Worksheet – Case #5 – Calculating the standard deviation interval around a mean

Finding Data

For this example, you need to use US corporate benchmarks from Moody’s. A good way to start is to go into Country &Region.

Go to:

Country & Region > United States > Interest & Exchange Rates > Corporate Benchmarks > Moody’s.

Locate and add:

  • Seasoned, Aaa rated, Average of period
  • Seasoned, Baa rated, Average of period

You will also need the time series displaying recession periods. Go to

Country & Region > United States [us, Region] > Surveys & Leading Indicators > Leading Indicators > NBER

Locate and add:

  • United States, NBER, Business Cycle Reference Dates

For this last series, you can also use the short code nber in Series List.

Analysis

Calculating the spread of the corporate benchmarks

The first step of this example is to calculate the spread between the two corporate benchmarks series.

A quick way to do so is to create a new expression under Series List:

  • Create a new expression in series list: usrate0233 – usrate0232
  • Delete the individual series (usrate0233 and usrate0232) in Series List, as we do not plan to use them.

Mean and standard deviation

You now have to calculate the mean of the spread series, and +1 / -1 standard deviation around it. You can do so using the Statistics Analysis:

  • On the time chart, click on “insert” and add Statistics
  • Besides the spread series click on “Add” and select Mean
  • Tick the box beneath “Std. Dev.” to display a band of +1 / -1 standard deviation around the mean

In the time chart, you will now find the standard deviation as a broad stripe along the chart, with the mean value as a line in the middle.

Creating recession bands

You can now use the recession dates series to display recession bands on the chart:

  • Right-click on the graph and select “Graph Layout”
  • Add a Fill by clicking on it at the top of the window
  • Drag and drop the nber-series beneath Fill
  • Drag and drop Fill above Stripe to move it to the background

Adding an axis value label

To add the last value of the series to the y-axis:

  • Click on the graph line in the chart
  • On the “Presentation properties” tab, locate the window “Content”
  • In the drop-down menu labeled “Axis value label”, select Show

Modifying the opacity of the bands

The recession and Stripe bands can be made slightly transparent:

  • Click on any recession band
  • In “Presentation properties”, change Graph style to Custom in the drop-down menu
  • Click on the button labeled “...” beside Color
  • Change color and opacity to your preference (for instance 30%)
  • Repeat the process for the Standard deviation-stripe

Other changes

  • Title: USA: Corporate Benchmarks spread
  • The legend has been moved to above the chart, centered, with its analysis text removed