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Category — Analytical Metrics
By Konstantin Vasilev Member of the Board of Directors of Cbonds, Ph.D. in Economics
Updated July 1, 2023

What is volatility?

Volatility, a crucial statistical measure, captures the extent of return dispersion for a specific security or market index. Typically, higher volatility signals greater risk associated with the security. Volatility is commonly assessed by calculating the standard deviation or variance among the returns of the aforementioned security or market index.

Within the realm of securities markets, volatility is frequently linked to substantial price swings in either direction. A market is deemed volatile when it experiences consistent fluctuations of over one percent over an extended duration. The volatility of an asset plays a significant role in the pricing of options contracts, recognizing its impact on the potential outcomes and associated risks.


Types of Volatility

Implied Volatility

Implied volatility (IV), or projected volatility, holds significant relevance for options traders as a key metric. It enables them to assess the expected level of market volatility in the days to come. This metric further empowers traders to calculate probability, aiding them in their decision-making process. However, it is important to note that implied volatility should not be mistaken for an exact science, as it does not offer a forecast of future market movements.

Diverging from historical volatility, implied volatility is derived from the price of an option itself and represents the market’s anticipated level of volatility in the future. Since it is based on implications, traders cannot rely on past performance to gauge future outcomes. Instead, they must estimate the option’s potential within the market environment, accounting for the expected levels of volatility.

Historical Volatility

Historical volatility (HV), also known as statistical volatility, offers insights into the price fluctuations of individual securities within the stock market over a given period. Analyzing price changes provides a measure of the security’s volatility relative to the broader market.

Volatility measures such as standard deviations and average price changes are employed in calculating volatility. These measures capture the price volatility experienced by stocks, which various factors, including market conditions and investor sentiment, can influence.

For investors, understanding volatility is crucial in formulating their investment strategies. While some may prefer low-volatility investments, such as fixed-income or treasury bonds, others may embrace volatility and seek growth stocks with the potential for higher returns.

Market participants often monitor market indexes, such as the S&P 500 index, as a benchmark to gauge overall market volatility. The Chicago Board Options Exchange (CBOE) Volatility Index, also known as the VIX, is a popular indicator used to track expected volatility in the market.

How to Calculate Volatility

Volatility is typically calculated using statistical measures such as variance and standard deviation. The standard deviation represents the square root of the variance and measures how values are spread out around the average price.

To calculate volatility, the standard deviation is multiplied by the square root of the number of periods in question:

vol = σ√T


vol = volatility over a specific time interval

σ = standard deviation of returns

T = number of periods in the time horizon

Let’s consider a simplified example using monthly stock closing prices ranging from $1 to $10. To calculate the variance, follow these steps:

  1. Find the data set’s mean by summing all values and dividing by the number of values. For instance, if we add $1, $2, $3, all the way up to $10, the sum is $55. Dividing this by 10 (number of values) gives us a mean of $5.50.

  2. Calculate the deviation of each data value from the mean. This is achieved by subtracting the mean from each value. For example, $10 - $5.50 = $4.50, $9 - $5.50 = $3.50, and so on. Negative deviations are also possible.

  3. Square each deviation to eliminate negative values.

  4. Sum up the squared deviations. In this example, the sum is 82.5.

  5. Divide the sum of squared deviations (82.5) by the number of data values.

The resulting variance, in this case, is $8.25. Taking the square root of the variance yields the standard deviation, which equals $2.87. The standard deviation measures risk and indicates how much the price may deviate from the average.

If prices follow a normal distribution, approximately 68% of data values will fall within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations. However, in our example, where the values are uniformly distributed rather than following a bell curve, these expected percentages do not hold true. Nevertheless, the standard deviation is commonly used in trading as price returns data sets often exhibit a more normal distribution than the given example.

Volatility and Options Pricing

Volatility is a key variable in options pricing models, estimating the magnitude of fluctuations in the underlying asset’s return from now until the option’s expiration. It plays a crucial role in determining the market price of options and is particularly important for volatility investors seeking to optimize their investment strategies.

In pricing models like Black-Scholes or binomial tree models, volatility is used to price options contracts. Higher stock market volatility and stock prices result in elevated options premiums. This is because increased volatility implies a greater probability of options ending up in the money at expiration. Consequently, volatility investors strive to predict the future volatility of an asset, as the market price of an option reflects its implied volatility.

Volatility can be measured using various methods, including analyzing historical prices and employing regression analysis techniques. It can be expressed as average volatility or annualized volatility, providing valuable insights into the risk appetite and performance of financial instruments.

Other Measures of Volatility


Beta (β) measures the relative volatility of a specific stock compared to the overall market. It approximates the overall volatility of a security’s returns relative to the returns of a relevant benchmark, often represented by a benchmark index like the S&P 500. For example, a stock with a beta value of 1.1 historically moves 110% for every 100% move in the benchmark’s stock price.

Conversely, a stock with a beta of 0.9 indicates that it historically moves 90% for every 100% change in the underlying index’s stock price.


Market volatility can also be assessed through the Volatility Index (VIX), which provides a numeric measure of broad market volatility. The Chicago Board Options Exchange introduced the VIX as a means to gauge the expected volatility of the U.S. stock market over a 30-day time period. It derives this estimate from real-time quote prices of S&P 500 call and put options.

The VIX effectively serves as an indicator of the future bets made by investors and traders on the direction of the markets or individual securities. A high reading on the VIX implies a higher level of volatility and risk in the market.

Traders have the option to engage in VIX trading using a variety of options and exchange-traded products, or they can utilize VIX values to price certain derivative products.

Tips on Managing Volatility

Periods of high volatility in the market can be unsettling for investors, as prices exhibit significant swings and sudden declines. However, long-term investors are often advised to maintain their course and overlook short-term volatility. This is because, over extended periods, stock markets generally experience upward trends. Emotions like fear and greed, which tend to intensify during volatile market conditions, can undermine a well-thought-out long-term investment strategy. Nonetheless, some investors view volatility as an opportunity to enhance their portfolios by capitalizing on price declines and purchasing assets at relatively lower prices.

To navigate through volatility, investors may consider employing hedging strategies. One such strategy involves purchasing protective puts, which act as insurance against downside losses without necessitating the sale of shares. However, it’s important to note that the cost of put options increases during periods of higher volatility. Therefore, investors should carefully assess the trade-off between protection and associated costs when implementing hedging strategies.

By maintaining a focus on long-term goals, staying disciplined amidst market fluctuations, and making informed investment decisions, investors can effectively manage volatility and strive for positive outcomes in their portfolios.

Example of Volatility

Imagine an investor who is in the process of constructing a retirement portfolio with a relatively short time horizon. As she prepares to retire in the next few years, her primary focus is on selecting stocks that exhibit low volatility and offer stable returns. In this context, she evaluates two companies:

  1. ABC Corp. has a beta coefficient of .78, indicating that it is slightly less volatile than the S&P 500 index.

  2. XYZ, Inc. has a beta coefficient of 1.45, signifying that it is considerably more volatile than the S&P 500 index.

Given her conservative investment approach, the investor may opt to include ABC Corp. in her portfolio. By choosing this company, she aims to mitigate the impact of potential market fluctuations and secure a more predictable short-term value for her retirement savings. The lower volatility of ABC Corp. aligns with her goal of seeking stability and minimizing risks associated with stock price fluctuations.


  • Is volatility the same as risk?

  • Is volatility a good thing?

  • What causes financial volatility?

  • What stocks are most volatile?

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