Calculating duration

[sridhar]

I saw a practice question from the FRM Practice 2007 (I got these either from your site or from the back of the FRM Handbook CD)– please see below.

In the explanation – it says that the approx duration is 7.0. How is this calculated?

--sridhar

74. Hong Kong Shanghi Bank has entered into a repurchase agreement with a client where
the client will sell a 10-year US treasury bond to the bank and repurchase it in 10 days.
The bond has a notional value of USD 10m, trades at par with the yield volatility for a 10-
year US treasury 0.074%. The swap’s maximum potential exposure at a 99% confidence
level is closest to:
a. USD 320,000
b. USD 380,000
c. USD 550,000
d. USD 1,200,000
CORRECT: B
The approximate duration for a 10 year bond is 7.0. The volatility of the swap value over
10 years is calculated as follows:
σ(V) = [market_value * duration * yield volatility *(10)0.5]
= 10,000,000 * 7.0 * 0.00074 * 3.16 = 163,806.
To get the 99% confidence interval, we multiply σ(V) by 2.33, which gives approximately
$380,000.

 

[David Harper CFA FRM]

Hi sridhar,

you can't, it's wrong. We can infer coupon = yield (i.e., priced at par) but duration varies with the coupon/yield: lower coupon gets the duration nearer to ten (b/c zero coupon has Macaulay duration @ 10 with, as you know, a modified duration of 10/[1+y/k] for a zero-coupon bond), and in the other direction, as you increase the coupon/yield, the duration is dropping further from ten. Duration here could be, roughly, anywhere from 5 (high yield/coupon) to near 10 (low yield/coupon). If that's the whole question, it's awful...(plus, YIELD VOLATILITY has not been in the AIMs/LOS at all in 2007/2008...not at all..i fret the introduction of these terms when they are not assigned)

David