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What is standard deviation?

Standard deviation definition

A simple standard deviation explanation is that it is a statistical measurement of how far data is spread out from the mean, or average. Standard deviation is calculated as the square root of the variance in the data points. It can be used to quantify certain outcomes relative to the average, so it is a useful measure in stock and options trading where a high standard of deviation is associated with high market volatility and, therefore, higher risk. Standard deviation is low when stock prices trade within a narrow range.

Where have you heard about standard deviation?

In an investment setting, you may have heard standard deviation explained in terms of analysing a company’s annual rate of return or the strike price of an option contract.

Standard deviation can also be used to show how the performance of a managed fund compares with its benchmark index.

What do you need to know about standard deviation?

Understanding the standard deviation definition can help you in researching stocks, funds and options to invest in or trade. There are several steps to calculating the standard deviation.

First, work out the average of a group of numbers – such as the annual rate of return on a stock over a few years. Next, subtract the mean from each number and square the result. Then work out the mean of the results and calculate the square root of the mean.

The standard deviation formula is expressed as follows:

Standard deviation formula

To take the standard deviation example of considering the annual rate of return of a company’s share price, using the return over several years, can help to measure volatility and predict trends in the performance of an asset. Investors adopting a low-risk strategy may opt for assets with low volatility, while investors with a higher risk appetite may look to invest in more volatile growth stocks and funds for a higher rate of return.

Standard deviation in options trading is based on a stock’s implied volatility. Strike prices within one standard deviation are closer to the share price and have a higher probability of being in the money on expiry.

In statistics, the empirical rule specifies that 99.7 per cent of data with a normal distribution sits within three standard deviations of the mean. In options trading, this equates to a 68 per cent probability of a stock closing within one standard deviation on expiry, a 95 per cent probability of the stock closing within two standard deviations and a 99.7 per cent probability of the stock closing within three standard deviations.

For example, if a stock is worth $100 per share and has an implied volatility of 30 per cent, then there is a 68 per cent probability that the price will close between $70 and $130, a 95 per cent probability that it will close between $40 and $160, and a 99.7 per cent probability that it will close between $10 and $190. Knowing this can help you decide which strike price to choose for an option contract.

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