Make better lending decisions through data analysis education.

Once we identify which market rates are our driver rates (market rates most strongly correlated with our deposit rates) for our deposits, we next need to determine how our deposits will react when these driver rates change.

A *pricing beta* quantifies the magnitude of *change* the credit union would likely make in response to changes in a driver rate. So if the driver rate increases by 100 basis points, how much of a change, and in what direction, can we expect the deposit rates to change? And how can we find this magnitude of change? Simple linear regression (SLR), of course! The SLR model can be expressed mathematically as

In this model, indexes our data going from 1 to the number of data points we have. The left side of the model, , is the response variable, or the deposit rate. The independent variable, or driver rate, is expressed by . Note that the reason simple linear regression is “simple” is because it only involves one , or input variable. The term is the error, or portion our model doesn’t quite capture. The term is simply an intercept. The most important term is ―the pricing beta.

With pricing betas, an important thing to consider is that deposit rates behave different in rising driver rate environments than in declining driver rate environments. Thus, we need to fit two separate SLRs. The first one uses data from the rising period, and the second uses data from the falling environment. Typically, if the driver rate and the deposit rate are positively correlated, then in rising environments deposit rates tend to respond slower. Conversely, in a declining environment, deposit rates tend to react quicker. If the driver rate is rising, the credit union does not want to have to raise its deposit rates any higher than necessary because that is a liability for them. On the other hand, if the driver rate is falling, then the credit union will want to lower its deposit rates quickly to lower expenses. Let’s just jump into a real example.

Here we have the 30-Year Mortgage Rate Average as our driver rate in blue and the aggregated regular share rate average in orange as our deposit rate. These are the same data used in the final plot in the first installment of this trilogy. This time, though, the plot shows how the two rates behave together over time. We already know the correlation is 0.94 from part I, so it’s no surprise that they essentially move together over time. In this plot, we see the 30-year mortgage rate generally increasing between 2004 and 2008, and beyond 2008 the rate generally declines. The point at which the market rate changes from increasing to decreasing will be the cutoff point that dictates which data points are used in fitting the regression model to get the pricing betas. It looks like somewhere around 2008 will be our cutoff point. Let’s first fit the model in the rising environment.

**2004 - 2008**

Here we have a scatter plot of the data between 2004 and 2008 indicated by the gray dots, and our regression line is indicated by the orange line. And it looks like the model fits the data pretty well when eyeballing it.

When we fit this model, we get a pricing beta of 0.29 (this is the slope of the orange line). Here’s one of the most important parts of this whole process―interpretation.

For every 100 basis point increase in the 30-year mortgage rate average, we expect a 29 basis point increase in the aggregated regular share rate average.

**2008 - 2016**

And here we fit the regression model in the falling driver rate environment above between 2008 and 2016. Again, looks like a pretty good fit.

The beta we obtain in this case is 0.38. Notice that the down beta is larger than the up beta. This isn’t surprising since we know that deposit rates generally react quicker in falling environments. Now, interpretation in this environment is a little trickier.

Recall that the correlation between the two rates was 0.94. Since the correlation was positive, we know the variables move together. And since we’re in a downward environment for the driver rate, we need to adjust our interpretation accordingly. So our interpretation would be for every 100 basis point *decrease* in the 30-year mortgage rate average, we expect a 38 basis point *decrease* in the aggregated regular share rate average.

In the conclusion of our trilogy, we will find the correlations and pricing betas for the four deposit types mentioned in the beginning of our journey.

Product Manager

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