What Is Volatility?

Volatility is a measurement of ho🎃w varied the returns of a given security or market index are over time. It is often measured from either the standard deviation or variance between those returns. In most cases, the higher the volatility, the riskier the security.

In the securities markets, volatil💖ity is often associated with big price swings, either up or down. For example, when the stock market rises and falls more than 1% over a sustained period of time, it is called a volatile market.

An asset’s volatiꦿlity is a key factor when pricing🐎 options contracts.

Understanding Volatility

Volatility often refers to the amount of uncertainty or risk related to the size�🥂� of changes in a security’s value.

A higher volatility means that a security’s value can potentially be spre🧜ad out over a laꩲrger range of values. This means that the price of the security can move dramatically over a short time period in either direction. A lower volatility means that a security’s value does not fluctuate dramatically, and tends to be steadier.

One way to measure an asset’s variation is to quantify the daily returns (percent move on a daily basis) of the asset. Historical volatility is based on historical prices and represents the degree of 澳洲幸运5官方开奖结果体彩网:variability in the returns of an asset. This number is without a unit and is expressed as a percentage.

While variance captures the 澳洲幸运5官方开奖结果体彩网:dispersion of returns around the mean of an asset in general, volatility is a measure of that variance bounded by a specific time period. Thus, we can report daily, weekly, monthly, or annualized volatility. It is useful to think of volatility as the annualized 澳洲幸运5官方开奖结果体彩网:standard deviation.

How to Calculate Volatility

Volatility is often calculated using varian🅰ce and standard deviation (the standard deviation is the square root of the variance). Since volatility descri⛄bes changes over a specific period of time, you simply take the standard deviation and multiply that by the square root of the number of periods in question:

Volatility = σ√T

where:

• σ = standard deviation of returns
• T = number of periods in the time horizon

Volatility and Stocks

For simplicity, let’s assume we have monthly stock 澳洲幸运5官方开奖结果体彩网:closing prices of $1😼 through $10. For example, month one is $1, month two is $2, and so on. To calculate variance, follow the five steps below.

1. Find the mean of the data set. This means adding each value and then dividing it by the number of values. If we add $1, plus $2, plus $3, all the way to up to $10, we get $55. This is divided by 10 because we have 10 numbers in our data set. This provides a mean, or average price, of $5.50.
2. Calculate the difference between each data value and the mean. This is often called deviation. For example, we take $10 - $5.50 = $4.50, then $9 - $5.50 = $3.50. This continues all the way down to the first data value of $1. Negative numbers are allowed. Since we need each value, these calculations are frequently done in a spreadsheet.
3. Square the deviations. This will eliminate negative values.
4. Add the squared deviations together. In our example, this equals 82.5.
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.

Next, take the square root of the variance to get the standard deviation. This equals $2.87. This is a measure of risk and shows how values are spread out around the average price. It gives traders an idea o♎f how far the price may de🐟viate from the average.

If prices are randomly sampled from a normal 澳洲幸运5官方开奖结果体彩网:distribution, then about 68% of all data values will fall within one standard deviation. Ninety-five percent of data values will fall within two standard deviations (2 × 2.87 in our example𒈔), and 99.7% of all values will fall within three standard deviations (3 × 2.87).

In this case, the values of $1 to $10 are not randomly distributed on a 澳洲幸运5官方开奖结果体彩网:bell curve; rather, they are uniformly distributed. Therefore, the expect🌠ed 68%–95%–99.7% percentages do not hold. Despite this limitation, traders frequently use standard deviation, as price returns data sets often resemble more of a normal (bell curve) distribution than in the given example.

Types of Volatility

Implied Volatility

Implied volatility (IV), also known as projected volatility, is one of the most important metrics for options traders. As the name suggests, it allows them to make a determination of just how volatile the market will be going forꦍward.

This concept also gives traders a way to calculate probability. One important point to note is that it isn't considered science and therefore does not forecast how the market will move in the future.

Unlike historical volatility, implied volatility comes from the price of an option itself and represents volatility expectations for the future. Because it is implied, traders cannot use past performance as an indicator of future performance. Instead, they have to estimate the potential of the option in the market.

Historical Volatility

Also referred to as statistical volatility, historical volatility (HV) gauges the fluctuations of underlying securities by measuring price changes over predetermined time periods. It is the less prevalent metric compared with implied volatility because it isn’t forward-looking.

When there is a rise i♚n historical volatility, a security’s price will also move more than normal. At this time, there is an expectation that something will or has changed. If the historical volatility is dropping,♋ on the other hand, it means any uncertainty has been eliminated, so things return to the way they were.

This calculation may be based on intraday changes, but ofte💝n measures movements based on the change from one closing price to the next. Depending on the intended duration of the options trade, historical volatility can be mea🏅sured in increments ranging anywhere from 10 to 180 trading days.

Volatility and Options Pricing

Volatility is a key variable in options pricing models, estimating the extent to which the return of the 澳洲幸运5官方开奖结果体彩网:underlying asset will fluctuate between now and the option’s expiration. Volatility, as expressed as a percentage coefficient within option-pricing formulas, arises 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 like the 澳洲幸运5官方开奖结果体彩网:Black-Scholes or 澳洲幸运5官方开奖结果体彩网:binomial tree models. More volatile underlying assets will translate to higher options premiums because with volatility, there is a greater probability that the options will end up 澳洲幸运5官方开奖结果体彩网:in the money at expiration.

Options traders try to 🀅predict an asset’s future volatility, so the price of an option in the market reflects its implied volatility.

Other Measures of Volatility

Beta

One measure of the relative volatility of a particular stock to the market is its beta (β). A beta approximates the overall volatility of a security’s returns against the returns of a relevant 澳洲幸运5官方开奖结果体彩网:benchmark (usually, the S&P 500 is used). For example, a stock with a beta value of 1.1 has moved 110% for every 100% move in the benchmark, based on 澳洲幸运5官方开奖结果体彩网:price level.

Conversely, a stock with a beta of 0.9 has moved 90% for every 100% move in the underlying index.

The VIX

Market volatility can also be seen through the 澳洲幸运5官方开奖结果体彩网:Volatility Index (VIX), a numeric measure of equity market volatility.

The Chicago Board Options Exchange created the VIX as a measure to gauge the 30-day expected volatility of the U.S. stock market derived from real-time quote prices of S&P 500 call and put options. It is effectively a gauge of future bets that investors and traders are making on the dirꦆection of the markets or i🧜ndividual securities. A high reading on the VIX implies a risky market.

Traders can trade the VIX using a variety of options and exchange-traded products. Or they can use VIX values to price certain derivative products.

Tips for Managing Volatility

澳洲幸运5官方开奖结果体彩网:Investors can find periods of high volatility to be distressing, as prices can swing wildly or fall suddenly. Long-term investors are best advised to ignore periods of short-term volatility and stay the course. This is because over the long run, stock 𓄧markets tend to rise. Meanwhile, emotions like fear and greed—which can become amplified in volatile ma✃rkets—can undermine your long-term strategy.

Some investors can use volatility as an opportunity to add to their portfolios by 澳洲幸运5官方开奖结果体彩网:buying the dips, when prices are relatively cheap.

You can also use hedging strategies to navigate volatility, such as buying 澳洲幸运5官方开奖结果体彩网:protective puts to limit downside losses without having to sell any shares. But note that put options will also b👍💖ecome pricier when volatility is higher.

Example of Volatility

Suppose that an investor is building a retirement portfolio. Since she is retiring within the next few years, she’s seeking stocks with low volatility and steady returns. 🧔She considers two companies:

1. ABC Corp. has a beta coefficient of 0.78, which makes it slightly less volatile than the S&P 500 index.
2. XYZ Inc. has a beta coefficient of 1.45, making it significantly more volatile than the S&P 500 index.

A more conservative investor may choose ABC Corp. for their 澳洲幸运5官方开奖结果体彩网:portfolio, since it has l💛ess volatility and more predictable short-term 🥂value.

The Bottom Line

Volatility is how꧒ much and how quickly prices move over a given span of time. In the stock market, increased volatility is often a sign of fear and uncertainty among investors. This is why the VIX volatility index is sometimes called the “fear index.”

At the same time, volatility can create opportunities for day traders to enter and exit positions. Volatility i🐻s also a key component in options pricing and tꦑrading.