Variance

Variance is a statistical measure that quantifies the degree of risk associated with an investment's returns by showing how much returns deviate from their expected value over time. It provides insight into the stability and predictability of investment performance. A low variance indicates consistent returns close to the mean, suggesting lower risk, while high variance reflects significant fluctuations and greater volatility.

Variance calculation begins by finding the mean return, which is the average return over a specified period. Next, calculate the deviation of each return from this mean and square these deviations to ensure all values are positive. Finally, divide the sum of squared deviations by the number of observations minus one (n-1) to compute the variance.

Squaring deviations ensures all values are positive, which prevents negative deviations from canceling out positive ones. This approach guarantees that variance accurately reflects the total variability in returns regardless of whether individual returns fall above or below the mean return.

A low variance indicates that returns are consistently close to the mean return, suggesting lower risk and more stable performance. This stability means the investment's returns are predictable and less volatile, making it a less risky choice for investors seeking steady, reliable returns over time.

By comparing the variances of various investments, investors can identify which ones are more stable and which are more volatile. This comparison helps investors understand the level of uncertainty and potential variability in different investment returns, enabling them to build a diversified portfolio that balances risk and return according to their risk tolerance.

High variance signifies significant return fluctuations from the mean, indicating higher risk and greater volatility. This means the investment's returns are less predictable and more uncertain, suggesting greater potential for both gains and losses compared to investments with lower variance.

Variance provides a quantitative measure of how much investment returns can vary, aiding investors in understanding the level of risk associated with different investments. This understanding is crucial for making informed investment decisions and managing risk effectively when selecting securities that align with financial objectives and risk tolerance.