The Lord of the Deposits: The Fellowship of the Rates

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Deposit accounts provide funds for credit unions, but these come at a cost to the credit unions in the form of deposit or dividend rates (note that not every credit union provides dividend rates, and this blog series will focus on those that do).  Thus, credit unions want to maintain an ongoing balance of rates that are low costs for them, but still attractive to their members. Because deposits provide funding for other areas of activity for credit unions, it’s important to maintain that balancing act with the dividend rates. An important factor that can help in understanding dividend rate behavior for maintenance is market or economic rates. Economic rates provide key insight into what credit unions can expect from their members in a general sense, and for asset/liability management.

 

Understanding deposit rate behavior in response to market rate behavior is crucial, and management must consider economic rates in deposit pricing. The question is, which economic indicators should we be paying attention to most? Furthermore, once identified, how can we quantify the reaction of deposit pricing to economic changes? We’ll address these issues in this three-part blog series.

 

This epic trilogy will focus on four deposit types. We chose these four because they are common amongst most credit unions.  The first three are non-maturing deposits: regular shares, share drafts, and money market shares. The last is share certificates.dep1.png

In the table above we can see some of the features of each deposit type along with their most recent average rates. Share drafts have the lowest current average of 0.19%, followed by regular shares at 0.24%, followed by money market shares at 0.27%, and ending with share certificates at the highest at 0.67%. It should be noted that the data used for this trilogy come from NCUA call report data with the most recent data coming from Q3 of 2016 and the earliest date going back about 13 years.

 

As previously stated, it’s important for managerial purposes to understand the relationship between economic or market rates and deposit rates. This relationship is what’s known as correlation.

 The correlation between two variables, such as deposit rates and market rates, is a statistic that measures the interdependence between the two variables, or rather, the linear relationship. That is, it is a standardized measurement of how two variables change together. For example, as one variable increases, the other variable will tend to either increase, decrease, or not change at all. Correlation exists on a continuous scale from -1 to 1. A correlation of 0 implies the two variables are independent of each other; that is, a change in one variable implies nothing about the change in the other variable. A correlation of 1 implies that as one variable increases, the other variable will increase exactly in a linear fashion. A correlation of -1 implies the opposite; as one variable increases, the other exactly decreases linearly. Though, due to variation in data and measurement error, getting exactly -1,1 or 0 just doesn’t happen in real life. But you can get close! Let’s go over the mathematical definition and how to interpret correlation coefficients.

dep2.png

dep5.png

 

The sample correlation coefficient symb1.png  is a measure of the direction and strength of the linear relationship between variables, symb2.png  and symb3.png.  The right side of the equation tells us exactly how to get the correlation coefficient. While it may look like a lot of math, it’s really just a bunch of multiplication, division, addition, and subtraction.

 The terms to be aware of in this formula are symb4.png, which indexes the data you input into the formula,symb5.png, which is the number of data points (or number of symb2.png,  symb3.png pairs),  symbol_xi.png and symbol_yi.png, which are the  symbol_ith.png values of the symbol_x.png and symb3.png variables respectively, and symbol_xbar.png and symbol_ybar.png (pronounced “x-bar” and “y-bar”), which are the respective averages of the symb2.png variable and the symb3.png variable.

 Again, this statistic exists on a continuous scale between -1 and 1, which makes it very nice for interpretation. The sign of the correlation coefficient indicates the direction of the relationship. For example, if symb3.png tends to increase as symb2.png tends to increase, then symb1.png will be positive. Conversely, if symb3.png  tends to decrease as symbol_x.png tends to increase, then symb1.png will be negative. To determine the strength of the linear relationship, we look to the magnitude of the correlation coefficient. And by magnitude we mean the number itself; ignore the sign of symb1.png. The closer the magnitude is to 1, the stronger the relationship is.

 One thing to point out is that up to this point we’ve been careful to highlight the word linear. The linear part is extremely important. The correlation coefficient is only good for measuring linear relationships. Let’s look at some examples to understand why this is important.

dep3.png

In the plot above, we see a bunch of simulated orange data points scattered about. Judging by the way the orange dots are distributed, you can easily make a straight line with your mind going from the bottom left to the top right of the plot. If we plug in the values of symb2.png and symb3.png from the plot into the mathematical definition, we get that the correlation is 0.98. This makes sense. As symb2.png (on the horizontal axis) increases, symb3.png (on the vertical axis) also increases, and it tends to do so in a constant manner. So clearly there is a positive trend, and as the 0.98 indicates, this is a very strong relationship (i.e. you can easily draw a straight line through the data in your mind). Let’s look at another example.

dep4.png

In this next plot above, we see a few things change. For one, as the symb2.png values increase, it appears the symb3.png values decrease. So we would expect a negative correlation. Also notice the spread of the data points. The data points in the first plot seem to be close together whereas the data points in this plot seem to be more spread out. Thus, we expect the strength of the relationship to be a little weaker. Now, if we use our formula again, we find that the correlation coefficient is -0.67, which again makes sense. It’s still pretty easy to draw a straight line in our minds, but this time the line is going in a downward direction. Let’s do a trickier and more extreme example that illustrates the importance of stressing that the correlation coefficient measures the strength of the LINEAR relationship between symb2.png and symb3.png.

deposit17.png

Now try to draw a line in your mind that follows the data in this next plot. That line is no longer straight. In fact, the line is pretty severely curved. However, the line is still following a positive trend. That is, as symb2.png values increase, the symb3.png values also increase. It’s just no longer in a constant manner.

 

Drawing the line this time was extremely easy. That’s because of how strong the relationship between symb2.png and symb3.png is. Another way to think about the relationship is for a given value of symb2.png, how strong of an idea do we have of what the symb3.png value is? In this case, for a given value of symb2.png, we know exactly what  will be. Clearly symb3.png is a function of symb2.png, which implies a perfect relation. However, if we use the correlation formula, we get a correlation of 0.86. Since the trend is positive, and we have a perfect relationship, shouldn’t the correlation be 1? Well, the formula from before is a expecting a linear relationship. The curve is throwing it off, so it fails to capture the truth in this situation. This is a clear case of when the correlation coefficient is not the best tool for measuring the relationship between two variables. As a side note, there do exist other cool tools we could use to measure a relationship like the one in this plot, but we’ll leave that for another time.

 

This example shows why it is extremely important when it comes to your own deposits data to examine the relationship between your deposit rates and market rates before deciding a correlation is the perfect way to summarize the relationship. Let’s look at one last example.

deposit18.png

Now try to draw a line in this plot above. Well, there isn’t a clear trend, so drawing a line is pretty difficult in this situation. As symb2.png increases, symb3.png could be just about anything. Using the formula, we get a correlation of -0.04, which is very close to 0. Thus, we have an extremely weak relationship, and since it’s so weak, the direction honestly doesn’t really matter all that much. Now let’s take a look at an example using actual data.

deposit19.png

Here we have a scatterplot of the 30-Year Fixed Rate Mortgage Rate Average along the horizontal axis, and the aggregated regular share rate average of all active credit unions along the vertical axis. This plot looks pretty similar to one of the examples we looked at earlier. It looks like we have a strong, positive linear relationship between the two rates. This means that as the 30-year mortgage rate tends to increase, the average aggregated regular share rate also tends to increase linearly. So we should expect a large positive number. And in fact, we get a correlation of 0.94. 

 Here’s an interesting scenario. If we’re in a declining market rate environment and want to get ahead of the curve, could we increase just one deposit rate to attract more members while keeping the other deposit rates really low to save on expenses? Well, no. That would result in that one deposit type cannibalizing the others. If one of your deposit rates is significantly higher than the others, then members are more likely to move their money into that account. Again, it’s all about that balancing act.

 Now that we know what correlation is, and how to calculate it, we want to find the correlation for various combinations of deposit and market rates to see which ones are most strongly correlated to help with asset liability management. In the upcoming sequel blogs, the market rates most strongly correlated with the deposit rates will be referred to as driver rates. Stay tuned for that in part III .


Keaton Baughan

Product Manager


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