Realized Volatility

Q: What is realized volatility?

The annualised standard deviation of an asset’s daily log returns over a past window, such as 10, 20 or 30 trading days. It measures how much the price actually moved, regardless of direction, and is also called historical volatility.

Q: How do you calculate realized volatility?

Compute the daily log returns ln(P today divided by P yesterday), take their sample standard deviation over the window, and multiply by the square root of 252. For ten Nifty returns with a daily standard deviation of 0.527%, the annualised figure is about 8.4%.

Q: Why multiply by the square root of 252?

Variance grows in proportion to time, so standard deviation grows with the square root of time. With about 252 trading days in a year, daily volatility times the square root of 252 gives the annual figure.

Q: What is the difference between realized and implied volatility?

Realized volatility is computed from past prices; implied volatility is the volatility that makes an option’s model price equal to its market price, so it reflects what the market expects. Implied usually exceeds realized.

Q: Which window should I use for realized volatility?

It depends on the horizon of the trade. Compare a 10-day realized figure with options expiring in about 10 days, and a 30-day figure with monthly options. Short windows react fast; long windows are stable.

Realized volatility is what the market actually did: the standard deviation of its daily returns, scaled to a year. It is the yardstick every implied volatility is measured against.

In short: realized volatility (also called historical or statistical volatility) is the annualised standard deviation of an asset’s daily logarithmic returns over a past window, usually 10, 20 or 30 trading days. It is computed from prices that have already happened, so it is backward-looking, while implied volatility is the market’s forward-looking estimate embedded in option prices. Daily volatility is annualised by multiplying by the square root of 252, the number of trading days in a year. A 20-day realized volatility of 12% on NIFTY means its daily moves over those 20 days had a standard deviation of about 0.76%.

The intuition

Volatility is a measure of how much a price wobbles, not which way it goes. Realized volatility answers the question with data: take the last N daily returns, measure how spread out they are, and express that spread as an annual number so it can be compared with the implied volatility quoted on the option chain. A high reading means the recent past was jumpy; a low reading means it was calm. It says nothing about tomorrow except that volatility tends to cluster, so a jumpy recent past is usually followed by a jumpy near future.

Formula

Daily log return: r_t = ln(P_t ÷ P_t−1)

Daily volatility: σ_d = √[ Σ(r_t − r̄)² ÷ (N − 1) ], the sample standard deviation over N returns

Annualised realized volatility: σ = σ_d × √252

Log returns are used because they add across days; the square root of 252 comes from variance scaling linearly with time, so standard deviation scales with its square root. Some practitioners drop the mean (set r̄ = 0) because over short windows it is noise; the difference is small.

Worked example (illustrative closes)

Suppose NIFTY’s last eleven closes were 24,000, 24,120, 23,950, 24,010, 24,200, 24,150, 23,980, 24,060, 24,180, 24,100 and 24,040, giving ten daily returns.

Day	Close	Log return	Day	Close	Log return
1	24,120	+0.50%	6	23,980	−0.71%
2	23,950	−0.71%	7	24,060	+0.33%
3	24,010	+0.25%	8	24,180	+0.50%
4	24,200	+0.79%	9	24,100	−0.33%
5	24,150	−0.21%	10	24,040	−0.25%

Mean return: +0.016%
Sample standard deviation of the ten returns: 0.527% per day
Annualised: 0.527% × √252 = 0.527% × 15.87 = 8.4%

If the at-the-money NIFTY option is quoted at an implied volatility of 13% on the same day, options are pricing future daily moves of about 0.82% against a recent reality of 0.53%: the implied-realized spread is positive, which is the usual state of affairs and the subject of implied vs realized volatility. The window matters: had the sample started three days earlier and caught a 2% fall, the 10-day figure could easily double while the 60-day figure barely moved.

Realized volatility is the width of the shaded band, scaled to a year. The direction of the bars does not enter the calculation.

Why it matters

It is the benchmark for implied volatility. An option is expensive or cheap only relative to what the underlying actually moves; the IV minus realized spread is the option seller’s margin of safety and the buyer’s hurdle.
It sizes hedges. A delta-neutral book rebalanced against realized moves earns or loses the difference between realized and implied; see gamma.
It feeds position sizing. A 20-day realized volatility of 12% implies a typical daily range of about 0.76%, or 180 NIFTY points; stops and strike selection follow from that.
It frames the VIX. India VIX is implied, not realized; comparing the two shows whether the market is paying for fear that is not yet in the data.

Common mistakes

Using simple returns instead of log returns over long windows; the two diverge for large moves.
Annualising with 365 or 250. NSE has about 252 trading days a year; using 365 inflates the figure by 20%.
Quoting one window as “the” realized volatility. The 10-, 20- and 60-day figures can differ widely after a single large move.
Comparing realized volatility with an implied volatility of a different tenor. A 10-day realized figure is best compared with the implied volatility of options expiring in about 10 days.
Ignoring overnight gaps. Close-to-close realized volatility includes them; an intraday range-based measure does not.

Indian specifics

NIFTY’s realized volatility is computed from the index’s official daily closes published by NSE; index options settle against a closing value computed from the last 30 minutes, so close-to-close returns are the natural basis. Because NIFTY weekly options expire every Tuesday, short windows (5 to 10 days) matter more than they do in markets with monthly-only expiries. Realized volatility on NIFTY has typically run in the 8% to 15% range in calm periods and spiked above 50% in March 2020. Stock-level realized volatility is also an input to NSE Clearing’s SPAN margin, which is why margins rise after a volatile week even for unchanged positions; see initial margin.

FAQ

What is realized volatility?

The annualised standard deviation of past daily log returns over a chosen window; also called historical volatility.

How do you calculate realized volatility?

Sample standard deviation of daily log returns, multiplied by the square root of 252.

Why multiply by the square root of 252?

Because variance scales with time, standard deviation scales with its square root, and a year has about 252 trading days.

What is the difference between realized and implied volatility?

Realized is measured from past prices; implied is what option prices expect for the future.

Which window should I use for realized volatility?

Match the window to the option’s time to expiry: short windows for weeklies, 20 to 30 days for monthlies.

Compare implied with realized on the chain

TradePulse’s option chain strip shows ATM IV, IV Rank and the Vol Spread of implied against 30-day historical volatility for the selected instrument.

Implied volatility pages Historical vs implied volatility

Related terms

Implied volatility, the forward-looking twin
Implied vs realized volatility, the spread between them
India VIX, the implied index
IV rank, where current IV sits in its range
Gamma, how realized moves pay a hedged book
What is volatility?, the beginner guide