[Long time readers know that I’m not a fan of currency hedging (See The Costs of Currency Hedging and The Costs of Currency Hedging: Taxes). I prefer to capture exposure to US dollar equities by investing in index mutual funds that do not hedge currency exposure and US-listed ETFs such as the Vanguard Total Market ETF (VTI). Not everyone agrees with my view. Reader AB sent the following note explaining why unhedged foreign stock market investing may not be suitable for everyone. I’ll have to think through the points raised in this post and will publish my take at a later date.]

Is it nobler in the mind to suffer the slings and arrows of outrageous fortune, or hedge against a sea of troubles? (aka To hedge or not to hedge.)

I noticed on this site that Canadian Capitalist has suggested that long term Canadian investors would be better off not hedging their USD currency exposure. Specifically, Canadian Capitalist examined the tracking error over the last few years between IVV and XSP (iShares hedged version of IVV) to illustrate the effects of hedging. It seems that the unhedged position is the superior choice with an expected return excess of over 1% per year. However, closer inspection of the facts demonstrates that hedging (or at least partial hedging) is probably the more appropriate choice for most middle class DIY investors. I would like to demonstrate the risk of using an unhedged position.

First, we need to dispel the myth that, over the long term, currency fluctuations average out and thus we do not have to worry about them. This is not true. Imagine flipping a coin 100 times where tails are worth -1 and heads are worth +1. Clearly, the expectation is 0 and thus we might conclude that over the long term (100 coin tosses) it would make no difference if we played this game or not. However, the probability that you would receive exactly 50 heads and exactly 50 tails is actually very small. You will almost certainly have an excess of heads or tails. This is at the heart of the currency hedging issue – the expectation of all the currency fluctuations might be 0, but you will experience a gain or a loss from the currency fluctuations almost surely. Thus, to make an informed decision about hedging, we need to understand the downside risk of not hedging. To carry the analogy with the coin tosses a little further, we need to understand how probable it is to see a large excess of tails. In the end, investors – especially DIY middle class investors who are using their earnings for retirement – need to understand that expected performance is only part of the investment equation. Volatility also plays a crucial role for rational investors. After all, risk and reward go hand-in-hand.

Imagine an investor who invests $10,000 CAD each year in XSP escalating her contribution by 3% each year for 30 years. Let us compare this investment strategy to an investor who invests $10,000 CAD each year (exchanging for USD) in IVV with the same escalation rate over the same investment horizon. Now, we need to lay out some assumptions to see the difference in the performance between these two strategies.

XSP has an extra MER of 0.15% over IVV for the currency hedge. Given the performance over the last few years, let us assume for argument’s sake that the real cost of the hedge is 10 times greater than the hedge part of the MER – i.e., a 1.5% drag in performance just from the currency hedge. Furthermore, let us add another 0.3% to the drag of XSP arising from the unrecoverable withholding tax for RRSP investors. Thus, we expect the XSP strategy to lag the performance of the IVV strategy by 1.8% per year. Over the next thirty years, let us assume that IVV has an expected growth rate of 7% per year with an annual volatility of 20%, and that the bid-ask spread on the USD averages 2%. Given that XSP closely tracks IVV on a daily basis, the volatility of XSP is the same as IVV, 20% per year, but the growth rate is only 5.2%. The USD experiences an annual volatility of about 15% per year relative to the CAD. We will assume that over the long run, the currency fluctuations “cancel out” which is to say that the expected exchange rate over the investment period sits at the currently observed rate. For simplicity, we assume that over the long term the returns of IVV are uncorrelated with the USD-CAD exchange rate.

If we Monte Carlo (using generalized geometric random walks as an approximation for the return distributions) the two investment portfolios over a thirty year investment horizon we find the following:

XSP strategy: Expected return $1.03 million CAD
IVV strategy: Expected return $1.37 million CAD

So we see that IVV strategy has a higher expectation. However, the variance of the two portfolios show how much more risk lies in the USD investment strategy.

XSP strategy: Standard deviation $818,000 CAD
IVV strategy: Standard deviation $1.68 million CAD

We see that the standard deviation of the USD investment strategy is about twice as large as the CAD investment. This represents the extra risk that Canadian investors assume by investing in IVV over XSP.

We can also examine the probability that the IVV investment strategy underperforms the XSP strategy. It turns out that the USD investment will underperform the hedged position roughly 40% of the time once the funds are converted back to Canadian dollars at the end of the investment period. Furthermore, if the USD investment does underperforms the hedged position after the investment period, the expectation is to have about only 75% of the hedged portfolio. Thus, the poor performance of a Canadian investor using an IVV-like strategy over the last 10 years (once the investment is converted to Canadian dollars) is not that atypical. Given that most middle class DIY investors will retire in Canada with Canadian dollar obligations, I am not sure that a completely unhedged position makes sense. The extra volatility from the unhedged position implies greater uncertainty in the size of the nest egg as retirement approaches. The picture that I present here represents a rather severe view in that the hedge always costs 10 times the stated MER. I suspect that over the long term, the cost will not likely be that high.

The unhedged position has more risk and while the currency fluctuations might be expected to cancel out, no investor will see that happen – even over a 30 year investment horizon. If the XSP strategy underperforms the IVV strategy with no actual risk from currency fluctuations, then arbitrage (or at least statistical arbitrage) exists between the two investments and hedge funds would be all over it, which would close the arbitrage. ETFs already require the work of arbitrageurs to properly track the underlying index. In the long term, the total cost of the hedge on XSP will be the fair value of the risk reduction (if you believe in any sort of market efficiency). Any discrepancy in performance that you see between the two strategies is simply reflecting a risk premium and/or the effect of transaction costs. There is no free lunch – not even with index ETFs.

As a side note, check out the performance of TSX60 stocks cross listed on the NYSE (eg. TD or RY). The difference in performance is not indicating a free lunch either.

This article has 26 comments

  1. Interesting analysis. It assumes that currency exchange rates have no memory. I don’t know if this is justified. The Canada-US rate seems to stay in a fairly narrow band despite the volatility. Another thing to consider is using a slightly lower allocation to IVV along with some fixed income (in proportions to give the same expected return as XSP) and see which approach has lower volatility.

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  4. My take, based on real data for a balanced passive ETF index portfolio from 1992 to 2009 in Canadian dollar terms – currency hedging NOT required, see my post here http://howtoinvestonline.blogspot.com/2009/12/historical-effect-of-inflation-and.html. I recently have gone 100% non-hedged.

  5. One major limitation to this analysis is the assumption that the retiree converts the entire portfolio to CAD$ at the end of the period. The average middle-class retiree is likely using their savings over the course of 20-30 years so is not handcuffed to making the exchange at inopportune rates.

    Maybe all the snowbirds out there are actually Canadians with significant positions in US$ investments who don’t want to get burned by currency risk 😉

  6. Thank you for this analysis. I am still comfortable with my decision to hold VTI, VEA and VWO. My total portfolio (equity, fi, cash, commodities, etc.) is currently 50% USD and 50% CAD. I am 33. I will ratchet down USD exposure during my annual rebalance so that when I retire only 10-15% will be in USD. THis is part of my plan and I am OK with my exposure to CAD appreciation.

  7. Canadian Capitalist

    I recall reading a couple of chapters in The Triumph of the Optimists on this topic and IIRC, the authors reached a different conclusion when looking at equity returns and currency fluctuations in the past. I’ll also have to look at how rebalancing affects the hedged and unhedged stock portfolios. My guess (a priori) would be that currency volatility boosts returns and/or reduces volatility of the portfolio as a whole but I have to work this out.

    I’m planning on continuing to hold VTI, VEA and VWO. It worked well during the crash of 2008-09 and I don’t see enough reason to change course now. Of course, some investors might choose to hedge but whether we hedge or not, I think that investors should simply pick a strategy and stick with it. The “sticking with it” might turn to be far more important than the decision to hedge or not. If history is any guide, investors will instead chase performance by hedging in some periods and not hedging in others.

  8. I can see that the answer for this could vary on a situational basis. Why not consider having both hedged and unhedged when available? This way, a good portion of your dollars could be in lower cost U.S. listed ETFs while some could be allocated to higher costs TSX listed hedged products. This way you can build up a reserve to either avoid the broker’s currency conversion charge or have it so far out that the impact of the cost incurred is very small.

    IMO – It makes sense to hedge against the U.S, currency but makes very little sense to hedge against a basket of int’l securities offered in 1 product like VWO. Claymore hedges against the US $ but does that make sense given that Vanguard’s is an unhedged position?

  9. For all you so-called passive investors, you have to know that currency hedging is active management, the stuff that you all claim is not supposed to work. So why you are engaging in it makes we question your commitment and faith in passive investing. That is a separate point though

    You can do the math all day but the bigger factor is when you hedge. Hedging is like buying fire insurance. There is little point buying fire insurance after your house burned down, and similarly there is less reason to hedge AFTER the currency has appreciated so much. There were very few poeple espousing hedging when the currency was at 66 cents. Now that it has appreciated to parity, everyone says you need to protect yourself (and introduces products to fill this sudden new ‘demand’). That’s a little after the fact.

    Realizing that hedxging currency is pure active management, the best time to hedge is when you feel the current exchange rates differ greatly from Purchasing Power Parity or PPP (PPP states that goods in different countries should cost the same when correct exchange rates are applied, so differences in the price of goods between countries can explain currencies that are over and under valued). Check out the big mac index for a great usable explanation http://www.economist.com/markets/bigmac/ There are also similar indexes using I-pods instead of Big Macs. (Great post idea if you haven’t done this subject yet CC)

    PPP is roughly at about $0.85 suggesting our CDN currency is overvalued to the US$. EVENTUALLY, everything reverts back to PPP (it can be off longer than many can stay solvent, but eventually it comes back to that) .

    So hedges should have been applied closer to PPP or below it, and then hedges should be reduced as CDN$ approached parity and I would think completely gone if the CDN dollar went beyond parity by a few cents.

  10. Canadian Capitalist

    @Rob: To add to your point, currency-hedged funds were not even available in 2002. They were first introduced in late 2005, after the dollar had moved from its low to 85 cents. Many of the currency-hedged funds in existence today began life as “clone” funds that used derivatives to skirt then RRSP foreign content rules. I have to agree that there is an element of performance chasing in investors wanting currency hedging with the bulk of the negative move probably already behind us.

  11. I’m with Rob on this one. While I’m on board with international equities for the long haul my approach involves swaps between hedged/non-hedged equivalents as the Canadian dollar moves between its historical trading range with the US dollar.

    While this is far from being a passive approach, I look at it as a way to gain some additional returns and don’t mind the additional time and risk. Then again, I’m not a 100% passive investor, preferring a core/satellite (80/20) approach which has served me well.

  12. Interesting post, and subsequent comments. I can’t say that I completely disagree with the analysis in the original post, mostly because I am quite a novice in the DIY investing arena. I can’t help but be skeptical with anyone’s results of a Monte Carlo simulation.

    I’ve only ever used it for estimating construction schedules, based on probabilities of certain events occuring along the critical path.

    This much I do know, which is that the outcome(s) of the simulation and the standard deviation (and consequently the confidence in the result) are entirely dependent on the probabilities associated with each event. The inputs can always be adjusted to give the desired result. Such doctoring of the simulation removes its usefulness, and I believe is completely self-serving. Further, and here is my ignorance and youth showing through, I find it very difficult to justify the values of the probabilities used in the analysis, thus making it even easier to run simulations that give self-serving results.

    Without knowing how many events, which events, the probablilities of occurance used for those events, or how those probabilities were determined for the Monte Carlo simulations that give the results outlined in the original post, I can not simply accept those results as valid. If I were an economist in academia, I would pursue this as a research topic. If any such research has already been done and published in a peer-reviewed journal (not that those are infallible either), I would be interested in reading that article.

  13. Avon Barksdale

    First of all, using the currency hedged iShares ETFs is NOT active management. Active management ALWAYS involves market timing. In active management, when you sell a stock because you think it will go down (or buy one because you think it will go up), you are market timing the security, period. The currency hedge is always in place on the Canadian version of the iShares ETFs – so no view on market direction or market timing is occurring. Let me state that again: the currency hedge is NOT active management – it is pure risk management (you are reducing the beta of the portfolio for a Canadian investor).

    The arguments about PPP etc. don’t hold water if you believe in market efficiency. The FX market is perhaps the most efficient market ever constructed – it is highly liquid, never closes, completely global, and has huge incentives to get it right (i.e. the FX market is hyper-competitive). Markets like that become efficient in a hurry. Thus, if the Canadian dollar is at parity, I will believe the market over economists or economic arguments any day of the week. Don’t forget, it is difficult to tell if PPP is being measured right or if in fact PPP is lagging the real strength of the currency. There is no guarantee that the Canadian dollar will ever revisit 80 cents US again. BTW, if you really want to see what professional FX traders as a whole think about market direction, look at the implied volatility of European calls and puts on the US dollar (no guarantees there either, but it might be closer to the truth that any weak PPP argument).

    Thank you for bringing RBC’s webpage to my attention. The graph they display is terribly misleading. The risk does not go to zero over 15 years. They are using historical data and looking at one 15 year period from actual data. If they would have been so kind to show the 14 year bar or the 16 year bar from the same data set, you would be unpleasantly surprised. These kinds of graphs are just terrible.

    Finally, if you really believe that iShares Canadian dollar hedged ETFs will consistently underperform their unhedged brethren on the NYSE then you need to act on that knowledge. What you are saying is that a bona fide market inefficiency exists between IVV and XSP (that is you are saying BlackRock does not know how to currency hedge). In that case the obvious arbitrage is to short XSP, take the proceeds and convert to USD, and buy IVV. Do this every day or month or whatever time period you want and close out your position at the end of the year. You will make money (without using any of your own) with probability approaching 1 if you are right on the inefficiency. Better yet, you can synthetically construct quanto spread options on the performance of XSP and IVV and again you will make riskless profits. Trust me, the hedge funds, the banks, and iShares (BlackRock) are completely aware of all these methods (and tons more) – and if any arbitrage opens up, you had better believe that it will be closed by program trading in an instant.

    As far as my Monte Carlo goes, it was just a simple approximation to the market (I am not going to attempt to construct a fully generalized Levy process model of the market to make the simple observation of increased volatility). The geometric random walks I use are standard fare for these kind of simple models (see Glasserman on Monte Carlo methods for financial engineering for more details and more advanced models – you might get a sense of what I do for a living if you look this book up on Amazon).


    • Canadian Capitalist

      @Avon: An arbitrage opportunity exists only when you can make riskless profits. I’m not convinced XSP and IVV falls under this category. If an investor goes short on XSP and long on IVV, she is still exposed to the risk of CAD-USD currency fluctuations. Even if she can hedge this exposure, a profit opportunity exists only when the delta between XSP and IVV is more than the cost of all the trading.

  14. Avon Barksdale,

    I respect your arguement that always buying a hedged version is not active management – I don’t agree with it, but I respect it. On a related notion, I would contend that buying “capped” indexes is also active management. I understand that many could disagree with me, and that’s fine. The fact remains however that most people actively flip back and forth on their hedged and non-hedged EFTs to suit their mood, outlook or tea leaves…. and this is probably my bigger point that most people don’t index even when they think they do.

    That said I can’t see your statement

    “Finally, if you really believe that iShares Canadian dollar hedged ETFs will consistently underperform their unhedged brethren on the NYSE then you need to act on that knowledge.”

    is anything other than active currency management.

    As for your comments on PPP, I can’t agree with what you are saying whatsoever. How do you explain the differences in the costs of identical goods. Currency markets can be and are efficient markets, but beyond the currency, the cost of goods in those different currencies are sticky. Cars, boats, etc all cost much less in the States right now (I know there are some non-fx reasons for this, but the differences are far greater than explained by those). Maybe I am misreading or misunderstanding your comments, but are you suggesting that PPP is not real?

    Lastly, I am a CFA Charterholder and have met several great investors over the years. I can confidently state that not a single one of them would know what a “fully generalized Levy process model of the market” is. But that is another point.

    You feel me?
    Stringer Bell (aka Rob)

  15. Interesting analysis. The modeling assumptions you have made are quite clear, and seem a very reasonable first approximation.

    Think I can bridge the gap between you and Rob on the active management part. A strategic choice to use hedged/unhedged (where the hedge protection rolls over, of course) is not active management. Jumping back and forth based whether you think the time is right would be.

    You lost me on the PPP.

    Think one needs to be careful on the assumption that your target is end-of-period stability in nominal Cdn$ (@Sampson). In an ideal world, you would do asset liability matching to the currency of determination of your retirement expenses. This means that you would want the portion of your retirement that will fund e.g. a Snowbird lifestyle to be unhedged while e.g. the part that funds property taxes on your Canadian house to be hedged. It goes even further – you would not want to hedge the part of your expenses that you may well spend in Canada but will go for goods or services indexed to the U.S. dollar. For better or worse, the latter includes most discretionary spending like durable goods.

    In my case, I have a 401k from the time I worked in the US, plus Canadian domiciled RRSPs. I live in Canada. I debated whether to hedge or not hedge Cdn $ exposures, and ultimately decided to hedge since my 401k gives me adequate USD exposure.

  16. Avon Barksdale

    Thank you all for your responses.

    My point is, whatever long term lag that you see in the iShares ETFs will be the fair cost of the hedge – there is no lag from market inefficiency. CC, you make my point about the lack of arbitrage. If iShares ETFs lagged on a risk adjusted basis, then there would be arbitrage (or as I said, at least statistical arbitrage) and countless ways to make money. Arbitrage closing program trading ensures you get what you pay for. In fact, we saw its effect across the global markets today.

    The criticisms of PPP are well documented. I wouldn’ t put too much stock in the cost of goods differences – goods sell at a wide spread of prices across the US as well (e.g. a basket a goods in NYC vs Baton Rouge). Overall, I believe in markets over active managers or economists who tell the market what it should be.

    Tracking errors cut both ways. Sometimes ahead and sometimes behind. Take short term tracking errors with a grain of salt. EFA and XIN are almost perfectly in line from Feb 15, 2008 to today. Tracking errors will wax and wane. But, to escape it, you will need to add volatility to your portfolio – and just because the expectation of the extra volatility might be zero, you will see an excess or deficit almost surely. There is simply no free lunch. Whatever price you end up paying for the hedge is the fair price of the risk reduction (the Sharpe ratio will reflect this). If you believe that markets are largely efficient, then no one is getting ripped off with the hedged ETFs – you pay for risk reduction and you get it, provided of course that you retire in Canada with Canadian dollar obligations. (Active management on the other hand just squanders money to rent seekers.)

    BTW, tracking errors appear in other places besides ETFs. Take dual listed companies like the formerly DLC Royal Dutch Shell. Shell and Royal Dutch should have always traded at a specific ratio but it often did not, separating sometimes widely. This tracking error appears to be arbitrage but in reality, the tracking error might reflect other real risks in the market. In fact, LTCM lost a bundle trying to exploit this arbitrage strategy in 1998.

    I admit that I don’t have a CFA or any other financial designation. But I do have a PhD in theoretical physics. If more fund managers knew about Levy processes and understood the full implications of risk neutral pricing – and did the work themselves – they would have been much more cautious about snapping up all those “undefaultable” MBSs in the American housing market 5 or 6 years ago.

    I feel you, Stringer. We just gotta hold those corners!
    Avon Barksdale

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  22. As a derivatives specialist and someone who hedges currency via futures, I thought this was an excellent, excellent article….The author was bang on in his coin toss analogy to illustrate the point that investors can’t just assume that over the long run currency hedging balances itself out. Furthermore, many people overestimate the cost of hedging. It is a fairly cheap process anyway.

    Moreover, I can tell you there are lots of times where it would be totally ludicrous not to hedge currency. For example, when it comes to fixed income instruments, I much prefer buying US denominated corporate bonds which trade electronically and offer better pricing than Canadian bonds which trade via Canada’s dealer network and are subject to large markups by the various financial institution.

    With that in mind, let’s say I own a US denominated bond that pays perhaps 6%-7% — why in the world would I want to subject myself to possible currency losses and expose myself to additional risk. The fact that the currency might balance out over the long run would bring me little comfort in an environment where the C$ were to appreciate against the US$.

  23. Niggly statistical point here that may have a significant effect on the result of the simulation. I’m guessing you assumed that CAD:USD exchange and S&P500 returns are uncorrelated/independent, when in history, they have been strongly inversely correlated. The net effect ought to be lower volatility of an unhedged S&P500 exposure in CAD terms.

  24. With an eye on total long term portfolio return and annual rebalancing, AFAIK, increased volatility of the unhedged in your portfolio should be a good thing, once the very long term trend of the unhedged fund is upwards.

    With the dividend withholding drag situation, should non taxable accounts not look for a more direct way to hedge, and hold the US based fund directly.

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