EWY, the South Korea ETF, was an interesting source of disagreement in our Discord about whether the vol was expensive or not. This is the IV vs trailing RV:
Based on realized vol calcs using daily sampling, IV approaching 50% looks rich.
But EWY had been grinding up since the beginning of the year. (It tanked along with the dollar this week after the Iran strikes.)
It was up 25% in February alone.
If we annualize that to a vol:
25% * √12 = 87% vol
More than 2x the realized vol and significantly higher than the “rich”IV.
The posts below discuss this sampling issue from several angles.
- Risk Depends On The Resolution | 4 min read
- Volatility Depends On The Resolution | 5 min read
- The Option Market’s Point Spread (Part 2) | 11 min read
- Thinking In N not T | 6 min read
- A Misconception About Harvesting Volatility | 3 min read
- The Coastline Paradox in Financial Markets | 11 min read
There’s no single “realized” volatility. Every time you delta hedge you sample a unique volatility such that is possible for a long delta hedger and a short delta hedger to both make or both lose money depending on the timing and size of their hedges.
Because we are cursed with memories, every good trade we do, we wish we did bigger, and every bad one we wish we did none of. Our memories, combined with the noise inherent in delta hedging is a recipe for madness. That’s why all option traders are unpleasant and wish they had chosen a career where they can simply clip a fee from the collective net worth of society, which has been steadily levitating for the past generation, raising (good) but compressing (boring) the fortunes of the clever and the dimwitted alike.😉
Since realized volatility is sensitive to how we sample it, it’s worth looking a bit closer to how it accumulates. This exploration is likely to inspire your own research or even guide your thinking on how to get your head around return behavior that, despite being common and familiar, remains, as my kids say, confuzzling.
In this post:
- The Trend Ratio — what the ratio of weekly-sampled to daily-sampled vol tells you about trending vs choppy regimes
- The Variance Contribution Ratio — a single number that tells you whether a trend was a slow grind or a one-day event
- Broad patterns across 35 liquid ETFs over a decade (~97K observations)
- What TR implies for delta hedging — the tradeoff between rebalancing noise and sampling bias
- What happens to forward vol after grinding trends, and what that means for pricing
- A self-contained Jupyter notebook that fetches from yfinance and reproduces everything
the shape of volatility
EWY had a grinding rally. You can describe this as momentum, autocorrelation, trend. These are all ways to say the stock went on a quite a run. These descriptions mask something even more fundamental that we should make explicit. The notability of this run, even before describing its steady behavior, is that it was volatile.
Even if it’s 1% per day for 20 days this is volatile in the sense that the movement in the stock was unusual. We do not expect EWY to find itself over 20% away from where it was a month ago. Plain and simple. If we tallied all monthly returns, a move of that size would stand out as an outlier.
If a dog is wearing a dress, we would acknowledge that unusual observation before describing the color or material of the garment. Similarly, before describing the shape EWY’s move, we take it in, “That’s pretty remarkable.” You’d need to have a narrow definition of volatility, a definition that is divorced from an honest view of reality, to think otherwise.
It’s settled then, EWY was volatile. Great. Now we can think about the shape of the volatility. I’m going to introduce 2 measures that we can use in conjunction to classify volatile moves.
Trend Ratio
A common way to compute a realized vol for say 20 trading days is to average the sum of squared daily returns, take the square root, then annualize by √251. We’ll call this 20d RV sampled daily or 20d_RV for short.
Now compute the same realized vol but sample weekly instead of daily. The method is the same except for 2 variables:
- 5-day returns instead of daily returns. Note that means only 4 data points, not 20.
- Since you sampled every 5 days, you annualize by √251/20
We will call this 20d RV sampled weekly or 20d_RV_w
The ratio of weekly-to-daily vol captures how much “trend” was present relative to chop. We can call this Trend Ratio (TR).
TR = 20d_RV_w / 20d_RV
When TR > 1, the market has been trending. The point-to-point displacement exceeds what you’d expect from the daily noise. When TR < 1, daily returns have been partially canceling or mean-reverting within the window.
As of the last day of February 2026:
EWY
20d_RV_w = 49.9%
20d_RV = 40.6%
TR = 1.23
Variance Contribution Ratio
Imagine 2 stocks.
Stock A: Moves 1% every day. Its vol annualizes to 16% if you sample daily
Stock B: Moves .60% 19 days, and 3.6277% on 1 day. Its vol also annualizes to 16% sampled daily
Both A and B accumulated the same amount of variance, but for A, each day contributed 1/20 of the variance. Stock B’s most volatile day contributed 65.8% of the total variance!
💡Variance is the square of returns. We care about variance because realized p/l in options is proportional to variance. If you are short gamma, a 6% move costs you more than 2x a 3% move.
We will define a Variance Contribution Ratio (VCR) as the fraction of total variance explained by the single largest squared daily return. Hence, the VCR for a 20d window:
VCR20 = max(r²) / Σ(r²)
If all 20 days contributed equally to variance, VCR would be 1/20 = 5%.
Snooping ahead for a moment, the median VCR across 35 liquid ETFs for the past decade is about 25%. This means one day typically explains a quarter of the whole month’s variance. A major departure from the uniform case. The real world is lumpy.
Boiling vs jumpy frogs
A high TR reading tells you the market trended, but not necessarily how. By filtering TRs by VCR or vice versa, we can distinguish grinding or frog-boiling trends versus a trend characterized by larger jumps. From there, we can study subsequent realized volatility behavior.
I grabbed 10 years of daily return data for 35 ETFs spanning equities, fixed income, fx, and commodities from yfinance (~97,000 observations)
The details of all the calcs and code are in this notebook:
🔗https://github.com/Kris-SF/public_projects/blob/main/vol_ratio_vcr_study1.ipynb
Here’s a high-level summary:
Across all tickers, we can see that the median trend ratio is ~95%. In other words, volatility sampled weekly is about 5% less than if you sample daily. More frequent sampling over the same time window generally leads to higher vol computations, so this is not a surprising result.
If VRPs are typically 10-15%, then VRPs are about 1/2 to 1/3 larger if you sample weekly. An interesting observation for someone debating how often to hedge. The trade-off, of course, is noise. We can see the distribution of trend ratios in the blue histogram. Again, that’s across all tickers. For individual tickers, you can look up the standard deviation of the Trend Ratio. We will look at them graphically below in a bit. The distribution of TR appears well-balanced.
On the other hand, we can see that VCRs have a strong positive skew. The median VCR is ~25%, meaning it’s normal for 1 out of 20 days to comprise 25% of the total variance! It’s never the case that the distribution is truly uniform, but there’s about a 1 in 20 chance that a single day can comprise 50% of the variance. Remember, there are no single stocks in this universe, so earnings are not a factor. If interested, you could change the tickers in the notebook to study single stocks.
What’s normal at the ticker level?
Trend Ratios by ticker:
Commodities seem to exhibit more trending behavior than equities, but the overall feels compact with a range of TRs from .9 to 1
VCRs by ticker:
It seems like SLV and FXY have had about 10 to 20% higher VCRs than the typical name suggesting they are more prone to a single jumpy move in their return stream. Because we are looking at the median VCR I don’t think the recent SLV chaos is skewing the data. If I exclude SLV data from June 2025 until now, the median VCR only drops from 29.5% to 29.4%.
Classification
Split TR and VCR at their medians to get a blunt classification framework:
Summary:
Grinding Trend: 20,744 (21.3%)
Spike Trend : 21,605 (22.1%)
Choppy Grind : 28,046 (28.8%)
Spike Revert : 27,150 (27.8%)
TOTAL : 97,545
EWY’s move was textbook upper-left quadrant grinding trend. High TR, low VCR.
Let’s set VCR aside for a moment. It’s nice that the recent VCR confirms that the variance was not especially lumpy, but we can see that with our eyes. The question that prompted this whole post was whether the elevated TR, the fact that the less frequently sampled vol was much higher than the daily vol, meant anything for future volatility? Is the high IV actually expensive, or does the option’s market somehow balance both measures of realized vol?
Phrased generally:
Does the elevated TR tell you anything about subsequent realized vol?
For every observation, I computed both the current TR and VCR, then looked at what happened to daily realized vol over the next 20 trading days. To be clear, this is the window that is 20 days hence, so there are no overlapping days between the TR reading and the subsequent volatility.
I’m specifically interested if daily sampled vol exhibits any tendencies. I sorted all observations into TR quintiles and measured the median percent change (technically the log change) in RV20d from the current window to the next window.
The pattern is monotonic and the direction of change is what I’d expect.
In Q1 (lowest TR, most choppy) forward daily RV declines. To be fair, I had no expectation about whether it would increase or decline, merely that as we increase the TR, the subsequent RV would increase.
[To articulate the logic: there’s additional information in the less frequently sampled vol at the margin, perhaps uncovered by splitting the data into quintiles. We are looking for benefit in the margins as we accept that there is less total information than more frequently sampled vol. After all, daily vol sample would converge to a good estimate of an asset’s true vol faster than once a year observations. This is also why you would prefer daily data about a trading strategy versus monthly.]
As we ascend quintiles, Q5 (highest TR, most trending) precedes a median increase of +3.4% in RV20d.
The daily estimator was understating the expectation of the next period’s vol if we assume it would be unchanged. The next period, daily RV partially “catches” up.
3.4% isn’t a huge number, but it’s material. If you thought 50% vol is fair, now you might pad that to 51.7% but…it’s highly variable and positively skewed. The mean vol increase is 14.9%, which would mean raising your fair vol from 50% to 57.5%!
This is the histogram of the percent vol increase in the subsequent period for the 5th quintile of trend ratio:
Be careful, the standard deviation of that vol change is huge. This is all the quintiles:
That EWY elevated IV over daily-sampled RV starts making a lot more sense because its trend ratio of 1.23 is in its top quintile.
VCR adds independent information
High VCR predicts vol decline, holding TR constant. This is partly mechanical. To take an extreme example, when one day accounts for half your variance budget, vol drops when it rolls out of the next window. But it’s also real: spike regimes tend to cluster and then subside.
To examine how VCR may interact with TR, we construct a heatmap. Each cell shows the median percent change in daily RV from the current 20-day window to the next, broken out by TR (columns) and VCR (rows).
Reading left to right (TR axis): Higher TR predicts vol increase, and this holds within nearly every VCR row. Look at the 15-20 VCR row: it goes from roughly flat at low TR to +11% at high TR. The pattern repeats row by row.
Reading top to bottom (VCR axis): High VCR predicts vol decline across every TR bin. The bottom row (VCR > 50) is negative across the board, ranging from -30% to -3%.
We would find EWY in the upper right corner (high TR, low VCR) the grinding trend zone. Subsequent vol rises from +8 to +12%.
Recall from the four quadrants that grinding trend is the least common, showing up about 21% of the time. But this is still frequent enough that you can easily bid an IV equivalent to the trailing daily-sampled vol.
I just doubt that the market will give it to you. But at least you know to screen for this and at the very least not be tricked into selling an insufficiently high IV.
It’s trivial to compute a VCR as well, so you can add this filter as confirmation that the trend is boiling a frog not just a jump.
The Notebook
Again, I’ve open-sourced the full Jupyter notebook behind this analysis.
🔗https://github.com/Kris-SF/public_projects/blob/main/vol_ratio_vcr_study1.ipynb
It fetches data directly from Yahoo Finance, constructs all the variables from scratch, and reproduces every chart above. You can change the ticker universe, the window length, or the sampling frequency and re-run the whole thing.
Note the code computes TR and VCR using a zero-mean estimator for realized vol (dividing by N, not N-1). This is deliberate, we’re measuring total quadratic variation including drift so the zero-mean formulation is standard in the vol trading world