# Hedging currency & market risk

Is point 2 below correct? 1) hedge price risk -> get foreign risk-free rate 2) hedge currency rate - > get interest rates differential: domestic risk-free rate - foreign risk-free rate 1)+2) hedge both - > get domestic risk-free return If I hedge the currency risk, why would I earn the interest rate differential?

Because you hedge the exchange rate risk. So you don’t benefit from currency appreciation and vice versa. So what you earn is interest rate differential - hedge costs.

what about the return on the investment though? How does it figure in that?

For calculating total return in DC: 1) do not hedge… Rdc = [V(dc,t)- V(dc,0)]/V(dc,t) 2) hedge only fx (principal) Rdc = R(dc, unhedged) + R(currency hedge) R(currency hedge) if you sold fc to hedge against fc depreciation = -(Ft-F0)/S0 3) hedge the underlying but not FX…if perfectly hedged…Rdc = Rf(fc) + R(currency) 4) hedge both…perfectly…Rdc = Rf(dc)

shanghaiexpo Wrote: ------------------------------------------------------- > For calculating total return in DC: > > 1) do not hedge… Rdc = /V(dc,t) > > 2) hedge only fx (principal) Rdc = R(dc, unhedged) > + R(currency hedge) > R(currency hedge) if you sold fc to hedge > against fc depreciation = -(Ft-F0)/S0 > > 3) hedge the underlying but not FX…if perfectly > hedged…Rdc = Rf(fc) + R(currency) > > 4) hedge both…perfectly…Rdc = Rf(dc) what are you referring to by R(dc, unhedged)? thanks! M.

R(dc, unhedged) is the equation in #1…your domestic unhedged return.

shanghaiexpo Wrote: ------------------------------------------------------- > R(dc, unhedged) is the equation in #1…your > domestic unhedged return. it does make sense! thanks!

what about foreign FI? I remeber having seen a hedged return computed as follows: ==> RFR (domestic) + (Return foreign - RFR Foreign) have you seen it before? thanks! M.

that is correct… for a bond, if you hedge the currency: R(foreign bond, DC) = R(LC) + [Rf(DC)-Rf(FC)] ==> R(LC) + FC premium/discount locked in one question I have is why is there a difference when you currency hedge a foreign asset vs currency hedge a foreign bond. When hedging foreign asset: hedged return = R(unhedged,DC)+R(fut) When hedging a foreign bond: hedged return = R(bond,LC)+FC premium/discount Why are the 1st terms different?? anyone?

nevermind…i think i figured it out.

shanghaiexpo Wrote: ------------------------------------------------------- > nevermind…i think i figured it out. Please advise why hedging foreign asset (equity) and hedging a foreign bond is different. TKVM in advance !

Open to other thoughts… in the questions far, when the hedging is in reference to a foreign asset, you are selling it at the expiration of the hedge. So you get the domestic unhedged return and return from the hedge. but in the bond questions, you are not selling the bond at the expiration of the hedge. So if you are holding the bond, then the return is only local return of the bond and the return on the hedge. I presume if you are told to sell the bond at the end of the hedge, then the calculation would be the same as the one for foreign asset. Does this make sense?

shanghaiexpo Wrote: ------------------------------------------------------- > So if you are holding the bond, then the return is only local return of the bond and the > return on the hedge. I presume if you are told to sell the bond at the end of the hedge, > then the calculation would be the same as the one for foreign asset. For bond, you can not hedge the capital gain because you don’t know the amount of the capital gain and this shall be same as the case for equity. So, only coupon payments (maybe with re-invested return) can be hedged, right ?

I think we might be making this more complicated than it needs to be. But for bonds, at maturity, you know what value you’d get, so that is hedge-able in theory. The coupon payments would be part of the local return part of the equation. I have not come across a question that ask to hedge coupon payments only for foreign bond. But I suppose you can do a currency swap for that. wtf…I dont even know if I’m making sense…brain overload…

OK, then it’s better for us not to go further. This portion is vague in CFAI text.

Hello everyone! I would have a question regarding 4)

I just can’t get how do you obtain the domestic risk free return when you hedge both the price and the currency risk. Here is how I see it:

Rf - return on foreign asset (in foreign currency)

RFf - risk free rate in foreign currency

RFd - risk free rate in domestic currency

S - spot exchange rate

F - future exchange rate

Pd - price of asset in domestic currency

1. Hedging the price risk of the foreign asset

a. the foreign asset produces some price return and pays some dividends: Rf + Div

b. you sell a futures on the foreign asset which yields you the foreign risk free rate less dividends: RFf - Div

c. you sell the foreign asset at the futures price and earn: RFf - Div + Div (from the held asset) so in the end you get RFf

So it’s fine up to here.

2. Hedging the currency risk.

a. Simultaneously to purchasing the foreign asset, you short a futures contract to be convert the equivalent of the asset’s worth in the future denominated in foreign currency ( S x Pd x (1+RFf) ) to domestic currency

b. From interest rate parity one would say that the future exchange rate (embedded in the futures contract) would be equal to: S x (1+RFd) / (1+RFf)

c. So at the contract maturity you convert your asset’s value in foreign currency to domestic currency (down the ask and divide) :

S x Pd x (1+RFf) / S x (1+RFd) / (1+RFf)

what you get is: Pd x (1+RFf)^2 / (1+RFd)

doesn’t look like domestic risk free return:) Any idea on what I am missing here?

By hedging price risk you earn the foreign risk free rate . RFf

If the foreign currency depreciates you will lose on the repatriation , so you hedge this depreciation by shorting currency futures to the extent of the expected gain in the deal : So you will short Pd*S*(1+RFf) in foreign currency futures . at the horizon the spot will be S*(1+RFf)/(1+RFd).

So when you repatriate your foreign asset gains which will be worth Pd*S*(1+RFf) in the future , you will have in domestic currency , using the implied future spot :

Pd*S*(1+RFf) / ( S*(1+RFf) /(1+RFd) )= Pd*(1+RFd)

You had everything right in your example , except part c where you convert foreign asset back to domestic

Thank you very much for the reply and for your help! Yet, I am not sure about the spot rate in the future that you propose: S*(1+RFf)/(1+RFd). Wasn’t the RFd supposed to be in the numerator and not RFf? Please have a look (I am not sure what this source actually is, but seems to be dedicated to CFA preparation):

http://tiny.pl/qp7cr

Your version of the equation definitely produces the right answer, but how did you get the (1+ RFf) in the numerator and the (1+RFd) in the denominator?