Standard deviation and variance: an overview
Standard deviation and variance are two basic mathematical concepts that feature prominently in various parts of the financial industry, from accounting to economics to investing. Both measure the variability of numbers within a data set using the average of a certain group of numbers. They are important in helping determine volatility and distribution of returns. But there are inherent differences between the two. While the standard deviation measures the square root of the variance, the variance is the average of each point relative to the mean.
Key takeaways
- Standard deviation and variance are two key metrics commonly used in the financial industry.
- Standard deviation is the deviation of a group of numbers from the mean.
- Variance measures the average degree to which each point differs from the mean.
- While the standard deviation is the square root of the variance, the variance is the average of the squared difference of each data point from the mean.
- Both concepts are useful and meaningful to traders, who use them to measure market volatility.
Standard deviation
Standard deviation is a statistical measure that looks at how far a group of numbers are from the mean. Simply put, standard deviation measures how far apart numbers in a data set are.
This metric is calculated as the square root of the variance. This means you need to determine how much variation each data point has from the mean. Therefore, calculating variance uses squares because it weighs more on outliers than on data that appears closer to the mean. This calculation also prevents differences above the mean from canceling out those below, which would result in zero variance.
But how do you interpret standard deviation once you understand it? If the points are further from the mean, the deviation in the data is greater. But if they are closer to the average, the difference is smaller. So, the more dispersed the group of numbers, the higher the standard deviation.
As an investor, make sure you understand how to calculate and interpret standard deviation and variance so you can create an effective trading strategy.
As an investor, make sure you understand how to calculate and interpret standard deviation and variance so you can create an effective trading strategy.
Variance
A variance is the average of the squares of the differences from the mean. To determine the variance, calculate the difference between each point in the data set and the mean. Once you understand this, square and average the results. Using software like Excel can help you with this process.
For example, if a group of numbers goes from one to 10, you get an average of 5.5. If you square the differences between each number and the mean and find their sum, the result is 82.5. To determine the gap:
- Divide the sum, 82.5, by N-1, which is the sample size (in this case, 10) minus 1.
- The result is a variance of 82.5/9 = 9.17.
Note that the standard deviation is the square root of the variance, so the standard deviation is approximately 3.03.
The mean is the average of a group of numbers and the variance measures the average degree to which each number is different from the mean. The extent of variance is correlated with the size of the overall range of numbers, meaning that the variance is greater when there is a wider range of numbers in the group, and is less when there is a narrower range of numbers.
The mean is the average of a group of numbers and the variance measures the average degree to which each number is different from the mean. The extent of variance is correlated with the size of the overall range of numbers, meaning that the variance is greater when there is a wider range of numbers in the group, and is less when there is a narrower range of numbers.
Key differences
Besides how they are calculated, there are a few other key differences between standard deviation and variance. Here are some of the most basic ones.
- Standard deviation measures how far apart numbers in a set of data are. Variance, on the other hand, gives a true value to the extent to which the numbers in a data set vary from the mean.
- The standard deviation is the square root of the variance and is expressed in the same units as the data set. The variance can be expressed in square units or as a percentage (especially in the context of finance).
- The standard deviation can be greater than the variance since the square root of a decimal is larger (not smaller) than the original number when the variance is less than one (1.0 or 100%).
- The standard deviation is less than the variance when the latter is greater than one (for example 1.2 or 120%).
The table below summarizes some of the main differences between standard deviation and variance.
Main Differences Between Standard Deviation and Variance | ||
---|---|---|
Standard DETOUR | Variance | |
What is this? | The square root of the variance | Mean squared differences from the mean |
What does this indicate? | The gap between numbers in a data set | The average degree to which each point differs from the mean |
How is he expressed? | Same as dataset units | In square units or as a percentage |
What does it mean? | A low standard deviation (spread) means low volatility, while a high standard deviation (spread) means higher volatility. | The extent to which returns vary or change over time |
Standard deviation and variance in investment
These two concepts are of paramount importance to both traders and investors. This is because they are used to measure market safety and volatility, which plays an important role in creating a profitable trading strategy.
Standard deviation is one of the key methods used by analysts, portfolio managers and advisors to determine risk. When the group of numbers is closer to the average, the investment is less risky. But when the group of numbers is further from the average, the investment presents a greater risk to a potential buyer.
Stocks close to their means are considered less risky because they are more likely to continue to behave as such. Stocks with wide trading ranges and a tendency to surge or change direction are riskier.
Risk in itself is not necessarily a bad thing when it comes to investing. This is because riskier investments tend to generate greater rewards and greater payout potential.
Risk in itself is not necessarily a bad thing when it comes to investing. This is because riskier investments tend to generate greater rewards and greater payout potential.
Example of Standard Deviation vs. Variance
To demonstrate how the two principles work, let's look at an example of standard deviation and variance.
Suppose you have a series of numbers and you want to determine the standard deviation of the group. The numbers are 4, 34, 11, 12, 2 and 26. We need to find the average of the numbers. In this case, we determine the average by adding the numbers and dividing it by the total number in the group:
(4 + 34 + 18 + 12 + 2 + 26) ÷ 6 = 16
So the average is 16. Now subtract the average from each number, then square the result:
- (4 – 16)^{2} = 144
- (34 – 16)^{2} = 324
- (18 – 16)^{2} = 4
- (12 – 16)^{2} = 16
- (2 – 16)^{2} = 196
- (26 – 16)^{2} = 100
Now we need to calculate the average of these squared values to get the variance. This is done by adding the squared results above, then dividing them by the total number in the group:
(144 + 324 + 4 + 16 + 196 + 100)^{ }÷6 = 130.67
This means we end up with a gap of 130.67. To calculate the standard deviation, we need to take the square root of the variance and then subtract one, which is 10.43.
What does variance mean?
The simple definition of the term variance is the difference between numbers in a set of data. Variance is a statistical measure used to determine how far each number is from the mean and from all other numbers in the set. You can calculate the variance by taking the difference between each point and the mean. Then square and average the results.
What does standard deviation mean?
Standard deviation measures how spread out the data is from its mean and is calculated as the square root of its variance. The further apart the data points are, the greater the deviation. Closer data points mean smaller deviation. In finance, standard deviation calculates risk, so riskier assets have a higher spread while safer bets have a lower standard deviation.
What is variance used for in finance and investing?
Investors use variance to assess the risk or volatility associated with assets by comparing their performance within a portfolio to the average. For example, you can use your portfolio variance to measure your stock returns. This is done by calculating the standard deviation of the individual assets in your portfolio as well as the correlation of the securities you hold.
What are the disadvantages of variance?
The variance of an asset may not be a reliable measure. Calculating variance can be quite lengthy and time-consuming, especially when many data points are involved. Variance doesn't account for surprise events that can eat away at returns. And variance is often difficult to use in a practical sense, not only is it a squared value, but so are the individual data points involved.
The essential
Standard deviation and variance are two different and closely related mathematical concepts. The variance is needed to calculate the standard deviation. These numbers help traders and investors determine the volatility of an investment and therefore enable them to make informed trading decisions.