What Is Standard Deviation?

Standard deviation is a statistical measure of how far a fund's returns stray from their average. In finance it is the most common way to put a single number on volatility — that is, on how much a price swings. The larger the deviation, the more widely the returns are flung around the mean, meaning the fund's path is more volatile. The smaller the deviation, the more the returns cluster near the mean, meaning a steadier path. Standard deviation does not indicate direction — it describes not whether the price went up or down, but how widely it scattered around its average.

What does it mean intuitively?

Think of it without heavy math. Take a fund's returns and find their average. Then look at how far each return departs from that average. Standard deviation is a single figure that summarizes the typical size of those departures:

• Small standard deviation: the returns are packed close to the mean. The fund moves along a relatively predictable, steady line.
• Large standard deviation: the returns are flung far from the mean, both up and down. The fund's day-to-day path is choppier.

A concrete example: two funds can have the same average return over a period, yet one moves close to that average each day while the other jumps sharply up on some days and falls sharply on others. Even with an identical average, the second fund's standard deviation is markedly higher; that difference makes visible the volatility the average hides. Standard deviation is preferred as a volatility measure because it weighs upward and downward deviations equally and summarizes the spread around the mean in a single, interpretable number.

How it is built from returns and annualized

Standard deviation is built step by step from the fund's periodic returns:

• Returns are computed over a set interval (for example, each day). In practice logarithmic (continuous) returns are often used, because their compounding behaves more cleanly.
• Each return's deviation from the mean is found, the average of the squared deviations is taken, and the square root of that result is the standard deviation.
• The result is the deviation for that interval: daily standard deviation if computed from daily returns.

To carry a daily figure onto an annual scale, you annualize: the standard deviation is multiplied by the square root of the number of periods in a year. This site multiplies the standard deviation of daily returns by √252 (about 15.87) to convert it into annual volatility; for weekly data the factor is √52, for monthly √12. The square root appears because variance (the square of standard deviation) grows roughly linearly with time, so standard deviation scales with the square root of time. This puts different funds — and different sampling frequencies — on a common annual scale for comparison.

Two measures that use standard deviation

Standard deviation is not just a result but a building block for other risk measures:

• Sharpe ratio — divides the fund's excess return over the risk-free return by its standard deviation. Standard deviation is thus the denominator of this ratio: it is used to measure how much return was earned per unit of fluctuation.
• Risk value (1-7) — the number from 1 to 7 assigned to every fund on TEFAS and in fund information documents is derived by mapping the annualized standard deviation of the fund's past returns onto seven bands. The larger the deviation, the higher the risk number; standard deviation is the core input to this scale.

That is why a money market fund usually sits at the low end of the scale and an equity-heavy fund at the top: the difference is mainly the difference in the standard deviation of their returns.

What standard deviation does not tell you

Standard deviation is powerful but limited, and on its own it is incomplete:

• It does not distinguish direction. It counts upside surprises and downside losses alike as "deviation." Yet for a saver, the asymmetry can matter; a sharp rise and a sharp fall are not the same experience.
• It does not measure the single worst moment. Standard deviation summarizes the average spread; the largest loss from a peak down to the following trough is a separate measure, called maximum drawdown.
• It is not a quality judgment. Low standard deviation does not automatically mean "safer" or "better"; a fund that loses value in real terms against inflation can also have a low standard deviation.

This page does not say which level should be preferred; it only explains what the concept measures. To view different funds' volatility and risk measures side by side, you can use the /fon-karsilastirma and /en-cok-kazandiran-fonlar pages; these pages offer no recommendation, they only display the figures.