By Sean Doherty

Beta calculations can sometimes be confusing, both in terms of how they are actually calculated and what the impact is on the Interest Rate Risk position of the institution.

In financial terms, the Beta (ß) is a number that describes the relation of a particular stock, or a portfolio of stocks, to the financial markets overall. A beta that is positive would indicate a positive correlation to the movement of the overall market; a negative beta would indicate an inverse relationship between the subject stock and the market as a whole. The closer to 1, the more correlated the relationship.

This is very similar to the way beta is used in interest rate risk models. The beta describes the relationship in the movement in price of a particular account type (NIB, NOW, MMDA, etc.) to the movement in the market overall. This is very important in controlling the rate of change in the offering rate for similar assets in a simulated rate movement. For example a beta (ß) of .35, would indicate that the change in a particular account can be expected to move 35 basis points for every 100 basis point move in the market.

This result can be further refined by calculating the beta for rising and declining rate environments independently. This will typically result in a more meaningful simulation and a better overall feel for the true interest rate risk position of the institution.

Understanding the results of the beta calculation should be tested for statistical relevance, generally accomplished through the use of the “coefficient of determination”, better known as the R^{2}, or R-squared. This number should be between 0 and 1, with 0 denoting that the beta does not explain any rate change, and 1 denoting that it perfectly explains the rate change. Although a high R^{2 }value does not necessarily *guarantee* that the data fits the beta, in a simple regression model, the higher the R^{2}, the better. We compensate for this by using a measure of 65% to test the fit of the data. An R^{2 }below this standard is said to be uncorrelated, and in our model, the default beta or one defined by the bank will be used instead.

We find this non-correlation factor to be present most often in accounts that do not track well with interest rates, for example High Yield NOW accounts or Savings accounts that rarely change in rate.

We have found some vendors that further modify the beta by the change in the balance in a particular account. We find this modification unnecessary, and oftentimes results in a worse statistical fit. Modifying the beta by the balance change introduces a less meaningful input into the analysis and considerably reduces its effectiveness.

Beta is not only an excellent tool for making an interest rate risk model more accurate, but it is also a window into your particular institution’s pricing behavior, both in terms of direction and magnitude.