Volatility analysis — historical, implied and the VIX
The answer
Historical volatility is how much a price actually moved. Implied volatility is how much the option market is charging for movement it expects. The VIX is that second number for an index, and it is usually larger than what happens next.
Why this costs you money
Two mistakes, in opposite directions.
The first is treating the VIX as a signal about direction. A reader sees the VIX at 30 and buys, because "high fear means a bottom". The VIX is high because prices already fell. It says the market expects large moves for the next month. It does not say which way, and large moves in a falling market are usually more falling.
The second is more expensive. A reader sees implied volatility is high, notices that option sellers usually make money, and sells options. It works for months. The average outcome is genuinely positive, for a documented reason. Then 1 day arrives on which the position loses more than the previous 2 years of profit.
Selling volatility is not a strategy that fails often. It is a strategy that fails once.
How it works
Historical volatility
Take daily percentage changes over a window, compute their standard deviation, and multiply by about 15.9 to put it in annual terms. The 15.9 is the square root of 252, the approximate number of trading days in a year.
Two things follow. Volatility always belongs to a window, so a 20-day figure and a 1-year figure on the same stock can differ a great deal. And volatility scales with the square root of time, not with time.
Implied volatility
An option's price depends on the strike, the time left, interest rates and how much the underlying is expected to move. Every input except the last one is observable. So you can run the pricing in reverse: take the price people are paying and solve for the movement it implies.
That output is implied volatility. It is not a model's forecast. It is a price, quoted in the units of movement.
The VIX
The VIX is not the implied volatility of 1 option. It is computed from a wide strip of out-of-the-money index options across 2 nearby expiries, weighted so the result targets a constant 30 days ahead. It does not depend on any particular option pricing model.
The number is quoted as an annualised percentage, representing 1 standard deviation over the coming 30 days. That definition contains the 2 conversions you need.
- Expected daily move = VIX ÷ 15.9. A VIX of 16 implies about a 1% move per day.
- Expected 30-day move = VIX ÷ 3.46, which is the square root of 12. A VIX of 16 implies about 4.6% over the month.
"One standard deviation" means roughly 2 days in 3 fall inside that range, if the distribution behaves. Real markets have fatter tails than the model, so the outside days are more common than the arithmetic suggests.
Volatility clustering, and why volatility is forecastable
Large moves follow large moves. Quiet days follow quiet days. This is one of the most reliably documented properties of financial prices, in every market anybody has measured, and it has a formal model going back to 1982.
That is why volatility is far more forecastable than direction. Tomorrow's direction is close to unpredictable, and if it were not it would be traded away. Tomorrow's size is substantially predictable, because today's size tells you a great deal about it. So a volatility estimate is a usable input to position sizing even though a direction forecast is not.
Volatility also mean-reverts. A very high reading tends to fall over the following weeks and a very low reading tends to rise. Neither happens on a schedule.
The variance risk premium
Compare implied volatility today against the volatility that actually occurred over the following 30 days, thousands of times. Implied is usually higher.
The reason is not a mistake. It is insurance. A person buying index puts is buying protection, and a person selling them accepts a very large obligation for a fee. Sellers demand payment above the fair statistical value, as an insurer charges more than the expected claim.
So the option seller is paid a real premium for a real risk. The premium is not free money and the risk is not theoretical. Holding both statements at once is the whole of volatility trading.
Term structure
Implied volatility differs across expiries. In calm periods, further expiries price higher than nearer ones, because more can happen in more time. In a crisis the shape inverts, and the nearest expiry prices the highest. That inversion is a useful regime marker: the market is pricing an event, not an atmosphere.
What it tells you, and what it does not
It tells you size, never direction. The formula uses puts and calls. It measures expected movement either way.
It is a 30-day number. Comparing today's VIX against today's index move is a category error. Divide by 15.9 first.
It is about the index, not your stock. A single company can have implied volatility of 45% while the index sits at 14%. Index volatility is damped by diversification. Your holdings are not.
A high reading is not a forecast of a crash. It forecasts large moves, and it is usually too high.
The average and the survival are different questions. A strategy with a positive average return and a catastrophic worst case is not described by its average. Volatility selling is the clearest example of that gap in finance.
The decision rule
Use volatility to set size, not direction.
- Convert the current reading into an expected daily move: VIX ÷ 15.9.
- Compare that against the average daily move of the last month. If the
implied figure is larger, options are expensive relative to recent behaviour. That is normal, not a signal.
- If expected volatility has doubled, your position size should roughly halve,
because the same number of shares now carries twice the daily movement.
- Never size a short option position by the premium received. Size it by what
a 5 standard deviation day would cost, and check that you would survive it.
Try this now
Five minutes. You are going to compare what the market is charging against what the market has been doing.
- Look up the current reading. For India, find India VIX on the NSE site or in your broker app. For the United States, find the CBOE VIX on any free quote site.
- Convert it to a daily move. Divide by 15.9. A reading of 14 gives about 0.88%.
- Convert it to points. Multiply that percentage by the current index level. This is the daily move the option market is pricing.
- Measure what actually happened. Open a daily chart of the same index and take the last 20 trading days. For each, compute the percentage change from the previous close, ignore the minus signs, and average them.
- Multiply that average by 1.25 to make it comparable to a standard deviation.
- Put the 2 numbers side by side. Implied from step 2, realised from step 5.
What you should see. In an ordinary month the implied number is larger, typically by 10% to 30% of itself. A VIX of 14 implies about 0.88% a day, while the index has been moving about 0.6% to 0.8% a day.
That gap is the variance risk premium, measured by you, on today's data. It is why selling options has a positive average return. It is also small, which is the part people miss. You are collecting a modest edge and accepting an enormous tail, and the arithmetic only works if the size is set so the tail cannot end you.
Then do the second half, which takes 1 minute. Find the worst single day in your 20 and divide its percentage move by the implied daily move from step 2. That is how many standard deviations that day was. Now ask what a day 3 times that size would do to a position you currently hold. Such days have occurred in both markets, more than once, in living memory.
Three real cases
1. 5 February 2018, United States — the day the short volatility trade ended The VIX rose from roughly 17 to roughly 37 in a single session, the largest 1-day increase on record at the time. An exchange traded note designed to profit from falling volatility, the VelocityShares Daily Inverse VIX Short-Term ETN, lost the large majority of its value after the close and was terminated by its issuer within days. The note had produced excellent returns for several years. Its holders were not wrong about the average. They were wrong about the worst case, and it arrived in a few hours.
2. 16 March 2020, United States, and March 2020 in India — the record, and what it did next The CBOE VIX closed at about 82.69, the highest close in its history, above the previous record set in November 2008. India VIX reached its own record in the same month. Two things followed. Realised volatility over the following weeks was also extreme, so the high reading was not simply wrong. And the index bottomed within days of the peak, which is why the level was never a timing tool: correct about size, silent about direction.
3. Robert Engle's work on clustering, 1982 and 2003 — the property that makes volatility usable An econometrician published a model in which today's expected variance depends on recent large errors, which is a formal way of saying turbulent periods follow turbulent periods. It fitted financial data well enough to become the foundation of modern volatility forecasting, and it was cited in the 2003 Nobel prize in economics. Carry the consequence: nobody can tell you where the index will be next month, and many people can tell you roughly how much it will move.
The question that resolves it
A novice sees a high reading and asks: is this a top or a bottom?
An expert asks: how large a daily move is now being priced, and does my position still fit inside that?
The first question has no answer. The second has an answer in 30 seconds, and it changes what you do today.
What would make this wrong
If realised volatility exceeded implied volatility on average over long periods, the variance risk premium would not exist and selling options would be a losing business on average. That is testable and it has been tested many times. The exercise above is a small version of the same test.
Three honest limits.
Volatility clustering can weaken. It is an empirical regularity, not a law. If a market's volatility became independent from day to day, forecasting it would stop working and volatility-based position sizing would lose its basis.
The VIX is not the same thing as VIX products. Futures, notes and funds linked to volatility hold contracts that must be rolled, and in normal conditions that roll costs money continuously. A long volatility fund can lose value over a year in which volatility rose.
The premium is not always positive. Implied volatility can be below what follows, and it usually is in exactly the periods that end accounts. The average is a statement about many months. Your account experiences 1 month at a time.
In India
India VIX is computed by NSE from the order book of NIFTY 50 index options, using a methodology licensed from CBOE, and has been published since 2008. It uses the best bid and ask of near-month and next-month contracts rather than last-traded prices, because a stale last trade would distort the reading.
Three features change how an Indian reader should use it.
There is no liquid volatility instrument for retail. NSE listed India VIX futures in 2014 and they never developed meaningful volume. So India VIX is an indicator you read, not an exposure you can take. To trade volatility in India you trade NIFTY options, which also carries direction and strike.
The expiry structure is unusual. Indian index option activity has been concentrated in very short-dated weekly contracts to a degree with few parallels anywhere. SEBI's October 2024 measures limited each exchange to 1 weekly index options expiry and raised minimum contract sizes. Short-dated options are the most sensitive to a sudden move, so the concentration is where the risk sits.
Realised volatility is structurally higher than the American index. The NIFTY 50 is more concentrated, and a shorter continuous trading day pushes more of the total movement into overnight gaps.
In the United States
The CBOE VIX has been published since 1993, in a form derived from S&P 100 options, and was redefined in 2003 to the current model-free calculation on S&P 500 options.
The United States has something India does not: a complete, tradable volatility market. VIX futures list across many months, so the term structure is directly observable rather than inferred. VIX options exist. A large family of exchange traded products offers long and inverse volatility exposure to anybody with a brokerage account.
That availability helps measurement and endangers execution. The term structure is visible on a free website, which is real information. The products built on it decay in normal conditions, and the inverse products can lose most of their value in a session, which is the lesson of 5 February 2018.
American realised volatility on the index has averaged in the mid-teens over long periods, with sustained stretches far below and short stretches far above.
Where they differ, and what that tells you
The levels are not comparable, and almost every commentary treats them as if they were.
India VIX is computed from NIFTY 50 options. CBOE VIX is computed from S&P 500 options. These are 2 different indices with different constituents, different concentration and different underlying movement. A reading of 15 says the market expects the NIFTY 50 to move a certain amount in one case, and the S&P 500 to move a certain amount in the other. Those are not the same amount.
So "India VIX is at 13, lower than the US VIX at 16, so India is calmer" is not a comparison. It is 2 unrelated numbers placed beside each other.
What to do instead. Compare each reading against its own history, as a percentile. India VIX at 13 might sit in the lowest 10% of its own last 5 years, which is a real statement. Or divide each reading by its own index's realised volatility over the same period. That ratio is comparable across markets, because it removes the underlying.
The second difference is what you can do about it. An American reader can observe the whole term structure and take a position in volatility itself. An Indian reader has no liquid volatility contract, so they must build the term structure by hand from implied volatilities across NIFTY expiries, and any volatility position also carries direction.
In India, volatility is an input to position sizing rather than a thing to trade. Advice imported from the United States assumes a tradable volatility market and quietly stops applying at the border.
Carry this
- VIX ÷ 15.9 is the expected daily move. VIX ÷ 3.46 is the expected 30-day move.
- Implied is usually higher than what follows. That gap is a payment for insurance, not a mistake.
- Volatility is forecastable. Direction is not. Use volatility to set size.
- India VIX and CBOE VIX are not comparable. Compare each against its own history.
- Selling volatility does not fail often. It fails once.