A Regression Approach to Estimate Credit Loss

Financial reporting in the U.S. is based on Generally Accepted Accounting Principles (GAAP). One of the pillars of these standards, issued by the Financial Accounting Standards Board (FASB) for private organizations, is the concept of prudence: Do not book future revenues, but do book any future losses that may be reasonably anticipated and quantified. Most accounting under U.S. GAAP aims to present a conservative picture of an entity’s financial position, lest overly optimistic accounting promise results that are unable to be sustained.

One of the recent pronouncements, Accounting Standards Update (ASU) 2016-13, Financial Instruments—Credit Losses (Topic 326), overhauled the accounting for current expected credit loss (CECL). CECL simply refers to credit that an entity does not expect to collect. Each reporting period, the entity is required to estimate and accrue the amount of uncollectible financial assets (such as loans) that will likely default. Whereas the now-superseded GAAP required recognition only if the loss met a probability threshold, ASU 2016-13 requires the reporting entity to recognize the estimated expected credit loss over the entire life of the asset, regardless of the probability of occurrence. For example, assume that an entity extends credit by purchasing a 10-year bond. Following the previous standard, the entity would accrue a loss only when, say, it was probable that a default would occur next year. Under the new standard, however, the entity is required to forecast and accrue the total expected credit loss over the bond’s entire 10-year term in the year of purchase.

The new accounting standard became applicable for public entities with reporting periods commencing after Dec. 15, 2019. Nonpublic entities have until after Dec. 15, 2022, to adopt the ASU. A modified retrospective adjustment with cumulative effects shown only to reporting-period financials is required, and early adoption is permitted.

ASU 2016-13 will have the greatest financial impact on lending institutions, such as banks, because of their businesses’ very nature. However, the ASU is applicable to any entity holding financial assets with contractual payment rights. More information on the impacts of ASU 2016-13 can found in this article by Mark D. Mishler.

The standard poses new challenges by requiring all future credit losses to be estimated and flow through the income statement each reporting period. Certain financial assets have very long holding periods. Circumstances that far into the future can seldom be estimated, but the standard nevertheless requires their consideration. Forecasts relying on a static loss percentage for the entire holding period (e.g., using a 3% loss rate per year) yield inaccurate results.

Moreover, the pronouncement itself provides very broad guidance on loss estimation. It requires losses to be estimated based on “relevant information about past events, including historical experience, current conditions, and reasonable and supportable forecasts that affect the collectability of the reported amount,” stating that an “entity must use judgment in determining the relevant information and estimation methods that are appropriate in its circumstances.” As explained by Arianna Pinello and Ernest Lee Puschaver in their article, ASU 2016-13 brings considerable uncertainty by requiring entities to estimate a variable that is both dependent on several other factors and too far out in the future.

Fortunately, statistical techniques exist that mitigate these challenges. This article presents a statistical approach to estimate credit losses through vector autoregression (VAR).

Basic Regression Equation

Regression modeling is extensively used in accounting research. A regression equation models a dependent variable as a function of one or more independent variables. A basic regression model is as follows:

y = β₀ + β₁(x₁) + β₂(x₂) +⋯ + β_n(x_n) + ε,

where y is the dependent variable and {x_n} (a common notation to denote a set of numbers) represents all independent variables. Changes in any x_n cause a change in y of magnitude β_n. The error term ε represents the part of y that is not explained by {x_n}.

In our context, each period’s expected credit loss is the dependent variable, to be modeled as a function of other variables. Whereas this sounds appealing in theory, a basic but challenging problem in practice is the selection of independent variables. Which variables does an entity choose to accurately estimate CECL? How can an entity be confident that most, if not all, relevant variables have been selected and that the error (ε) is sufficiently small? Both these questions inevitably lead to numerous differences in CECL modeling and widely varying estimates across the industry. The basic regression approach does little, then, to alleviate existing concerns related to applying ASU 2016-13.

Vector Autoregression (VAR)

Assume that company ABC holds debentures (unsecured loans) of another company. ABC regularly reports quarterly financial results and is currently preparing to report Q3 (July-Sept.) information. The issuer works in a dynamic industry, and ABC finds it tedious to ascertain the impact of innumerable factors on estimating Q3 credit loss. However, one thing the company knows for certain is the credit loss incurred on the debentures in Q2. The Q2 credit loss has occurred in the past. Intuitively, it already reflects the impact of all possible factors that could have impacted it. It is much more feasible and accurate to model the Q3 loss as some function of the already occurred Q2 loss because most information value has already been captured by the latter.

This is the fundamental concept of the forecasting technique known as autoregression (AR). AR techniques model future values of a variable as a function of its past values. An AR(p) model, with  lags, has the following equation:

y_t = β₀ + β₁(y_t-1) + β₂(y_t-2)+...…+ β_p(y_t-p) + ε,

where y_t denotes the value of the variable at time t, and the independent variables are lagged (past) values of the variable itself. Assuming the data is monthly, (y_t-1) denotes the variable’s value for the previous month, (y_t-2) for the month before that and so on. AR is particularly suited for estimating variables such as the CECL because it alleviates uncertainty concerns that come with longer periods of time. In addition, two or more variables are frequently correlated to each other, in which case each variable’s AR model can incorporate the other’s lagged values in addition to its own. Both variables are then simultaneously forecasted in a single system of equations, a process known as vector autoregression (VAR).

Case Example

Company ABC holds three types of asset portfolios: Portfolio A is a collection of credit card debt receivables. Portfolio B is composed of mortgage-backed securities (MBS), and Portfolio C contains other miscellaneous debt and off-balance sheet items. Assume, for simplicity, that all assets across each portfolio have the same holding period. ABC knows from experience that the three portfolios tend to be correlated (borrowers defaulting on mortgage payments also likely default on credit card payments, and vice versa). ABC also finds the macroeconomic employment rate to impact the performance of all portfolios. ABC has been in business for 10 years and currently applies a probability threshold before recognizing credit loss, with the intention to adopt ASU 2016-13 in the next reporting year.

Instead of individually estimating the initial and subsequent adjustments for each portfolio, ABC can use a VAR approach to forecast all losses in a combined system. A three-dimensional VAR(1) process is modeled as follows:

A_t = β₀ + β₁(A_t-1) + β₂(B_t-1) + β₃(C_t-1) + β₃(E_t-1) + ε
B_t = β₀ + β₁(A_t-1) + β₂(B_t-1) + β₃(C_t-1) + β₃(E_t-1) + ε
C_t = β₀ + β₁(A_t-1) + β₂(B_t-1) + β₃(C_t-1) + β₃(E_t-1) + ε,

where A_t, B_t and C_t represent estimated credit loss amounts at time t for each portfolio, respectively, as a function of their single-period lagged values and that of the employment rate E.

ABC will initially train the models on the 40 actual credit loss amounts from previous periods (10 years with four quarters each). Based on this data, the VAR system will estimate the magnitude of correlation coefficients ({β_n}). Assume that after training, the system produces the following equation for Portfolio A:

A_t = 1.23 + 2.54(A_t-1) + .38(B_t-1) - .15(C_t-1) + 1.86(E_t-1) + ε.

Based on actual loss data, the VAR model estimates that the current period’s expected credit loss amount for Portfolio A is the sum of $1.23, 2.54 times the previous period’s credit loss for Portfolio A, .38 times that for Portfolio B, -.15 times that for Portfolio C, 1.86 times the previous period’s unemployment rate and some unknown error. It is important to note here that the data consists of actual credit loss amounts and not expected credit loss amounts/allowances. ABC has likely carried a separate CECL allowance for each of the prior periods, but these are not suitable for the system’s initial training.

ABC estimates the credit loss for the next period by plugging in the actual credit loss from the current period. These estimated values now become the basis for forecasting credit losses for the period after, and so on, until losses for each portfolio’s holding period have been estimated.

A_t+1 = β₀ + β₁(A_t) + β₂(B_t) + β₃(C_t) + β₃(E_t) + ε

After adding expected credit losses across the three portfolios, ABC arrives at a total of $50,000 in CECL. Because the current allowance on the balance sheet is $42,000, ABC records an initial $8,000 upward adjustment to CECL via retained earnings. At the next reporting period, ABC reruns the VAR system, this time incorporating the actual credit loss amounts for the initial adoption period. CECL is estimated to be $48,000, but write-offs for the adoption period have reduced the allowance to $46,000. ABC records a $2,000 credit loss expense, increasing the CECL allowance by the same amount.

The VAR approach to estimating CECL has several benefits for ABC:

1. With some initial planning, data preparation and implementation, ABC finds it relatively simple to run the VAR system each reporting period and update the CECL allowance.
2. ABC (and likely the regulator) feels confident that substantial relevant information is being captured by each variable’s past values.
3. ABC can add or remove variables to the VAR model as circumstances change.

Caveats

VAR is a sophisticated forecasting technique that requires considerable testing before implementation. The first step is to analyze the autocorrelation and partial autocorrelation functions (PACFs) of the underlying series, two concepts that are beyond the scope of this article. Typically, tests for trends, seasonality and stationarity around the mean are conducted to implement the optimal number of lags. The system is also typically developed in a statistical software such as R. Knowledge of forecasting techniques and data analysis is a prerequisite to train informative VAR models.

Underlying Concept is Key

Despite numerous variations associated with the VAR process, the underlying concept remains the same: Past values of a variable are strong predictors of future values because they represent the impact of all other factors that could have impacted them. This article presents an overview of VAR modeling that can be valuable to financial reporting professionals who wish to further explore nuances of the technique for implementation purposes. There are also several other forecasting techniques that practitioners can explore to alleviate estimation concerns around ASU 2016-13. It is important to understand that under the new standard, practitioners’ options are not limited to currently established processes for estimating credit losses.