Duration based hedging
- Thread starter arteja
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Hi A Ravi
That's from Hull Chapter 6, so generically it refers to a duration hedge against *any* interest rahte sensitive asset; i.e., and the hedge is therefore a hedge against the interest rate factor, while the portfolio may certainly be exposed to other factors. And further, even against the interest rate factor, it's only the single-factor (approxiate) hedge given by a duration. So, in the context, Hull's example is:
Ex 6.6. Portfolio manager is long $10 MM in government bonds
So he shorts Treasury bond futures given by the formula
IMO, the way to think about the formula is, just like Tuckman's DVO1 hedge. They are essentially similar. The idea is to hedge by setting the *dollar duration* or *value duration* to equality; i.e., the hedge achieves: dollar duration of portfolio = dollar duration of hedge....in DVO1 terms, a basis point shock implies that both change in value in an equal but offsetting amount.
Re: interest rate swap: I think i did skip the criticism of the comparative-advantage argument (not of i rate swaps per se). I am not in a good position (nor is anyone, I think) to predict, with high confidence, what is relevant to the 2009 exam. Due to the density, in the videos, i do occassionally (I hope rarely) skim or skip segements of AIMs. In this case, yes, the argument against comparative advantage, I admit it hasn't come up in years so it slipped in my imagination. I could be wrong, it could be tested.
Thanks, David
That's from Hull Chapter 6, so generically it refers to a duration hedge against *any* interest rahte sensitive asset; i.e., and the hedge is therefore a hedge against the interest rate factor, while the portfolio may certainly be exposed to other factors. And further, even against the interest rate factor, it's only the single-factor (approxiate) hedge given by a duration. So, in the context, Hull's example is:
Ex 6.6. Portfolio manager is long $10 MM in government bonds
So he shorts Treasury bond futures given by the formula
IMO, the way to think about the formula is, just like Tuckman's DVO1 hedge. They are essentially similar. The idea is to hedge by setting the *dollar duration* or *value duration* to equality; i.e., the hedge achieves: dollar duration of portfolio = dollar duration of hedge....in DVO1 terms, a basis point shock implies that both change in value in an equal but offsetting amount.
Re: interest rate swap: I think i did skip the criticism of the comparative-advantage argument (not of i rate swaps per se). I am not in a good position (nor is anyone, I think) to predict, with high confidence, what is relevant to the 2009 exam. Due to the density, in the videos, i do occassionally (I hope rarely) skim or skip segements of AIMs. In this case, yes, the argument against comparative advantage, I admit it hasn't come up in years so it slipped in my imagination. I could be wrong, it could be tested.
Thanks, David
cash king
New Member
Hi David,
I'm confused by two points in Hull's charpter 6.
1.Why we calibrate the hedge ratio based on duration of the underlying asset of the futures, instead of the futures themselves? In some cases, e.g. Eurodollar futures do not have explicity underlying asset, though we know the duration of the futures is typically 0.25 year.
2.I notice that the duration of the portfolio to be hedged is measured at the maturity of the hedge, and the duration of the underlying asset is measured at the maturity of the futures. Why none of them is measured by the begining of the hedge, which seems a natural choice?
I'm confused by two points in Hull's charpter 6.
1.Why we calibrate the hedge ratio based on duration of the underlying asset of the futures, instead of the futures themselves? In some cases, e.g. Eurodollar futures do not have explicity underlying asset, though we know the duration of the futures is typically 0.25 year.
2.I notice that the duration of the portfolio to be hedged is measured at the maturity of the hedge, and the duration of the underlying asset is measured at the maturity of the futures. Why none of them is measured by the begining of the hedge, which seems a natural choice?
Hi @cash king
- I think you can hedge based on the futures; for example, Kolb's method (unassigned) does include so-called basis point (BP) model hedge for interest rate futures which is basically the same thing as Hull (i.e., a dollar duration based hedge) but he uses the DV01 of the futures instrument, not the asset. So, I infer that's merely Hull's choice. You make a good point because I am not aware of anywhere that he justifies this choice, as better than the duration of the futures themselves.
- I think this choice can also vary, but (1) the end is better than the beginning and (2) please note that he's being consistent with his approach to commodity hedges. I say the end is better than the beginning because you don't put on a hedge to mitigate instantaneous losses; e.g., If the exposure is a trade enter today and the position will be held for 90 days, you don't experience an instantaneous loss. Rather, you want to hedge your outcome (with the respect to the underlying position) at the end of 90 days. Sort of like, corporate P/L losses don't occur on Jan 1st, they occur as a flow over the year, and are "realized" cumulative at the end of the year. So, i think the idea is: we expect to have a position (exposure) through such and such time frame, and we want our hedge to offset our cumulative losses (if) when we get to the end of the expected holding period, at which time the losses will most likely be realized. That said, I think the actual hedge can be more dynamic such that you'd neither calibrate to the end (or the beginning) but something like a weighted average, to reflect the hedge wants to be ongoing over a period. In this way, I think Hull is actually simplifying from "weighted average" to "end of exposure." I hope that helps!
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