## Standard Deviation

### Standard Deviation

In mathematics, standard deviation is the degree of the dispersion from a set of data’s mean. The SD is higher when the data is more stretched. In other terms, the square root of the variance is the standard deviation.

In finance, the representation of standard deviation is associated with the risk in trading securities, such as bonds, property and stock. It is also the risk of ‘portfolio securities’. Therefore, risk is a fundamental tool in evaluating, and managing the portfolios of investments. This as a result determines different returns associated to the assets/portfolio, and helps investors to make the best decision. Overall, investors can expect higher returns when an investment is attached with higher risk levels.

SD can also be used in determining how huge the market movements are if returns are at normal distribution.

An Example:

A mutual fund X gains 1% every month historically, for the past 36 months. The SD is at 0 because of no changes in the returns monthly. However, if the fund X loses 1% each month then it would still have SD at 0. This is because the returns did not vary. On the other hand, if a mutual fund Y gains a return of 5% one month, 25% the second month and suddenly loses 7% the third month it will have a higher SD, because the returns have been very fluctuating.

In most cases, the monthly returns of the funds will fall within a SD of the average returns. The probability of this happening is 68%of the times. While, for returns to fall within 2 SD, the probability of it happening lies at 95%

### Why does SD matter?

SD is not intuitive in nature, and therefore it is not useful for comparisons to make with other trading funds. For this reason, SD should be used with some context. In determining the SD of your funds, first look at the SD of similar funds, and in the same category as yours.

Technical indicators make use of SD as a way to evaluate the future of the stock, whether it is good to sell it off or buy. However, SD is just one way to measure the risk, it should be used with other indicators in deciding whether the worth of stock is risky or not.

### Further Reading

**Multiscale behaviour of volatility autocorrelations in a financial market**

www.sciencedirect.com [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**The forecasting performance of the implied standard deviation in currency options**

www.emerald.com [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**A note on a simple, accurate formula to compute implied standard deviations**

www.sciencedirect.com [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**Isolating the systematic and unsystematic components of a single stock's (or portfolio's) standard deviation**

www.tandfonline.com [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**GINI RATIO AND STANDARD DEVIATION: THE DIFFERENCE OF INDICATING REGIONAL DISPARITY [J]**

en.cnki.com.cn [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**Event studies in economics and finance**

www.jstor.org [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**Multinational corporations vs. domestic corporations: Financial performance and characteristics**

link.springer.com [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**Deregulation and bank financial policy**

www.sciencedirect.com [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**Power laws in economics and finance**

www.annualreviews.org [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …

**Estimating mean-standard deviation ratios of financial data**

www.tandfonline.com [PDF]

… exponent 2β(1)≃0.38 is obtained by the previous scaling analysis of the standard deviation … 1995 R Mantegna, HE StanleyScaling behavior in the dynamics of an economics index. Nature … 1996 A PaganThe econometrics of financial markets. Journal of Empirical Finance, 3 (1996 …