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Anyone vaguely aware of the stock market operations has undoubtedly come across the term “volatility”. It is an ambiguous term which most often implies risk or uncertainty concerning how the stock markets will move.

## What is Volatility?

Volatility denotes more than just risk or uncertainty.

It is a statistical measure of the dispersion that a security or market index’s returns witness around its mean or Moving Average (MA).

In simpler terms, it is the gauge of how fast the value of securities or market indexes moves.

Volatility is typically measured using either standard deviation or variance. In either case, the higher the value, the more volatile are the prices or the returns.

It means that a high standard deviation value suggests that prices are spread across a wide spectrum. Conversely, a low standard deviation value indicates that prices are closely knit across a narrow range.

In the stock market context, rapid price fluctuation in either direction is considered as volatility. Therefore, a high standard deviation value means prices can dynamically rise or fall and vice versa. In most cases, a surge or dive of 1% in market indexes classifies it as a “volatile” market.

Nevertheless, volatility is not a singular concept or measurement but rather multi-faceted.

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## Historical Volatility

As the name suggests, historical volatility refers to the measurement of volatility over a sustained period based on historical movements in returns or prices. It is also known as statistical volatility due to its heavy reliance on scientific measures.

In practice, historical volatility is used by investors to determine a security’s performance in the past based on its underlying asset’s price movements over different periods.

Rising historical volatility implies that prices of accounted securities will fluctuate at a greater scale, more than usual. Contrarily, falling statistical volatility will indicate that prices will witness contained and low-scale deviation from the mean or average.

• Calculation of historical volatility

Since this measure of dispersion is based on past and concrete data, institutional investors follow a rule of thumb when calculating it. This dispersion is measured using a variance, as mentioned earlier.

Let’s understand the procedure with the help of a simple example.

Example – A dataset containing the closing prices of ABS stocks over 5 weeks is mentioned below.

 Week 1 Rs. 13 Week 2 Rs. 11 Week 3 Rs. 12 Week 4 Rs. 10 Week 5 Rs. 14

Step 1: Mean calculation

Mean = (13 + 11 + 12 + 10 + 14)/5 = 60/5 = 12

Step 2: Difference between the mean value and each component in the dataset

Subsequently, it is required to calculate the deviation between 12 and the rest of the elements in that dataset.

1. 13 – 12 = 1
2. 11 – 12 = – 1
3. 12 – 12 = 0
4. 10 – 12 = – 2
5. 14 – 12 = 2

Step 3: Add the deviations after squaring them

Step 4: Divide the squared deviations by the total number of elements in the dataset to calculate variance (ơ2)

Since it is the variance, the dataset’s standard deviation will be reached by square rooting this value.

Standard deviation of ABS stocks = √2 = 1.414

However, this process only holds in case of uniform distribution. In the case of random sampling from a voluminous dataset, only 68% of this data agrees with or falls within the SD mentioned above.

## Implied Volatility

As opposed to historical volatility, its implied counterpart is a future projection of probable movements in values of securities.

It is used by investors across global stock markets to determine where a particular stock’s value is headed without accounting for historical data.

Implied volatility is a critical metric in the determination of prices of options contracts. Analysts take into account numerous factors to project the likely movements in securities’ prices. It is expressed in percentages; however, implied volatility does not clarify in which direction prices will move.

A high IV simply suggests that the price of specific security will dramatically swing, either to rise or depreciate in value. Conversely, a low IV indicates that specific security will not witness any dramatic increase or decrease in value, save slight deviations.

When applied to stock markets, a bearish market will show a high implied volatility rate as opposed to a bullish market, where implied volatility will be low. The primary reason behind this is, in a bullish market, investors expect prices to increase over time and therefore, IV goes down. Conversely, in a bearish market, prices are predicted to decline over time and hence, IV increases.

• Implied volatility with regard to options contracts

Options contracts are of two types – call and put. In a call option, an investor is entitled to purchase stocks at a strike price within the contract’s expiration date. Conversely, in a put option, an investor is entitled to sell stocks at a strike price within the contract’s expiration date.

Implied volatility of the underlying security is used to price options contracts. One of the most widely-regarded pricing models for options contracts is the Black-Scholes model. The model takes into account the IV of an underlying asset, its current market price, its strike price, and the date of expiration to determine its price.

## Different Measures of Volatility

Alongside standard deviation and variance, volatility can also be measured in other terms as well. These are –

• Beta

It shows the relativity between the value of stocks and their relevant market index. Therefore, beta is a concrete representation of stock volatility. Beta represents the approximate volatility in returns of securities against that of its relevant benchmark index.

For instance, if a specific stock shows a beta value of 1.2 and its relevant benchmark index is Nifty 50, then it denotes that for a 100% change in the Nifty 50 index, that stock will move 120% in value. On the other hand, a beta value of 0.8 denotes that for a 100% change in the Nifty 50 index, its stock price will move by 80%.

A higher beta value implies a high correlation with the index and therefore, high volatility, i.e. market dependency.

• Volatility Index (VIX)

It is dependent on investor’s predictions concerning the movement of specific securities or the broader market. It was developed by the Chicago Board Options Exchange. VIX takes into account investor opinion; therefore, a high VIX indicates a volatile and risky market and vice versa.

### What is Volatility Smile?

A volatility smile is a graphical shape that comes about from plotting the implied volatility and strike price of a bunch of contracts. These contracts all have the same underlying asset and expiration date. When an underlying asset moves far from out-of-the-money to in-the-money or vice versa, its implied volatility first declines. It thereafter reaches a low at an at-the-money point and then rises.

Due to this phenomenon, the shape seems like a smile. An options contract witnesses the lowest implied volatility when it is at the money; i.e. the underlying asset’s strike price and market value are similar.

### What is a Volatility Skew?

Volatility skew, as the name suggests, is more skewed rather than being balanced as a volatility smile. It shows the different IV among an out-of-the-money option, in-the-money option, and an at-the-money option.

A graphical skew appears when one phenomenon is assigned higher implied volatility compared to another.

## What are the Factors affecting Volatility?

Numerous factors affect stock market volatility as well as its securities counterpart. These are –

• Supply and demand for securities
• Geopolitical factors prevalent in an economy
• Socioeconomic factors
• Expiration date of an options contract

Nevertheless, a volatile market does not always imply losses but risk. And seasoned investors can potentially leverage market volatility in their favour by making timely use of their options contracts, either to make considerable gains or hedge their portfolio against probable downsides.

FAQ

• What is meant by market volatility?

Market volatility denotes the dispersion witnessed in the returns of a market index around its mean or Moving Average.

• What are the types of volatility?

Volatility is primarily of two types – historical volatility and implied volatility.

• What is implied volatility?

Implied volatility refers to the predicted movements of returns of securities or market index based on supply and demand and other relevant factors.

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