Tracking ETF error

The 1 kg of stewing beef I bought ended up tasting like pork. When confronted, the butcher retorted “Well buddy, it’s meat isn’t it?”

Most consumers would be incensed at this response, but for some reason, investors are far more tolerant. It may be that mutual funds have dulled our expectations by underperforming their benchmarks for decades.

But for exchange-traded funds (ETFs), the standards should be higher, because their benchmarks are transparent indices and—for the most part—the goal is replication.

Tracking error: what is it and why is it important?

Mathematically, a tracking error is the standard deviation of the difference between index and ETF returns. For example: a 4% tracking error means annual ETF returns will be within ±4% of index return, two times out of three.

Ioulia Tretiakova, director of quantitative strategies, PUR Investing Inc., affirms that while tracking error can be important if ETFs are used to hedge a portfolio, understanding tracking error helps individual investors employ these vehicles more effectively.

There are three ways to replicate an index:

• Stratified sampling: buy only some of the underlying securities. Think of it as ordering a chicken and getting one wing, one breast, one leg, and one thigh.
• Optimization: use underlying securities and/or derivative instruments to mimic an index’s return. In other words, you’re buying chicken fingers.
• Full replication: buying all the components of an index is the most effective way to minimize tracking error. So, you order a chicken and you get the whole bird.

Ordering a chicken and getting chicken fingers may not bother some investors, but it’s important that they understand the possibility that this is what can happen.

To be fair, stratified sampling and optimization can be the only practical approaches given size and liquidity considerations. For example, the DEX Universe Bond Index has 1,058 holdings, while the popular iShares CDN Bond Index Fund (XBB) that mirrors it holds only 301 issues.

“Regulation has an impact,” Tretiakova observes. “There is no maximum security weight for ETFs in Canada, but in the U.S. there is a 19.99% cap. Hence the return of Vanguard’s Information Technology ETF (VGT) lagged its benchmark MSCI U.S. Investable Market Information Technology Index, by 50% since inception (1/26/2004 to 1/3/2010) in part because the index weight of AT&T was 49% and only 19.99% for VGT.”

That’s sort of like ordering three chickens and getting the two-bird maximum.

Should daily returns be used to calculate tracking error?

The index underlying the iShares MSCI EAFE Index Fund (EFA) and its “Loonie-hedged” cousin, XIN, does not have a contemporaneous closing time, so using daily closing NAVs and index values for tracking error calculations makes little sense; like roosters crowing dawn in each time zone.

On the other hand, the tracking error of leveraged ETFs (in Canada, the Horizon BetaPro series) should be calculated using periods no longer than daily.

Over the longer term, daily rebalancing will cause divergence made all the greater by volatility. The investor orders an egg and gets a two-egg omelette.

The multiple-of-daily-index-return objective of leveraged ETFs is not completely accurate, warns Tretiakova.

What actually happens, in the case of a 2X ETF, is that “there is twice the total return minus one times the cost of capital. Currently, this is slightly better for investors than the stated objective of twice the price return because dividend yields are slightly higher than the cost of capital. However, when these two rates vary, the difference may be more significant,” she adds.

ETFs with unusual tracking error

Some ETFs operate without a specifically stated benchmark, defining only broad asset class exposure.

For example, the Claymore Broad Emerging Markets ETF (CWO, launched April 7, 2009) states, “The manager will select an Emerging Markets Benchmark Index such as the MSCI Emerging Markets Index, the FTSE RAFI Emerging Index or another widely recognized emerging markets index in order to provide such exposure and may change the Emerging Markets Benchmark Index at its discretion without unitholder approval.” The challenge is trying to determine the tracking error when the target index is changing. One comfort these unitholders have is that the indices for groups of emerging markets will likely have similar volatility (risk), which means the advertised chicken will unlikely end up being pork chops!

Finding tracking error information

Most ETF sponsors offer tracking error information on their Web sites. Often shown in chart form, price movements of ETFs are easily compared with their underlying index.The actual tracking error of Canadian-traded ETFs and how they compare to others is available at http://purinvesting.com/demo/Screen.htm.

A cost to investors, tracking error is well worth monitoring. It’s one way of keeping ETF sponsors honest and assuring you don’t get salt pork when you expected steak.

Mark Yamada

Investments

Mark Yamada is president of PÜR Investing Inc., a software development firm specializing in risk management and defined contribution pension strategies.