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Unformatted text preview: llar duration,
dY Fixed Income II: R. J. Hawkins d 2P
≡ Dollar convexity
dY 2 Econ 136: Financial Economics 5/ 19 Duration Hedging:
Let’s hedge one bond with another.
We deﬁne a bond hedge to be a bond portfolio that doesn’t
change in value when the yield changes.
The P&L of the portfolio:
Let Qi be the quantity of bond i .
Let dPi be the price change of bond i .
Then the proﬁt and loss or P&L of the portfolio is:
P&L = Q1 dP1 + Q2 dP2 Fixed Income II: R. J. Hawkins Econ 136: Financial Economics 7/ 19 Duration Hedging: To determine the hedge set the P&L to zero:
The the P&L of the portfolio is
P&L = −dY Q1 D$1 + Q2 D$2 = 0
Clearing dY and solving for Q2 :
Q2 = − D$1
D$2 If the original position is long then the hedge is short.
If the original position is short then the hedge is long. Fixed Income II: R. J. Hawkins Econ 136: Financial Economics 10/ 19 The Perfect Hedge: Background We know that bonds with ﬁxed coupons have a ﬁnite
Bonds with ﬂoating-rate coupons have a duration of zero.
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This note was uploaded on 01/23/2014 for the course ECON 136 taught by Professor Szeidl during the Fall '08 term at University of California, Berkeley.
- Fall '08