Tracking error explained

by , 1st January 2018

In truth, we are starting this article from a false premise. To call what we are investigating ‘tracking error’ is a piece of jargon that deserves further precision in its description. And the word precision helps explain some of the concepts that we go into below.

The issues around fund performance relative to the benchmark, and the degree to which these might not correlate, is the result of the way that ETFs can be composed.

In order to track an index, the fund must replicate its constituents and there are a number of ways this can be done, each with their own risk when it comes to matching precisely the performance of the underlying stocks.

According to an EDHEC paper on the subject written back in 2012, there are three ways to replicate an index:

  • Full replication
  • Sampling replication
  • Swap-based replication

We shall look at these three options in turn:

Full replication

The first of these is relatively easy to understand. It involves a fund establishing a portfolio that contains all the constituents of the underlying index in the same proportion as the benchmark index. The problem with undertaking such a strategy, however, is that this approach can be costly and difficult to implement, particularly if it comprises a large number of securities.

The management of a large number of constituents can be time-consuming with the chopping and changing that comes from periodic rebalancing and corporate actions adding to problems with liquidity, clearing and settlement issues.

They can all lead to performance deviations between the tracked index and its tracker fund, and these can be widened further by the differences between the index provider’s assumptions relating to tax and reinvestment of dividends and the actual conditions faced by a fund.

To reduce the expenses it has to pass on to the investor an index fund may look to securities lending and this is particularly prevalent among full replication funds.

Sampling replication

Another cost-reduction measure is sample replication. This is when a fund invests in a fraction of the index constituents and other securities, which are selected for their overall correlation with the tracked index and their higher levels of liquidity. While such an approach is less costly than full replication, it results in higher levels of tracking discrepancy due to the trade-offs between liquidity and simplicity on the one hand and variable correlation on the other.

Swap-based replication

The last variant is swap replication which attempts to track the performance of the underlying index by entering into swap agreements with third-parties to deliver index returns to the ETF in exchange for the returns on a portfolio which is either held by the ETF or held in its name as collateral plus a fee.

The ETF holds a claim to a portfolio of physical securities that are different from the index constituents, and the swap counterparty delivers the return difference between the physical portfolio and the index tracked by the ETF.

Through this arrangement, ETF providers transfer the tracking error risk to the swap counterparty and assumes counterparty credit risk, in particular the risk that the counterparty fails to deliver the promised return differential. Hybrid replication ETFs combine physical and synthetic replication techniques.

More reasons for error

The method of replication is not the only reason behind tracking error. One classic paper of the subject by Raman Vardharaj, Frank J. Fabozzi, CFA, and Frank J. Jones pointed out that tracking error is also caused by:

Differences in market capitalisation and style (e.g., growth and value) between the portfolio and the benchmark. With respect to size effects, the tracking error increases as the average market cap of the portfolio deviates from the benchmark. The same idea holds for deviations in style relative to the benchmark.

Another area of error comes form sector deviation from the benchmark. Increased differences in sector allocation between the portfolio and the benchmark, or sector bets, generally increase tracking error.

Further issues arise from the effect of benchmark volatility. Because managed portfolios generally hold only a small fraction of the assets in their benchmarks, a volatile benchmark, as measured by standard deviation, is more difficult to track closely. Moreover, tracking error tends to increase during periods of higher market volatility.

Because these various factors all have an impact on tracking error, it is useful to understand the sensitivity of tracking error to small changes in potential portfolio over- or underweight portfolio bets. Marginal contributions to tracking error can be observed as a manager makes small incremental changes to portfolio bets. By analyzing these marginal contributions over time, a manager can efficiently reduce tracking error by selecting those factors that would be most effective in reducing tracking error while minimizing portfolio turnover and expenses.

Defining tracking error

The EDHEC paper makes the point that despite the size of the passive funds sector, there is no legal definition for what makes a tracker. This is understandable given how tricky definition would be in this area, and particularly in light of the above variances in how tracker funds can be composed.

Still, it means that there is therefore no standardised measure of tracking error and no mandated disclosure of the quality of index replication. Unsurprisingly, perhaps, providers have avoided focusing on the issue and instead switch the spotlight in their promotional material to questions of replication method.

EDHEC suggests the regulator should provide a formula for tracking error to be used across all index tracking products, impose a maximum tracking error for a fund to qualify as a tracker (different limits could be applied to different underlying), and enforce initial and ongoing disclosure of targeted and realised tracking error.

None of this advice has yet been taken up. EDHEC suggest that in the context of the acceleration of the growth of passive investment, the European regulator has, for the time being, focused its attention on how an index is tracked while largely ignoring the need for a minimum level of disclosure and standardisation with respect to what index exactly is tracked and how effective and efficient the tracking is.