# Price Volatility

## Price Volatility Definition

Volatility is a measure of how much something tends to change. Unlike the usual way people look at prices of securities and their changes – up or down, the volatility point of view does not care about the direction so much. In fact it does not distinguish between up and down.

When you hear that volatility of a stock increased from 20% to 30%, you have no idea whether the stock price actually went up or down. You can just conclude that its moves got bigger and more variable.

## Volatility Usually Means Standard Deviation

When people talk about volatility of security prices, they (almost always) think of standard deviation of price changes. There are various approaches to the exact calculation of volatility. Calculating standard deviation from day-to-day percentage changes is the most commonly used approach.

If you are familiar with the basics of probability and statistics, you know that standard deviation is the square root of variance, and variance is the average of individual observations' squared differences from average value. If you don't really understand what we are talking about now, you may refer to the article on variance and standard deviation on this website. But for understanding the point of this article, it is enough to know that:

1. There is something like volatility of security prices.
2. It is also called standard deviation.
3. It means how much security prices tend to move.

## How to Calculate Volatility

Here you can see a step-by-step explanation of historical volatility calculation.

## Units of Volatility

In general, standard deviation of something (security prices, time intervals, temperature, size, or anything around us that can be measured with numbers) is measured in the same units as that something.

For example, time intervals between trains are measured in minutes and seconds, and standard deviation of these time intervals is also measured in minutes and seconds. Daily high temperatures are measured in Celsius or Fahrenheit and the standard deviation of daily high temperatures is also measured in Celsius or Fahrenheit.

## Units of Volatility of Stocks and Other Securities

Security prices are usually measured in dollars (or other currency). Their changes can be measured in dollars or in percent (more common). Volatility of security prices can therefore also be measured in currency units or percent.

Measuring stock volatility in percent is more common, as there is one big advantage over using currency units – comparability. There are stocks which cost 5 dollars and there are other stocks which cost 200 dollars.

By using percentages you can directly compare their volatility – more percent always means greater volatility. If you used dollars, you would most likely get a much larger dollar amount of volatility for the 200 dollar stock, even when the 5 dollar stock were a much bigger mover in relative terms. This is the same logic as that of measuring day-to-day price changes in dollars vs. percent.

## Volatility Can't Be Negative

Volatility (standard deviation) can't be negative. As mentioned above, volatility is the square root of variance, which is the average squared difference between individual observations and the average value. A squared value is always non-negative.

The lowest possible volatility level is zero. This would be the volatility of a stock that doesn't move at all and stays at a fixed price level all the time, or a security that has exactly the same return every day (like, for example, bank deposits or fixed interest short term "riskless" government debt).

The more (differently over time) a security moves, the higher its volatility.

## Using Range to Measure Price Volatility

Range is another measure of volatility of security prices. Compared to standard deviation, it is much more straightforward and you see it immediately just by looking at a chart. You take the highest price in a period, then the lowest price in the same period, and subtract the low from the high.

For example, the minimum price of Bank of America stock in the last month was let's say 17.50 and the maximum price was 21.80. The range in that month was therefore 4.30 dollars (21.80 less 17.50).

## Range and Comparability Issues

Because you are working with dollars here, range is not a good measure for comparing stocks with substantially different prices. For example, let's compare Bank of America to Google stock. Minimum price of Google in the same month was 515.30 and the maximum was 552.30. Google's range was therefore 37 dollars (552.30 less 515.30), much higher than the range of Bank of America stock. But which stock was really more volatile?

## Measuring Range in Percent

If you express range in percentage terms, 4.30 dollars on a roughly 20 dollar stock is something around 20%, while 37 dollars on a 500+ dollar stock is less than 10%. Bank of America was much more volatile than Google in that particular month.

You have multiple options for calculating the percentages. You can divide each stock's dollar range by:

• the stock's closing price in the particular period,
• the maximum price (top of the range),
• the minimum price (bottom of the range),
• the average of the maximum and the minimum (the centre of the range, which probably makes most sense of all four methods).

The important thing is to be consistent and use the same method for all stocks you want to compare.

Also note that range percentages are of course not comparable to percentages we get by using standard deviation as a volatility measure, as the calculations are very different.

## Conclusion: Comparing Volatility of Two Stocks

For both standard deviation and range as measures of stock price volatility, percentages are comparable, while absolute dollar amounts are not if the stocks have different price levels.

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