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Core Volatility Beginner Past dispersion, close-to-close Backward-looking

Historical Volatility HV

A backward-looking number whose answer is decided by a choice you barely noticed making.

Quick answer: Historical Volatility is the annualised standard deviation of an asset's past close-to-close log returns over a chosen window — a purely backward-looking measurement of how much price actually moved, in which the length of the window silently determines the answer you get.

In simple words

Historical volatility is what volatility looks like after the fact. You take a run of past closing prices, measure how spread out the daily percentage changes were, and annualise it — and you have a number describing how bumpy the recent past actually was. Suppose you compute it on the last 20 NIFTY closes and get 12%. That 12% is not a forecast and not an opinion; it is a measurement of a period that has already finished, the way a thermometer reads a temperature that already happened. The subtle part hides in the phrase 'last 20 closes': change 20 to 10 or to 60 and you will get a different number from the very same market, and every one of those numbers is correct.

Think of it as the width of the recent wobble. A 20-day historical volatility answers the question 'how much did this market typically move, per day, over the last 20 trading days, expressed as an annual rate?'. Because it only ever looks at closing prices, it is blind to everything that happened during each day — the day NIFTY fell 300 points by lunch and clawed it all back by the close counts, to historical volatility, as a quiet day. That blindness is not a bug you can patch; it is the definition of a close-to-close estimator.

Not to be confused with: Implied volatility, which is extracted from option prices and describes a future that has not happened, and realised volatility, which can use richer intraday data than close-to-close. Historical volatility is the plain, close-to-close, backward-looking member of the family — the measurement of a past that is finished, computed from the one price per day that everyone can agree on.

The same market at three window lengths

The window length is not a detail — it is the question

10-day, 20-day and 60-day historical volatility of the same NIFTY series, plotted together.

0%10%20%30%40%20d60d100d140dperiod mean 14.2%one shock, then months of elevated readings — because the window still contains itTrading day20-day annualised historical volatility
Three lines, one underlying, three different stories. The 10-day line spikes highest and recovers fastest; the 60-day line barely notices the same shock but stays elevated for a quarter. None is more correct than the others — they are answers to three different questions, and quoting 'NIFTY's historical volatility' without a window is quoting nothing at all.

Professional explanation

The window length is not a parameter, it is the question you are asking

Beginners treat the lookback window as a technicality to be set and forgotten. It is the opposite: the window defines what 'volatility' even means for that calculation. A 10-day historical volatility asks how turbulent the last two weeks were; a 60-day asks how turbulent the last quarter was; and in a market that has just calmed down after a scare, those are genuinely different and genuinely correct answers. A short window is responsive and noisy — it reacts fast and jumps around. A long window is stable and sluggish — it smooths the noise but carries old news for a long time. There is no universally right choice, only a choice matched to a horizon. A trader comparing a 30-day implied volatility against a 10-day historical volatility, and concluding options are expensive, has not found an edge; they have compared two different questions and blamed the answer on the option market.

A shock stays in the reading for exactly one window length

This is the single most misunderstood mechanical feature of historical volatility. A large move enters the window the day it happens and remains one of the window's observations for exactly as many more days as the window is long. During that entire time it inflates the reading, holding volatility up long after the market itself has gone quiet. Then, on the day it finally rolls off the back of the window, the volatility drops — sometimes sharply — with no corresponding event in the market. Traders routinely misread that scheduled cliff as fresh information, as if the market suddenly calmed on that specific morning. It did not. The estimator's memory simply expired. The rolling-vol chart on this page is built to make that artefact impossible to miss: the step down happens on the calendar, not in response to price.

It is close-to-close, and therefore blind to the entire trading day

Historical volatility, in its standard form, uses one price per day — the close — and measures the return from one close to the next. Everything that happens between the closes is invisible to it. A day on which NIFTY opened flat, plunged 400 points by midday on a rumour, and recovered every point by the close is, to close-to-close historical volatility, an utterly calm day: the return from close to close was zero. This is why the concept has cousins — realised volatility using high-low or intraday data — that try to see what close-to-close cannot. The trade-off is honesty about scope: close-to-close is robust and unambiguous because everyone agrees on the closing price, but it measures only the drift between two daily snapshots, not the distance travelled in between.

It is a measurement, not a forecast — but it is used as one

Nothing in the arithmetic of historical volatility looks forward. It is a summary statistic of prices that have already printed, as purely descriptive as an average. And yet it is used, constantly and reasonably, as the naive forecast of future volatility, because volatility clusters: a market that has been turbulent recently tends to stay turbulent for a while. This is the uncomfortable middle ground the page has to be honest about. Historical volatility is a legitimate and often hard-to-beat baseline forecast, and it is simultaneously guaranteed to be wrong at every turning point, because by construction it can only ever describe the regime that has just ended and never the one about to begin. It sees the last crisis perfectly and the next one not at all.

Overlapping windows make the HV series look smoother than the volatility is

When you plot a rolling historical volatility day after day, consecutive readings share almost all of their data — a 20-day window and the next day's 20-day window differ by only one observation in and one out. That overlap induces strong autocorrelation in the historical volatility series itself, so the line looks smooth, trending and well-behaved even when the underlying volatility is jumping around. It is easy to look at a gently sloping historical volatility line and believe volatility is changing gradually, when in fact the smoothness is manufactured by the overlapping windows. The line is a heavily filtered view of the truth, and the filter is doing more of the work than most chart-readers realise.

A shock leaves on a schedule, not when the market calms

A rolling 20-day historical volatility around a single large down day.

0%10%20%30%40%0d60d120d180d240d300da shockTrading dayAnnualised realised volatility10-day20-day60-day
Watch the step down that arrives with no news. The shock day sits inside the 20-day window holding the reading up, then on the twenty-first day it drops out of the window and the volatility falls in one jump — even though nothing happened in the market that morning. That cliff is an artefact of the estimator, not an event, and mistaking it for one is a classic error.

Formula

Historical volatility — annualised standard deviation of close-to-close log returns

HV = √( (1 / (n − 1)) × Σ (r_t − r̄)² ) × √252, with r_t = ln(P_t / P_{t−1})

The sample standard deviation of the last n daily close-to-close log returns, annualised by √252. The n−1 denominator (Bessel's correction) makes the estimate unbiased on a finite window. Over short windows the mean return r̄ is often assumed to be zero, which barely changes the result and simplifies the arithmetic. The choice of n — the window — is not incidental to the formula; it is the most consequential decision in it.

  • HVHistorical volatility — the annualised figure, expressed as a percentage (0.135 = 13.5%).
  • nThe window length: the number of daily returns used, e.g. 10, 20 or 60. This choice determines the answer.
  • r_tThe close-to-close log return on day t: the natural log of that day's close divided by the previous close.
  • P_tThe closing price on day t; P_{t−1} is the previous close. Only closing prices enter — the day's high and low are ignored.
  • r̄The mean of the r_t over the window; often taken as zero for short windows.
  • ΣSummation over the n days in the window.
  • √Square root — of the variance to get the standard deviation, and of 252 to annualise.
  • 252Approximate number of trading days in an Indian market year — the annualisation factor.

How to compute a historical volatility on NIFTY

  1. Decide the window first, because it is the question. A 10-day window measures the last two weeks; a 60-day window measures the last quarter. Match it to the horizon you actually care about.
  2. Collect that many-plus-one consecutive daily closing prices for NIFTY. A 20-day historical volatility needs 21 closes to produce 20 returns.
  3. Compute each close-to-close log return: r_t = ln(P_t ÷ P_{t−1}).
  4. Take the standard deviation of those returns with an n−1 denominator. Over a short window you may assume the mean is zero and simply use the root-mean-square of the returns.
  5. Multiply the daily standard deviation by √252 ≈ 15.87 to annualise, and report it as a percentage.
  6. Label it with its window. '20-day HV = 13.5%' is a complete statement; 'HV = 13.5%' is not, because the reader cannot reproduce or compare it.
  7. Before reading anything into a change, check whether a large day just entered or just left the window — a jump in HV with no market event is usually the window rolling, not new information.

Practical example

NIFTY worked example

Take a 20-day window in which NIFTY was quiet — say every day's log return was about ±0.5% — and then a single 3% down day lands. Watch what each window length does with that one shock. Assuming the mean is roughly zero, historical volatility is √(Σr² ÷ (n−1)) × √252. For a 10-day window holding nine 0.5% days and the one 3% day: Σr² = 9 × (0.005)² + (0.03)² = 0.000225 + 0.0009 = 0.001125; divide by 9 to get 0.000125; the square root is 0.01118; annualise by 15.87 and you get 17.7%. For a 20-day window (nineteen quiet days plus the shock): Σr² = 0.000475 + 0.0009 = 0.001375; ÷19 = 0.00007237; root 0.008507; annualised 13.5%. For a 60-day window: Σr² = 0.001475 + 0.0009 = 0.002375; ÷59 = 0.00004025; root 0.006345; annualised 10.1%. One market, one shock, three readings — 17.7%, 13.5% and 10.1% — and all three are correct. The interpretation is the lesson: there is no such thing as 'the' historical volatility, only a historical volatility for a stated window, and the shorter the window the more violently that single day dominates it.

BANKNIFTY worked example

BANKNIFTY teaches the flip side — that the reading is a property of what the window happens to contain as much as of the market. Say BANKNIFTY normally posts ±0.7% days, giving a placid 20-day historical volatility of 0.7% × 15.87 ≈ 11.4%. Now suppose the window happens to straddle a scheduled event — an RBI policy decision or the Union Budget — on which BANKNIFTY moved 4% in a session. Recompute: Σr² = 19 × (0.007)² + (0.04)² = 0.000931 + 0.0016 = 0.002531; ÷19 = 0.0001332; root 0.011542; annualised 18.3%. The historical volatility has jumped from 11.4% to 18.3% not because the market's character changed but because the window now contains an event day it did not before. This is why comparing today's 20-day historical volatility against last month's can mislead: if one window caught the Budget and the other did not, you are comparing two windows with different event content, not two states of the same market. The reading answers 'what did the last 20 days contain', and calendars, not just markets, decide that.

Lot sizes used above (NIFTY 75, BANKNIFTY 30) are those in force at the time of writing; NSE revises them periodically. Figures exclude brokerage, STT, exchange charges, stamp duty and GST. Examples are teaching scenarios built on round numbers — they are not historical quotes, not backtests and not trade calls.

Risk note. Because historical volatility is a clean, backward-looking measurement, it is tempting to size positions or set risk limits directly from it — the market has been calm, so run more leverage. That is exactly the trap volatility clustering sets. Historical volatility is lowest right after the quietest stretches, which are the periods in which leverage and short-volatility positioning accumulate, and it cannot rise to warn you until after the move that ends the calm has already printed. A risk framework anchored solely on trailing historical volatility is structurally guaranteed to be most permissive immediately before it should have been most cautious.

Advantages & limitations

What it is good for

  • It is a measurement, not an opinion. Given the same prices and the same window, everyone computes the same number, so it is reproducible, auditable and free of anyone's forecast or bias.
  • It needs only closing prices, which are public and free. Anyone can compute it for any instrument with a price history, which makes it the universal baseline against which richer estimators are judged.
  • It is an honest, often hard-to-beat naive forecast. Because volatility clusters, recent historical volatility is a legitimate first estimate of near-term volatility and a benchmark that fancier models frequently fail to improve on.
  • It is unambiguous about scope. Close-to-close historical volatility measures exactly one thing — the dispersion of daily closing returns — and does not pretend to capture intraday travel it cannot see.
  • It is directly comparable across instruments and periods once the window is fixed, so a 20-day NIFTY historical volatility and a 20-day BANKNIFTY historical volatility sit on the same scale.

Where it breaks down

  • It is entirely backward-looking. It describes a period that has finished and, at every turning point, describes the regime that has just ended rather than the one beginning — it sees the last crisis perfectly and the next one not at all.
  • Its answer is decided by the window, which is often chosen thoughtlessly. The same series gives 17.7%, 13.5% or 10.1% depending on whether you picked 10, 20 or 60 days, so an unlabelled historical volatility is uninterpretable.
  • It is close-to-close and blind to the trading day. A session that plunged and fully recovered registers as calm, so historical volatility can badly understate the risk actually experienced intraday.
  • It steps discontinuously as shocks enter and leave the window. A large drop in the reading can occur with no market event, purely because an old shock rolled off the back — an artefact routinely misread as fresh calm.
  • Overlapping windows make the plotted series artificially smooth. Consecutive readings share nearly all their data, inducing autocorrelation that disguises how abruptly the true volatility is actually changing.
  • It cannot see a scheduled event before it happens. A window that has not yet reached the Budget or an RBI decision reads exactly as calm as one in a genuinely quiet market, offering no warning of the known event ahead.

Common mistakes

  • Quoting 'NIFTY's historical volatility' without stating the window. The number is meaningless without its lookback, because 10-, 20- and 60-day figures on the same series can differ by seven percentage points and all be right.
  • Reading the scheduled roll-off of a shock as a market event. When a big day leaves a 20-day window and the reading drops on the twenty-first day, that cliff is the estimator's memory expiring, not the market calming — trading it as news is trading an artefact.
  • Comparing a 30-day implied volatility against a 10-day historical volatility and concluding options are expensive. You have compared two different horizons and blamed the gap on the option market. Compare like tenor with like tenor.
  • Sizing positions from a low historical volatility just after a calm stretch. Volatility clusters, so the lowest readings sit right before the accumulated leverage unwinds, and the number cannot warn you until after the damage has printed.
  • Assuming a smooth historical volatility line means volatility is changing gradually. The smoothness is manufactured by overlapping windows; the underlying volatility can be jumping while the filtered line glides.
  • Trusting close-to-close historical volatility to capture a whipsaw day. A session that fell hard and recovered by the close reads as flat, so a book that took real intraday pain sees none of it in the historical volatility.
  • Using too short a window and mistaking its noise for signal. A 5-day historical volatility reacts to everything and settles on nothing, so its swings are mostly estimator noise, not changes in the market's true volatility.

Professional usage

On a desk, historical volatility is the reference point against which the tradeable number — implied volatility — is judged. A volatility arbitrage trader compares implied volatility against a forecast anchored on recent realised and historical volatility, and the whole trade is a bet on the gap between the two, delta-hedged so the residual profit and loss depends on volatility rather than direction. Risk managers keep a suite of historical volatilities at several window lengths precisely because a single window hides the term structure of recent movement — a rising 10-day against a flat 60-day flags a fresh disturbance the long window has not yet absorbed. And every serious desk treats the choice of window as a modelling decision to be justified, not a default to be inherited, because they have all been burned by a shock rolling off a window at the wrong moment.

Quant researchers rarely use plain close-to-close historical volatility as an endpoint; they use it as the input to a forecasting model — an exponentially weighted moving average that down-weights old data, or a GARCH model that formalises clustering and mean reversion — precisely to fix the two defects the raw measure has: its equal weighting of a three-week-old shock and yesterday's move, and its cliff-edge roll-off. The honest admission the best of them make is that these refinements improve the forecast at the margin and still cannot see a regime change before it arrives, because no estimator built purely on past prices ever can. Historical volatility is where volatility forecasting starts, not where it ends.

Key takeaways

  • Historical volatility is the annualised standard deviation of past close-to-close log returns over a chosen window — a backward-looking measurement of what the market already did.
  • The window length is the question, not a setting. A 10-, 20- and 60-day historical volatility of the same series can read 17.7%, 13.5% and 10.1%, and all three are correct, so an unlabelled HV means nothing.
  • A shock inflates the reading for exactly one window length and then drops out on a schedule, producing a cliff in the volatility line with no market event behind it. Do not trade that artefact as news.
  • It is close-to-close and blind to intraday movement, so a day that whipsawed and recovered by the close registers as calm.
  • It is a measurement used as a forecast: a hard-to-beat naive baseline because volatility clusters, and yet guaranteed to be wrong at every turning point because it can only describe the regime that just ended.

Historical volatility is the most honest and the most misleading number in the volatility family at the same time. Honest, because it is a pure measurement with no forecast smuggled inside it — everyone who has the prices gets the same answer. Misleading, because that answer is completely determined by a window most people choose without thinking, and because the number's every movement can be an artefact of a shock entering or leaving that window rather than anything the market did. Learn to always state the window, to check the roll-off before you read meaning into a change, and to remember that a low reading is a description of a calm that has ended, never a promise of one that will continue.

Frequently asked questions

What is historical volatility in simple terms?
Historical volatility is a measurement of how much a market actually moved over some past window, expressed as an annualised percentage. You take the daily close-to-close returns over, say, the last 20 days, measure how spread out they were, and annualise. It describes the past, not the future, and everyone with the same prices gets the same number.
How is historical volatility calculated?
You compute the log return between each pair of consecutive daily closes over your window, take the standard deviation of those returns with an n−1 denominator, and multiply by the square root of 252 to annualise. For short windows the average return is usually treated as zero, which simplifies the sum without meaningfully changing the answer.
What window should I use for historical volatility?
There is no universal answer, because the window is the question. A 10-day window measures the last two weeks and reacts fast; a 60-day window measures the last quarter and moves slowly. Match the window to the horizon you care about, and always state which window you used, because different windows give genuinely different numbers.
Why do 10-day and 60-day historical volatility differ so much?
Because they are answering different questions over different periods. A short window is dominated by recent days and reacts sharply to any single large move, while a long window dilutes that same move among many quiet ones. After a shock, a 10-day reading can sit seven or more percentage points above a 60-day reading on the identical series.
Is historical volatility a forecast of future volatility?
No, though it is often used as one. It is strictly a measurement of the past. Because volatility clusters, recent historical volatility is a reasonable naive forecast of near-term volatility, but it is guaranteed to be wrong at turning points, because it can only ever describe the regime that has just ended.
Why does historical volatility drop suddenly with no news?
Because a large past day rolled off the back of the window. A shock stays in the reading for exactly one window length, holding it up, and on the day it finally exits, the volatility falls in a step. That cliff is an artefact of the estimator's fixed memory, not a market event, and it is a classic thing to misread.
What is the difference between historical and implied volatility?
Historical volatility is computed from past prices and describes a period that has finished; implied volatility is extracted from option prices and describes a future that has not begun. Historical volatility is a measurement; implied volatility is a price. The gap between them is called the volatility risk premium.
What is the difference between historical and realized volatility?
They overlap heavily, but historical volatility conventionally means the plain close-to-close standard deviation, while realised volatility often uses richer data — high-low ranges or intraday sampling — to see movement that close-to-close misses. Historical volatility is the simplest, most agreed-upon backward-looking estimator; realised volatility is a broader family of them.
Why does historical volatility only use closing prices?
Because the close is the one price per day that everyone agrees on and that settles contracts, which makes close-to-close historical volatility robust and unambiguous. The cost is that it is blind to the trading day: a session that plunged and fully recovered by the close counts as a calm day, because its close-to-close return was near zero.
Can historical volatility be zero?
Only if every return in the window was identical, which for a real market effectively never happens. A standard deviation floors at zero, so historical volatility cannot be negative, and a computed zero or negative value signals an arithmetic error or a stale, unchanging price series rather than a genuinely motionless market.
Does a low historical volatility mean the market is safe?
No. It means the recent past was calm, which is a description, not a promise. Because volatility clusters, the lowest historical volatility readings often sit just before the largest moves, when leverage and complacency have built up on the assumption that the calm will continue. Low historical volatility is a measure of recent quiet, not future safety.
How many days of data do I need to compute historical volatility?
You need one more closing price than your window length, because n closes produce n−1 returns — a 20-day historical volatility needs 21 closes. Beyond that minimum, using a longer history only lets you compute longer windows or a rolling series; it does not make a given window's reading more 'accurate', because each window is a self-contained answer.
Why is historical volatility annualised?
So it can be compared with other volatilities — implied volatility, other instruments, other periods — all of which are quoted annually by convention. The annualisation multiplies the daily standard deviation by the square root of 252, the approximate number of trading days in a year, because variance adds linearly with time and volatility scales with its square root.
Does historical volatility predict market direction?
No. Like all volatility measures it is sign-blind — it squares the returns before averaging, so a rising market and a falling market of the same daily size produce the same historical volatility. It tells you how much the market moved, never which way, and reading a rising HV as bearish imports information the number does not contain.
Why does a rolling historical volatility line look so smooth?
Because consecutive readings share almost all their data — a 20-day window and the next day's differ by only one observation swapped in for one swapped out. That overlap induces strong autocorrelation in the series, so the plotted line glides even when the underlying volatility is jumping. The smoothness is a property of the estimator, not of the market.
Should I assume the mean return is zero when computing historical volatility?
For short windows, yes, and most practitioners do. The average daily return over a few weeks is tiny compared with the day-to-day dispersion, so subtracting it or not barely changes the standard deviation. Over long windows with a strong trend the assumption matters more, but for the typical 10-to-60-day HV it is a harmless simplification.
How does historical volatility handle a scheduled event like the Budget?
Badly, before the fact, and mechanically after. Before the event, a window that has not yet reached it reads exactly as calm as a genuinely quiet market — no warning. Once the event day is inside the window, it inflates the reading for a full window length and then rolls off with a cliff, so the same event distorts the series twice: on the way in and on the way out.
Is a shorter window always more responsive and better?
More responsive, not better. A short window reacts fast to real changes but also to noise, so much of its movement is estimator jitter rather than genuine shifts in volatility. A 5-day historical volatility is mostly noise; the right window trades responsiveness against stability for the horizon you actually trade.
How does historical volatility relate to India VIX?
They measure different things on different sides of time. Historical volatility is the backward-looking standard deviation of NIFTY's own past returns; India VIX is a forward-looking, model-free summary of NIFTY option prices over the next 30 days. Comparing the two — implied against historical — is one of the standard ways traders judge whether options look rich or cheap.
Can two people get different historical volatility for the same stock?
Yes, easily, if they made different choices. Different window lengths, different treatments of the mean return, using log versus simple returns, or including versus excluding a corporate-action-adjusted price can all shift the number. The calculation is deterministic once every choice is fixed, which is exactly why the window and the conventions must be stated.
Why does the same shock affect a short window more than a long one?
Because in a short window the shock is a larger fraction of the observations. In a 10-day window one big day is a tenth of the data; in a 60-day window it is one part in sixty, diluted among many ordinary days. The arithmetic on this page shows a single 3% day reading as 17.7% on 10 days but only 10.1% on 60 days.
Is historical volatility useful if it is always backward-looking?
Yes — a great deal of practical work rests on it. It is the reproducible baseline against which implied volatility is judged, the input to volatility forecasting models, and a hard-to-beat naive forecast in its own right because volatility clusters. Its backward-looking nature is a limitation to respect, not a reason to discard the most auditable number in the family.

Voice search & related questions

Natural-language questions people ask about historical volatility.

What is historical volatility?
Historical volatility is a measurement of how much a market actually moved over a past window, annualised into a percentage. It uses only closing prices, so it is a clean, reproducible number describing a period that has already finished rather than a guess about what comes next.
Which lookback should I pick for historical volatility?
Pick the window that matches your horizon and then always state it. A 10-day reading tells you about the last couple of weeks and jumps around; a 60-day reading tells you about the last quarter and barely moves. Neither is more correct — they answer different questions, so 'HV' without a window is an incomplete sentence.
Why did historical volatility fall today when nothing happened?
Almost certainly because a big past day just rolled out of the window. A shock stays in the reading for exactly one window length, then drops out on schedule, and the volatility steps down with it. The market did not calm this morning; the estimator simply forgot an old day.
Does historical volatility see what happens during the day?
No. Standard historical volatility is close-to-close, so it only sees the move from one day's close to the next. A day that crashed at lunch and recovered by the bell looks completely calm to it, because the close-to-close return was near zero. For intraday movement you need a range-based or realised-volatility estimator instead.
Can I use historical volatility to predict tomorrow?
As a rough baseline, yes, because turbulent periods tend to be followed by turbulent periods — volatility clusters. But it is a measurement of the past being borrowed as a forecast, and it will be wrong at exactly the moments that matter most, the turning points, because it can only describe the regime that has already ended.
Is low historical volatility a green light to add leverage?
It is the opposite of a green light in disguise. Historical volatility is lowest right after the calmest stretches, which are precisely when leverage and short-volatility bets pile up, and the number cannot rise to warn you until after the move that ends the calm has already happened. Nothing here is investment advice.
Why do my broker and I get different historical volatility numbers?
Because one of the choices differs. Different window lengths, log versus simple returns, whether the mean is subtracted, or how corporate actions were adjusted will all move the figure. The math is exact once every convention is pinned down, which is why two 'HV' numbers only match when the windows and methods match too.

Sources & references

Last reviewed 10 July 2026. Educational content only — not investment advice.

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What is Volatility?
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