Question

1) Describe how the Standard Deviation of a Stock is calculated. (15 points) a. What does the Standard Deviation measure?

Answer 1

Ans 1

1. When we talk about investment the concept of risk measurement place very important role in the finance industry. Traders and analyst use many matrix to measure the relative risk of potential investment, one of the most common being standard deviation.
2. In other words standard deviation is a basic concept that measures volatility in the market, the average amount by which separate data points differ from the mean. Simply put, standard deviation determines the spread of stock prices from their mean price.
3. High standard deviation means high volatility i.e. the prices swing up or down and when there is slight movement in price of a stock it is said to be low volatility and has low standard deviation.

Calculation of standard deviation :-

Step-1 Select the stock.

Step-2 Collect the historical data of stocks closing price over the past five years or so.

Step-3 Calculate the mean of the stocks closing prices.

Step-4 Subtract the mean from individual stock prices and square the results.

Step-5 Now add all the squared values and calculate average by dividing it by the total no. of data points less 1 to obtain the variance.

Step-6 The square root of this variance provides the standard deviation.

The Formula for standard deviation is:-

$\begin{aligned} &\text{Standard Deviation} = \sqrt{ \frac{\sum_{i=1}^{n}\left(x_i - \overline{x}\right)^2} {n-1} }\\ &\textbf{where:}\\ &x_i = \text{Value of the } i^{th} \text{ point in the data set}\\ &\overline{x}= \text{The mean value of the data set}\\ &n = \text{The number of data points in the data set} \end{aligned}$