Duration Calculation

[DJS05101985]

Reading 50 Question 20:
Suppose that the coupon curve of prices for a passthrough security for some month is as follows:
7% –> 94
8%–> 97.06
9%–> 99.50
10%–>102.60
11%–> 105.25
12%–>106.19
Calculate duration for 9% coupon passthrough?
Ok - so duration = [(V-)-(V+)]/(2*V0*dY) , right? Now this bond has a negative duration, i.e. as yield is increasing so is the price. Compared to the “usual” curve which has an inverse relationship between yield and price. So V- = 97.06 and V+ = 102.60, duration = -2.78. But the book says V-=102.60 and V+=97.06. What am I missing?

 

[S2000magician]

If the numbers are correct as you’ve given them, then your duration calculation is correct, and their explanation is wrong.
Is there an erratum posted on this?

 

[ro424]

It’s because you need to calcuate coupon curve duration, see p. 573 of the reading.
The premise here is that the higher the coupon the lower the YTM, so when yields tighten, the price change will be to the higher coupon (and lower yielding) bond.

 

[Kirtika]

%Change in price= - D *%change in yield.
The negative sign denotes the inverse relationship of the yeild and bond price,
Correct me if I am wrong

 

[S2000magician]

Kirtika wrote:%Change in price= - D *%change in yield.
The negative sign denotes the inverse relationship of the yeild and bond price,
Correct me if I am wrong

This is true as along as D is effective duration (and Δy is small enough that the effective convexity adjustment doesn’t matter).

 

[Kirtika]

Sure thanks S2000magician

 

[S2000magician]

My pleasure.

 

[cfa2014]

Concur with ro424 and Kirtika- The notation and its respective value reflects the inverse relationship
V(-) if the yield is increased and V(+) if the yield goes up
V(-) > V(+) due to the inverse relationship, so V-=102.60 and V+=97.06 is correct. There are quite a few examples across the FI reading