hedge ratio, so called optimal?

[puneet_]

Hi,

I have very basic questions or doubt on option hedge ratio. i am taking below question as example for my doubt.

154.1. The standard deviation of monthly changes in the spot price and futures price of silver is, respectively, $3.20 and $5.10. The correlation between them is 0.80. An industrial firm will need to purchase one million ounces of silver in six months, but wants to hedge their price risk with silver futures (contract specifications are here http://www.cmegroup.com/trading/metals/precious/silver_contract_specifications.html). If the firm does not “tail its hedge,” how many long contracts are optimal?

i believe, difference between spot and future price is cost of carry i.e. interest or storage cost would make spot of 3.20 to future of 5.10. so if we know that company is going to need million ounce of silver in six months then the company should go for long future position for 1 million ounce of sliver. why should it hedge 501,960 ounce only (h*1million where h is optimal hedge ratio= 3.2/5.1*.8).

I think, i am laking basic understanding of hedging with futures. can someone please clarify? thanks in advance.

 

[ShaktiRathore]

Hi,
please see these links carefully:
https://forum.bionicturtle.com/threads/optimal-hedge-ratio-correlation-understanding.9482/
https://forum.bionicturtle.com/thre...ore-than-one-type-of-futures.6872/#post-25926
https://forum.bionicturtle.com/threads/optimal-hedge-ratio-and-beta-are-they-the-same.6832/
thanks

 

[David Harper CFA FRM]

Hi @puneet_ You make a good point. The question really should query a cross-hedge rather than a direct hedge of silver on silver, because you are totally right, you would likely hedge with one million ounces, just as you say. The question is really just testing the minimum variance hedge ratio so the ex post justification could be that (i) the correlation is almost 1.0 but not one and (ii) the futures price is more volatile than the spot. This latter assumption is reasonable: the cost of carry is a model of the theoretical price, if the inputs into COC are varying (stochastic), like the risk-free rate or convenience yield, the futures price can more volatile.

But that's just an excuse. The question should be corrected to introduce a cross-hedge, even if slight, to completely justify the use of the assumptions given. Thanks!

 

[puneet_]

Thanks David. understood that if it is cross hedge then 3.2 to 5.1 hedge ratio would make sense if correlation is 1. if correlation is not 1 then 3.2 to 5.1 has to be adjusted with respect to correlation. but it is ONLY true for cross hedging . if it is exactly same underlying and hedge (with same grade/quality) then hedge has to be for total 1 million ounce (minus COC). i hope it's correct.

 

[David Harper CFA FRM]

Hi @puneet_

Yes, that's correct (although, minorly, I don't think you need to deduct COC)! If the underlying spot exposure is for the same exact commodity as the futures contract, then the simplest hedge is to simply match the quantity. For example, to hedge an exposure of a quantity of silver ounces (Q), where (F) is the number of ounces per futures contract, use Q/F contracts, such that at maturity, you are exposed to the same number of ounces as you have hedged (cost of carry does not need to factor into this: both the exposure and the hedge are in the future, at maturity, when the future price will be presumed to converge on the spot price).

The optimal hedge ratio, then, is broadly a matter of cross-hedging. The only nuance here is the following: even when the spot and future contract share identical commodities, it is not necessarily the case that both (i) the ρ = 1.0 and (ii) that σ(F) = σ(S). In order for the basis risk to be zero, both of the conditions (strictly speaking) must be true. So, this is an issue of whether the hedge seeks any mark-to-market (M2M) protection; i.e., do we care about volatility of the net hedged position in the interim? The minimum variance hedge is "merely" about minimizing the variance of the net hedged position. But this would be a "more sophisticated hedge." My question is still flawed for introducing the tension. If the spot exposure and futures commodity are exactly the same, the presumption should be a quantity-on-quantity hedge. It would be the burden of the question to introduce the additional assumptions and state that is was seeking a mark-to-market (i.e., interim price volatility) hedge via the minimum variance hedge ratio. I hope that is clarifying, thanks!