Beta and volatility
How far a price moves, how much of that moving goes with the market, and what India VIX measures
Index figures as on 31 August 2026
Verified 12 October 2026
For training and education only. Not investment advice.
Trainer notes
Ask the room what they mean when they call a fund 'risky'. Most answers are about how much its value goes up and down. This deck gives that idea three measures: standard deviation, beta and India VIX. None of them says what will happen next.
Volatility says how much a price moves. Beta says how much of that moving goes with the market.
Both are worked out from past returns. India VIX is different: it is worked out from option prices and shows the volatility the market expects over the next 30 days.
Trainer notes
Keep three questions apart through the deck. How bumpy was it (standard deviation)? How closely did it follow the market (beta)? How bumpy does the options market expect the next month to be (India VIX)? Exception to 'past returns': some analysts estimate a forward-looking beta, but the beta in a fund factsheet is historical.
Four terms to know first
Volatility
How widely returns spread around their average, up or down. Standard deviation is the usual measure.
Beta
How sensitive a share's or fund's returns have been to the market's returns. The market's own beta is 1.
Correlation
How consistently two sets of returns move together, on a scale from −1 to +1.
India VIX
NSE's volatility index. It shows the volatility expected over the next 30 days, drawn from Nifty option quotes.
Sources: NSE Indices, Methodology Document for Equity Indices, September 2026 (beta); NSE white paper 'India VIX: Computation Methodology'.
Trainer notes
The 'market' in a beta is whichever index is chosen: NSE Indices uses the Nifty 50 for its High Beta 50 index, and a fund factsheet normally uses the scheme's benchmark. Standard deviation is covered step by step in the deck on risk-adjusted return ratios. An option is a contract whose price rises when traders expect bigger moves; that is why option quotes carry information about expected volatility.
Working out a beta
FOUR ASSUMED MONTHS
Market, monthly returns: +4%, −2%, +4%, −2%.
Fund F, monthly returns: +5%, −2.2%, +5%, −2.2%.
- Averages. Market: (4 − 2 + 4 − 2) ÷ 4 = 1%. Fund F: (5 − 2.2 + 5 − 2.2) ÷ 4 = 1.4%.
- Gaps from the average. Market: +3, −3, +3, −3. Fund F: +3.6, −3.6, +3.6, −3.6.
- Multiply the gaps month by month and average them: 10.8 each month, so 10.8. Square the market's gaps and average them: 9.
- Beta = 10.8 ÷ 9 = 1.2.
Result: In these four months Fund F moved 1.2 times as far from its average as the market did, the same way.
Illustration with an invented fund and assumed figures. Real calculations use many more returns.
Trainer notes
The first average (10.8) is called the covariance of the fund with the market; the second (9) is the market's variance. Beta is covariance divided by market variance. Real data seldom lines up this neatly: here the fund's gaps are exactly 1.2 times the market's in each month, so the fit is perfect. Slide 6 shows what happens when it is not.
Reading a beta figure
Arithmetic on a 10% market move. It shows what the past link implies by itself; it is not a forecast.
| Beta | What it describes | Market +10% | Market −10% |
|---|---|---|---|
| 1.0 | Has tended to move in step with the market. | +10% | −10% |
| 1.2 | Has tended to move further than the market, in the same direction. | +12% | −12% |
| 0.8 | Has tended to move less far than the market, in the same direction. | +8% | −8% |
| 0 | Its moves have shown no link with the market's. It can still move for reasons of its own. | No link | No link |
Illustration: beta × market move. Actual returns also carry moves that are not linked to the market, so they differ from these figures.
Trainer notes
Each cell is beta multiplied by the market move: 1.2 × 10 = 12, 0.8 × 10 = 8. Strictly, beta applies to returns above the risk-free rate, and the fund's own non-market moves come on top. A negative beta, which is uncommon, would mean the returns have tended to move against the market. Do not let the room read 0.8 as 'loses less': it is a description of the past link only.
Beta is not the same as volatility
TWO ASSUMED FUNDS
Market: standard deviation 10%.
Fund G: standard deviation 20%, correlation with the market 0.5.
Fund H: standard deviation 12%, correlation 0.9.
- Beta can also be written as: correlation × (fund's standard deviation ÷ market's standard deviation).
- Fund G: 0.5 × (20 ÷ 10) = 0.5 × 2 = 1.00.
- Fund H: 0.9 × (12 ÷ 10) = 0.9 × 1.2 = 1.08.
- G is the bumpier fund: 20% against 12%. H has the higher beta: 1.08 against 1.00.
Result: Beta counts only the movement that goes with the market. Standard deviation counts all of it.
Illustration with two invented funds and assumed figures. Not a view on any scheme.
Trainer notes
A correlation of 1 means the two sets of returns moved in perfect step; 0 means no link. Much of Fund G's movement comes from things other than the market, such as a few large holdings or one sector. That part does not show in its beta. This is why a factsheet shows standard deviation and beta side by side.
Betas of seven NSE indices
| Beta against the Nifty 50 | |
|---|---|
| High Beta 50 | 1.38 |
| Bank | 1.16 |
| Midcap 150 | 1.06 |
| Low Vol 50 | 0.84 |
| IT | 0.82 |
| FMCG | 0.70 |
| Pharma | 0.55 |
What the year shows
- Our own calculation: 247 daily returns, 29 Aug 2025 to 31 Aug 2026.
- Nifty 50: volatility about 13% a year over this period.
- Nifty IT: beta 0.82, yet volatility about 25% a year.
- A different year or benchmark gives different betas.
Source: Trustner calculation (not an NSE figure) from NSE Indices daily close files, 29 Aug 2025 to 31 Aug 2026; price indices.
Trainer notes
Refresh these at each month-end, using market figures that are at least 30 days old. These betas are our own arithmetic on NSE Indices' published closing values, not figures published by NSE; index factsheets may differ because of the period or method. Volatility here is the standard deviation of daily returns multiplied by the square root of 252 trading days. The Nifty IT bar is the real-data version of slide 6: its correlation with the Nifty 50 was 0.43, so a high volatility went with a beta below 1. Do not read the chart as a view on any sector. Market figures are shown with a lag of at least 30 days, under Trustner's own rule for price data used in education.
How India VIX is worked out
A price index is built from share prices. A volatility index is built from option quotes.
What goes in
The best bid and ask quotes of Nifty option contracts for the near month and the next month, taken from NSE's order book.
What comes out
The volatility the market expects over the next 30 calendar days.
How it is stated
As an annualised percentage. A reading of 15 means 15% a year, not 15% over the next month.
How it tends to behave
It usually rises when the market moves steeply up or down, and declines as volatility subsides.
Source: NSE white paper, 'India VIX: Computation Methodology'. The method follows that of the Cboe volatility index, adapted to the Nifty option order book.
Trainer notes
Bid is the highest price a buyer is quoting and ask is the lowest price a seller is quoting. The index mainly uses out-of-the-money options, and NSE takes the Nifty futures price as the forward level of the index. 'VIX' is a trademark of Cboe, used by NSE under licence. Nobody needs the formula; the point is that India VIX reads expectations from option quotes and does not look at past returns.
From a yearly figure to 30 days
ASSUMED READING
A volatility index reads 15.
The share index it is based on stands at 20,000.
Both figures are assumed.
- 15 is an annualised figure: 15% a year.
- Volatility scales with the square root of time. A month as 1/12 of a year (approximate): √12 = 3.4641.
- 15 ÷ 3.4641 = 4.33% for about a month.
- 4.33% of 20,000 = 866 points, up or down.
Result: Roughly one standard deviation of the implied move, either way; larger moves are possible. No direction.
Illustration, assumed figures. The range is a statistical measure, not a limit or a forecast. Source: Cboe, 'Inside Volatility Trading: Breaking Down the VIX Index and Its Correlation to the S&P 500 Index' (÷ √12 for a month); not in NSE's paper; approximate.
Trainer notes
Dividing by the square root of 12 is a common rule of thumb, not part of NSE's document; Cboe's education material uses it for its own VIX. It treats a month as one-twelfth of a year. NSE's paper counts time in minutes over a 365-day year, so 30 days is 30/365 and the figure would be 4.30%, not 4.33%. The result is roughly one standard deviation: moves larger than this are quite possible. Using 15 ÷ 3.4641 gives 4.3301%, and 4.33% of 20,000 is 866. Say clearly that this is not a prediction of where the index will be.
India VIX over twelve months
| India VIX | |
|---|---|
| Sep 25 | 11.1 |
| Oct | 12.2 |
| Nov | 11.6 |
| Dec | 9.5 |
| Jan 26 | 13.6 |
| Feb | 13.7 |
| Mar | 27.9 |
| Apr | 18.5 |
| May | 16.2 |
| Jun | 13.6 |
| Jul | 11.8 |
| Aug | 11.2 |
Where things stand
- 31 August 2026: India VIX closed at 11.19.
- Highest close in the 12 months: 27.89, on 30 March 2026.
- Lowest close in the 12 months: 9.15, on 26 December 2025.
- Nifty 50 closed at 24,080.40 on 31 August 2026.
Source: NSE Indices daily index close files, 1 September 2025 to 31 August 2026 (closing values of India VIX and the Nifty 50).
Trainer notes
Refresh these at each month-end, using market figures that are at least 30 days old. The chart shows only month-end closes, rounded to one decimal (exact closes: 11.07, 12.15, 11.62, 9.48, 13.63, 13.70, 27.89, 18.46, 16.19, 13.60, 11.76, 11.19), so moves within a month do not appear; the highest and lowest figures are from all 247 daily closes. Do not explain the March 2026 reading with a cause unless you have a source for it, and do not describe any level as high, low, calm or fearful. Market figures are shown with a lag of at least 30 days, under Trustner's own rule for price data used in education.
Four things people get wrong
Misconception'A low beta means low risk.'
What is trueBeta counts only movement that goes with the market. A fund with a beta below 1 can still swing widely for reasons of its own.
Misconception'A fund's beta is a fixed number.'
What is trueIt changes with the period, the benchmark and whether daily or monthly returns are used. Check all three before comparing.
Misconception'A high VIX means a fall is coming.'
What is trueIndia VIX measures the size of moves the options market expects, not their direction. It usually rises on steep market moves either way.
Misconception'Volatility means loss.'
What is trueStandard deviation counts rises and falls alike. It describes how bumpy returns were, not what an investor gained or lost.
Trainer notes
On the first point, use the Nifty IT figures from slide 7. On the second, a beta is an average over a period and assures nothing about the next period. Older material often gives fixed VIX levels that are said to mark a 'complacent' or a 'fearful' market; NSE's document gives no such levels, so do not quote them. Returns are not assured, whatever a fund's beta or standard deviation.
Check yourself
Question 1: The market's standard deviation is 10%. Fund K's is 15% and its correlation with the market is 0.8. What is K's beta, and what does it describe?
Answer: 0.8 × (15 ÷ 10) = 0.8 × 1.5 = 1.2. Over the period measured, K's returns tended to move 1.2 times as far as the market's, in the same direction. It describes the past link only.Question 2: A volatility index reads 12. Roughly what move over one month does that correspond to, and does it say which way?
Answer: 12 ÷ √12 = 12 ÷ 3.4641 = 3.46%, up or down. It is an annualised figure scaled to a month by a rule of thumb. It says nothing about direction and is not a limit.Question 3: A client says: 'This fund has a beta of 0.7, so it cannot fall much.' What would you explain?
Answer: Beta shows how the fund's returns have moved with its benchmark in the past. It leaves out moves that are not linked to the market, it changes with the period and benchmark, and it assures nothing about the future. Returns are not assured; the fund's value can fall.
Sources and disclaimer
Sources for the figures in this explainer
- Beta as the sensitivity of returns to market returns, with the Nifty 50 as the market: NSE Indices, Methodology Document for Equity Indices, September 2026 (Nifty High Beta 50).
- India VIX: inputs, 30-day horizon, annualised percentage, behaviour: NSE white paper, 'India VIX: Computation Methodology' (undated; file created June 2014).
- India VIX and Nifty 50 closing values, 1 September 2025 to 31 August 2026: NSE Indices daily index close files.
- Index betas, correlation and volatility on slide 7: Trustner calculation from the same daily files, 247 daily returns to 31 August 2026.
- Beta = covariance ÷ market variance = correlation × ratio of standard deviations (standard statistics). ÷ √12 for one month: Cboe article, approximate.
- Funds F, G, H and K, the assumed market and the assumed index readings are invented for illustration. They do not refer to any real scheme.
This material is for training and investor education only. It is not investment, tax or legal advice and is not a recommendation to buy, sell or hold any security or scheme. Examples use assumed figures unless a source and date are shown. Mutual fund investments are subject to market risks; read all scheme related documents carefully. Trustner Asset Services Pvt. Ltd. is an AMFI-registered Mutual Fund Distributor (ARN-286886).