What is volatility?

Volatility is a statistical measure of the dispersion of returns for a given security or market index. In most cases, the higher the volatility, the riskier the security. Volatility is often measured as the standard deviation or variance between the returns for that same security or market index.

In securities markets, volatility is often associated with large swings in either direction. For example, when the stock market rises and falls more than one percent for a sustained period of time, it is called a “volatile” market. The volatility of an asset is a key factor when evaluating options contracts.

Understanding volatility.

Volatility often refers to the amount of uncertainty or risk associated with the size of changes in the value of a security. Higher volatility means that the value of a security can potentially be spread over a wider range of values. This means that the price of the security can change dramatically in a short period of time in either direction. Lower volatility means that the value of a security does not fluctuate dramatically and tends to be more stable.

One way to measure the change in an asset is to quantify the daily returns (percentage movement on a daily basis) of the asset. Historical volatility is based on historical prices and represents the degree of variability in an asset’s returns. This number is unitless and is expressed as a percentage. While variance captures the dispersion of returns around the mean of an asset in general, volatility is a measure of that variance bounded by a specific time period. Therefore, we can report daily, weekly, monthly or annualized volatility. It is therefore useful to think of volatility as the annualized standard deviation.

How to calculate volatility.

Volatility is often calculated using variance and standard deviation. The standard deviation is the square root of the variance.

For simplicity, suppose we have monthly closing stock prices from €1 to €10. For example, the first month is €1, the second €2, and so on. To calculate the variance, follow the five steps below.

Find the average of the data set. This means adding up each value and then dividing it by the number of values. If we add €1, plus €2, plus €3, up to €10, we get €55. This is divided by 10 because we have 10 numbers in our data set. This gives an average, or mean price, of €5.50. Calculate the difference between each data value and the average. This is often called the deviation. For example, we take €10 - €5.50 = €4.50, then €9 - €5.50 = €3.50. This continues until the first data value of €1. Negative numbers are allowed. Since we need every value, these calculations are often done in a spreadsheet. Elevate the deviations to the square. This will eliminate the negative values. Add the deviations squared. In our example, this equals 82.5. Divide the sum of the squared deviations (82.5) by the number of data values. In this case, the resulting variance is 8.25. You take the square root to get the standard deviation. This is equivalent to 2.87 euros. This is a measure of risk and shows how values are distributed around the average price. It gives traders an idea of how much the price may deviate from the average.

Other measures of volatility.

One measure of the relative volatility of a particular security relative to the market is its beta (β). A beta approximates the overall volatility of a stock’s returns relative to the returns of a relevant benchmark (usually the S&P 500 is used). For example, a stock with a beta value of 1.1 has historically moved 110% for every 100% movement in the benchmark, based on price level.

In contrast, a stock with a beta of .9 has historically moved 90% for every 100% movement in the underlying index.

Market volatility can also be seen through the VIX or volatility index. The VIX was created by the Chicago Board Options Exchange as a measure to gauge the expected 30-day volatility of the U.S. stock market, derived from real-time call and put option prices on the S&P 500.1 It is effectively an indicator of the future bets investors and traders are making on the direction of markets or individual stocks. A high reading of the VIX implies a risky market.

A variable in option pricing formulas that shows the extent to which the return on the underlying asset will fluctuate between now and the option’s expiration. Volatility, expressed as a percentage coefficient in option pricing formulas, is derived from daily trading activities. How volatility is measured will affect the value of the coefficient used.

Volatility is also used to price options contracts using models such as Black-Scholes or binomial tree models. More volatile underlying assets will result in higher option premiums because with volatility there is a higher probability that options will end up in-the-money at expiration. Options traders try to predict the future volatility of an asset, so the price of an option in the market reflects its implied volatility.

Key Conclusions.

• Volatility represents the magnitude of an asset’s price fluctuation around its average price-it is a statistical measure of its dispersion of returns.
• There are several ways to measure volatility, including beta coefficients, option pricing models, and standard deviations of returns.
• Volatile assets are often considered riskier than less volatile assets because price is expected to be less predictable.
• Volatility is an important variable for option pricing.

Original source of this article: www.investopedia.com