 # Foreign Bond Exposure

I don’t understand why currency performance even comes into play (in some calculations in fixed income). Unless I somehow missed the gist of the vignette, there was one I read where:
-reporting currency is USD
-we buy the Mexican 5-year, & hedge it back to the home currency using currency FCs.
My first Q: Isn’t currency risk & performance eliminated by this? Clearly not, because we go on to calculate the return as: 5% Mexican 5 year rate + 2% loss on currency from peso appreciating relative to the USD (& we bought USD forward) + 3% difference between financing rates in the countries (US rate higher by 3%)
There is another reading that introduces the:
Return in home currency = (1+its return)*(1+currency return)
So, if we add a hedge to this- doesn’t it just become (1+its return in the foreign country)?

That means all returns are converted back to USD (including the MXN bond), that’s why you need to compute currency performance.

Depends on what forward rate you hedged at (using the forward contract), versus the current spot rate.

If there is a currency hedge using forward contracts (to sell MXN and buy USD), the currency return would be:

Hedged ~Currency ~return = \frac {Forward ~rate_{USD/MXN} - Spot ~rate_{USD/MXN}}{Spot ~rate_{USD/MXN}}

Note: The exchange rates are in DC/FC format (DC = USD, FC = MXN)

If the forward rate = spot rate, then the hedged currency return = 0.

If the forward rate > spot rate, then the hedged currency return > 0.

If the forward rate < spot rate, then the hedged currency return < 0.

A useful formula to approximate the hedged currency return is based on uncovered interest rate parity.

Hedged ~Currency ~return = \frac {Forward ~rate_{USD/MXN} - Spot ~rate_{USD/MXN}}{Spot ~rate_{USD/MXN}}

Hedged ~Currency ~return \approx r_{USD} - r_{MXN}

There was no hedge done here, so the currency return is based on:

Expected ~Currency ~return = \frac {Expected ~spot ~rate_{USD/MXN} - Spot ~rate_{USD/MXN}}{Spot ~rate_{USD/MXN}}

Note: The exchange rates are in DC/FC format (DC = USD, FC = MXN)

If the expected spot rate = spot rate, then the expected currency return = 0.

If the expected spot rate > spot rate (peso appreciates against USD), then the expected currency return > 0.

If the expected spot rate < spot rate (peso depreciates against USD), then the expected currency return < 0.

The situation in which currency performance comes into play in a hedged investment occurs when the amount of currency hedged is different from the actual cash flow from the investment. This commonly occurs with stocks, because you don’t know what the price of the stock will be when you sell it, and it can occur with bonds if you don’t hold the bond to maturity, for the same reason.