### Historical Volatilities1

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Phil Walsh
Keymaster

This exercise works through an example of importing historical price data, so that it can be used to calculate historical returns and volatilities.

Market Manager > Time Series > Data Configuration

Select the index as below.

Simply press Next at this stage.

From the screen below, deselect all the grid-points and only check the 4lom grid-point. We will only import historical prices for this grid-point.

After pressing Finish from this screen, File > Save Data Cfgs.

From the main menu in the Market Manager:

Time Series > Analysis Configuration

From this screen, click ‘Series List’.

From the query screen, select the index.

From the resulting screen, we see that there is only one grid-point for this index that we can select.

From the main screen, save this configuration definition, ensuring that historical volatilities will be calculated as a simple average.

From the main menu in the Market Manager:

Time Series > Import > Data

Import the following file:

Return to Analysis Configuration screen and check that the historical values can be view from the menu item below. Check that the data matches the data in the import file

From the menu item below, examine the Log Returns of the historical prices. Can you reconcile the returns in a spreadsheet?

From the menu item below, examine the statistics.

Can you reconcile the standard deviation in Excel?

Under Histogram, double-click on the matrix icon and open the graphical viewer, as shown below.

Plot a graph as shown below. (Optionally – can you replicate the same chart in Excel?)

From the menu item below, examine the Historical Volatility.

Try to reconcile the Historical Volatility in Excel, by following these steps:

• Firstly, for each return value, raise it to the power of 2
• Calculate the average of the squared returns
• Take the square root of this average

The important point to note is that the Historical Volatility, using the simple moving average approach, is not the standard deviation of the returns, but is calculated as described above.

Return to the Time Series Analysis Configuration screen and change the method for calculating Historical Volatility to be an Exponentially Weighted Moving Average.

View > Volatilities > Data

The following spreadsheet can be used to both reconcile the historical volatility using the EWMA approach and, if you were not able reconcile the historical returns or the historical volatility using the simple moving average approach, this spreadsheet can be used.

Ensure that you can follow the workings in the spreadsheet and, for the EWMA, the following tutorial can be revisited if uncertain as to how the EWMA is calculated.

[videoembed type=”youtube” ratio=”sixteen_by_nine” url=”http://www.youtube.com/watch?v=njDi2PMh688&#8243; width=”560″ height=”315″ autoplay=”yes” loop=”yes”]

EWMA

[videoembed type=”youtube” ratio=”sixteen_by_nine” url=”http://www.youtube.com/watch?v=P_tr9_Ue220&feature=channel_page” width=”560″ height=”315″ autoplay=”yes” loop=”yes”]

Optionally – If you are comfortable with the GARCH (1,1) approach to calculating historical volatility, you can attempt to reconcile Endur’s calculation in a spreadsheet.

Now attempt to work through this exercise again, attempting to generate historical returns and volatilities for the 3lom point. Note that the actual data that is imported is not important. Instead focus on ensuring that you can repeat the same relevant steps as earlier AND determine what differences are required for another grid-point.

Finally, for information, it is possible to download actual historical prices as published by the OTC broker Specton,  from the following site.

http://www.spectrongroup.com/

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