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Annualizing Tracking Error from Monthly Relative Returns

Article Quant Q&A · Author: mHelpMe
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Summary

This exchange considers how to estimate annualized tracking error from a series of monthly relative returns. It identifies multiplying the monthly dispersion by the square root of twelve as the usual annualization step, reflecting aggregation across twelve months under standard assumptions about returns.

The answer also questions whether ordinary sample standard deviation is the right measure. It presents tracking error as the square root of the annualized average squared difference between benchmark and portfolio returns, without subtracting the mean active return first. This focuses on the total size of deviations, including any persistent bias. The brief response does not discuss assumptions such as independence or serial correlation, nor clarify estimator conventions or how missing observations should be handled, so implementations should align the formula with the intended definition and data frequency.

Key ideas

  • Monthly tracking error is commonly annualized using the square root of twelve.
  • Tracking error can be calculated from benchmark minus portfolio returns for each month.
  • The presented formula uses root mean squared active return rather than centering deviations around their average.
  • The exchange does not address serial correlation or alternative estimation conventions.

Tags

StatisticsRisk managementPortfolio construction
Full text
# How to calculate annualised tracking error?


# How to calculate annualised tracking error?












I have 36 months of relative returns and I need to calculate the annualised tracking error.

So, using 36 months of returns is it simply like below:

```
stdev(36 months of returns) * sqrt(12)
```

Why the `sqrt(12)`?

## Answer by hvedrung (score 2)

https://quant.stackexchange.com/a/19602

$\sqrt{12}$ annualizes monthly deviations.

But I don't understand why you measure tracking error with stdev. It should be $$ ATE = \sqrt{\frac{12}{36}\sum_{i=1}^{36}(r_{b,i}-r_{t,i})^2}$$ where $r_{b,i}$ is benchmark return for month $i$ and $r_{t,i}$ is tracking portfolio return for same period. So you shouldn't substract average error inside square.

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