Duration price shock

[LMFRM]

Hi David,
I don't know how to find the duration price change regarding a shock (up dans down), could you help me?
Thank you.
For example on Tuckman, chapter 4, p42

Par value $1,000.00
Years to Maturity 10
Coupon, % 4.0%
Yield 6.0%
Semiannual equivalents:
Coupon, % 2.0%
coupon, $ $20.00
Periods 20
Semiannual Yield 3.0%
Bond Price (PV) $851.23
Modified Duration
Shock, bps 20
Shock, % 0.20%
Yield up 6.20%
Price (Shock up) $837.85
Yield down 5.80%
Price (Shock down) $864. 86
Duration 7.931

 

[ShaktiRathore]

Duration=(-1/P(6%))*[P(6+.2%)-P(6-.2%)]/[2*.2%]
Duration=(-1/851.23)*[837.85-864.86]/.4%
Duration=(27.01/851.23)/.4%
Duration=27.01/.0034=7.9

 

[LMFRM]

Hi ShaktiRathore,
In fact my question is to know how to find 837.85 and 864.86 (just the price shocks)?
Thanks,

 

[David Harper CFA FRM]

Hi LMFRM to get the price inputs that ShaktiRathore used, you only need to re-price the same bond but with the yield input changed. Here is a tip (I am using the TI BA II+): you only need to change the I/Y input, as the others are already in the calculator. So ...

For the initial price, keystrokes (left to right, 3rd row)
20 N
3 I/Y
20 PMT
1000 FV
CPT PV then +/- returns 851.2253

Now to re-price with the +20 bps shock, we only need to re-key the [I/Y] and re-compute:
3.1 I/Y (or, I like to do: 6.2/2 = )
CPT PV then +/- returns 837.85

Hope that explains, thanks!

 

[LMFRM]

Hi,
Thank you.