标题: Durations of Non-USD Bonds [打印本页] 作者: JPSem 时间: 2011-10-14 22:27 标题: Durations of Non-USD Bonds
Does anyone have any thoughts on estimating the duration of non-US denominated bonds, i.e. adjust the raw durations of these bonds to incorporate the FX effect? Would calculating the historical correlation of FX moves and interest rate moves and then adjusting the raw duration using that correlation be one of the options? Thanks.作者: ohai 时间: 2011-10-14 22:33
What is your definition of "duration" for non-US bonds? Also, are you calculating the payoff in USD? Otherwise, it doesn't seem like you will need FX.作者: bodhisattva 时间: 2011-10-14 22:38
My definition of "duration" for non-US bonds is the change in the non-USD bond's value in response to 1% change in the U.S. yields. Yes, I am calculating the payoff (returns) in USD, and given that the change in the U.S. rates are not perfectly correlated with the changes in foreign rates (these, in fact, will also be influenced by the FX rates - interest rate parity), I am assuming that I will need to adjust each non-USD bond duration by a factor, which will show the correlation between the U.S. yield curve and non-U.S. curve in question...?作者: economicz 时间: 2011-10-14 22:44
i guess the question is why are you trying to incorporate the effects of fx in your duration number............seems to be mixinig two concepts into one...............duration analysis and Break even analysis.............作者: maratikus 时间: 2011-10-14 22:49
Just hedge the principal and interest payments back into USD and calculate the duration based on that.作者: malbec 时间: 2011-10-14 22:55
Ok. Normally, you would measure duration (US rate sensitivity) and FX deltas separately, particularly since you can hedge these two things independently. As a parallel example, imagine you are pricing some other security like a call option. Call options have rates sensitivity, but you would never include this in the same risk measure as other risk components: delta, vega, etc.作者: DSquaredSlim 时间: 2011-10-14 23:00
OK, currency hedging will take care of the FX risk, but in terms of managing your duration risk with respect to the change in the U.S. rates, shouldn't there be an adjustment made to the raw duration of the foreign bonds? Say you invest in 10 year Russian zero coupon bond (duration = 10 years), denominated in Russian rubles, and 10 year UST yields go up by 50 bps, your regular duration measure will tell you that your bond will loose ~5% in value, but in reality the pricew of this bond depends mainly on the change in Russian yield curve. So if the Russian yields have, say, +0.7 correlation with the U.S. yields (this is just a made up number, for illustration purpose only), then your bond is actually going to loose 3.5% only. This is the kind of asjustment I am talking about.作者: cfalevel2011 时间: 2011-10-14 23:07
You're not completely off track, but what you're describing goes beyond the definition of "duration". You're basically trying to infer a predictive relationship between US rates and Russian rates. This is more of a regression analysis than a duration measurement.作者: bpdulog 时间: 2011-10-14 23:12
I guess you could use US rates as a proxy hedge for Russian rates, but this would probably not be reliable. For instance, in a bearish environment, US rates will probably decline, but Russian (swap) rates might increase due to higher credit spreads.
I think the appropriate answer really depends on what you are trying to do. If you are trying to construct a hedge, then you will probably need to find some kind of Russian rates swap. RUB is non-deliverable, so NDFs might not be a good hedge for Russian rates exposure. If you are trying to write some kind of academic article, then maybe regression analysis is sufficient.作者: troymo 时间: 2011-10-14 23:18
Well, it is not a "traditional" duration measure, but if you're managing a global bond portfolio then I guess you need to come up with some sort of "adjusted" durations, I assume.作者: pawn 时间: 2011-10-14 23:23
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.作者: sabre 时间: 2011-10-14 23:29
For a broad overview, beta adjustment might be ok. You would not want to use this for actual hedging though.作者: sabaruch 时间: 2011-10-14 23:34
OK, thanks for your input.作者: bolligerallstar 时间: 2011-10-14 23:40
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.作者: MarginofSafety 时间: 2011-10-14 23:45
Thanks BangBusDriver, very helpful.作者: malbec 时间: 2011-10-14 23:51
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.
