Question

A stock had returns of 16.39 percent, ?6.31 percent, and 23.51 percent for the past three years. What is the standard deviation of the returns?

Answer 1

Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. In finance, standard deviation is a statistical measurement; when applied to the annual rate of return of an investment, it sheds light on the historical volatility of that investment. The greater the standard deviation of a security, the greater the variance between each price and the mean, indicating a larger price range.

Standard deviation = ?[?(X-µ)^2/N-1]

Where,

                X = Value in the data set

                 µ= Sum of all the data sent divided by number of data

               N = Number of data points

Let's find the mean of the numbers

µ = (Sum of numbers in data set)/number of data

   = (0.1639 + -0.0631 + 0.2351)/ 3

   = 0.3359/ 3

   = 0.112

Data (X)	(X-µ)	(X-µ)^2
0.1639	0.0519	0.00270
-0.0631	-0.1751	0.0307
0.2351	0.1231	0.0152
	Total	0.0486

Let's put the values in the formula to find standard deviation

Standard deviation = UNDROOT[0.0486/ (3- 1)]

                                         = UNDROOT[0.0486/ 2]

                                         = UNDROOT[0.0243]

                                         = 0.1559

So standard deviation of numbers is 0.1559 or 15.59%