Trading term

What is Standard deviation?

Standard deviation is one number for how far a set of returns typically strays from its own average. The S&P 500 has averaged 11.86% a year since 1928 with a standard deviation of 19.40%, so an ordinary year lands anywhere between a 7.5% loss and a 31% gain. When someone calls an investment volatile, this is usually the number behind it.

Start with a list of yearly returns and work out the average. Standard deviation then measures how far the individual years sat from that average. It squares each miss first, so the big ones count for more, then takes the square root at the end to put the answer back into percent. You end up with a single figure in the same units as the returns themselves. That's why you can read it at a glance.

Here's what that figure tells you in practice. The S&P 500's average year since 1928 is 11.86% and its standard deviation is 19.40%. Add and subtract, and an ordinary year runs anywhere from a 7.5% loss to a 31.3% gain. That's an enormous spread, and roughly two years in three land inside it. The unusual years are wider still. 1931 finished down 43.84% and 1954 finished up 52.56%, both well outside that band.

The spread also predicts something about your balance. The wider it is, the further your compounded return falls below your average return, because a loss takes a bigger bite than the same-sized gain gives back. Fall 30% and you need a 42.9% gain just to get level again. That's why the S&P's 11.86% average turned into 10.02% compounded over those 98 years. The compounded figure is called CAGR, and it's the one your money actually followed.

Keep one thing in mind. This is measured from returns that already happened, over whatever window somebody chose. Pick a different decade and you get a different number. There's a forward-looking version too, built on what the market expects rather than what it delivered, and it's called implied volatility. For the S&P 500 as a whole, the VIX is what reports it.

For example

Two funds each average 8% a year over 20 years, and you put $10,000 into both. The steady one returns exactly 8% every year and ends at $46,610. The other one swings hard in both directions, with a standard deviation of 30.78%, and ends at $20,880. Same average return, less than half the money. The spread is the only thing that separates them.

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Why it matters to you

Standard deviation is the risk number on almost every fund fact sheet, and it's what the Sharpe ratio divides your return by. Two funds can post the same return and still be completely different things to own. It also tells you what a bad year feels like before you're living through one. That's worth knowing, because most long-term plans don't die from a bad year. They die from someone selling in the middle of one.

⚠ It counts your best years as risk too

Standard deviation measures spread in both directions and has no idea which way a return went. A fund that jumped 40% in a year scores exactly as risky as a fund that dropped 40%, and nobody has ever complained about the first one. So a high figure on its own doesn't mean dangerous. It means wide. If it's the downside you care about, look at drawdown alongside it, because that one only counts the falls.

Frequently asked questions

What is standard deviation in investing?

It's a single number for how spread out an investment's returns have been around their own average. A low figure means the years cluster close together; a high one means they scatter. It's quoted in the same units as the returns, so a 19.4% standard deviation on an 11.9% average return means an ordinary year ran between a 7.5% loss and a 31.3% gain.

Is standard deviation the same thing as volatility?

In practice, yes. When a fact sheet or a news story calls an investment volatile, standard deviation is almost always the number behind the word. Volatility is the plain-English term; standard deviation is the specific calculation. You'll occasionally see variance quoted instead, which is the same thing before the square root, and the S&P's 19.4% works out to a variance of 376. That number means nothing to a human. The square root is what makes it readable.

What's a normal standard deviation for the stock market?

For a broad stock index, somewhere around 15% to 20% a year is typical, and the S&P 500's figure since 1928 is 19.40%. A bond fund usually lands in the single digits, and cash sits near zero. There's no universally right level, because it depends on what you own and how long you're holding it. But the further above 20% a fund sits, the wider its year-to-year range.

Does a high standard deviation mean a bad investment?

No. It means a wide range of outcomes, and that range includes the good ones. The S&P 500's 19.40% standard deviation came alongside an 11.86% average return over 98 years. What a high figure does tell you is that the ride is rough and that your compounded return will lag your average return by more. Whether that's a problem depends on how long you can leave the money alone.