Question

1. Estimate the historical volatility of a stock using the following data. The data show the stock price at the end of each of week over ten consecutive weeks.

12.0, 13.3 11.2, 12.0, 12.7, 13.1, 13.3, 14.5, 14.9, 14.1

Please don't use excel, and show all the calculation steps.

Answer 1

Historical volatility = estimated volatility * (h)^0.5

Where, h = 52 for weekly data

And estimated volatility is the standard deviation of the given data that is given by, sigma,

Where, n is total number of observation

Ui is weekly stock price

U bar is the mean value

Here, mean = (12+13.3+11.2+12+12.7+13.1+13.3+14.5+14.9+14.1)/10

= 13.11

Now let us calculate the standard deviation, ie, estimated volatility,

= (((12-13.11)^2+(13.3-13.11)^2+(11.2-13.11)^2+(12-13.11)^2+(12.7-13.11)^2+(13.1-13.11)^2+(13.3-13.11)^2+(14.5-13.11)^2+(14.9-13.11)^2+(14.1-13.11)^2)/(10-1))^0.5

= (12.469/9)^0.5

= 1.17704

Now, historical volatility is,

= 1.17704 * (52)^0.5

= 8.4878