What is Variance?
Variance refers to the degree to which an investment’s returns vary over time –- This metric gives investors an idea of how predictable the performance of an asset may be.
Variance statistics help investors determine how to allocate their assets in a way that aligns with how they wish to balance risk and potential returns. Volatility is associated with risk, so variance can help you understand what kind of risk an investment involves. Calculating variance gives you a tangible benchmark for asset allocation (how much of each asset you wish to hold). The variance formula looks complex and involves several steps, but it’s not as scary as it seems –- Excel has a function that helps you calculate variance. If you’ve ever taken a statistics class, you may be familiar with variance’s first cousin, the standard deviation. The standard deviation is the square root of the variance.
To calculate variance, we look at the difference between each number in the data set and the mean (average), square the differences, then divide the sum of the squares by the total number of values in our data set.
Let’s look at the fictional company ABC Widget Corp., for example. What is variance with regard to this fictional stock?
To answer this question, we begin with the returns ABC yielded in previous years. Let’s say that during the years spanning 2016 – 2018, ABC saw year-over-year returns of 300%, 400%, and - 40%.
The average of the returns in this data set is 220%. The differences between each return and the average are 80%, 180%, and - 260%. The squares of these deviations equal 6,400, 32,400, and 1,600. The sum of these squared deviations is 40,400. Dividing 40,400 by the number of returns we used (3) arrives at a variance of 13,467.
The square root of the variance yields a standard deviation of 116%. This number suggests that the fictional ABC Widget Corp. is a very volatile stock.
Variance is like a nutrition label for a financial asset...
Just as a nutritional label might tell you if a product contains things you may or may not wish to eat as part of a balanced diet, variance will tell you something about how risky an asset might be. And just as different people might draw different conclusions from the same nutritional label, based on different goals and preferences, different investors will have different appetites for the level of risk a variance reveals.
In the investment world, the variance of returns among different assets is used as a factor that helps you figure out the best asset allocation. How do investors make the best choice when figuring out how much of their total portfolio to put into each specific asset they want to own? Variance is one useful measuring stick that can help inform such decisions.
The higher the average variability of an asset, the higher-risk it is. Assets and securities that are low-risk tend to have lower returns and less variance. Their performance is simpler to predict because there’s less of a chance it’s going to vary from the average.
At the same time, securities that vary from their average a lot can produce higher returns, but can also produce higher losses.
Using Microsoft Excel, it’s easy to calculate the sample variance. There are several different formulas, but the best one in most cases for users of Excel 2019 will be =VAR.S(sample data). For example, if the sample data you wanted to use was contained in cells B10 through B20, the formula would be:
(Unless you have all the data sets of all time, you’re assessing the variance of an asset-based on a smaller ‘sample’ set of data –- That’s why it’s called ‘sample variance.’)
What is the variance in statistics? By itself, the number that you come up with after calculating variance isn’t particularly useful. You’ve figured out how much a data set varies, which is cool, but it’s hard to interpret that one number.
When you take the square root of the variance, however, you arrive at the standard deviation.
This unit gives statisticians (or investors) something they can more easily work with because it’s expressed in the same manner as the data set. From there, it’s possible to figure out how the data points relate to each other.
For example, say you were to calculate the variance of a stock over the last five years. There were some wild swings in price during that time, and you come up with a number like 10,000. What does this mean? It looks like the price of this stock can vary a lot, but that’s a broad generalization that doesn’t give you much to work with.
The square root of the variance (standard deviation) in this fictional example would be 100%. This number is expressed as a percentage, which is the same way the numbers in your data set would be represented (as a percentage of returns).
While sample variance is a way to assess how to best allocate your assets, it’s not a magical panacea. To be effective, this variable needs to be considered against the backdrop of many other market conditions.
Over-reliance on variance can make someone avoid a worthwhile investment or become too invested in another.
When you answer the question, “what is variance?”, you aren’t considering the broader market horizon, nor are you examining the more in-depth aspects of a specific company or asset.
The variables that might have contributed to the numbers you’re looking at remain hidden. That’s why investors seldom look to any single metric or calculation when making informed decisions.
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