4.8:
Variance
Variance is a measure that reflects the degree of risk in an investment's returns.
It provides insight into the variation of investment returns from their expected value over a period.
Consider Peter. He has invested in two stocks, Stock A and Stock B. They have exhibited different returns in the first five months of the year.
Peter finds the mean return, which is the average return of each stock. Stock A has a mean return of six percent, and Stock B's mean return is four percent.
Next, he calculates the deviations and squared deviations from the mean return for each month for Stock A and B.
To calculate variance, the total of squared deviations is divided by one less than the number of observations. Here it is calculated as four which is one less than the number of observations.
For Stock A, the variance is relatively low, at two point five percent, indicating stable performance. Stock B, however, shows a higher variance of thirty-five point five percent, reflecting high volatility in monthly returns.
Variance helps Peter understand the risk profile of his investments, where Stock A is less risky than Stock B.
4.8 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.