How do I Measure the Volatility of the Stock Exchange in Pakistan?

The volatility of Pakistan's stock exchange can be calculated with the standard deviation of its key stock indices.

Volatility of a stock exchange is measured by calculating the historical volatility of the exchange's main stock indices. In this context, volatility refers to the fluctuations of the stock index on a daily, weekly or monthly basis versus its historical average or, in other words, its standard deviation. In looking at the emerging markets, Pakistan's Karachi Stock Exchange has been subject to periods of high volatility because of social unrest in the country.

Instructions

1. Look up historical prices for Pakistan's key stock index, the KSE-100, on the Internet.

2. Download data for the KSE-100 and input the data into a spreadsheet (via the available .pdf file or .lis file). It is important to gather enough data points to make the volatility calculation meaningful. If you wish to measure daily volatility, for example, download daily stock index closing prices for at least one year of trading days.

3. Calculate the average historical price for the KSE-100 stock index by adding up the data and dividing the sum by the number of data points. This is also called the "mean" and the calculation is significantly easier if it is done in a spreadsheet, such as Excel, instead of using a calculator. Calculating the mean can be achieved in Excel with the "AVERAGE" function.

4. Subtract the mean from each stock index data point collected to calculate the deviation.

5. Calculate the square of each deviation by taking it to the power of 2. In other words, multiply each number by itself.

6. Add up all of the squared deviations.

7. Divide the sum by the total number of data points less 1. For example, if there are 365 pieces of data, divide the sum of the squared deviations by 364.

8. Compute the square root of the number from the prior step. The result of these calculations is the standard deviation.

9. Interpret the results of the standard deviation calculation. For example, a higher number indicates a higher level of volatility for the KSE-100 or, in other words, more significant fluctuations in the KSE-100 index from its average historical closing price.

Tips & Warnings

• The "STDEV" function in Excel will perform the exact same calculation in one step.

References

• The Karachi Stock Exchange
• Stock Charts.com: Standard Deviation (Volatility)