With a larger standard deviation, a security’s price varies more from its mean, resulting in a greater spread between its high and low prices and a wider price range for that asset. Example: The standard deviation of an unstable stock is often higher than the standard deviation of an equally steady blue-chip company.
What Is Historical Volatility (HV) and How Does It Work?
The statistical dispersion of returns for a certain investment or market index over a period of time defined in years or months is referred to as historical volatility (HV). A financial instrument’s average deviation from its average price during a certain time period is often used to determine this statistic.
The standard deviation is the most often used method of calculating historical volatility, although it is not the only one. The greater the historical volatility number, the riskier the investment is considered to be. However, this is not always a negative outcome since risk may function in both directions—both positively and negatively.
Understanding the Historical Volatility of the Stock Market (HV)
Historically, historical volatility hasn’t been used to directly evaluate the chance of a loss, but it may be used to do so. But what it does measure is the distance that a security’s price has moved away from its mean value in the past.
The historical volatility of a market’s prices reflects how much prices have moved away from a central average, or moving average, price over a period of time. This is how a market with a strong trend but a smooth trading pattern may maintain minimal volatility even though prices shift drastically over time. Unlike other investments, its value does not vary substantially from day to day, but rather changes in value at a consistent rate over time.
This indicator is typically used in conjunction with implied volatility to analyze if option prices are over- or undervalued in the market. Historical volatility is also employed in all sorts of risk estimates, including financial risk valuations. Stocks with a high level of historical volatility often need a greater level of risk acceptance. Furthermore, high volatility markets necessitate the use of larger stop-loss levels as well as the use of potentially greater margin needs.
Aside from being employed in option pricing, HV is often used as an input in other technical studies, such as Bollinger Bands, to determine the volatility of an asset. Depending on how volatile the market is as assessed by standard deviations, these bands shrink and widen around a central average.
Using Historical Volatility as a Measure
When it comes to trading and investing, volatility has a negative image, although many traders and investors may benefit from increased volatility. Because a stock or other investment that does not move is considered low-volatility, it also has a minimal possibility for financial gains.
As an example, a stock or other investment with a very high degree of volatility may have a large profit potential, but at the expense of a significant amount of volatility. It would also have a significant financial impact. A flawless market call is required for all transactions, and an incorrect market call may result in a loss of money if the security’s large price fluctuations trigger a stop-loss or margin call.
As a result, volatility levels should be somewhere in the medium, and the exact location of that middle relies on the markets and even the equities under consideration. In order to assess what amount of volatility is “normal,” it is useful to do comparisons across similar securities.
Calculating the standard deviation may be accomplished using the following formula:
1.) To compute the mean value, add all of the data points together and divide the total number of data points by the total number of data points.
2.) As demonstrated in the example, the variance for each data point is calculated by subtracting the mean from the value of the data point. Those numbers are then squared, and the results are added together to get a final total. The result is then divided by the number of data points less one, resulting in a final result of one.
3.) The standard deviation is calculated by taking the square root of the variance, which is the result of step 2.
When Calculating Standard Deviation, Consider the Following:
Among the most helpful tools in investing and trading techniques, the standard deviation is particularly valuable since it helps to gauge market and securities volatility, as well as anticipate performance patterns. In the context of investment, an index fund, for example, is likely to have a low standard deviation when compared to its benchmark index, since the fund’s purpose is to duplicate the index.
A large standard deviation from comparable stock indexes is expected of aggressive growth funds, on the other hand, since their portfolio managers take calculated risks in order to create returns that are greater than the average.
It is not always beneficial to have a smaller standard deviation. Every aspect of the investment, as well as the investor’s willingness to take risks, is determined by the investments themselves and the investor. To determine their tolerance for volatility and the overall investing goals of their portfolios, investors should take into account the amount of variance present in their portfolios. Greater risk-adverse investors may be comfortable with an investing plan that includes investments in vehicles with higher-than-average volatility, but greater risk-averse investors may not be so comfortable.
Among the primary fundamental risk measurements that analysts, portfolio managers, and financial advisers use is the standard deviation (or standard deviation). The standard deviation of mutual funds and other products is disclosed by investment companies to investors. If the fund’s return deviates significantly from predicted normal returns, this indicates a big dispersion. The fact that this data is simple to comprehend ensures that it is consistently presented to end customers and investors.
The Relationship Between Standard Deviation and Variance.
Take the mean of the data points and subtract it from each one separately. Square each of these values, and then take another mean of the squares. This is how you calculate the variance of a data set. When calculating the standard deviation, take the square root of the variance.
With respect to mean value, variance assists in determining how wide the data spreads. More variety in data values occurs as the variance increases, and there may be a greater difference between one data value and another as the variance increases. A lesser variation will be seen if the data values are all relatively close together. In contrast to the standard deviation, variances indicate a squared result that may not be effectively displayed on the same graph as the original dataset, making them more difficult to comprehend.
It is frequently simpler to see and apply standard deviations. Unlike the variance, the standard deviation is stated in the same unit of measurement as the data, but this is not always the case with the standard error. It is possible for statisticians to identify whether the data follows a normal curve or any other mathematical connection by calculating the standard deviation.
For example, if the data follows the behavior of a normal curve, then 68 % of the data points will be within one standard deviation of the average, or mean, data point. Because to higher standard deviations, more data points fall outside of the normal distribution. Greater amounts of data that is near to the average are produced by smaller variations.
An Illustration of The Standard Deviation
Consider the following data points: 5, 7, 3, and 7, for a total of 22 data points. The mean is calculated by dividing 22 by the number of data points, in this instance four, which results in a mean of 5.5. As a result, the following conclusions are reached: x = 5.5 and N = 4 are the values of the variables.
By subtracting the mean from each data point, the variance can be determined, resulting in values of -0.51, 1.51, 2.51, 1.52, and 1.53, respectively. Every one of those numbers is then squared, giving in the values 0.25, 2.25, 6.25, and 2.25, respectively. Afterwards, the square values are put together, yielding a total of 11, which is then divided by the value of N minus 1, which equals 3, yielding a variance of around 3.67 %.
The square root of the variance is then computed, yielding a standard deviation measure of about 1.915 as a consequence of this calculation.
Consider the performance of Apple (AAPL) stock over the previous five years. Following the release of the most current available data, Apple’s stock returned 12.49 % in 2016, 48.45 % in 2017, -5.39 % in 2018, 88.98 % in 2019, and, as of September, 60.91 % in 2020. Over the course of five years, the average return was 41.09 %.
The value of each year’s return minus the mean is 21.2 %, -21.2 %, -6.5 %, 29.6 %, and -23.3 %, respectively, in percentage terms. All of those numbers are then squared to provide 449.4, 449.4, 42.3, 876.2, and 542.9, which are the results of the calculations. 590.1 is the variance calculated by adding all of the squared values together and dividing them by four (N minus 1). It is necessary to calculate the square root of the variance to get the standard deviation of 24.3 %.