Same average, different ride
Standard deviation (SD) measures how spread out returns are around their average. It is the usual number behind a fund's "volatility".
Here are two funds with five years of returns each. Both average 10% a year.
| Year | Fund A | Fund B |
|---|---|---|
| 1 | 8% | 0% |
| 2 | 10% | 20% |
| 3 | 12% | −10% |
| 4 | 10% | 30% |
| 5 | 10% | 10% |
| Average | 10% | 10% |
Working it out
Take each year's gap from the average, square it, add them, divide by one less than the number of years, then take the square root.
- Fund A: gaps −2, 0, 2, 0, 0. Squares: 4, 0, 4, 0, 0, total 8. 8 ÷ 4 = 2. Square root: 1.41%.
- Fund B: gaps −10, 10, −20, 20, 0. Squares: 100, 100, 400, 400, 0, total 1,000. 1,000 ÷ 4 = 250. Square root: 15.81%.
Fund A's years stay within a couple of points of 10%. Fund B swings between −10% and 30%. Same average, very different experience, and SD is the number that tells them apart.
Reading the number
As a rough guide, about two-thirds of yearly outcomes fall within one SD of the average, if returns are spread fairly evenly. For Fund B that is roughly −6% to 26%. It is a guide, not a promise, and real returns have fat tails: bad years can be worse than the maths suggests.
From daily moves to a yearly figure
Fund pages quote volatility as a yearly number built from daily returns. The daily SD is scaled by the square root of the trading days in a year, about 252, which is roughly 15.9. A daily SD of 0.8% becomes 0.8 × 15.87 = 12.7% a year. WealthTicker's volatility figure is the annualised daily SD over the trailing three years.
What it misses
- It counts up and down alike. A big gain raises SD as much as a big loss. The Sortino ratio uses only downside swings for this reason.
- It is not a worst case. The deepest fall is in max drawdown.
- It is only useful against return. The Sharpe ratio divides excess return by SD; our Sharpe ratio post shows the ranking.
Use SD to compare funds within a category over the same period, not across very different kinds of fund.
This post is educational, not financial advice. The worked example uses made-up yearly returns to show the method; it is not data on any fund.
Frequently asked questions
What does standard deviation tell me about a fund?
How far its returns typically stray from their average. A higher number means a bumpier ride; a lower number means returns that stay closer to the average.
Is a higher standard deviation always worse?
Not by itself. It measures the size of swings in both directions, so it is a cost only when the extra swings are not matched by extra return.
Is standard deviation the most I can lose?
No. A fall can be several times larger than one standard deviation. For the worst real fall, look at maximum drawdown.
This is commentary on published data, not investment advice. WealthTicker is not a SEBI-registered adviser or distributor. Figures are WealthTicker’s own calculations from public data — AMFI’s fund NAVs and disclosures, NSE’s index and FII/DII files, and the fund houses’ monthly portfolios (how we calculate). They are as of the dates stated and can be revised by their source.
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