Variance and standard deviation are two important statistical measures used to quantify the risk associated with investment returns.
Variance is often used to describe the degree of spread or dispersion of a set of data points. In the context of investment returns, variance provides a measure of how much the actual returns deviate from the expected or average returns. Specifically, variance is calculated by finding the average of the squared differences between each data point and the mean. The formula for variance is as follows:
$$Variance = \sqrt{(\sum(x_i - x)^2) / (n -1))}$$
where xi is each data point, x is the mean, and n is the total number of data points.
Standard deviation, on the other hand, is the square root of variance. It measures the amount of dispersion of a set of data from its mean, expressed in the same units as the data. Standard deviation is more commonly used than variance as it provides a more easily understandable measure of risk.
In investment terms, standard deviation provides a measure of the volatility or uncertainty of investment returns. A higher standard deviation indicates a wider range of possible outcomes, which means there is a greater potential for both positive and negative returns. Conversely, a lower standard deviation indicates a narrower range of possible outcomes, which means there is less uncertainty and generally less risk involved.
In summary, variance and standard deviation provide a quantitative way to measure the level of risk associated with investment returns. Knowing these statistical measures can help investors understand the potential risks and rewards of different investment options, and make more informed decisions.