About Variance Of Returns Calculator (Formula)
The variance of returns calculator is a fundamental tool in finance and statistics used to measure the spread or dispersion of investment returns. It provides investors and analysts with a quantitative way to assess the risk associated with an investment or a portfolio of investments. The variance of returns helps individuals understand how much an investment’s returns tend to deviate from its expected or average return.
The formula for calculating the variance of returns is relatively straightforward. To compute the variance, you need a dataset of historical returns for the investment in question. The formula is as follows:
Variance (σ^2) = Σ [(Ri – R̄)^2] / (N – 1)
Where:
- σ^2 represents the variance of returns.
- Σ denotes the summation symbol, meaning you will sum up the values within the brackets for all data points.
- Ri represents each individual return in the dataset.
- R̄ (pronounced “R-bar”) represents the average return or expected return of the investment.
- N represents the total number of data points in the dataset.
Here’s a step-by-step breakdown of how to use this formula:
- Gather your historical returns data: Collect a dataset of past returns for the investment or portfolio you want to analyze. The more data points you have, the more reliable your variance calculation will be.
- Calculate the average return (R̄): Add up all the individual returns in your dataset and divide by the total number of data points (N). This gives you the expected or average return.
- Calculate the squared differences: For each return in your dataset (Ri), subtract the average return (R̄) and square the result [(Ri – R̄)^2].
- Sum up the squared differences: Add up all the squared differences calculated in step 3 using the summation symbol (Σ).
- Divide by (N – 1): Divide the sum of squared differences by (N – 1), where N is the total number of data points. This correction factor (N – 1) is used to make the variance estimator unbiased and reflects the sample size.
The result is the variance of returns (σ^2), which is expressed in the same units as the original returns but squared. To get the standard deviation of returns (σ), which is a more interpretable measure of risk, simply take the square root of the variance: σ = √σ^2.
In summary, the variance of returns calculator is a valuable tool for assessing the risk associated with an investment or portfolio by quantifying how much the actual returns tend to deviate from the expected or average return. This measurement plays a crucial role in portfolio management, risk assessment, and investment decision-making.