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Back in the "old days" (ie 5-10 years ago) when we wanted to be long or short an emerging currency (say the ZAR, BRL, or TRY) we simply did everything against the pre-eminent currency of the day, the dollar. So for example to be long the Turkish Lira, we sold USDTRY. Short the rand, we bought USDZAR. Most of the return was attributable to the RHS of the pair.

Nowadays, the dollar is not the universally dominant hard currency, and so the relative strength or weakness of the USD itself "pollutes" a USD-EMFX position. In practise, for example, the correlation between EURUSD and USDXXX where XXX is an EM currency, has increased (in absolute terms):

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Thus, if I am short USDZAR, I am significantly long of EURUSD through the correlation. The question is, how do I hedge this developed-currency cross rate risk out? How do I get back as close as possible to a pure-play on the emerging currency?

Obviously the answer will be that I have to fund my emerging currency position with a basket of hard currencies (candidates being say, USD, EUR, GBP, CHF, CAD, AUD, and JPY). But how do I best calculate the weights of this basket? Multiple regression of USDZAR against USDEUR, USDGBP, USDCHF, USDCAD, USDAUD, and USDJPY? Is that the right approach? Is there anything better? I've seen bloomberg using PCA for example in their Bloomberg Correlation Weighted Indices.

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@moderator: How can I start a bounty on this question? It doesn't seem to be letting me do so. –  Thomas Browne Jun 4 '11 at 21:48
    
A question has to be at least two days old to offer a bounty. –  chrisaycock Jun 6 '11 at 3:09
    
Is there anything wrong with the two approaches you mentioned, regression and PCA? Those would be my first two choices for this problem. –  Tal Fishman Aug 18 '11 at 19:18
    
nothing wrong. Bloomberg has a correlation weighted set of indices (BCWI <go>} but they average the weights on each optimal basket - which to me doesn't make a huge amount of sense - takes away from the pureplay of each currency as we deviate from its optimal weights. I was just wondering at the time if there was something more interesting being done out there. I have gone with PCA bloomberg-style, without weight averaging. –  Thomas Browne Aug 19 '11 at 23:04
    
Doesn't it depend on the currency you calculate your P/L in? If it's USD, why hedge it all? You may still want to hedge, I suppose, but it is unrelated to the EM trade. Correct me, I I'm wrong, please. –  Anatoliy Aug 22 '11 at 14:53

3 Answers 3

up vote 3 down vote accepted

Short answer - Use the betas from a multiple regression to create a hedged portfolio.

In a single factor model (i.e. hedging with only one other currency), you can interpret the Beta as the proportion of the factor that you would need to short. So if Beta = .5 then for every 1MM you are long, you would go short $500K on your currency pair hedge. The same idea extends to multiple betas.

Long answer - Naturally, a host of questions open up here -- what is the window for estimating the beta? What regression procedure to use (LAD, OLS, GLS, robust methods)? Are the currency correlations stationary?

Whether to use PCA or multiple regression depends on which model is more stable. (Technical note: PCA and multiple regression assumes your errors are i.i.d. Also, the history of past returns is an approximation of Beta only if the returns are invariants - i.i.d. across time. Therefore, regressing with realized returns is not actually a true representation of the true forward distribution.).

You might try a rolling multiple regression test and measure the significance and consistency of the factors out-of-sample. If you do PCA, asymptotic PCA (see Stock & Watson 2002) is preferable for time-series with many factors.

Also, you might want to consider time-series factor analysis (see package TSFA in R) if you believe there is a latent factor structure that explains the covariance of currency pairs traded.

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Thanks - it's what I suspected. I'll look at Stock & Watson. I think the multiple regression route that I suspected is the way to go. I am going to have to look at the multicolinearity aspects though if I include a lot of other EMFX in there. Perhaps a PCA first? –  Thomas Browne Sep 1 '11 at 16:06
    
If you are only hedging the risk one security and you have a view on the most suitable hedges then PCA is not necessary as you can specify your model. If you aren't clear about what the best hedges are then you can use PCA notwithstanding the issues with PCA I noted above. Personally I would explore hedging using the factors produced from TSFA since there will be time-series autocorrelation in your data. By explore I mean test the performance of the hedge out of sample vs. a very simple approach (one factor regression). –  Quant Guy Sep 1 '11 at 20:16

It depends on what aspect of ZAR you are trying to take a position on.

As A K pointed out, if your book is in USD and you want to take a position on the spot rate itself, then just have a USDZAR position. Yes, it is correlated with EURUSD because of both EUR-ZAR correlations and because of USD variations, but that's part of the USDZAR tradeoff.

If, instead, you want to play the ZAR internal interest rates, then choose your period and do the fx swap instead; you do a USD for ZAR exchange at the beginning and a ZAR for USD exchange at the end. Since you've set the exchange rates today at the spot and outright rates, the deal is only dependent on the interest rate differential between USD and ZAR, not on the spot rate variations.

Alternatively, if you do want exposure to the spot variation, you could do a ZAR IRS plus an FX option on the spot price at 1y and if you haven't needed it just do another at 1y. For a more fixed period, do a Bermudan.

Basically, choose your instrument. There is no immovable object in finance, and you actually don't need one; if you make a basket of currencies that's really stable against market movements, you'll just have exposure to the variation of the currency of your book.

I think.

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Yep - not looking at the rates - could use IRS too of course. or fund bonds in FX forwards or repo. Looking for the pureplay on ZAR so your last para kind of answers the question. –  Thomas Browne Sep 1 '11 at 16:05

Pay close attention to what factors your model is actually predicting (or trying to predict). In the case of ZAR, a good model could be identifying mispricing in the USD factor, or it could be gold, overall EM currency risk, risk tolerance, etc. A complex model could easily be predicting all of these factors to some degree. You should strive to hedge out only those factors for which you do not have an edge. Isolate exposure to the risk you want, hedge out the risk you don't want. Ideally, you will want to do this using both a theoretical understanding of how your model should work as well as empirical work (backtests, regressions, etc.) confirming that this is how it works in practice.

Once you have isolated your desired risk factors, using either method you mention above (regression and PCA) should work fine at eliminating undesired risks.

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