a cleaner way to compute seasonal vol

Vivek emailed me a simple question after reading yesterday’s does revenue seasonality translate to vol seasonality? post:

Why not just compute volatility from the daily returns within each calendar month instead of using a trailing 20-day window?

Um, well, eh. I don’t know. I guess just had a blind spot. I think of rolling realized vol instinctively. But for a seasonality study, it has a problem I already flagged in the post: a big earnings move in August gets recounted ~20 times as the window slides over it, smearing that vol into September.

It’s just unnecessary. So I added a section to the notebook that computes calendar-month realized vol directly: take each month’s daily log returns, compute √(mean(r²)) × √252, and you get one clean RV number per month per year without overlap.

Did the calendar month realized vol (CMRV) method change the story?

The earnings effects and their seasonal patterns does look sharper.

 

• May, June, August, and November are now the clear relative-vol peaks. Feb earnings are not important as the May and Aug earnings are capturing the bulk of the year’s revenue recognition.
• September, which looked like a peak in the rolling version, drops to a trough. It was borrowing August’s earnings move through the sliding window. Once you measure September’s own returns, it’s quiet.
• The late-year volatility surge now concentrates in November, an earnings month, where the rolling method showed strong effects in December.

• August is now the single largest effect size, the only month exceeding the “medium” threshold. June is close.
• September flips to a quiet month once you stop smearing.
• The scatter plot confirms it’s not one wild year: August dots are consistently elevated across the sample. All 3 of these charts are controlling for IWM.

A few more charts just to round it out:

 

The updated notebook is here: 👉 HRB Seasonality Study

Thanks again to Vivek for the feedback. Vivek was one of the senior quants at SIG when I was there. He’s also a chess genius if you’re into that.