pawn

This is not for an academic article, this is for an ongoing monitoring/management of a global bond portfolio. I just want to derive an overall portfolio duration that will be a meaningful measure of the sensitivity of the entire portfolio to the U.S. yield changes.

sabre

For a broad overview, beta adjustment might be ok. You would not want to use this for actual hedging though.

sabaruch

OK, thanks for your input.

bolligerallstar

Duration (D) = d(P)/d(i)
P = S*Pf
Pd = price in foreign currency, S = Spot exchange rate, i = foreign interest rate

D = S*d(Pf)/d(i) + Pf*d(S)/d(i)

= (Spot Exchange Rate)*(Duration in foreign currency) + (Price in foreign currency) * (Rho)

Rho = interest rate sensitivity of exchange rate............. (Rho is just a classification)

For practical purposes, lets not keep it Quant intensive. So, you can now obtain rho with 2 methods.


1) If you aren't hedging, then assume a linear relationship: Regress interest rates with Forex rate and get the slope. If you are not satisfied with linear relationship assumption, you can assume higher order.

2) If you are hedging, then get the term structure of local interest rates and foreign interest rates. Give them a parallel bumps taking different possible scenarios, take the foreign currency gilt and local treasury, use no arbitrage relation (i.e. you'll have no profit or loss attributable to Forex movement so you can offset any gain or loss to get the implied spot). Take the average change in spot for all scenarios and you have your Rho.

Using second method is bit better than first but it needs hedging, what I have outlined is the simple case, you can go more sophisticated with higher and point wise bumps or customizing it for china and India, which will get your value very close to actual. First method uses estimation from historical data, if you want forward looking Rho, then you have to get the forward estimates, because your position is uncovered, you can't have it easily as you are beneficiary of Forex movement being un-hedged.

This can be easily implemented in excel and easy to maintain.

MarginofSafety

Thanks BangBusDriver, very helpful.

malbec

The PM really wouldn't care about any number you came up with this way as it wouldn't replicate out of sample. The PM of a global bond portfolio would be much more interested in sources of alpha: duration (local interest rates), currency, and credit. Every shop will have its own proprietary models to come up with fundamental values for these numbers, and those models will often take U.S. rates into account (the differential specifically). A simple linear correlation between U.S. rates and a bond from another country isn't going to tell you anything.



Edited 1 time(s). Last edit at Sunday, September 25, 2011 at 10:30AM by buybuybuy.