Correcting Variance Estimates from Overlapping Return Windows
Summary
The document addresses bias in volatility analysis when return observations come from overlapping windows. Overlap makes the window estimates dependent, so the observed variance across them can be biased. It presents the Hodges and Tompkins adjustment factor, based on the window length and the number of available subseries, as a correction for variance measured from an overlapping return series.
The answer suggests applying that factor when calculating average volatility over a period and points to a published study as the derivation. The original question also asks whether percentiles and extrema should be adjusted, but the supplied response does not explain how to correct those distribution statistics. Its guidance therefore centers on variance and average volatility; it does not establish that the same multiplier applies to minima, maxima, or quantiles, or address the assumptions needed for a particular asset and sampling design.
Key ideas
- Overlapping return windows introduce dependence between volatility observations.
- The Hodges and Tompkins factor adjusts variance estimates for overlap using window length and sample count.
- The response recommends applying the adjustment when averaging volatility over a period.
- The document does not resolve how overlap affects extrema or percentile estimates.
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Full text
# Adjusting for variance bias when using overlapping data
# Adjusting for variance bias when using overlapping data
I'm in the process of constructing volatility cones for several assets and I want to make sure the data is free of biases.
I know that using overlapping data introduces an artificial degree of correlation between samples and I have the formula for adjustment however I'm unsure how to apply it to the data set.
I'm not necessarily concerned with looking at the mean and variance of the entire data set as I am in looking at the absolute values (min, max, 90th percentile, etc)
I'm wondering if each sample (i.e. 30 day window) needs to be adjusted or whether the bias only applied to the variance of entire data set (the variance of variance of overlapping returns)
Any clarification is greatly appreciated. Thank you very much
## Answer by quantum_poster (score 1)
https://quant.stackexchange.com/a/78929
For anyone looking this up 10 years later, you can reference Euan Sinclair's Volatility Trading pg 40.
He says that
> we need to know how much bias is introduced into our volatility estimates by using overlapping data. This problem was studied extensively by Hodges and Tompkins Volatility Cones and Their Sampling Properties, Journal of Derivatives 10:27–42 (2002). They find that variance measured from overlapping return series need to be multiplied by the adjustment factor
$$m = \frac{1}{1-\frac{h}{n}+\frac{h^2-1}{3n^2}}$$
> where $h$ is the length of each subseries (for example, 20 days), $n = (T − h) + 1$ is the number of distinct subseries available for a total number of observations $T$
So if you're calculating, say, average volatility across some time period, you would adjust that mean by the adjustment factor $m$.
The formula ought to be referenced as the Hodges and Tompkins formula. It is derived in their paper (link), see Equation (12) page 12.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.