# Volatility

## Key Takeaways:

• Volatility of an asset is the dispersion in the prices of the asset and is synonymous with the risk associated with the asset in the market.
• Volatility is of two types: Historical volatility and Implied volatility
• Standard deviation is the most popular measure of volatility. Another measure is Beta.

## What is Volatility?

Volatility of an asset is the dispersion in the prices of the asset and is synonymous with the risk associated with the asset in the market.

Volatility is measured by variance or standard deviations of the past returns of the asset.

Higher the volatility of the asset or security, higher is the risk in investing.

## What is Historical and Implied Volatility?

Volatility can be calculated using two methods.

The first is historical volatility — Data on returns in the recent past is studied, with the assumption that what has happened recently is indicative of the future. It is studied to gauge short term price changes in stock.

The second is implied volatility — Market prices of the security’s derivatives (futures and options) are studied. It’s mainly based upon the market’s perception on how volatile a stock is.

## What is Price Volatility?

Price volatility refers to fluctuations in the prices of a commodity. It is often used in the investment world to refer to the price fluctuations in an investment opportunity. Often it is observed that investment opportunities with higher price volatility offer higher return on investment and those with comparatively stable prices offer lower return on investment.

Many investors make decisions based on the price volatility of an investment opportunity. As price volatility is directly related to risk, they compare their risk appetite with the return they are seeking to make a decision.

## How to calculate Volatility?

Variance and standard deviation are usually used to calculate volatility. Variance and standard deviation are related by the formula:

Standard Deviation = (Variance)1/2

Follow the below steps to calculate variance:

·       Find out mean of the given data set

·       Measure the difference between each value and mean value and find out the deviation

·       Take square of the deviations

·       Take sum of all the squared deviations

·       Divide the sum by total number of data points

Let’s consider an example to understand this better. Let’s say we have a stock with monthly closing prices of \$2 to \$20 as evident from the table below.

Let’s follow the above steps to calculate its variance.

1.     Calculating mean: Firstly, mean is calculated which came out to be 11.

2.     Calculating deviations: Difference between individual prices and mean is calculated in the table with column heading ‘Deviation’.

3.     Squaring the deviations: Individual deviations are squared, and they are represented in the column with heading ‘(Deviation^2)’.

4.     Summation of the squared deviations: The results from the above step are added to get the sum of the squared deviations which came out to be 330, as represented in cell D12.

5.     Dividing by number of data points: Result from the previous step is divided by total number of data points available, which is 10, to get 33.

As volatility is generally represented by standard deviation, we can find out standard deviation in the above example by taking square root of variance, which came out to be 5.744563 as mentioned in cell F12

## What are the measures of Volatility?

The most commonly used measure of Volatility is standard deviation as mentioned above. Other than that, Beta is another measure used to calculate volatility. It compares fluctuations in a security’s return with benchmark value. For example, a beta value of 1.2 denotes that the stock has historically moved 120% for every 100% movement in benchmark.

## What does the Volatility Index (VIX) mean?

Volatility index refers to the market’s expectation regarding next 30-days volatility. It indicates the short-term mood of the market. It is the percentage change that investors predict about the next 30 days movement in the market.

If the volatility index is 25, then it says that investors are anticipating that markets will move by 25%. VIX differs from other market indicators as it is forward looking.

Volatility index is inversely related to the market. When the market is fearful, VIX increases. On the other hand, when the market looks stable in the future, VIX goes down.

Know More

Year 2019 saw much lower volatility than what usually is. Only 37 days saw changes of 1% or more in S&P 500 Index as compared to 64 days in 2018. Historical average of such days has been 53 days. So, it’s expected that 2020 would have much more volatility.