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tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### Duration of Inflation Linked Bonds

Is the duration of indexed linked bonds calculated the same as for fixed interest bonds?i.e. like sum(t_i x payment_i x (1 + yield)^-t_i) / sum(payment_i x (1 + yield)^-t_i)

Gmike2000
Posts: 801
Joined: September 25th, 2003, 9:49 pm

### Duration of Inflation Linked Bonds

It depends on your understanding of the word duration. If you mean duration in the sense of how the price changes as the (nominal) curve shifts around, then linkers are a bit different. Basically, there is a correlation between the real yield and the nominal yield curve. For example, if the (nominal) curve shifts up, a nominal bond will lose in value. A linker, however, will lose a bit less, because an upward shift in the (nominal) curve incorporates rising inflation expectations, for which the linker bond holder will be compensated. And vice versa. So the linker duration is usually lower than the nominal bond duration.The other day, while travelling, I met a salesperson from a third tier bank who claimed linkers slowly become like zero bonds, because the notional accumulates up to the maturity of the linker. That was the most ridiculous thing I have ever heard from anyone in the business....clearly, that person does not understand duration (actuallly, does not understand fixed income.).

tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### Duration of Inflation Linked Bonds

Could I not:1) use the current inflation expectations curve to project each coupon payment and the redemption payment2) calculate the GRY based on these derived cashflows3) use the standard duration formula ?

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### Duration of Inflation Linked Bonds

It's a complex subject, with mucho academic brouhaha around it, if memory serves... I remember seeing papers flying around that discuss the proper approach to calculating linker duration when it's done as a leg of an asset swap trade. The basic problem is the inability to separate inflation risk premium from actual inflation expectations. As a result the operative concept of inflation trading is breakeven inflation (bei), which effectively is a lump measure of everything.At any rate, issues of correlation between nominal rates and real rates are theoretical, really, since there's a million complex points in there. In practice, when linkers are traded, their dv01 = dv01(as if it were nominal) * Index Ratio. This works out OK, because subsequently bei also effectively incorporates the increased convexity of linkers to which I think Gmike is referring.