# 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.

• 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

• 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
• 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