
- Yields on intermediate-term issues are above the yields on the short-term issues and the rates on long-term issues decline to levels blow those for the short-term issues before levelling out.
- Precursor to a recession.
3 Basic theories on the shape of the yield curve.
Expectations theory
Liquidity preference theory
Segmented Market theory
Expectations theory
o Most widely accepted yield curve theory.
o Forward rates are solely a function of expected future spot rates.
o Expectations of rising short-term rates create a positive yield curve.
Liquidity preference theory
o Forward rate reflect investors’ expectations of future rates plus a liquidity premium to compensate them for exposure to interest rate risk.
Segmented Market theory
o Proposes that lenders and borrowers are confined to certain maturity segments due to restrictions on their maturity structure and will therefore not be enticed to shift out of these maturity ranges.
o Shape of yield curve is thus a function of supply and demand.
Interest rate risk
Risk that changing market rates will impact negatively on the return of a bond.
Duration of a bond
- Duration captures the risk attributes of a bond in a single number that measures the sensitivity of a bond’s market price to changes in the market rate.
Generalisations to bonds’ interest rate risk:
o Long-term bonds are subject to more interest rate risk than short-term.
o Low-coupon bonds are subject to more interest rate risk than high-coupon.
o Low-yield bonds are subject to more interest rate risk than high-yield.
Properties of bond duration
o Duration of zero-coupon bond = maturity
o Duration of coupon bond
Effective duration
- Interpreted as the approximate percentage change in a bond’s price for one percent change in the market rate.
- Duration becoming longer implies higher interest rate sensitivity.
Duration effect
- Approximates a change in price given a specific change in yield.
- %∆PD = – D(∆y)
