Reading 46: Understanding Fixed-Income Risk and Return Flashcards
What does the Macaulay duration represent?
Give the formula for modified duration as well as the formula used to estimate the annual modified duration if the Macaulay duration is not already known.
The Macaulay duration is the weighted average of the time it would take to receive all the bond’s promised cash flows, where the weights are calculated as the present value of each cash flow divided by the bond’s full price.
ModDur =MacDur/(1+r)
ApproxModDur=((PV−)−(PV+))(2×(ΔYield)×(PV0))
Describe callable bonds when interest rates are low relative to the coupon rate.
It becomes more likely that the issuer will call the bond, so the embedded call option gains value for the issuer.
As interest rates fall, the callable bond suffers “price compression” as it becomes likely that the bond will be called, with the call price serving as a cap on the callable bond’s value.
The effective duration (slope of the price-yield profile) of the callable bond is lower than that of an otherwise identical noncallable bond—its expected life shortens as the weighted average time to receipt of cash is reduced.
What can generally be stated when the investment horizon is greater than, less than, and equal to the Macaulay duration of a bond.
When the investment horizon is greater, coupon reinvestment risk dominates market price risk. In this case, the investor is concerned about interest rates falling.
When the investment horizon is less, market price risk dominates coupon reinvestment risk. In this case, the investor is concerned about interest rates rising.
When the investment horizon is equal, coupon reinvestment risk and market price risk offset each other.
What does the price value of a basis point (PVBP) estimate? Give the formula.
The change in the full price of a bond in response to a 1-basis point change in its yield-to-maturity.
PVBP=((PV−)−(PV+))/2
Describe the dimensions added to a bond purchased at a premium/discount.
A discount bond offers a coupon rate that is lower than the required rate of return, so amortization of the discount serves to enhance the return to bring it in line with the market discount rate.
A premium bond offers a coupon rate that is higher than the required rate of return, so amortization of the premium serves to lower the return to bring it in line with the market discount rate.
Describe putable bonds when interest rates are high relative to the coupon rate.
It becomes more likely that the investor will put the bond back to the issuer, so the embedded put option gains value for the investor.
As interest rates rise, the putable bond does not lose as much value as an otherwise identical nonputable bond. The put price effectively serves as a floor on its value.
The effective duration (slope of the price-yield profile) of the putable bond is lower than that of an otherwise identical nonputable bond—its expected life shortens as the weighted average time to receipt of cash is reduced.
Explain money convexity.
While money duration indicates the first-order effect on the full price of a bond (in dollar terms) given a change in the yield-to-maturity, money convexity (MoneyCon) is the second-order effect. The money convexity of a bond is its annual convexity multiplied by the full price of the bond.
Note: The convexity of a putable bond is always positive.
Differentiate modified duration and money duration.
While modified duration is a measure of the percentage change in the price of a bond in response to a change in its yield-to-maturity, money duration is a measure of the dollar (or whichever currency the bond is denominated in) price change in response to a change in yields.
List the factors that lead to greater duration and also lead to greater convexity for a fixed-rate bond.
The longer the term-to-maturity, the greater the convexity.
The lower the coupon rate, the greater the convexity.
The lower the yield-to-maturity, the greater the convexity.
