{"id":143,"date":"2023-06-16T17:05:21","date_gmt":"2023-06-16T21:05:21","guid":{"rendered":"https:\/\/api.tiingo.com\/blog\/?p=143"},"modified":"2023-06-16T17:05:23","modified_gmt":"2023-06-16T21:05:23","slug":"how-to-calculate-volatility","status":"publish","type":"post","link":"https:\/\/www.tiingo.com\/blog\/how-to-calculate-volatility\/","title":{"rendered":"Unclear on How to Calculate Volatility? Here\u2019s What You Need"},"content":{"rendered":"\n
\"A<\/figure>\n\n\n\n

If you\u2019ve spent any period of time participating in the stock market, you\u2019ve no doubt noticed that stock prices can fluctuate wildly. This is part of what makes it exciting \u2014 dramatic upward price changes can make you a fortune in a few minutes. But it also makes it unnerving \u2014 a price collapse can wipe out years of returns in just as short a time.<\/p>\n\n\n\n

The fluctuations of a given stock, index, or a financial instrument like an option, or another type of derivative, are known as volatility, and it\u2019s an important concept to understand if you intend to do any investing.<\/p>\n\n\n\n

In this piece, we\u2019ll start by defining volatility. Then, we\u2019ll discuss several different methods of how to calculate volatility. This should arm you with an important piece of the puzzle required to understand the financial markets.<\/p>\n\n\n\n

What Is <\/strong>Volatility<\/strong>?<\/strong><\/h2>\n\n\n\n
\"How<\/figure>\n\n\n\n

<\/a>There are a number of ways of thinking about volatility. In simple terms, you might call it uncertainty about the market price fluctuations or valuation of a given security. Higher volatility means being less sure about where a stock is going in the future, while lower volatility means being more sure about the stock\u2019s direction for the future.<\/p>\n\n\n\n

This isn\u2019t a bad place to begin, but it\u2019s possible to be more precise. In mathematical terms, volatility is a metric that captures the statistical measure of the dispersion of returns.<\/p>\n\n\n\n

Note the use of the word \u201creturns\u201d in this definition. Though it\u2019s not uncommon to calculate the price volatility for something like option price movements, volatility is often focused on returns. We\u2019ll adopt this practice from here on because we usually care more about returns than price, but the math is the same either way.<\/p>\n\n\n\n

Volatility can be calculated over a different number of trading days, depending on the time frames you\u2019re interested in examining. Daily returns can be used to calculate daily volatility, annualized returns can be used to calculate annualized volatility, and so on.<\/p>\n\n\n\n

What these calculations all have in common, however, is that you\u2019re looking to quantify the frequency and magnitude of shifts in returns over a given set of data points.<\/p>\n\n\n\n

Why Is Understanding How to Calculate <\/strong>Volatility<\/strong> Important?<\/strong><\/h3>\n\n\n\n

There are several reasons why understanding volatility is important. Perhaps the biggest is that volatility is a huge factor in shaping investment decisions. When contemplating how you want to deploy funds as part of an investment strategy, you have to think carefully about your risk tolerance and your future plans.<\/p>\n\n\n\n

Though risk and volatility aren\u2019t the same thing<\/a>, they\u2019re closely related. Generally speaking, high-volatility investments are riskier than low-volatility investments. This reflects the general fact that risk and reward go together in finance, or to put it in poetic terms: The road to riches is usually paved with many successful rolls of the dice.<\/p>\n\n\n\n

You\u2019d probably want to put your life savings in extremely low-volatility, low-risk investments, like government bonds. In this scenario, the chances of both a huge upside and a catastrophic downside are minimal \u2014 you\u2019re unlikely to become a prince or a pauper playing it safe in this way.<\/p>\n\n\n\n

In an alternate scenario, if you have a fund set aside for taking big chances on startups productizing emerging technologies like quantum computing, for example, it\u2019s fine to pursue a high-volatility, high-risk plan. This offers the chance of earning a bunch of money very quickly, but you could also lose every dime if the startup goes bankrupt.<\/p>\n\n\n\n

Another reason why understanding market volatility is important is that it\u2019s one of the main tools you have for forecasting. Like other market phenomena, volatility tends to exhibit certain important regularities<\/a>. One of these is the fact that volatility tends to \u201ccluster\u201d on successive days.<\/p>\n\n\n\n

It\u2019s always possible, of course, to have random spikes in volatility in otherwise torpid price charts. But it\u2019s more likely that you\u2019ll see several days in a row of high volatility, owing perhaps to a major news story<\/a> about the Federal Reserve, a war, or a similarly disruptive event.<\/p>\n\n\n\n

Another important regularity is what\u2019s known as \u201cautoregression\u201d or \u201cregression to the mean.\u201d Like returns, price, etc., volatility will tend to move back toward its long-term mean after a while.<\/p>\n\n\n\n

While it\u2019s never possible to calculate future returns with total certainty, if you understand how to calculate the volatility of an asset, and if you understand clustering and autoregression, you can make better-informed decisions.<\/p>\n\n\n\n

How to Calculate the <\/strong>Volatility of a Security<\/strong><\/h2>\n\n\n\n
\"How<\/figure>\n\n\n\n

Hopefully, you now see the importance of understanding volatility measures, but that still leaves the question of how to actually calculate them.<\/p>\n\n\n\n

Before we get to that, we\u2019ll make some broad comments about getting the data you need to calculate volatility over a given period of time.<\/p>\n\n\n\n

You can get quality data sets from sources like your broker or the Tiingo API<\/a>. From these, it\u2019s possible to calculate volatility on returns or prices for individual stocks, a market index, or any other financial instrument.<\/p>\n\n\n\n

There are also sources that offer time series data where volatility has already been calculated, such as these feeds from the St. Louis Fed<\/a>.<\/p>\n\n\n\n

Assuming you\u2019re curious about learning about how these calculations work, read on!<\/p>\n\n\n\n

Calculating <\/strong>Volatility<\/strong> With the <\/strong>Standard Deviation<\/strong><\/h3>\n\n\n\n

Arguably the simplest volatility calculation is the one that\u2019s done with the standard deviation<\/a>. Here are the basic steps:<\/p>\n\n\n\n

    \n
  1. First, calculate the average price for the financial asset over the period of time you\u2019re interested in.<\/li>\n\n\n\n
  2. Next, figure out how much the asset\u2019s price deviates from this amount by subtracting the mean from each of the data points in your dataset. If you\u2019re calculating daily volatility for Apple, for example, you\u2019d subtract the average daily price of AAPL from its daily closing price<\/a>.<\/li>\n\n\n\n
  3. After you\u2019ve got this difference, square it so that the positive and negative deviations don\u2019t cancel each other out.<\/li>\n\n\n\n
  4. Then, you take the average of these squared deviations. This is a quantity known as the variance.<\/li>\n\n\n\n
  5. Finally, you take the square root of the number (you might see the square root abbreviated as \u201csqrt\u201d in other articles). In our example, taking the square root of the variance gives you the daily standard deviation, but it could also be the weekly, monthly, or annual standard deviation if you\u2019re looking at data for those time frames.<\/li>\n<\/ol>\n\n\n\n

    This standard deviation gives you an estimate of the volatility an asset has experienced. When it\u2019s done on historical data in the way just described, it\u2019s known as historical volatilit<\/a>y.<\/p>\n\n\n\n

    Calculating <\/strong>Realized Volatility<\/strong><\/h3>\n\n\n\n

    Standard deviation is an easy quick approximation, but most practitioners use what\u2019s called \u201cRealized Volatility.\u201d It\u2019s a modification of the standard deviation formula. In fact, Tiingo uses this formula internally and for several realized volatility products, including the recently launched realized volatility crypto feeds that are used to help power the new Chainlink Realized Volatility products<\/a>.<\/p>\n\n\n\n

    Here is the formula:<\/p>\n\n\n\n

    \"How<\/figure>\n\n\n\n

    This formula removes the subtraction of the mean from the standard deviation formula. It also annualizes the volatility, which is standard practice when quoting volatility. <\/p>\n\n\n\n

    You can take the annualized volatility and then convert back to any time period by simply dividing by the square root of the number of time periods in one year. For example, you could figure out the monthly volatility from the annualized volatility by dividing by the square root of 12.<\/p>\n\n\n\n

    This method is the standard formula used in variance swaps and institutional trading firms. While standard deviation tends to be a good approximation, this method is considered a standard when discussing realized (historical) volatility. <\/p>\n\n\n\n

    Calculating <\/strong>Implied Volatility<\/strong><\/h3>\n\n\n\n

    Another way of calculating volatility is using the Black-Scholes-Merton (BSM) option pricing model to estimate the implied volatility<\/a>. If historical volatility is backward-looking, implied volatility is forward-looking \u2014 it\u2019s a forecast<\/em> of expected<\/em> volatility in the future<\/em>, from the time the option has been purchased until its expiration. That\u2019s why it\u2019s called \u201cimplied\u201d volatility.<\/p>\n\n\n\n

    The fair price of a call option or a put option can be calculated with the BSM model. This requires us to know the spot and strike prices of the underlying asset, as well as its volatility, the risk-free rate, the time to maturity, and a few other parameters.<\/p>\n\n\n\n

    The way to calculate implied volatility with the BSM formula is to plug in all the other parameters (strike price, time to maturity, etc.) and solve for volatility.<\/p>\n\n\n\n

    Calculating <\/strong>Volatility<\/strong> With <\/strong>Excel<\/strong><\/h3>\n\n\n\n

    When it comes to how to calculate volatility, one of the tools of the financier\u2019s trade is Excel. As you might imagine, there are many ways of using it to calculate volatility.<\/p>\n\n\n\n

    If you\u2019re interested in historical volatility, you\u2019ll need historical data points for the security or option you\u2019re analyzing. You can use the Excel function STDEV.S to calculate it directly, or if you want to work through the steps to cultivate a deeper understanding of the math, you can also use Excel\u2019s AVERAGE, SUM, squaring, and SQRT functions to do it manually and to calculate realized volatility.<\/p>\n\n\n\n

    Naturally, it\u2019s also relatively easy to calculate implied volatility using Excel. You\u2019ll need to find the relevant values for the asset to fill in the BSM model\u2019s parameters, and then you\u2019ll use Excel\u2019s \u201cGoal Seek\u201d to perform the actual calculation.<\/p>\n\n\n\n

    What Is the <\/strong>VIX<\/strong>?<\/strong><\/h2>\n\n\n\n
    \"Storm<\/figure>\n\n\n\n

    <\/a>Sometimes called the \u201cfear index,\u201d the volatility index (VIX)<\/a> of the Chicago Board Options Exchange is a prominent way of capturing the expected volatility of the broader stock market by looking at how much traders expect the S&P 500 to move over the next 30 days.<\/p>\n\n\n\n

    This is assessed by looking at the going premium on options. If you think of options as being a kind of insurance against downside risk, this makes intuitive sense; the more people are paying for options, the more uncertain they perceive the market to be.<\/p>\n\n\n\n

    Making Decisions Based on <\/strong>Volatility<\/strong><\/h2>\n\n\n\n

    Volatility receives a lot of attention because it\u2019s so crucial to making good decisions with respect to financial investments. Just as you\u2019d need to understand how tempestuous the ocean is expected to be before you take a boat out, you need to know how to calculate volatility. Then you\u2019ll have an estimate of past and future volatility, which will help you to understand the risks you\u2019re taking with a particular asset.<\/p>\n\n\n\n

    If you\u2019d like to access high-quality data to perform your own volatility calculations, sign up for access to the Tiingo API<\/a>. We work hard to ensure that our financial data is cleaned and preprocessed to the highest standards \u2014 this way you can focus on doing analyses and building your models.<\/p>\n","protected":false},"excerpt":{"rendered":"

    If you\u2019ve spent any period of time participating in the stock market, you\u2019ve no doubt noticed that stock prices can fluctuate wildly. This is part of what makes it exciting \u2014 dramatic upward price changes can make you a fortune in a few minutes. But it also makes it unnerving \u2014 a price collapse can […]<\/p>\n","protected":false},"author":1,"featured_media":144,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"osom_blocks_metabox":"","inline_featured_image":false,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-143","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-uncategorized","8":"entry"},"yoast_head":"\nUnclear on How to Calculate Volatility? 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