Choosing a Lookback Window for Ex-Ante Tracking Error

Summary

The question concerns selecting historical data for the covariance matrix used to forecast portfolio tracking error. The calculation is refreshed quarterly and annualized, and the author is comparing forecasts with realized post-period values while considering lookback windows from one to five years.

The response offers a rule of thumb attributed to a derivatives textbook: estimate covariance from daily closing prices over a recent window of roughly 90 to 180 days. It also suggests matching the number of observations to the horizon over which volatility is to be applied. This is practical guidance rather than a demonstrated optimization procedure: the note provides no empirical comparison of competing windows, no forecast-error results, and no treatment of changing market regimes or asset-specific data needs. The proposed window should therefore be understood as a starting point, not a universally best choice.

Key ideas

• Ex-ante tracking error forecasts depend on the covariance matrix estimated from historical returns.
• The response suggests using recent daily closes over a window of roughly 90 to 180 days.
• A rule of thumb links the observation count to the horizon for which volatility is applied.
• The note does not establish which window minimizes forecast error for a particular portfolio.

Tags

# Ex-Ante tracking error how to determine the look back period


# Ex-Ante tracking error how to determine the look back period












I am looking to compare the ex-ante predictions against the post values. I am using a look back period of ranges from 1 year to 5 years to construct my covariance matrix that I am using for my ex-ante predictions (calculation below). I am unsure of how to determine the best look back period?

```
   te_ante = sqrt(relative_wgts * cov_matrix * relative_wgts') * sqrt(4)
```

- I'm calculating the te_ante every quarter hence the sqrt(4) to give me an annualised te_ante.

## Answer by TLP (score 1)

https://quant.stackexchange.com/a/10570

As pointed out by Hull (2012). Options, futures and other derivatives. (8th edition, p305):

"A compromise that seems to work reasonably well is to use closing prices from daily data over the most recent 90 to 180 days. Alternatively, as a rule of thumb, n can be set equal to the number of days to which the volatility is to be applied."

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