Market volatility is measured by means of identifying the price change standard deviation for a certain period of time. The statistical concept of standard deviation allows seeing how something differs from an average value.
We will show you how to identify volatility through an example.
Task. To calculate volatility of XYZ stock for the past four days. The stock prices are shown below:
Day 1 – USD 10.
Day 2 – USD 12.
Day 3 – USD 9.
Day 4 – USD 14.
The volatility calculation formula will become clear from the following solution.
In order to calculate the price volatility, we need to take 6 simple steps.
Step 1. Calculate an average price:
USD 10 + USD 12 + USD 9 + USD 14 / 4 = USD 11.25
Step 2. Calculate the difference between each price and average price:
Day 1: 10 – 11.25 = -1.25
Day 2: 12 – 11.25 = 0.75
Day 3: 9 – 11.25 = -2.25
Day 4: 14 – 11.25 = 2.75
Step 3. Raise each difference from the previous step to the square:
Day 1: (-1.25) squared = 1.56
Day 2: (0.75) squared = 0.56
Day 3: (-2.25) squared = 5.06
Day 4: (2.75) squared = 7.56
Step 4. Sum up squared differences:
1.56 + 0.56 + 5.06 + 7.56 = 14.75
Step 5. Calculate dispersion:
Dispersion = 14.75 / 4 = 3.69
Step 6. Calculate standard deviation:
Standard deviation = the square root of 3.69 = 1.92
Standard deviation shows that the ABC Corp. stock price usually deviates from the average stock price by USD 1.92. This is the solution to the task.
Standard deviations are important because they do not only tell you how much a value can change, but they also provide the ground for a probability of its occurrence. Values will be within one standard deviation from an average one in 68% of cases, within two in 95% of cases and within three in 99.7% of cases.
Traders calculate standard deviations of market values based on trading values at the end of the day and intraday volatility or forecasted future value changes during a trading session.
Outside market observers, perhaps, are better acquainted with the last method, which is used by the Chicago Board Options Exchange volatility index that is usually called VIX.