When you buy an index fund, you are buying a portfolio with real shares in weights that reflect a miniature version of the underlying market or index (see here and here for more). We also know that if the portfolio has the exact same stock weights as the index, not only should returns be equal, but also the index fund doesn’t have to trade.
Of course, when it comes to exchange-traded funds (ETFs), it’s not just the portfolio that needs to track the index — the ETF price also needs to track the portfolio. That’s where ETF market makers and ETF arbitrageurs come in.
Chart 1: ETFs tracking the index is a two-step process involving portfolio managers and arbitrageurs
They use creations and redemptions, which make arbitrage easier, to keep ETFs tracking their underlying portfolio closely, as we show today.
Do ETF returns match index returns?
If an ETF follows its index “perfectly,” you might expect the returns each day for the index and the ETF to be exactly equal. So, if the:
- Index rises exactly 1%, then the
- ETF rises exactly 1%, too.
We can show in Chart 2 how this works for real ETFs by plotting returns for both the index and the ETF, each day, on a chart for a few ETFs.
Chart 2: Most domestic ETFs track their index very well; international ETFs have larger differences in daily tracking error
We chose three very different ETFs:
- QQQ: A large and liquid, market cap-weighted, U.S. Nasdaq-100® Index ETF.
- RSP: An equal-weighted version of the U.S. S&P 500, which is harder to manage as it has more stocks and more corporate actions. Additionally, the equal weighting means the stocks need to be traded more to keep all the weights equal.
- FXI: An ETF that holds international (Chinese) stocks, which can’t be arbitraged at the same time as the ETF trades.
The data shows that the daily returns of the ETFs with U.S. stock holdings (QQQ and RSP) both track the daily returns almost perfectly. That shouldn’t be a surprise — in this study, we saw that even if an ETF doesn’t trade, the bid and offer track the underlying portfolio, with a tight spread, all day.
However, the chart looks very different for FXI, with many dots away from the diagonal. In fact, sometimes the index goes up when the ETF goes down, and vice versa.
But before you start to worry, this does NOT mean those ETFs have a tracking problem or are mispriced (they are not rich or cheap). It is normal for almost any international ETF – and caused by different closing times as the trading clock moves around the world – as we show later.
What is a “tracking error”?
We can re-plot the charts above to show the difference in daily returns for each date (Chart 3), which effectively makes the diagonal line flat. Now:
- Daily difference in returns: Each dot in the chart below shows whether the ETF return was higher or lower than the index on that day.
- Standard deviation of these differences can be calculated (grey zones with labels).
- Tracking error is an “annualized” version of the standard deviation of the daily differences in returns. The math for annualizing is shown in Chart 4 here. That makes it comparable to how we think about portfolio returns (which are often measured % per-annum).
Note that this is different to how you calculate a portfolio’s volatility and market risk (which we discuss here).
Chart 3: Daily difference in returns for a selection of ETFs above
Clearly, the U.S. ETFs holding U.S. stocks have very low tracking error compared to international ETFs. But, as we noted above, that doesn’t mean the international ETFs are mispriced or mismanaged.
Why are international ETFs different?
The difference in tracking error for the international index is usually due to the different times that the index — and the ETF — returns are calculated. In short, this has more to do with how time zones work.
For example, we know that:
- U.S. ETFs close when the U.S. market closes at 4 p.m. New York time. That means ETF returns are calculated from 4 p.m. today to 4 p.m. the next day.
- International indexes close when the local market closes. That’s often a different to US market hours.
That means the start and end times used to calculate ETF and index returns are very different.
Chart 4: A 24-hour trading day and how it impacts international stocks vs. U.S. listed ETF
The infographic above shows how this works in practice — as trading moves around the world, it passes through different trading time zones of each country in the world. For example, for FXI which we saw above:
- Economic and other news that affects stock prices comes out all day (including overnight). We can see this is true by watching the prices of U.S. S&P 500 futures, which trade on CME almost 24 hours a day (green line).
- Chinese stocks only trade during the Chinese day (solid red line).
- Returns on Chinese stocks (and the Chinese stock index FXI tracks) are calculated from Chinese close to Chinese close (dashed red line) – down on this day.
- U.S. stocks officially only trade during the U.S. day (solid black line).
- Returns on FXI ETF are calculated from U.S. close to U.S. close (dashed black line) – up on this day.
As the diagram shows, even if the ETF’s index and the ETF both follow the “beta” of the market (shown by the futures price), their actual prices and returns can be very different due to the different times each market is open.
It’s also worth noting that when markets are closed, both the black and red lines go flat. That’s not because the value of the stocks isn’t changing – but because there are no “official” trades to update the prices.
As a result, the close times for Chinese stocks and FXI ETF are very different. In the example above, the Chinese index is up, while the FXI is down, even though over the 24-hour period, the market rose.
Tracking difference matters more for international ETFs
A better way to look at the performance of international ETFs is to remove these timing differences.
One way to do that is to look at the difference in annual returns. This metric is often called tracking difference.
As we see in Chart 5, on this metric, even FXI tracks its underlying stocks well.
Importantly, this shows that the daily “over and underperformance” we see in chart 2 does not reflect the ETF being over or undervalued. For example, when the market is trending up, the index and ETF both rise over time (we don’t see mean reversion).
Chart 5: Most ETFs track their underlying index well over the longer term, too
Most ETFs track their indexes exceptionally well
For ETFs that close at the same time as their index, daily returns are typically almost identical. For all the other ETFs, with different closing times, which can include commodity and bond indexes, tracking difference is a more relevant calculation to use.
It shows that the skilled portfolio managers and dedicated market makers help ensure most ETFs track the value of underlying stocks well, regardless of whether those underlying stock markets are open or closed.
It’s another reason why ETFs work well for investors.