Calculating Annualized Tracking Error from Daily Returns

Summary

The document asks how to estimate an index fund’s tracking error from five years of daily fund and benchmark values. Its proposed procedure is to calculate each series’ daily percentage returns, subtract benchmark returns from fund returns, and take the standard deviation of those active returns. It then asks whether that result should be annualized by compounding over the full period or by scaling for the number of trading days in a year.

The questions also raise how to interpret a small standard deviation expressed as a percentage and whether daily observations provide a more accurate estimate than monthly observations. No answer or empirical comparison is included, so the document does not resolve the annualization choice or data-frequency tradeoff. The calculation also depends on using consistent return definitions and an appropriate annualization convention; the sample itself supplies no tracking-error estimate.

Key ideas

• Tracking error is estimated from the variability of fund returns relative to benchmark returns.
• The proposed inputs are daily percentage returns for both the fund and its benchmark.
• The document asks whether daily tracking error should be annualized using a square-root-of-time factor.
• It raises the effect of observation frequency but provides no comparison or conclusion.

Tags

# How to calculate Annualized tracking error of an Index fund given daily historical data?


# How to calculate Annualized tracking error of an Index fund given daily historical data?












Let's say I have Fund A and Benchmark B and the daily data for both, stretching back 5 years.

To find the Annualized Tracking Error (ATE), would this method be correct:

- Compute percentage change of A's daily value relative to its previous day's value

- Compute same for B

- Compute the difference between 1 and 2

- Do this for all 5 years worth of daily data. Step 3 will look like a column with ~1250 rows of data

- Compute the standard deviation of this whole column (stdev.s). Per my understanding this would be the Tracking error for the entire 5 years. Let's call it K

- To find the Annualized tracking error, annualize the above i.e. Annualized TE= (1+k)^(1/5) - 1

Questions:

- My confusion is in the annualizing step. Instead of my formula in step 6, should I be using k * sqrt(250)?

- Let's say the result is 0.000142. Does this mean TE is 0.01%?

- Would I be right in assuming that calculating all this with daily data would yield a far more accurate TE than with monthly data?

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