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Why ETF Tracking Error Can Exceed Futures Tracking Error

Article Quant Q&A · Author: Mariska
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Summary

The document compares the tracking error of an ETF and a futures instrument relative to the same equity index. It measures tracking error as the standard deviation of daily return differences and reports that the ETF’s measured value is larger in the example. This challenges the assumption that futures always hedge an index more closely than an ETF.

The answer explains that tracking error depends on the product and the measurement period. Some ETFs obtain synthetic index exposure, with a predictable cost that can lower net asset value over time without necessarily adding variability to tracking error. Futures can diverge from the index because of basis changes, shifts in implied dividends and short-term interest rates, and roll costs. The response says futures may track especially closely between roll dates, but it does not examine the specific instruments, data, or calculation choices in the question. Its explanation is therefore a general guide, not a diagnosis of the reported result.

Key ideas

  • Tracking error is the variability of the return difference between a hedge and its reference index.
  • A larger ETF tracking error than futures tracking error is possible and depends on the instruments and period measured.
  • Predictable ETF costs can reduce its value without necessarily increasing return-difference volatility.
  • Futures tracking can be affected by basis, dividend and rate expectations, and rolling costs.

Tags

EquitiesFuturesStatistics
Full text
# ETFs have lower tracking error than Futures?


# ETFs have lower tracking error than Futures?












I used the daily returns of SPX Index, SPY US Equity, and SPA Index. I then calculate their standard deviation as hedging instruments with respect to SPX Index, i.e., (spx_ret - spy_ret) or (spx_ret - spa_ret). However, the results I obtained were strange:

```
SD (spx_ret - spy_ret) = 0.0012959
SD (spx_ret - spa_ret) = 0.0006794
```

How can an ETF have a larger tracking error? I thought Futures are almost like a "perfect hedge" and ETFs have huge tracking error due to management and rebalancing fees. Am I missing something in the calculation?

## Answer by Matt B. (score 3)

https://quant.stackexchange.com/a/14059

It depends on your ETF. Some have synthetic exposure to the index sold by a sponsor (ie someone give them exactly the performance of the index) but this has a cost (a constant / deterministic drag on the NAV of your ETF which doesn't appear in your tracking error).

Futures on the other hand have basis, are sensitive to changes in implied dividends and short term rates, and rolling costs, so they only perfectly track your index if you look at them between 2 rolling dates.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.