# CFAI Book 6 pg. 167

Can someone please explain the calculation in example 3 part 2? When I calculate it I get: Rh=R + S(1-h) R=4.05% S= -5.0% Rh=-4.05% + (-5.0%)(1- -.2) Rh=-10.05% Am I missing a negative? Should the hedge ratio be .8 the minimum variance hedge ratio?

I am not sure, but thats how I understood it: h (minimum-variance hedge ratio) = 0.8 (as you wrote) R (return in foreign currency terms; \$) = 1.01 / 1 = 1% (Where did you get the 4.05%?) using the equation you mentioned: Rh = R + S (1-h) becomes Rh = 0.01 + (-0.05) (0.8) Rh = 0

Thanks for the direction! I was using -4.05% which is return in the domestic currency. Thanks for catching my mistake. Just to clarify for anyone else interested: minimum variance hedge ratio = translation risk + econ risk Translation risk is always = 1 and econ risk in this problem is -.20 so 1-.2=0.8.

didn’t you guys notice that this minimum-variance hedge ratio is not helping? becuase of the under-hedge (hedge ration h = 1 - 0.2 = 0.8), the 1% foreign return was gone. the dollar investor ends up 0% ( 1% - 5% * (1 - 0.8) ). so, where’s the proof that economic risk was minimized? however, if we could turn it around, when security return is negatively correlated to fx (-0.2 in this case), instead of under-hedge, we do over-hedge. i.e. we flip the sign. so h = 1 + 0.2 = 1.2, in this case, dollar investor would receive 2% ( 1% - 5% * (1 - 1.2) ).

Most aren’t hedging for a gain, you are trying to minimize the currency effect…no hedge is perfect remember that. If you were speculating that the currency was going to appreciate then you wouldnt hedge at all, if you were speculating that the currency was going to depreciate, then why not just buy an option and if it does depreciate then you lose the premium.

bigwilly Wrote: ------------------------------------------------------- > Most aren’t hedging for a gain, you are trying to > minimize the currency effect…no hedge is perfect > remember that. If you were speculating that the > currency was going to appreciate then you wouldnt > hedge at all, if you were speculating that the > currency was going to depreciate, then why not > just buy an option and if it does depreciate then > you lose the premium. you missed my point. minimum-variance hedge ratio is to “minimize the exposure of exchange rate moment” (cfai, book6, p164). there were two currency exposures being discussed. one exposure is translation risk. one can hedge out this risk by hedging on principal. by doing so, the dollar investor of example 3 can still pocket 0.95% out of 1% foreign gains. another exposure is economic risk (or corrlation risk). in order to control this risk, our dollar investor of example 3 gave up the easy 0.95%. under this context, there are two ways of hedging, one is the simple way (hedging on principal), another is the fancy way (variance-covariance). but, the example 3 failed to show that the fancy way reduces currency exposure for the dollar investor. on the contrary, it increases exposure by a factor of 20 such that all the foreign gains were wiped out. this is my whole point.

Accordign to this from above: Rh = 0.01 + (-0.05) (0.8) Rh = 0 --------------------------------------------- Not sure why Rh = 0, my math says 0.01 + (-0.04) = -0.03 or -3%. If we change .8 to 1, my math says 0.01 + (-0.05) = -0.04 or -4% It appears the decision to only hedge 80% of the principal was better than hedging 100%. Also Translation risk and Economic Risk go hand in hand. It is assumed Translation Risk = 1, unless specified as other. Anyways, I’m off track, I dont see how you say it failed?? If the local currency appreciated, thats GOOD and you want to be exposed to that, you dont’ want to be exposed when the LC depreciates.

your math is indeed wrong. Rh = R(local) + (1 - h) * R(FX) = 1% + (1-0.8) * (-5%) = 0% if using principal hedge, h = 1, Rh = R(local) = 1% (but if consider the loss in unhedged capital gain, Rh = 0.95%) compare outcomes of two hedges, which way would you prefer?

Ok, how is my math wrong… if the Econ risk is -.20 , then 1+ -.2 is 0.8. So… 1% + -5%(.8) = -3%. Why are you subtracting .8 from 1?? Teh Hedge ratio is .8, not 1-.8.

Ok, I apologize, I used the formula from above and didn’t resort to the book to see the formula up top was incorrect. It should be 1% + -5%(1-.8) = 0. Sorry, i was confused b/c of the original equation. I’m incorrect on this one

haha… pal, time to re-read the book… equation (46-10) at p165. basically, the math says if hedge ratio is 0.8, then one has 0.2 unhedged. that 0.2 of currency exposure is for the dollar investor to take to “minimize the overall exchange risk”. huh … back to my original argument, “really?” !

If you see my last post, I did re-read, hence teh apology :). My whole argument was going off a formula that someone else posted int eh beginning that i took for granted. Anyways, I think its supposed to minimize the volatility of the portfolio, but I think that was a paraphrase from Stalla can’t remember.

FYI, rand0m, the variation of the formula I was using is correct however you must use the Domestic return (or Unhedge return) vs the LC return. So it should have been this: -4.05% - (-5%*.8) = -0.05% or ~0. My mistake was using the 1% without figuring out what the 1% was

ok, if you promise not to ban me from this forum then I promise to go back to my maths elementary school books… I will revisit the issue later, after work, I guess and check what happened… sorry for the confusion!

just to make sure: You can use either Rh = R* - h x Rf, where R* is measured in Domestic Currency for the investor (here: 0=-4.05% - 0.8 x (-5%) ) and the cross product term is assumed to be 0. or you can use Rh = R + s (1-h), where R is measured in Local Currency of the Portfolio (here: 0=1% + (-5%) (1 - 0.8) ) Thanks and again my apologies for the confusion.