# The "Standard Gauge" and ETF Tracking Errors

The "standard gauge" is the distance of 1,435 mm (4 feet, 8.5 inches) between the rails of a train. It is called "standard" because it is the most common worldwide standard. This measure was created by George Stephenson, the engineer who built the first railway linking the cities of Liverpool and Manchester in 1830. Stephenson "invented" the train: cars on rails dragged by a steam engine. A practical man, he was still illiterate at the age of 18 because his family had no money for schooling. Working in coal transportation and studying day and night, he overcame his cultural handicaps to finally become a precursor of the second industrial revolution, created by vast movements of men and goods. The "standard gauge", however was not original. It is said that Stephenson used the same wheel distance as horse drawn carriages, which was virtually unchanged since Roman times. The constant distance between rails is crucially important: the ties, which serve to keep the rails at the right distance, are the key element to preventing a train derailment.

In finance, we had no problems similar to those of equidistant rails until the arrival of exchange traded funds (ETFs) in the 1990s. ETFs are an exact replica of an index. For example, the XIU.TO is a copy of the S&P/TSX 60, the SPY is the exact replica of the US S&P500 and XSP.TO is the replica in Canadian dollars of the US SPY. So in principle, if the index S&P/TSX 60 is up 10 points, the XIU must rise by the equivalent of 10 points: the standard gauge of the ETF. In financial jargon, this is called "tracking efficiency". In the vast majority of cases, ETFs accurately reflect the movements of the underlying index. However, the standard gauge between the two rails (the index and the ETF) is sometimes not respected and the price of an ETF gets "derailed". This is called the "tracking error". In the case of XIU, this temporary anomaly rarely exists and its duration is very limited, but for other ETFs, temporary derailment is more serious. Here are some reasons why this may occur:

1. Periodic rebalancing of the index (that is, a return to the original allocation of the securities comprising the index) causes the ETF to suffer the same fate. This translates into added costs as well as a delay between the time of rebalancing by the index and the ETF.
2. The addition of a new issue replacing another in the index, which means that the ETF must readjust accordingly. While the change in the index is instantaneous, the ETF must adjust through buy and sell transactions.
3. Distributions of dividends and coupons which can cause a variation in the standard gauge. ETF issuers hold one or more months of dividends and coupons before distributing or reinvesting them. This means that they have short-term capital that generates a profit which may alter the normal responsiveness to movements of the ETF's underlying index, creating a variance in tracking efficiency.
4. Sometimes ETF issuers lend securities to other institutions and collect a profit in addition to the performance of the ETF.
5. Foreign securities in an ETF may be subject to foreign taxes while the index does not have this issue since it doesn't actually own any securities.
6. For US listed ETFs in Canada (e.g. XSP.TO = SPY), the exchange rate risk is borne by the issuer. A significant variation in the difference between interest rates of the two countries can momentarily affect hedge effectiveness.
7. For ETFs replicating the behaviour of futures such as natural gas, oil or leveraged ETFs (double, triple up or down) repositioning for new futures expiries generates variations in tracking.

The list could be longer. Those interested in looking into this further can read an excellent Morningstar publication titled, "On the Right Track: Measuring Tracking Efficiency in ETFs" available free online.

Periodically, issuers are obliged by regulations to show the variation of the tracking error as a percentage. This information is publicly available. To access the source directly, visit SEDAR, the official documentation site available at this link: http://www.sedar.com/search/search_form_mf_en.htm NOTE - This link will open in a new tab.. Enter the issuer's name: e.g. "iShares" under "Investment Fund Name" and then in "Type of Material" choose "Management Report of Fund Performance." From the list of documents that appears, select "iShares S&P/TSX 60 Index ETF," that is to say XIU. On page 9 of the document, the historical performance of the index and that of XIU will be displayed. For example, at December 31 2014, the XIU (ETF) return for the year was 12.04% while the index had a return of 12.27%. Two factors are responsible for the negative difference of 0.23%: the annual management fee (0.15%) and the tracking error (0.08%). Note that the this tracking efficiency is very good. During the years before 2014, the difference between the index and the ETF was much the same. This proves that the XIU ETF is a faithful representation of the behaviour of the S&P/TSX 60.

Here is another example: XHY is an ETF that replicates in Canadian dollars the behaviour of the US ETF HYG. The latter has an underlying index of US high yield corporate bonds (Markit iBoxx USD Liquid High Yield Index). The official document of the issuer, iShares, on SEDAR says that the one-year performance at December 31 2014, was 2.64% for the ETF and the underlying index had a return of 3.22%, a negative difference of 0.58%. Annual management fee is 0.60%. Once we remove these charges we see that the ETF has a tracking that is virtually perfect: the difference of 0.02%, insignificant but in favour of the ETF, probably indicates a gain from holding coupon payments before distributing them monthly to unit holders. In contrast, the longer period of three years (2012-2014) shows a difference of -1.34% between the fund's performance and that of the index. Over three years, the tracking efficiency was not as good on average as that of 2014. By removing the 0.60% management fee, a tracking error of 0.74% remains, which is not as good as that of XIU. However, this does not negate the ability of this ETF to accurately track the movements of the underlying index.

A third example is that of the iShares XIN.TO ETF. This fund is a replica in Canadian dollars of US funds following the MSCI EAFE (quality stocks from 21 markets worldwide, excluding the US and Canada). At the end of 2014, the return for the year of XIN was 4.15%, while that of the index was 6.45%, a negative difference of 2.30%. If we remove the annual management fee of 0.48%, we have a 1.82% tracking error. This is more than double the previous ETFs mentioned. This shows that the more complex the index an ETF replicates (subject to frequent changes in the underlying securities, managing many exchange rates, etc.), the greater the tracking error, creating uncertainty about the ETF's tracking ability.

Issuers like BMO show tracking error graphics on their websites, which is interesting because at a glance, you see the sometimes variable distance between the index and the ETF throughout the time. At the following site (http://www.etfs.bmo.com/bmo-etfs/trackError?fundId=92494 NOTE - This link will open in a new tab.) there is a chart of the tracking error between the S&P500 index and the BMO ETF for this index over the past 12 months. It is the same for all other BMO ETFs.

The conclusion here is that tracking error is an important factor that investors should not overlook when selecting ETFs for their portfolio.

## The author

### Charles K. Langford

PhD, Fellow CSI

Charles K. Langford is President of Charles K. Langford, Inc, Portfolio Managers. He teaches portfolio management at School of Management (École des Sciences de la Gestion), University of Québec (Montréal). He is the author of 14 books on portfolio management, derivatives strategies and technical analysis.

Until 2007 he has been vice-president overlay risk management for Visconti Venosta Teaspoon Approach Management, Ltd. Until 1990 he was portfolio manager for Refco Futures (Canada) Ltd.

He has received a Bachelor degree from Université de Montréal, a Master degree and the PhD from McGill University (Montreal); he is Fellow of CSI (Canadian Securities Institute).