What Is Variance?
Variance is a fundamental statistical measurement representing the spread between numbers in a data set. It quantifies how far each number in the set is from the mean (average), and by extension, from every other number in the set. Represented as σ², variance is crucial for analysts and traders in assessing market volatility and security.
The square root of variance is known as the standard deviation (SD or σ), a critical metric used to evaluate the consistency of an investment’s returns over time.
Key Takeaways
- Variance measures the spread of numbers in a data set.
- It helps quantify the degree of dispersion relative to the mean.
- Investors utilize variance to assess investment risk and potential profitability.
- In finance, variance aids in comparing the performance of individual assets within a portfolio for optimal asset allocation.
- The square root of variance is the standard deviation.
Understanding Variance
In statistical analysis, variance measures variability from the mean. It is calculated by determining the differences between each number in the data set and the mean, squaring these differences, and dividing the sum of the squares by the total number of values in the data set.
Variance is determined using the formula:
Variance can be computed for various fields beyond investments and trading by making slight formula adjustments. For example, when calculating a sample variance to estimate population variance, the formula’s denominator changes to N − 1 to avoid underestimating population variance.
Advantages and Disadvantages of Variance
Advantages: Variance allows statisticians to understand how individual numbers within a data set are related without resorting to broader techniques like quartiles. It treats all deviations (regardless of direction) equally, ensuring that squared deviations don’t cancel each other out, which might falsely suggest no variability in the data.
Disadvantages: Variance has the drawback of giving added weight to outliers—extreme values far from the mean—potentially skewing the data. Moreover, variance can be less intuitive to interpret directly; it is often used to calculate the standard deviation, which is easier to understand and apply in practical scenarios.
Example of Variance in Finance
Consider a hypothetical example of stock returns for Company ABC over three years: +10% in Year 1, +20% in Year 2, and −15% in Year 3. The average return over these three years is 5%. The differences between each return and the average are +5%, +15%, and −20% respectively.
Squaring these deviations results in 0.25%, 2.25%, and 4.00%. Summing these squared deviations yields 6.5%. Dividing this sum by the number of returns minus one (since this is a sample: 2 = 3−1) gives a variance of 3.25%. Taking the square root of the variance yields a standard deviation of 18% (√0.0325 = 0.180).
Frequently Asked Questions
How Do I Calculate Variance?
Calculate variance through the following steps:
- Calculate the mean of the data.
- Subtract the mean from each data point.
- Square each resulting value.
- Sum all the squared values.
- Divide this sum by n-1 (for a sample) or N (for the population).
What Is Variance Used for?
Variance indicates the degree of spread or dispersion around the mean value in a data set. Its larger values suggest greater involvement. In finance, high variance is often interpreted as higher risk or volatility for an investment.
Why Is Standard Deviation Often Used More Than Variance?
Standard deviation, being the square root of variance, strip away unit definition, allowing easier and direct comparisons between different entails. For instance, standard deviation enables recognition of relationships regardless of differing units of variables by abstracting scale and measure units.
Related Terms: standard deviation, mean, risk assessment, data analysis.
