### Volatility Calculations and Perceptions

Contents

## Understanding Volatility

Volatility indicates the variation in market prices. The volatility calculations (and perception) depends upon the trading instrument or market. We first look at the reasons why understanding volatility has prime importance.

- Price volatility presents opportunities to buy assets cheaply and sell when overpriced.
- Market moves in a cyclical fashion from phase of low volatility to high volatility and so on. These phases result in most technical chart patterns such as trading range compression, buying climax etc.
- Volatility itself is a primary measure of risk.
- Higher volatility of returns while saving for retirement results in a wider distribution of possible final portfolio values.
- Market moves in cycle of high volatility and low volatility. Consequently traders may have to adjust their entry/exit rules of their strategy
- Measuring volatility is essential for proper timing of trades. Particularly Options have a time value and hence entering the trade at proper time is crucial for profit.
- When certain cash flows from selling a security are needed at a specific future date, higher volatility means a greater chance of a shortfall.

## Volatility Calculations

Volatility calculations depend upon the market segment being traded as well as the trading style. For example, each of the following traders may have different volatility calculations (and perception):

- TraderA who trades short-term price movements in stocks
- TraderB who invests in stocks for a short time horizon (3 to 12 months)
- TraderC who is an option buyer/seller
- TraderD who manages portfolios of investment stocks

There is significant overlap in these definitions of volatility while categorizing by the types of traders.

## Short-term Traders

Short-term trading includes intraday trading and swing trading.

**Standard Deviation**: The s.d. of price returns over a certain period is the most popular measure of volatility. Popular technical indicators for trading breakouts (like Bollinger Bands) use standard deviation.

**Average True Range:** ATR is a measure of how much prices are expected to move in a single bar. It is calculated as the max movement since previous bar or current bar’s range. Traders use ATR to determine how far they need to place stop loss.

**Bands:** The width of price bands like Bollinger Bands, Donchian Channels, Keltner Channels, regression channels etc. serve as a good indication of underlying volatility.

## Option Traders

**Actual Future volatility:** It refers to the volatility of a financial instrument over a specified period starting at the current time and ending at a future date (normally the expiry date of an option)

**Implied Volatility:** it is the volatility that, when used in a particular pricing model, yields a theoretical value for the option equal to the current market price of that option. It is a forward looking measure.

**Historical Implied volatility:** it refers to the implied volatility observed from historical prices of the financial instrument (normally options)

**Current implied volatility:** it refers to the implied volatility observed from current prices of the financial instrument

**Future implied volatility:** it refers to the implied volatility observed from future prices of the financial instrument

## Investors

**Historical Volatility:** or actual historical volatility refers to the volatility of a financial instrument over a specified period but with the last observation on a date in the past.

**VIX:** It is a weighted blend of prices for a range of options on the Nifty index. The current market prices of all out-of-the-money calls and puts for the front month and second month expirations are used in calculation. It is the most popular measure of volatility for most people

**Market Capitalization:** Small caps tend to be more volatile than large caps.

**Share Holding Pattern**: Amount of shares privately hold versus publicly hold is a good measure of stability.

**Leverage:** the operating leverage which a company is employing also affects its volatility.

**Industry Groups:** Business in certain industries is inherently more volatile than the others. For example, stocks of retailers are less volatile than those of internet companies.

## Portfolios Managers

**Beta:** The beta is an important measure of risk. It is calculated by comparing the changes in returns of the portfolio with a benchmark.

**R-Squared:** It is the correlation of a portfolio’s movements to that of its benchmark. It measures the degree to which a portfolio’s volatility is a result of the day-to-day fluctuations experienced by the overall market.