In a previous blog post, I had estimated that the residual currency effect (RCE) of Canadian-listed S&P500 funds has cost investors 0.99% since January 2000 and 0.67% since May 1993. In this post, I will provide more details on how I came to that finding. I conclude that hedging the currency exposure of U.S. equity holdings systematically reduces expected returns for Canadian investors.
In Canada, there are six pairs of hedged and unhedged S&P500 mutual funds and ETFs with a reasonable history.
| Name | Ticker | Launch Date | Current Management Expense Ratio |
| RBC U.S. Index Fund A | October 1998 | 0.34% | |
| RBC U.S. Index Currency Neutral Fund A | October 1998 | 0.47% | |
| TD US Index e | November 1999 | 0.66% | |
| TD US Index Currency Neutral – e | November 1999 | 0.61% | |
| National Bank Inv. U.S. Index | January 1999 | 0.69% | |
| National Bank Inv. U.S. Cur. Neutral Index | November 1998 | 0.69% | |
| BMO S&P 500 ETF (CAD) | ZSP | November 2012 | 0.09 % |
| BMO S&P 500 Hedged to CAD ETF | ZUE | May 2009 | 0.09 % |
| iShares Core S&P 500 ETF | XUS | April 2013 | 0.10 % |
| iShares Core S&P 500 ETF (CAD-Hedged) | XSP | May 2001 | 0.10 % |
| Vanguard S&P 500 ETF | VFV | November 2012 | 0.09 % |
| Vanguard S&P 500 ETF CAD-H | VSP | November 2012 | 0.09 % |
This Table is almost identical to Table 1 in my previous post, except for one difference: This time, I have added a pair of National Bank of Canada mutual funds. We will see later on why I excluded this pair from my analysis.
There is very little difference between these pairs of funds: They all hold exactly the same portfolio of stocks, denominated in the same single currency; their fees are very close when not identical, and they are impacted by U.S. withholding taxes in exactly the same way. The only material difference is that the currency-hedged funds hold long positions in Canadian dollar forwards to hedge the currency fluctuation impacts on the portfolio.
To estimate the RCE, we must first estimate what the returns of these (FX-hedged) funds would be if the hedging operations were completely accurate. In a perfect world, these returns would be very close to the local currency returns of the index, after accounting for fees and withholding taxes, of course. To achieve this result, I created a data series that mimics a perfect currency hedging transaction using 1-month forward contracts. At the end of the month, 1-month forwards do settle for cash at the spot rate, which results in a positive or negative hedge return. In other words, the 1-month forward rate converges towards the spot rate as the month advances. The hedge return is computed as follows1:
Now that we have a hedge return, we can calculate the returns of a perfectly hedged S&P500 fund2:
Another benefit of our methodology is to eliminate the effect of cross-currency interest rate differentials on the calculated RCE, since currency forward contract pricing accounts for these differences.
To check the accuracy of our reasoning, we compared the cumulative returns of the hedged mutual funds and ETFs to our simulated “perfect hedge” fund returns. The results are shown in Charts 1 to 6. These Charts display the monthly return difference between the actual currency-hedged funds and their calculated “perfect-hedge” returns. In general, returns track their theoretical value very closely with one exception: The National Bank fund. While all the other funds rarely deviate from their “perfect-hedge” estimates by more than 0.50%, the National Bank fund deviates by as much as 6%. This result is virtually impossible for a fund that systematically hedges currency risk. Our conclusion is that the National Bank fund currency hedging is actively managed and, as a result, the fund is not suitable for the purpose of this study. It is also worth mentioning that all funds had correlation coefficients of 1 except for the National Bank fund, which had a (still high) 0.95 correlation between the actual and estimated hedged returns.
Table 2 provides the RCE statistical analysis. We compiled data into two periods: January 2000 to June 2020 for the (oldest) RBC and TD funds. We also analyzed the May 2013 to June 2020 common data period for all five funds.
All funds display statistically significant negative average RCE with t-stats below minus-2, with the exception of the iShares ETF. This ETF has a negative RCE in the same order of magnitude as the other funds, but its high standard error reduces the t-stat to -1.1. In other words, its RCE is sizeable, but much more volatile than those of other funds.
To conclude, RCE has cost S&P500 currency-hedged funds 67 basis points since 5/2013, a statistically significant underperformance. As explained in my previous post, I believe this underperformance is mostly explained by the effect of the negative correlation between the S&P500 and the value in U.S. dollars of the Canadian dollar. This underperformance could decline or increase in the future depending on the future correlation and market volatility: the greater the negative correlation and volatility, the greater the negative RCE.
| Fund Manager | Period | Annualized RCE | Monthly RCE | t stat |
| RBC | 2000-2020 | -0.95 | -0.08 | -3.8 |
| 2013-2020 | -0.66 | -0.05 | -2.0 | |
| TD | 2000-2020 | -1.02 | -0.08 | -3.7 |
| 2013-2020 | -0.74 | -0.06 | -3.9 | |
| BMO | 2013-2020 | -0.65 | -0.05 | -3.5 |
| iShares | 2013-2020 | -0.72 | -0.05 | -1.1 |
| Vanguard | 2013-2020 | -0.60 | -0.05 | -2.8 |
| Average | 2000-2020 | -0.99 | ||
| 2013-2020 | -0.67 |
The Canadian-domiciled DFA US Core and DFA US Vector funds have existed in hedged and unhedged versions since February 2009 and February 2010, respectively. We have prepared the RCE analysis for these funds, both since the February 2010 common period and since May 2013.
| Fund | Period | Annualized RCE | Monthly RCE | t stat |
| DFA US Core Equity | 2010-2020 | -0.74 | -0.06 | -4.1 |
| 2013-2020 | -0.44 | -0.03 | -2.6 | |
| DFA US Vector Equity | 2010-2020 | -0.85 | -0.07 | -4.3 |
| 2013-2020 | -0.50 | -0.04 | -2.8 |
The results for DFA funds in Table 3 confirm our results for S&P500 funds: The RCE is negative and statistically significant in all periods. DFA has apparently been able to hedge the currency more effectively than the S&P500 funds over the comparable 2013-2020 period. Indeed, its RCE ranged between -0.44% and ‑0.50% compared to a -0.60% to -0.74% range for S&P500 funds.
Based on 20 years of fund returns, as well as the negative correlation we observe between the USD/CAD exchange rate and U.S. stock returns since the end of the Bretton Wood system back in 1971, we see evidence of a persistent negative Residual Currency Effect for Canadians who invest in currency-hedged U.S. equity funds. We believe that hedging the currency on U.S. equity holdings systematically subtracts from the expected returns for Canadian investors.
