Standard deviation is a statistical measurement in finance that, when applied to the annual rate of return of an investment, sheds light on the historical volatility of that investment. The greater the standard deviation of a security, the greater the variance between each price and the mean, which shows a larger price range.

– Standard deviation measures the dispersion of a dataset relative to its mean.

– A volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low.

– As a downside, it calculates all uncertainty as risk, even when it’s in the investor’s favor, such as above average returns.

It is an especially useful tool in investing and trading strategies as it helps measure market and security volatility, and predict performance trends. As it relates to investing, for example, one can expect an index fund to have a low standard deviation versus its benchmark index, as the fund’s goal is to replicate the index.

On the other hand, one can expect aggressive growth funds to have a high standard deviation from relative stock indices, as their portfolio managers make aggressive bets to generate higher-than-average returns.

A lower standard deviation isn’t necessarily preferable. It all depends on the investments one is making, and one’s willingness to assume the risk. When dealing with the amount of deviation in their portfolios, investors should consider their personal tolerance for volatility and their overall investment objectives. More aggressive investors may be comfortable with an investment strategy that opts for vehicles with higher-than-average volatility, while more conservative investors may not.

It is one of the key fundamental risk measures that analysts, portfolio managers, advisors use. Investment firms report the standard deviation of their mutual funds and other products. A large dispersion shows how much the return on the fund is deviating from the expected normal returns. Because it is easy to understand, this statistic is regularly reported to the end clients and investors.

**Limitations**

The biggest drawback is that it can be impacted by outliers and extreme values. Standard deviation assumes a normal distribution and calculates all uncertainty as risk, even when it’s in the investor’s favor, such as above average returns.

**Differences from Variance**

Variance is derived by taking the mean of the data points, subtracting the mean from each data point individually, squaring each of these results and then taking another mean of these squares. Standard deviation is the square root of the variance.

The variance helps determine the data’s spread size when compared to the mean value. As the variance gets bigger, more variation in data values occurs, and there may be a larger gap between one data value and another. If the data values are all close together, the variance will be smaller. This is more difficult to grasp because variances represent a squared result that may not be meaningfully expressed on the same graph as the original dataset.

Standard deviations are usually easier to picture and apply. They are expressed in the same unit of measurement as the data, which isn’t necessarily the case with the variance. Using them, statisticians may determine if the data has a normal curve or other mathematical relationship. If the data behaves in a normal curve, then 68% of the data points will fall within one standard deviation of the average, or mean data point. Bigger variances cause

more data points to fall outside the standard deviation. Smaller variances result in more data that is close to average.

**How is it Calculated?**

- The mean value is calculated by adding all the data points and dividing by the number of data points.
- The variance for each data point is calculated, first by subtracting the value of the data point from the mean. Each of those resulting values is then squared and the results summed. The result is then divided by the number of data points less one.
- The square root of the variance (result from number 2 above) is then taken to find the standard deviation.

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