The formula to calculate the Variance of Returns (V) is:
\[ V = \frac{\sum (R_i - R_m)^2}{N} \]
Where:
Variance of returns is a statistical measurement used in finance that quantifies the dispersion of returns of a financial instrument such as a stock or a portfolio. It measures the degree to which the returns deviate from the mean or average return over a certain period. A high variance indicates that the asset's returns are spread out over a larger range of values and thus, the asset is more volatile or risky. Conversely, a low variance indicates that the returns are closer to the mean and the asset is less volatile.
Let's assume the following returns:
Using the formula:
\[ R_m = \frac{5 + 10 + 15 + 20}{4} = 12.5 \]
Calculating the squared differences:
\[ (5 - 12.5)^2 = 56.25, \quad (10 - 12.5)^2 = 6.25, \quad (15 - 12.5)^2 = 6.25, \quad (20 - 12.5)^2 = 56.25 \]
Summing up the squared differences:
\[ 56.25 + 6.25 + 6.25 + 56.25 = 125 \]
Finally, dividing by the number of returns:
\[ V = \frac{125}{4} = 31.25 \]
The Variance of Returns (V) is 31.25.