Annualised volatility is a crucial statistic for comparing the riskiness of different investments such as stocks, commodities and bonds. Any investor deciding how to allocate resources among a basket of different investment products would be well served to annualise the volatility of each product. The statistical information obtained from the annualised volatility will allow the investor to assess the level of risk that can be attributed to the various different investments under consideration. Once the level of risk is known an investor can begin to build a portfolio of investment products tailored specifically to her own risk tolerance.

- Skill level:
- Moderate

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## Instructions

- 1
Select the time period for which you want to measure volatility. For example, you could calculate volatility of a financial instrument over the course of a month, a quarter, or half a year. The shorter the time period the more sensitive the volatility measure will be toward the current market's price swings, whereas the longer time periods will be less sensitive toward current market's price swings. If you are just starting out to use volatility try using a month of price data which is approximately 20 trading days.

- 2
Calculate the daily percentage change for each day of your chosen time period. For example, if you had chosen a month's worth of daily closing prices for the company General Electric you would want to know what the daily percentage change for every day of the month your are evaluating. The calculation goes this way: subtract yesterday's closing price from today's closing price and then divide this number by yesterday's closing price. Next, multiply by 100 to arrive at the daily percentage change.

- 3
Calculate the standard deviation for the entire set of daily percentage changes by first calculating the average daily percentage change for your chosen time period. Then take each individual daily percentage change and subtract from it the average daily percentage change, which will then be raised to the power of 2. For example, if the average daily percentage change is 2.5 and the first daily percentage change number you calculated was 1.2 you would want to subtract 2.5 from 1.2 and then square this difference for an answer of 1.69 (1.2 - 2.5)^2. You would repeat this same calculation for each daily percentage change for your chosen time period and then add them all up and divide this final number by the total number of calculations you did minus 1. For example, if you had done 20 separate calculations you would subtract 1 from 20 to arrive at 19. Once you have completed this calculation you must then take its square root to arrive at the standard deviation.

- 4
Multiply the standard deviation by the square root of 252 to arrive at the annualised volatility. For example, assume you had a monthly standard deviation of 2.0. You would multiply 2.0 by the square root of 252 to arrive at an annualised volatility of 31.75.