**Standard Deviation**

**What is Standard Deviation?**

• Standard deviation is a commonly-used measurement of diversity or variability in statistics, finance and probability theory. More specifically, standard deviation will show how much variation is present from the mean or expected value—in finance, it can be applied to transactions or maneuvers. A low standard deviation will indicate that the given data points are very close to the mean, while a high standard deviation indicates that the data are spread over a vast spectrum of values.

• In addition to expressing variables of a given population, standard deviation is also used to measure confidence in statistical conclusions. For instance, the margin of error in polling data is typically determined by calculating the standard deviation, as if the poll were conducted several times.

**Why is Standard Deviation used in Finance?**

• Standard deviation is critical in finance, because the technique can elucidate the rate of return for an investment or transaction. In essence, the standard deviation will yield the underlying investment or transaction’s volatility.

• In finance, standard deviation is used to represent the risk associated with a given security (such as a stock or bond etc.) or the risk of actively managed bundles of securities (such as hedge funds, mutual funds, or ETFs).

• Risk is a primary factor when determining how to manage or invest in securities; risk determines the variation in returns on the investment, which in turn offers a mathematical basis for the investment decision.

• The basic concept of risk is that, as it increases, the expected rate of return for the underlying asset will increase to entice potential investors. Investors, should thus, expect a higher potential rate of return for a riskier investment to obfuscate the uncertainty latent in the purchase. In essence, standard deviation will provide a quantified estimation regarding the uncertainty of future returns.

**Example of Standard Deviation in Finance:**

• Let’s assume that you are choosing between two stocks: stock A and stock B. Over the past 20 years, Stock A has yielded an average return of 10% per year, with a standard deviation of 20 percentage points and Stock B, over this timeframe, has averaged 15% with a standard deviation of 30 percentage points.

• Using this example, on the basis of analyzing risk and return, an investor should decide that Stock A is the safer play because Stock B’s 10 percentage point increase in standard deviation yields a greater risk of uncertainty. As a result, Stock B is more likely to fall short of the initial investment more often than Stock A.

• In this example, Stock A is expected to earn roughly 10 percent, plus or minus 20 percentage points per year—thus the range that Stock A can yield is 30% gains to -10% losses.