Minimum varaince hedge
- Thread starter vakshay
- Start date
Hi @vakshay They are the same really. If you need a preference, the latter is John Hull's and very well established. But they are not really different, it's one of those occasions (sort of like VaR is mathematically a negative/loss but generally expressed as a positive, such that we often need to think about the sign before plugging into something) where the sign (+/-) is effectively "delegated" to the user.
The context of the two is (slightly) different: Miller (the former) solves for the hedge in a two-asset portfolio (setting the weight of one asset equal to 1.0 or really by investing $1.0 in the first asset; so, Miller's use-case is slightly less relevant in my opinion), whereas Hull (the latter) hedges spot position with a future contract. (Not really different as both are minimum variance frameworks depending on linear correlation, but Hull's use-case just lends itself to delegating the sign). In this way, Miller's formula (conditional on positive correlation) lets the hedge ratio make explicit the short position, compared to Hull who effectively "delegates" the short position (as a hedge) to the user because, in the case of a futures, it's generally the case that you want to "step back" and think about "is this hedge of X contracts a short or long futures position?" rather than skip the a priori common sense step. I hope that helps!
The context of the two is (slightly) different: Miller (the former) solves for the hedge in a two-asset portfolio (setting the weight of one asset equal to 1.0 or really by investing $1.0 in the first asset; so, Miller's use-case is slightly less relevant in my opinion), whereas Hull (the latter) hedges spot position with a future contract. (Not really different as both are minimum variance frameworks depending on linear correlation, but Hull's use-case just lends itself to delegating the sign). In this way, Miller's formula (conditional on positive correlation) lets the hedge ratio make explicit the short position, compared to Hull who effectively "delegates" the short position (as a hedge) to the user because, in the case of a futures, it's generally the case that you want to "step back" and think about "is this hedge of X contracts a short or long futures position?" rather than skip the a priori common sense step. I hope that helps!
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