6.8 : Variance

Variance is a statistical measure that quantifies the degree of risk associated with an investment's returns by indicating how much the returns deviate from their expected value over time. It provides essential insights into the stability and predictability of an investment's performance. The variance calculation involves determining the mean return, which is the average return over a specified period, and then calculating the deviations of each return from this mean. These deviations are squared to ensure all values are positive, which prevents negative deviations from canceling out positive ones. The sum of these squared deviations is then divided by the number of observations minus one (n-1), where n is the total number of observations, to compute the variance.

Interpreting variance is crucial for understanding an investment's risk profile. A low variance indicates that the returns are consistently close to the mean return, suggesting lower risk and more stable performance. Conversely, a high variance signifies significant return fluctuations from the mean, indicating higher risk and greater volatility. This interpretation helps investors assess the level of uncertainty and potential variability in their investment returns.

Variance is an essential tool for investment decision-making and risk management. It provides a quantitative measure of how much investment returns can vary, aiding investors in understanding the level of risk associated with different investments. By comparing the variances of various investments, investors can identify which ones are more stable and which are more volatile. This understanding is crucial for building a diversified portfolio that balances risk and return in line with the investor's risk tolerance and financial objectives.