Minimum Variance Hedge Ratio

For hedging currency risk of a foreign asset, I understand that you could sell a forward contract on the initial principal of the amount you are trying to hedge. This is called a “naive” hedge and will not account for changes in the asset value after the hedge has been set. This is why the MV Hedge ratio is introduced. Do we need to be able to do any calculations w/regard to the MV ratio? What are the main concepts on this? My take is the MV ratio will be lower for exporters since there is already a “natural” hedge since they would be helped by a depreciating domestic currency. What say you AF?

leon, there is a formula – from my memory it is Ht+He

And Ht always = 1, right?

Yes. Which is the principal. He is the cov of (Rlc + Rcurrency)/Var Rlc

What is Rlc? Return local currency?

You got it Smarshy. BTW, I loved part II of JJ. Almost better than the real thing (even in high def).

What is JJ? Do you mean the Jenna Jameson thing? Would love to take credit for the genious, but wasn’t me.

Smarshy Wrote: ------------------------------------------------------- > What is JJ? Do you mean the Jenna Jameson thing? > Would love to take credit for the genious, but > wasn’t me. Oops, yes, it was Slash. Sorry, short term memory problems!

The second term accounts for the covariance of the local currency return and the asset returns (economic risk). If there is no assumed relationship between the two then the optimal decision will be to just hedge the principal (as we usually do) as there is no bias in either direction (you can’t know if you should hedge more or less than principal). If there is a relationship between the two then by only hedging principal you are going to leave yourself exposed to more/less currency risk then desired. For example, if when the local currency appreciates the underlying asset is more likely to appreciate too then you would want to hedge less than the principal amount. I guess the optimal amount will be function of the strength of the relationship.

So the crux of this is that if LC and asset returns are correlated then use a MV Hedge. The principal portion (HT) always equals 1, and HE will increase with correlation between the asset return and LC return. Am I in the ballpark?

That sounds right to me ozzy.

What if the LC and asset returns are perfectly negatively correlated? In that case, the correlation equals to -1 and hE = (-1) * stdev(RL) / stdev(Rc). If we assume that the stdevs are same, then hE = -1 and min hedge ratio = 0. It means that if the asset and currency returns are negatively correlated, then do not hedge at all? Is my interpretation accurate?

Vegas Wrote: ------------------------------------------------------- > What if the LC and asset returns are perfectly > negatively correlated? > In that case, the correlation equals to -1 and hE > = (-1) * stdev(RL) / stdev(Rc). > > If we assume that the stdevs are same, then hE = > -1 and min hedge ratio = 0. > > It means that if the asset and currency returns > are negatively correlated, then do not hedge at > all? > > Is my interpretation accurate? I don’t think so. Your return will likely not be as large as your principal so it would reduce the amount of hedge needed but won’t totally wipe out the 1 for the Ht.

I think this can be done on the fly with a bit of common sense. If you aren’t given a relationship, then just hedge the principal - if you are given a relationship, it’s likely to be in the form of “if currency strengthens by 10%, the market goes down by 4%” So you just hedge the difference.

good job chris, that common sense is much easier to digest

chrismaths Wrote: ------------------------------------------------------- > I think this can be done on the fly with a bit of > common sense. > > If you aren’t given a relationship, then just > hedge the principal - if you are given a > relationship, it’s likely to be in the form of “if > currency strengthens by 10%, the market goes down > by 4%” So you just hedge the difference. Chris, can you give an example of your rational, I think I can follow your thought, but just want to make sure. Thx