Module 57 Yield Based Bond Duration Measures and Property Flashcards
(13 cards)
What is modified Duration?
It is the anticipated percentage change in bond price (The Full Price) for a 100 bps change in yield
Calculation: Macauley Duration / 1+YTM (needs to be per coupon period e.g. divided/2 if semiannual)
What does Duration try to show us?
Duration tries to show us the slope of the bond yield curve at any given time, so for a given level of yield and price - it looks to happen what would happen to the price if the yield goes up or down.
(However it is just a single measure at a point on the curve)
How do you workout the percentage change of the full price of the bond
(minus) Annualised modified duation * change in annualised yield
What is Approximately Modified Duration?
A bond can have embedded options that make it hard to compute Macauley Duration, so better to use approximate modified duration
What is the Money Duration?
Taking the modified duration and multiplying by the full price of the bond?
What can we use money duration to do?
Use it to calculate the change in PV of the full price
PV change of full price = Mon Dur x Change in Yield
What is the Price Value of a Basis Point (PVBP)
It gives you an estimate price change, given a 1 basis point change in yield (using something simlar to the approx modified duration)
What is the calculation of the PVBP
PV of bond if yield go down (by 1 basis point) - PV of bond if yield goes up (by 1 basis point) / 2
Why is it useful?
It is useful to calculate for bonds with embedded options
How do you treat Zero Coupon Bonds
The weight of the final bond payment is 1 (as there’s no coupon)
So the Mac Dur is the Time to maturity
Mod Dur = Time To Maturity / 1+YTM
How do you treat Perpetual Bonds
Mac Dur = (1+r) / r
How do you treat FRNs?
Interest Risk arises only between reset dates, so the MacDur = (T-t)/T
T = Numbrt of days in the Coupon Period
t = days since last coupon
Represents proprtion of the period until the next reset date
What are the properties of duration
Coupon side: Higher Coupon means Lower Duration (Less sensitivity to interest changes)
YTM: Higher yields leads to Lower Duration (Less Sensitivity to Interest Changes)
Time-to-maturity: Longer Time to Maturities results in higher Duration (More sensitive to interest changes)
* exception: Long-Term bonds with low coupons, but trades at a discount but a longer maturity will not trade at a discount
Fraction of current coupon period: As the fraction increase of current coupon period, duration decreases
