[Long time readers know that Im 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. Ill 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 arguments 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.