Annualizing Rolling Realized Variance from Daily Returns

Summary

The document asks how to calculate annualized realized variance from daily market returns over a rolling 126-trading-day window. The proposed calculation takes the logarithm of one plus each daily return, squares it, and sums those squared log returns across the window. The author clarifies that the window ending on day 126 includes that day's observation, so the first complete estimate can be viewed as available for day 127.

The central question is whether to multiply the half-year sum by 252 or by 2 when expressing it on an annual basis. The excerpt contains no answer or supporting derivation, so it does not resolve the annualization convention or discuss assumptions such as the number of trading days per year, serial dependence, or whether variance versus volatility is being reported. It is useful as a focused measurement question, but readers need an additional explanation before relying on it as a complete calculation guide.

Key ideas

• The proposed rolling measure sums squared daily log returns over 126 observations.
• The stated window includes its ending day's return, and the author assigns that estimate to the next day.
• The document asks whether annualization should use a 252-day factor or a factor of two.
• The excerpt provides no answer, derivation, or caveats resolving the annualization choice.

Tags

# 46386


# Is this the right way to compute "realized daily market return variance, annualized, over the preceding 126 trading days”?












```
Realized.Variance<-rollapply((log(Fama.French.daily$Mkt+1)^2) ,126,sum,by=1)
```

So Fama.French.dail$Mkt is my daily Market return.

To calculate the realized Variance over the preceding 126 days, i took the sum of the squared log returns of the past 126 observations. (Using the approach above the value on day 126 includes day 126, so its the preceding value for day 127.) Anyway, How can i annualize them ? Is it times 252 or do i just multiply by 2 since i already summed up half a year?

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