Investment in the financial markets is done in the form of stocks, bonds and currencies. The sole purpose of investment is to gain a positive return, but every investment has inherent risk to losses. In quantitative finance, statistical tools like mean, standard deviation and coefficient of variance are used to determine the performance of stocks and also to make investment decisions.

## Mean and Standard Deviation

Mean and standard deviation are the basic tools used in investing. In statistics, standard deviation determines how much an individual data point deviates from the mean of the total data points, where mean is the arithmetic average of sample points. Arithmetic average or mean is calculated by adding the values of individual data points and then dividing by the total number of sample points.

Mean= (Sum of sample points/total number of sample points). Standard deviation (SD) is determined by taking the square root of variance.

SD= sqrt(variance)

Variance = sum(mean-individual sample point)^2

## Standard Deviation in Investment

Though standard deviation in investment is determined the same way as in statistics, it implies different meaning in investing. It is a measure of risk of individual stocks and the portfolios of assets. The risk inherent in any investment is determined in terms of the volatility of returns. The volatility means the fluctuation in returns of an individual stock over time and also with respect to the portfolio. It is measured in percentage. Large cap individual stocks have standard deviation on average of about 35 percent, while the aggregate large cap stocks have about 20 percent. The standard deviation of large cap stocks is comparable with the standard benchmarks like S&P and NASDAQ.

## Standard Deviation and Rules of Thumb

A practical estimation rule is used to calculate the probabilistic determination of the returns on investment using the average return and the standard deviation. For example, if the average return on investment is 10 percent and the standard deviation is 17 percent, using the rules of thumb, the probability of 10 +/- 17 percent is 68 percent, 10 +/- 34 percent is 95 percent and 10 +/- 51 percent is 98 percent.

## Standard Deviation in Investment Decisions

Standard deviation provides the quantitative information in investing which is indirectly used to reduce the risk of investments. The risk in investment is reduced by diversifying the portfolio which involves buying equities that are negatively co related in terms of returns. The negative co relation means if one stock in the portfolio is performing bad, the other stock does well and vice versa. A good portfolio usually includes small cap and large cap stocks, bonds, commodities and currencies.