 # Volatility

A measure of the rate of fluctuations in the prices of a security over time

## What is Volatility?

Volatility is a measure of the rate of fluctuations in the price of a security over time. It indicates the level of risk associated with the price changes of a security. Investors and traders calculate the volatility of a security to assess past variations in the prices to predict their future movements. Volatility is determined either by using the standard deviation or beta. Standard deviation measures the amount of dispersion in a security’s prices. Beta determines a security’s volatility relative to that of the overall market. Beta can be calculated using regression analysis.

### Types of Volatility

#### 1. Historical Volatility

This measures the fluctuations in the security’s prices in the past. It is used to predict the future movements of prices based on previous trends. However, it does not provide insights regarding the future trend or direction of the security’s price.

#### 2. Implied Volatility

This refers to the volatility of the underlying asset, which will return the theoretical value of an option equal to the option’s current market price. Implied volatility is a key parameter in option pricing. It provides a forward-looking aspect on possible future price fluctuations.

### Calculating Vol

The simplest approach to determine the volatility of a security is to calculate the standard deviation of its prices over a period of time. This can be done by using the following steps:

1. Gather the security’s past prices.
2. Calculate the average price (mean) of the security’s past prices.
3. Determine the difference between each price in the set and the average price.
4. Square the differences from the previous step.
5. Sum the squared differences.
6. Divide the squared differences by the total number of prices in the set (find variance).
7. Calculate the square root of the number obtained in the previous step.

### Sample calculation

You want to find out the volatility of the stock of ABC Corp. for the past four days. The stock prices are given below:

• Day 1 – \$10
• Day 2 – \$12
• Day 3 – \$9
• Day 4 – \$14

To calculate the volatility of the prices, we need to:

1. Find the average price:
\$10 + \$12 + \$9 + \$14  /  4  = \$11.25
2. Calculate the difference between each price and the 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
3. Square the difference from the previous step:
Day 1: (-1.25)2 = 1.56
Day 2: (0.75)2 = 0.56
Day 3: (-2.25)2 = 5.06
Day 4: (2.75)2 = 7.56

4. Sum the squared differences:
1.56 + 0.56 + 5.06 + 7.56 = 14.75
5. Find the variance:
Variance = 14.75 / 4 = 3.69
6. Find the standard deviation:
Standard deviation = 1.92 (square root of 3.69)

The standard deviation indicates that the stock price of ABC Corp. usually deviates from its average stock price by \$1.92.

Thank you for reading CFI’s explanation of volatility. CFI is the official provider of the Financial Modeling & Valuation Analyst (FMVA)™ designation for financial analysts. To continue learning and advancing your career, these additional resources will be helpful:

• Guide to Beta in Finance