# Guide to Standard Deviation in Finance and How to Calculate

By Indeed Editorial Team

Updated November 14, 2022

Published October 18, 2021

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Investments are among the most complex financial activities, leading experts to adopt various tools to determine associated risk. One of such tools they adopt to determine the volatility of assets is the standard deviation. Understanding standard deviation in finance can help you make smarter investment decisions and grow your wealth. In this article, we explore standard deviation in finance, discuss standard deviation versus finance, explain the relationship between standard deviation and risk, highlight the drawbacks of standard deviation, and outline how to calculate the standard deviation.

## What is standard deviation in finance?

Standard deviation in finance is a statistic measuring the dispersion of datasets relative to their mean for financial analysis. Precisely, when determining the standard deviation of a dataset, it involves identifying the degree of deviation between the values of the observations present within the dataset. In turn, it provides a valuable element to help investors and financial analysts determine the risk associated with an investment, including the minimum returns required on such investment to make it profitable and reasonable for the investor. For instance, volatile stocks often have high standard deviations while stable blue-chip stocks have a low standard deviation.

Related: What Is Quantitative Analysis?

## Standard deviation vs. variance

Variance is a measure to determine the extent to which units in a dataset vary from the mean value. A high variance value signifies a large gap between units, and a low variance value suggests the opposite. You can calculate the variance of a data set by subtracting the mean of the values from each value and squaring the results. Next, calculate the mean of the squared result to get your variance.

While both variance and standard deviation help calculate risk, variance is more challenging to understand. The variance isn't in the same measurement unit as the initial data due to the squaring, which may be challenging to reflect on a graph.

Related: What Is Sum of Squares? (With Examples, Formula, and Types)

## The relationship between standard deviation and risk

Investors and financial analysts rely on standard deviation to measure risk, as it shows the volatility of an asset. Generally, the smaller the standard deviation, the lesser the volatility and risk of the asset. Conversely, a high standard deviation is a sign of a volatile asset. As a result, financial assets with a limited range of movement have low standard deviations. In contrast, assets that experience massive spikes and drops in price have a high standard deviation. This allows investors can to use standard deviation to inform their investments based on their aversion to risk.

While many investors avoid it, risk in investment is not always a bad thing. Also, standard deviation only measures the disparity in data units rather than tell you whether to invest in an asset or not. An asset can have a low standard deviation and still be in loss. Similarly, an asset with a high standard deviation can be profitable. It's essential for investors and analysts to remember that standard deviation only depicts the volatility of an asset, not its value. Regardless, the standard deviation is still an essential tool as it helps investors manage risks.

Related: Understanding How To Complete a Risk Analysis

## Drawbacks of standard deviation

While standard deviation is an excellent tool for informing investment choices, it has limitations. The major flaw of this tool is that it assumes a normal distribution and interprets any volatility as risk. This happens even when the volatility favours the investor, such as when an asset experiences spikes in price. In addition, the tendency for extreme values to affect the standard deviation makes it an unreliable tool to use alone. For the best results, it's essential investors pair the standard deviation with other measurements and analysis of an asset's value.

Related: Guide: How To Become a Stockbroker

## Calculating standard deviation

Here are some steps you can follow to calculate standard deviation:

### 1. Determine the formula for standard deviation

Having the right formula is essential for accurately determining the standard deviation. The formula for standard deviation is:

Standard deviation (σ) = √[∑(x - mean)²/N-1]

### 2. Calculate your mean of returns

This refers to the average of all your returns within a specific period. To calculate the mean, simply add up all your returns, and divide the total by the number of returns. For example, a stock can make 5%, 10%, 15%, and 20% over a particular period. To calculate the mean of returns, you'll add 0.05 + 0.10 + 0.15 + 0.20 and divide the total by four (number of returns) to get your mean of returns.

### 3. Find the variance

This is the rate at which data sets vary from the mean. This is the first part of applying the standard deviation formula. To find the variance, subtract the mean of returns from each data set individually. Next, square the subtraction results, add the squared results together and divide them by the number of results minus one. For example, using the same data set in step 2, you can calculate the variance as:

(0.05 - 0.125)2 + (0.10 - 0.125)2 + (0.015 - 0.125)2 + (0.2 - 0.1250)2/ 4-1

That gives:

0.0056 + 0.00063 + 0.00063 + 0.0056/3 which equals 0.01246/3

That gives a value of 0.004153.

### 4. Calculate the standard deviation

After finding your variance, simply calculate the square root to obtain your standard deviation. When calculating the variance, the squaring of the values changes the unit of measure. This means, by finding the square root to obtain the standard deviation, you return the values to the original unit of measure. For example, following the data set from the previous step, the standard deviation is the square root of 0.004153. That gives a standard deviation of 0.064. Meaning the data set has a standard deviation of 6.4%.

## Examples of standard deviation

Here are some examples of standard deviation to guide you:

### Example 1

If Gary invested in Garrison company's stock and received returns of $7, $55, $36, $23, and $63 over five months, calculate the standard deviation of Garrison company's stocks.

Mean: The first step to solving this problem is to find the mean of returns. This is 7+55+36+23+63/5, which equals 36.8.

Variance: Next, you can use the value of the mean of returns to solve for the variance. To calculate the variance, subtract the mean from each value, square the results, add all the values, and divide by the number of values minus one. That is (7 - 36.8)2 + (55-36.8)2 + (36 - 36.8)2 + (23 - 36.8)2 + (63 - 36.8)2 / 5 - 1 and it gives 888.04 + 331.24 + 0.64 + 190.44 + 686.44/ 4 which gives a result of 524.2 as the variance.

Standard deviation: After finding the variance, calculate the standard deviation by finding its square root. That gives a standard deviation of $22.9. This means Gary's return on investments can vary by $29 from its average.

### Example 2

If the returns on Fabrik Retail Services were 13.23%, 45.7%, 8.7%, 78.65%, and 56.8% over five years, what is the standard deviation?

Mean: The first step is to solve the mean of returns by adding all the values and dividing the result by the number of values. In this case, that is 13.23 + 45.7 + 8.7 + 78.65 + 56.8 / 5 and it gives a value of 40.6 as the mean of returns.

Variance: The next step is to calculate the variance by subtracting the mean of returns from each value, squaring the results, adding all the values, and dividing by the number of values minus one. In this case, that's (13.23 - 40.6)2 + (45.7 - 40.6)2 + (8.7 - 40.6)2 + (78.65 - 40.6)2 - (56.8 - 40.6)2 / 5 -1 and it gives 749.12 + 26.01 + 1,017.6 + 1,447.8 + 262.44 / 4 = 875.74.

Standard deviation: To obtain the standard deviation, simply find the square root of the variance, in this case, that gives a standard variation of 29.6%.

### Example 3

If the value of GFT cryptocurrency was $21, $8, $42, $15, and $5 over five months, calculate the standard deviation.

Mean: The first step is to find the mean of these values by adding them and dividing them by the number of values. That gives 21 + 8 + 42 + 15 + 5/ 5 and 18.2 as the mean.

Variance: The next step is to calculate the variance. You can do that by subtracting the mean from each unit and squaring the results. Next, add all the squared results and divide them by the number of values minus one. In this case, that's (21 - 18.2)2 + (8 - 18.2)2 + (42 - 18.2)2 + (15 - 18.2)2 + (5 - 18.2)2 / 5-1 and that equals 7.84 + 104.04 + 566.44 + 10.24 + 174.24/ 4 which gives a variance of 215.7.

Standard deviation: The standard deviation is the square root of 215.7, which is $14.7.

The model shown is for illustration purposes only, and may require additional formatting to meet accepted standards.

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