6.9 : Standard Deviation

Standard Deviation

Standard deviation is a statistical measure quantifying the degree of variation or dispersion in a set of values. It is particularly useful in finance for assessing the volatility and risk associated with investment returns. By calculating the standard deviation, investors can gain a clearer understanding of how much an investment's returns deviate from the mean return over a given period, thus providing insight into the investment's overall risk profile.

To compute the standard deviation, one must first determine the variance, which is the average of the squared deviations from the mean return. The standard deviation is then obtained by taking the square root of the variance. This transformation makes standard deviation a more intuitive measure of volatility, expressed in the same units as the original data, typically percentage points.

A higher standard deviation indicates a greater level of risk, as it reflects wider variations in returns. Investments with high standard deviations are more volatile, meaning their returns can fluctuate significantly from the average. This implies a higher potential for both substantial gains and considerable losses. In contrast, a lower standard deviation signifies more consistent returns, with less deviation from the mean, suggesting a lower risk level. Investments with low standard deviations are more stable and predictable, making them more suitable for risk-averse investors.

One downside of using standard deviation as a risk measure is that it treats all deviations from the mean—both positive and negative—as risk. This means that above-average returns, which are beneficial to investors, are also considered risky. Consequently, the standard deviation does not differentiate between upside and downside volatility, potentially leading to a conservative risk assessment in scenarios where positive returns are frequent.