Expected Loan Loss Provisioning: An Empirical Model*

Yao Lu The University of Chicago Booth School of Business

yao.lu@chicagobooth.edu

Valeri Nikolaev The University of Chicago Booth School of Business

valeri.nikolaev@chicagobooth.edu

Abstract Understanding the economic consequences of untimely provisioning for loan losses is of significant interest to accounting academics and bank regulators. We argue that the existing approach to understanding the timeliness (i.e., quality) of loan loss provisioning developed under the incurred loss standard (FAS 5) is not applicable under the newly adopted expected loss standard. To address this, we develop and validate a model of expected loan loss provisioning that relies on concurrent bank- and macro-economic indicators of future losses. The estimated allowance for expected losses following from the model is an order of magnitude more powerful in explaining future losses compared to the reported numbers, and it also possesses a significant amount of value-relevant information not reflected in the reported numbers. Our model provides insights into the pro-cyclicality of loan loss provisioning. Unlike the reported provisions for loan losses, the estimated provisions for expected losses behave in a counter-cyclical fashion. We also offer and validate a bank-year measure of under-provisioning for loan losses, which is a direct measure of the timeliness of loan loss provisioning. We apply this measure and find evidence consistent with under-provisioning having real effects with respect to banks’ lending, financing, and dividend decisions and, ultimately, their viability.

First version: November 2017 This version: May 2018

____________________ *We gratefully acknowledge financial support from the University of Chicago Booth School of Business. We thank John Gallemore, Sudarshan Jayaraman, Thomas Rauter, Stephen Ryan, Sehwa Kim, and seminar participants at the Ohio State University for helpful comments.

1

1. Introduction

Loan loss provisioning has been the subject of a long-standing policy debate because of

its pro-cyclical impact on banks’ regulatory capital. At the center of this debate is the question of

the timeliness of loan loss provisioning. The lack of timely reporting of loan losses overstates a

bank’s true economic capital and, arguably, increases the pro-cyclicality of banks’ lending

(Laeven and Majnoni 2003). Some observers argued that the delays in loan loss provisioning

magnified the severity of financial crisis of 2008 (GAO 2013). The Financial Accounting

Standards Board recently made a historic change in how banks and other financial institutions

must account for losses on their loan portfolios (ASC 326-20). The new standard (effective as of

the end of 2019) requires provisioning for expected losses. It replaces the incurred loss approach

(FAS 5), under which losses are accounted for only after a loss impairment event, i.e., when

probable. This model has been subject to criticism that it limits a bank’s ability to record losses

that do not yet meet the probable threshold but that are expected. Thus, the new standard aims to

improve the timeliness of loan loss provisioning by incorporating information about expected

losses. Similar changes in loan loss accounting are taking place internationally, with the adoption

of IFRS 9.

The economic consequences of expected vs. incurred loan loss provisioning are of

significant interest to academics, accounting standard setters, and bank regulators (Dugan 2009,

Acharya and Ryan 2016). The key questions of interest include the following: Does the

recognition of expected vs. incurred losses on a bank’s portfolio affect banks’ behavior outside

of recessionary periods? Does expected loan loss provisioning reduce the severity of economic

downturns? Are provisions for expected losses reported under the new regime more likely to lead

to regulatory capital manipulations? Academic studies relevant for answering these questions

2

have started to emerge over the past decade (e.g., Beatty and Liao 2011; Bushman et al. 2012,

2015). These studies find that delayed recognition of loan losses under the incurred loss

approach adversely affects banks’ solvency and stability. However, our knowledge in this area is

still limited. To further understand the economic consequences of expected loan loss

provisioning and answer the above questions, it is necessary to use an empirical model of

expected loan loss provisioning. The existing approach to measuring the timeliness of reported

losses, which was developed under the current accounting standards (FAS 5), is not applicable to

evaluating the quality and timeliness of loan loss accounting under the new reporting regime.

The timeliness of loan loss provisioning under the incurred loss approach is conceptually

distinct from the notion of timeliness under the expected approach. A bank can be timely in

recognizing incurred losses while untimely with respect to expected losses. Under the incurred

(expected) loss approach, the timeliness of reported provisions must be judged by the extent to

which reported provisions reflect incurred losses (expected losses). Incurred losses are expected

losses conditional on loans being subject to adverse credit events and are typically realizable

within the next accounting period (year or a quarter), or soon thereafter. Accordingly, the

timeliness of incurred loss provisioning is judged by the extent to which provisions reflect the

current and one-period-ahead non-performing loans, i.e., proxies for incurred losses (Beatty and

Liao 2011). This approach is not suitable for measuring the timeliness of expected provisioning

because future non-performing loans or future realized losses, when measured over a relatively

long period, cannot be used as a proxy for expected losses without assuming perfect foresight.1

1 Timeliness is measured by regressing LLP on future loan losses and other control variables. This approach is generally problematic because a low coefficient on future losses (or low R-squared) need not imply poor timeliness (or a failure to incorporate information about expected losses). A low coefficient is also consistent with provisions rationally incorporating all available forward looking information about future losses, but with losses being difficult to predict. The more difficult it is to predict future losses based on current information, the lower the coefficient on future realizations (and R-squared) will be.

3

Consequently, the inability of future non-performing loans (or realized losses) to explain current

provisions is directly linked to the predictability of future losses, i.e., uncertainty. Predictability

(uncertainty) is very different from timeliness as it has little to do with accounting measurement.

Hence, measuring the timeliness of expected loss provisioning requires a different approach – the

one that measures expected losses.

We propose and validate an empirical model useful for estimating expected loan loss

allowances and provisions and for evaluating reporting timeliness under the expected loss

approach. The model generates a firm-year measure of the degree to which banks’ reported

numbers under-provision for expected losses and hence overstate their real economic capital.

We use this model to take a step towards understanding the economic consequences of expected

vs. incurred loan loss provisioning, including their effects on the pro-cyclicality of provisioning

and on banks’ real decisions.

Under the expected loss approach, the balance sheet allowance must reflect the present

value of future expected losses on the existing loans, conditional on forward-looking information

available to accountants as of that time. Provision for expected losses, in turn, is equal to losses

realized in a given period plus change in expected losses over this period. To estimate the

expected loan losses, we model future expected default rates on a given portfolio of loans as a

function of concurrent bank-specific and macro-economic forward-looking indicators. We apply

the estimated default rates to expected loan balances, adjusted for attrition due to defaults to

estimate future expected losses, and calculate their present value to determine the allowance and

provision for expected losses. We acknowledge that our approach relies on several strong

assumptions which are discussed in more detail in Section 2. One such assumption is that,

conditional on the information at a given point in time, expected loan losses over our prediction

4

horizon are on average uncorrelated with changes in loan portfolio composition.2

We estimate the model and perform two sets of tests to validate its performance. First, we

show that the estimated allowance for expected losses is significantly more effective at

anticipating medium run losses than is the reported allowance, which has very little power to

predict loan losses measured over extended horizons. Second, we show that the estimated

allowance and provision for expected losses contains significant amounts of value-relevant

information not reflected in the reported numbers. Overall, our model considerably outperforms

the current provisioning.

We use our model to investigate the pro-cyclicality of expected loan loss provisioning,

which has been a widely debated issue. Acharya and Ryan (2016) pointed out that the proposed

expected loss model might not be able to suppress the volatility of banks’ operations over the

business cycle because it requires accurate forecasts of cycle turns and other factors affecting

future loan losses. We find that the estimated provision for expected loan losses is counter-

cyclical, in contrast to the reported pro-cyclical provision for incurred losses. We also observe

that expected provisions exhibit a more pronounced “income smoothing” property – a positive

correlation between earnings before provision and provisions for expected loan losses. Such

result, however, cannot be attributed to earnings manipulations but is a natural property of

expected loan loss provisioning. These findings are in line with an improved timeliness of

expected loss provisions and with the conventional wisdom that more forward-looking

provisions vary less with the business cycle.

To get at the notion of the timeliness of loan loss provisioning, we use our model to

construct a firm-year measure of under-reserving (under-provisioning) for expected loan losses:

2 The reader needs to bear this assumption in mind when interpreting the results. Ryan and Keeley (2013) show that portfolio composition changes over time. However, the assumption that portfolio composition is relatively stable for a given bank and over given five year periods (which are our prediction horizons) is a useful approximation.

5

the difference between expected and reported allowance for loan losses computed at a given

balance sheet date. To demonstrate that this proxy measures the timeliness of expected losses, we

show that banks with a higher degree of under-reserving predictably report lower earnings and

capital levels in the subsequent three years (which indicates that the lack of timeliness in

reported provisions is predictable). We also show that banks with a greater degree of under-

reserving for expected losses at the end of 2007 suffered a significantly more negative stock

performance and significantly lower loan growth as the financial crisis of 2008 unfolded. This

effect, however, is not present outside of the financial crisis period.

We use the measure of under-reserving for expected losses to further our understanding

of the real effects of under-provisioning for expected loan losses. First, we explore whether the

degree of under-provisioning is associated with banks’ real decisions. We take the perspective

that managers of financial institutions understand expected losses on their loan portfolios even if

they are not required to report them (Benston and Wall 2005). Thus, banks’ lending and

financing decisions should be based on the level of expected losses, not just on the portion of

these losses that banks are required to report. In a world without agency problems, a bank’s

economic decisions are expected to depend on the level of true economic capital, which reflects

expected losses in general and not just their incurred portion. For example, greater expected

losses translate into lower economic capital and hence should adversely affect banks’ willingness

to extend new loans. However, if we hold the amount of real capital constant, i.e., controlling for

expected losses, does the degree of under-reserving for expected losses explain banks’ decisions?

Since capital requirements are based on reported, not expected, numbers, under-reserving for

expected losses (which amounts to overstating real capital) gives a bank incentive (and

opportunity) to expand its balance sheet by issuing more loans and increasing liabilities thereby

6

leading to increased risk-taking outside recessions (Bertomeu, Mahieux, and Sapra 2017). We

show that (controlling for the amount of expected losses), the degree of under-provisioning

exhibits a significant positive association with the amount of new loans issued, an increase in

banks’ liabilities and leverage, and a higher level of dividend payouts in the subsequent year.

Furthermore, under-reserved banks exhibit slower reactions to GDP shocks, i.e., they are

less likely to cut back on lending and reduce leverage when the economy slows down, and they

are less likely to expand lending in response to new investment opportunities. Finally, we

explore whether under-provisioning for expected losses affects banks’ viability. If under-

provisioning distorts banks’ real decisions, it should also be associated with banks’ higher

probability of failure in the subsequent years. We find evidence in support of this prediction.

Provisioning for loan losses, which is the banks’ dominant accrual, is one of the key

determinants of the informativeness and transparency of banks’ financial statements (Bushman

2016). We contribute to the literature in several ways. First, we develop and validate a new

approach to measuring the allowances and provisions for expected loan losses on a bank’s loan

portfolio. This approach addresses limitations of the existing measure of loss timeliness when

applied under the new reporting regime. Our study complements Harris, Khan, and Nissim

(2018), who model an expected loss rate over a 12-month period as a function of bank portfolio

characteristics. Our approach differs in several important ways: First, it reflects the present value

of long-run (life-time) expected losses and, as a result, it generates an estimated allowance and

provision for expected losses; second, due to the focus on long-run losses, it combines regression

with elements of a structural approach; third, it incorporates macro-economic fluctuations in

expected loan losses to address the pro-cyclicality of loan loss provisioning. Accordingly, we

show that the estimated expected loan loss provisions are not pro-cyclical and exhibit a greater

7

positive correlation with earnings before provision.

Second, based on our model, we offer a firm-year measure of banks’ under-reserving for

expected losses, which is also a bank-year measure of the timeliness of provisioning for expected

losses. Our validation tests indicate that under-reserving banks exhibit lower future accounting

performance and capital and were also more severely affected by the financial crisis of 2008.

Third, we provide evidence consistent with under-provisioning for expected losses (under the

current reporting practice) distorting banks’ investment, financing, and payout decisions. Under-

provisioning banks appear to be more aggressive in their lending and financial policies and are

more likely to fail. These results complement recent evidence that forward-looking provisioning

reduces risk taking and improves bank stability (Beatty and Liao 2011; Bushman and Williams

2012, 2015). However, these studies investigate the timeliness (forward-looking nature) of

provisioning for incurred/probable losses (i.e., losses reflected in changes to current and

subsequent period’s non-performing loans) and do not evaluate the degree of provisioning for

expected loan losses. The latter is a different construct, as timely provisioning for incurred losses

can be rather untimely under the expected loss approach.

Our study should be of interest to accounting standard setters and financial regulators.

We provide evidence that a simple model of the expected loan losses generates provisions and

allowances that are significantly timelier compared to the current reporting practice. Additionally,

our evidence supports the view that provisioning for expected loan losses exhibits lower pro-

cyclicality and is in fact counter-cyclical. In line with this finding, our evidence also indicates

that expected loss recognition reduces the cyclicality of banks decisions.

The rest of the paper is organized as follows. Section 2 lays out the model. Section 3

describes the data and implementation. Section 4 validates the model and explores expected loss

8

pro-cyclicality. Section 5 explores the pro-cyclicality of expected loan loss provisioning. Section

6 validates the measure of under-reserving for expected losses. Section 7 explores possible

economic consequences of under-reserving on banks’ decisions and bank failures. Section 8

concludes.

2. Modeling expected loan losses.

In this section, we lay out our empirical approach to modeling expected loan losses.

Subsequently, we will discuss how this approach reconciles with prior models that measure the

timeliness and forward-looking nature of loan loss provisioning.

2.1. A model of expected loan losses.

Expected losses 𝐸𝐸𝐸𝐸𝑡𝑡 on portfolio of loans 𝑤𝑤𝑡𝑡 can be written as:

𝐸𝐸𝐸𝐸𝑡𝑡 = E𝑡𝑡[𝐸𝐸𝑡𝑡𝑡𝑡+1 + 𝐸𝐸𝑡𝑡𝑡𝑡+2 + 𝐸𝐸𝑡𝑡𝑡𝑡+3 … |𝐼𝐼𝑡𝑡], (1)

where 𝐸𝐸𝑡𝑡𝑡𝑡+𝑘𝑘 are losses on the portfolio of loans in place at the end of period 𝑡𝑡 realized during the

period 𝑡𝑡 + 𝑘𝑘, and where 𝐼𝐼𝑡𝑡 is the information available at time 𝑡𝑡. Expected losses on a loan

portfolio are not the same as expected (net) charge-offs:

E𝑡𝑡[𝐸𝐸𝑡𝑡𝑡𝑡+1 + 𝐸𝐸𝑡𝑡𝑡𝑡+2 + 𝐸𝐸𝑡𝑡𝑡𝑡+3 … |𝐼𝐼𝑡𝑡] ≠ E𝑡𝑡[𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+1 + 𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+2 + 𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+3 … |𝐼𝐼𝑡𝑡].

This is because 𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+𝑘𝑘 are associated with portfolio 𝑤𝑤𝑡𝑡+𝑘𝑘, which reflects changes in the

portfolio 𝑤𝑤𝑡𝑡 due to new issuance, defaults, or repayments. The two sides of the above equation

are only equal if a bank continues to hold its current portfolio, allowing loans to default or

mature (and does not issue new loans).

To model expected losses, it is thus necessary to fix the portfolio of loans in place at time

𝑡𝑡 and only allow for changes due to attrition (accumulation of defaults) and maturities. This

necessitates using elements of a structural approach. We begin by noting that 𝐸𝐸𝑡𝑡𝑡𝑡+𝑘𝑘 = 𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+𝑘𝑘

holds for 𝑘𝑘 = 1 since portfolio changes within the year 𝑡𝑡 + 1 are unlikely to cause defaults

9

within the same year (and are relatively small). Thus, we can compute the following default (loss)

rate:

𝑝𝑝𝑡𝑡+1 ≡𝐿𝐿𝑡𝑡𝑡𝑡+1

𝐵𝐵𝑡𝑡= 𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+1

𝐵𝐵𝑡𝑡

This rate is useful because it allows for modeling the expected default rate 𝑝𝑝𝑡𝑡+1|𝑡𝑡 =

𝐸𝐸 �𝐿𝐿𝑡𝑡𝑡𝑡+1

𝐵𝐵𝑡𝑡�𝐼𝐼𝑡𝑡� = 𝐸𝐸 �𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+1

𝐵𝐵𝑡𝑡�𝐼𝐼𝑡𝑡�, as well as the future expected default rate

𝑝𝑝𝑡𝑡+𝑘𝑘|𝑡𝑡 = 𝐸𝐸�𝑝𝑝𝑡𝑡+𝑘𝑘|𝑡𝑡+𝑘𝑘−1�𝐼𝐼𝑡𝑡� = 𝐸𝐸 �𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+𝑘𝑘𝐵𝐵𝑡𝑡+𝑘𝑘−1

�𝐼𝐼𝑡𝑡� as a function of information 𝐼𝐼𝑡𝑡. We apply these

expected default rates to the gross book value 𝐵𝐵𝑡𝑡 of loans in the portfolio to obtain the following

estimates of expected losses:

𝐸𝐸[𝐸𝐸𝑡𝑡𝑡𝑡+1|𝐼𝐼𝑡𝑡] = 𝑝𝑝𝑡𝑡+1|𝑡𝑡𝐵𝐵𝑡𝑡, (2a)

𝐸𝐸[𝐸𝐸𝑡𝑡𝑡𝑡+2|𝐼𝐼𝑡𝑡] = 𝑝𝑝𝑡𝑡+2|𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝐸𝐸[𝐸𝐸𝑡𝑡𝑡𝑡+1|𝐼𝐼𝑡𝑡]) = 𝑝𝑝𝑡𝑡+2|𝑡𝑡(1 − 𝑝𝑝𝑡𝑡+1|𝑡𝑡)𝐵𝐵𝑡𝑡, (2b)

𝐸𝐸[𝐸𝐸𝑡𝑡𝑡𝑡+3|𝐼𝐼𝑡𝑡] = 𝑝𝑝𝑡𝑡+3|𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝐸𝐸[𝐸𝐸𝑡𝑡𝑡𝑡+1|𝐼𝐼𝑡𝑡]− 𝐸𝐸[𝐸𝐸𝑡𝑡𝑡𝑡+2|𝐼𝐼𝑡𝑡]) = 𝑝𝑝𝑡𝑡+3|𝑡𝑡(1 − 𝑝𝑝𝑡𝑡+2|𝑡𝑡)(1 − 𝑝𝑝𝑡𝑡+1|𝑡𝑡)𝐵𝐵𝑡𝑡,

… (2c)

𝐸𝐸[𝐸𝐸𝑡𝑡𝑡𝑡+𝑘𝑘|𝐼𝐼𝑡𝑡] = 𝑝𝑝𝑡𝑡+𝑘𝑘|𝑡𝑡(1 − 𝑝𝑝𝑡𝑡+𝑘𝑘−1|𝑡𝑡) × … × (1 − 𝑝𝑝𝑡𝑡+1|𝑡𝑡)𝐵𝐵𝑡𝑡, (2d)

where 𝑝𝑝𝑡𝑡+𝑘𝑘|𝑡𝑡 = 𝐸𝐸 �𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡+𝑘𝑘𝐵𝐵𝑡𝑡+𝑘𝑘−1

�𝐼𝐼𝑡𝑡� is an expected future default rate for the period 𝑡𝑡 + 𝑘𝑘, conditional

on the information at time 𝑡𝑡.

This formulation is intuitive. Expected losses in period 𝑡𝑡 + 𝑘𝑘 are equal to the

corresponding expected default rates times the beginning-of-period loan balance adjusted for

prior expected defaults. This approach allows holding the current loan portfolio fixed while

taking into account the reduction in portfolio balance due to attrition (we discuss how we deal

with maturities later).

10

An important assumption that underlies the model above is that the expected default rates

𝑝𝑝𝑡𝑡+𝑘𝑘|𝑡𝑡 are applicable to current portfolio book value 𝐵𝐵𝑡𝑡 adjusted for expected defaults. This

requires that the composition of loans in a bank’s portfolio does not systematically change over

the prediction horizon 𝑘𝑘. This would be the case if changes in loan portfolios were non-

systematic or proportional (𝑤𝑤𝑡𝑡+𝑘𝑘 ∝ 𝑤𝑤𝑡𝑡) so that the composition stays, on average, the same over

time. We acknowledge that this is a strong assumption. Relaxing this assumption would require

adjusting expected default rates for expected changes in portfolio composition. However,

implementing such adjustments is difficult as it would require observability of loan losses by

loan vintages and type, which is not currently a reporting requirement.

The model of expected loan losses allows us to define and calculate the allowance for

expected losses:

𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡 = 𝐸𝐸 �𝐿𝐿𝑡𝑡𝑡𝑡+1

1+𝑟𝑟𝑡𝑡+ 𝐿𝐿𝑡𝑡

𝑡𝑡+2

(1+𝑟𝑟𝑡𝑡)2 + 𝐿𝐿𝑡𝑡𝑡𝑡+3

(1+𝑟𝑟𝑡𝑡)3 + ⋯+ 𝐿𝐿𝑡𝑡𝑡𝑡+𝑇𝑇

(1+𝑟𝑟𝑡𝑡)𝑇𝑇 |𝐼𝐼𝑡𝑡�, (3)

where 𝑇𝑇 is the average remaining time to maturity for the loans in the current portfolio. For

practical considerations, we set 𝑇𝑇 to five years (estimating expected losses over longer horizons

is likely unreliable and so we do not explore this in the current version of the paper).

Once we have estimated the amount of expected losses at a given point in time, we can

also estimate the provision for expected losses, 𝐸𝐸𝐸𝐸𝐿𝐿𝐸𝐸𝑡𝑡. The provision for expected loan losses is

defined as losses realized over a period plus an increase (decrease) in the present value of

expected loan losses:

𝐸𝐸𝐸𝐸𝐿𝐿𝐸𝐸𝑡𝑡 = 𝐸𝐸𝑡𝑡−1𝑡𝑡 + 𝐸𝐸 �𝐸𝐸𝑡𝑡𝑡𝑡+1

1 + 𝑟𝑟𝑡𝑡+

𝐸𝐸𝑡𝑡𝑡𝑡+2

(1 + 𝑟𝑟𝑡𝑡)2… |𝐼𝐼𝑡𝑡� − 𝐸𝐸 �

𝐸𝐸𝑡𝑡−1𝑡𝑡

1 + 𝑟𝑟𝑡𝑡−1+

𝐸𝐸𝑡𝑡−1𝑡𝑡+1

(1 + 𝑟𝑟𝑡𝑡−1)2 … |𝐼𝐼𝑡𝑡−1�

≡ 𝑁𝑁𝑁𝑁𝑁𝑁𝑡𝑡 + 𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡 − 𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡−1, (4)

11

In order to implement the model, we need to estimate the bank specific expected loss

rates 𝑝𝑝𝑖𝑖𝑡𝑡+𝑘𝑘|𝑡𝑡. Suppose the information set 𝐼𝐼𝑖𝑖𝑡𝑡, available to accountants at the time when they

estimate losses, consists of a vector of variables, 𝑦𝑦𝑖𝑖𝑡𝑡. We model expected default probabilities by

running the following non-linear regression for subsamples of different bank size:

𝑝𝑝𝑖𝑖𝑡𝑡+𝑘𝑘 = 𝑝𝑝𝑖𝑖𝑡𝑡+𝑘𝑘|𝑡𝑡 + 𝜖𝜖𝑖𝑖𝑡𝑡+𝑘𝑘 = exp(𝑦𝑦𝑖𝑖𝑡𝑡𝛽𝛽𝑘𝑘) /(1 + exp(𝑦𝑦𝑖𝑖𝑡𝑡𝛽𝛽𝑘𝑘)) + 𝜖𝜖𝑖𝑖𝑡𝑡+𝑘𝑘, (5)

where 𝑝𝑝𝑖𝑖𝑡𝑡+𝑘𝑘 = 𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖𝑡𝑡+𝑘𝑘/𝐵𝐵𝑖𝑖𝑡𝑡+𝑘𝑘−1 is the realized charge-offs rate, 𝑘𝑘 = 1,2, … ,𝑇𝑇. We use the

estimated regression coefficients to calculate expected future default probabilities conditional on

the information available at time 𝑡𝑡:

𝑝𝑝𝑖𝑖𝑡𝑡+𝑘𝑘|𝑡𝑡 =𝐸𝐸[𝑝𝑝𝑖𝑖𝑡𝑡+𝑘𝑘|𝐼𝐼𝑖𝑖𝑡𝑡] = exp�𝑦𝑦𝑖𝑖𝑡𝑡′ �̂�𝛽𝑘𝑘� /�1 + exp�𝑦𝑦𝑖𝑖𝑡𝑡′ �̂�𝛽𝑘𝑘��. (6)

We subsequently substitute these quantities from equations (2a)-(2d) into equation (3) to

calculate future expected losses and their present value, 𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸𝑖𝑖𝑡𝑡. To measure the discount rate,

we use the concurrent interest rate on the loans in portfolio 𝑟𝑟𝑡𝑡.3 Subsequently, we use equation (4)

to estimate 𝐸𝐸𝐸𝐸𝐿𝐿𝐸𝐸𝑖𝑖𝑡𝑡.

We include the following variables into the information set used to estimate the model:

𝑦𝑦𝑖𝑖𝑡𝑡′ = (𝑝𝑝𝑖𝑖𝑡𝑡,∆𝑝𝑝𝑖𝑖𝑡𝑡, 𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝑖𝑖𝑡𝑡 ,∆𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝑖𝑖𝑡𝑡,𝑁𝑁𝐴𝐴𝐸𝐸𝑖𝑖𝑡𝑡 ,𝐿𝐿𝐼𝐼𝑃𝑃𝑡𝑡𝑃𝑃𝑃𝑃𝐼𝐼90𝑖𝑖𝑡𝑡 ,∆𝑟𝑟𝑖𝑖𝑡𝑡,∆𝐺𝐺𝐺𝐺𝐿𝐿𝑡𝑡,

𝑈𝑈𝐼𝐼𝐼𝐼𝑈𝑈𝑝𝑝𝑈𝑈𝑈𝑈𝑦𝑦𝑈𝑈𝐼𝐼𝐼𝐼𝑡𝑡𝑡𝑡,∆𝑈𝑈𝐼𝐼𝐼𝐼𝑈𝑈𝑝𝑝𝑈𝑈𝑈𝑈𝑦𝑦𝑈𝑈𝐼𝐼𝐼𝐼𝑡𝑡𝑡𝑡,𝑁𝑁𝐶𝐶𝐼𝐼𝐼𝐼𝑡𝑡𝑡𝑡),

where 𝑝𝑝𝑖𝑖𝑡𝑡 = 𝑁𝑁𝑁𝑁𝑡𝑡 𝑁𝑁ℎ𝑎𝑎𝑟𝑟𝑎𝑎𝑁𝑁−𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑡𝑡𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑖𝑖𝑡𝑡−1

, where 𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝑖𝑖𝑡𝑡 = 𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑟𝑟𝑁𝑁𝑜𝑜𝑡𝑡 𝑟𝑟𝑁𝑁𝑟𝑟𝑁𝑁𝐿𝐿𝑟𝑟𝑁𝑁𝑖𝑖𝑡𝑡𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑖𝑖𝑡𝑡−1

,

𝑁𝑁𝐴𝐴𝐸𝐸𝑖𝑖𝑡𝑡 = 𝑁𝑁𝑜𝑜𝐿𝐿−𝑎𝑎𝑎𝑎𝑎𝑎𝑟𝑟𝑟𝑟𝑎𝑎𝑎𝑎 𝑎𝑎𝑜𝑜𝑎𝑎𝐿𝐿𝑜𝑜𝑖𝑖𝑡𝑡𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑖𝑖𝑡𝑡−1

, 𝐿𝐿𝐼𝐼𝑃𝑃𝑡𝑡𝑃𝑃𝑃𝑃𝐼𝐼90𝑖𝑖𝑡𝑡 = 𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑜𝑜 𝑝𝑝𝑎𝑎𝑜𝑜𝑡𝑡 𝑑𝑑𝑟𝑟𝑁𝑁 90 𝑑𝑑𝑎𝑎𝑑𝑑𝑜𝑜𝑖𝑖𝑡𝑡𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑖𝑖𝑡𝑡−1

, 𝑈𝑈𝐼𝐼𝐼𝐼𝑈𝑈𝑝𝑝𝑈𝑈𝑈𝑈𝑦𝑦𝑈𝑈𝐼𝐼𝐼𝐼𝑡𝑡𝑡𝑡 is the

unemployment rate, 𝑁𝑁𝐶𝐶𝐼𝐼𝐼𝐼𝑡𝑡𝑡𝑡 = 𝑁𝑁𝐶𝐶𝐼𝐼𝐿𝐿𝑑𝑑𝑁𝑁𝐶𝐶𝑡𝑡−𝑁𝑁𝐶𝐶𝐼𝐼𝐿𝐿𝑑𝑑𝑁𝑁𝐶𝐶𝑡𝑡−1𝑁𝑁𝐶𝐶𝐼𝐼𝐿𝐿𝑑𝑑𝑁𝑁𝐶𝐶𝑡𝑡−1

, 𝑁𝑁𝐶𝐶𝐼𝐼𝐼𝐼𝑃𝑃𝐼𝐼𝐶𝐶 is the Case-Shiller real estate index,

and ∆ is the difference operator: ∆𝐶𝐶𝑡𝑡 = 𝐶𝐶𝑡𝑡 − 𝐶𝐶𝑡𝑡−1.

3 Since we do not observe the interest rate on the loans, we approximate it by calculating the ratio of interest revenue less loan loss provision to the sum of total loans, held-to-maturity securities, available-for-sales securities, and trading assets.

12

To construct a bank-year measure of the level of under-reserving for the expected losses,

we use the difference between the reported allowance for loan losses, 𝐴𝐴𝐸𝐸𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡, and 𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸𝑖𝑖𝑡𝑡:

𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑖𝑖𝑡𝑡 = 𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸𝑖𝑖𝑡𝑡 − 𝐴𝐴𝐸𝐸𝐸𝐸𝐼𝐼𝑖𝑖𝑡𝑡, (7)

The higher the value of 𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑖𝑖𝑡𝑡, the less timely a bank is in recording expected losses in year

𝑡𝑡. In our empirical analysis, we scale the estimated (the reported) allowance and provision by the

lagged gross amount of loans, 𝐵𝐵𝑖𝑖𝑡𝑡.

2.2. Conceptual differences from prior models.

While the prior literature has not offered a model that allows measuring the allowances

and provisions for expected loan losses, several models have been offered to measure the degree

to which loan loss provisioning reflects forward-looking information about future expected

losses (see Beatty and Liao 2014 for a review). This approach can be conceptually understood by

looking at the following regression model:

𝐸𝐸𝐸𝐸𝐿𝐿𝐼𝐼𝑡𝑡 = 𝛼𝛼0 + 𝛼𝛼1∆𝑁𝑁𝐸𝐸𝐿𝐿𝑡𝑡+1 + 𝛼𝛼1∆𝑁𝑁𝐸𝐸𝐿𝐿𝑡𝑡 + 𝑁𝑁𝑡𝑡ℎ𝐼𝐼𝑟𝑟 𝐺𝐺𝐼𝐼𝑡𝑡𝐼𝐼𝑟𝑟𝑈𝑈𝐷𝐷𝐼𝐼𝐼𝐼𝐼𝐼𝑡𝑡𝑃𝑃𝑡𝑡 + 𝜀𝜀𝑡𝑡 (8)

where 𝐸𝐸𝐸𝐸𝐿𝐿𝐼𝐼𝑡𝑡 is current provision and where ∆𝑁𝑁𝐸𝐸𝐿𝐿𝑡𝑡+1and ∆𝑁𝑁𝐸𝐸𝐿𝐿𝑡𝑡are future and current changes

in non-performing loans that aim to proxy for incurred (probable) losses. The incremental R-

squared from the first two regressors in this model (or the magnitude of the coefficient 𝛼𝛼1) has

been used in the literature to measures the timeliness of provisioning for expected losses (e.g.,

Bushman and Williams 2015).

There are two important considerations behind this research design. First, it assumes that

the managers (accountants) know or can accurately estimate the changes in non-performing loans

realized in the subsequent period (𝑡𝑡 + 1). Second, non-performing loans, which is a proxy for

incurred losses, only reflect losses likely to be realized within a relatively short time frame and

do not capture long-run expected losses. These considerations mean that this approach is not

13

applicable to modeling expected long-term losses or measuring the timeliness of loan loss

provisioning under the expected loss approach. Instead, it measures the timeliness of (expected)

losses conditional on such losses being probable (and known to management). Probable losses

and expected losses are different and need not be positively correlated.

One could consider modifying the model (8) to incorporate some measure of non-

performing loans or realized losses over a number of periods (i.e., 𝑡𝑡 + 2, 𝑡𝑡 + 3, …). However,

under such modification, the assumption that the manager knows or can precisely measure future

non-performing loans (realized losses) is no longer plausible. As a result, low incremental R-

squared in the modified version becomes a proxy for a portfolio’s loan loss predictability rather

than timeliness. Thus, measuring the timeliness of loan loss provisioning under the expected loss

approach is conceptually distinct from the notion of timeliness under the incurred loss model and

requires a model that allows investigating the mapping of expected losses (as opposed to realized)

losses into reported numbers, which is what our model does.

3. Data and sample selection.

Our data comes from several sources. We obtain accounting information for bank holding

companies from FR Y-9C reports available on the Federal Reserve Bank of Chicago website.

These data cover both private and public banks and are available on both a quarterly and annual

basis starting in 1986. We use annual information to construct the variables used in our analysis.

We obtain monthly stock returns (for listed bank holding corporations) from the Center for

Research in Security Prices (CRSP). Finally, data on bank failure comes from the Federal

Deposit Insurance Corporation (FDIC) website.

Our sample covers the period from 1986-2017, the years for which the data is available.

We require bank holding companies to have at least 15 years of available data during this sample

14

period to ensure sufficient historical data needed to estimate expected loan losses, i.e., to

determine the estimated allowance (ALLE) and provision (LLPE) for expected loan losses. The

exception to this requirement is the bank failure tests, in which we do not restrict data

availability by year. To reduce the impact of extreme observations, we truncate the top and

bottom 1% observations for all the variables that appear in our regressions, except for

macroeconomic and bank failure variables.

Table 1 presents the descriptive statistics for the variables used in our analysis. Banks in

our sample have average total assets (Asset) of $7.7 billion and average total loans (Loans) of $4

billion. The reported allowance of loan losses (ALLR) is 1.6% of lagged total loans, which is

about three times larger than the provision for loan losses (LLPR). Descriptive statistics are

similar to other studies that use US bank holding company data (e.g., Beatty and Liao 2011,

Bushman and Williams 2015, Laux and Rauter 2017).

4. Baseline tests.

4.1 Descriptive analysis of model estimated variables.

We use the methodology discussed in Section 2 to estimate the allowances (ALLE) and

provisions (LLPE) for expected loan losses. The estimated coefficients for the prediction model

are reported in the Appendix (Table A1). The future default ratios exhibit an intuitive relation

with concurrent information in firm and macro indicators. They are significantly, positively

associated with historical losses, past-due and non-accrual loans, changes in the interest rates,

growth in unemployment, and real GDP growth. Default rates exhibit negative associations with

interest rates, unemployment, and the return of Case-Shiller Home Price Index. The positive

association between future default probability and GDP growth and the negative association with

unemployment is an indication of banks’ lending pro-cyclicality, i.e., banks adopt a more liberal

15

credit policy in good times, extending loans to lower quality borrowers. Better market conditions

lead to new, lower quality loans being extended, which results in a higher default probability in

the future. The results also point to the presence of bank-specific effects in loan losses, i.e., a

high default rate or low-asset-quality banks that are more likely to default in the future.

Table 2 presents the percentiles for the distribution of the estimated allowances and

provisions for loan losses, and describes the distribution of the reported numbers. The

distributions can also be seen in Figure 1. ALLE has a mean of 0.019 and a median of 0.017.

Both quantities are somewhat larger than the corresponding quantities based on the reported

allowance ALLR, which are 0.016 and 0.015 respectively, however, the differences are not very

large on average. In part, this is due to the fact that the levels of reported allowance are relatively

high as they constitute about 3 years’ worth of reported provisions. Similar patterns are observed

for all other percentiles of the distribution of estimated allowances as compared to reported

allowances. Finally, the mean and median level of UNDER is positive, in line with the

expectation that the current reporting practice on average under-reserves for loan losses.

4.2 Model performance and validation.

We begin by validating the model of expected loan losses and contrasting its performance

to the reported numbers. First, we explore the predictive ability of the estimated allowance for

expected losses (ALLE) to explain future realized losses and to compare it to the predictive

power of the reported allowance (ALLR). We focus on the medium run because the reported

allowance is expected to have some power to predict losses in the medium run, but not in the

longer run (recall that the level of reported allowance is sufficient to cover three to four years of

provisions or realized losses). Second, we explore the value relevance of the estimated expected

vs. reported loan loss allowances and provisions.

16

4.2.1 Predictive ability tests.

We regress the cumulative net charge-offs measured over the following three years

(Future losses) on the current year allowance for expected vs. reported loan losses:

𝐹𝐹𝑃𝑃𝑡𝑡𝑃𝑃𝑟𝑟𝐼𝐼 𝑈𝑈𝑈𝑈𝑃𝑃𝑃𝑃𝐼𝐼𝑃𝑃𝑖𝑖,𝑡𝑡+3 = 𝛽𝛽0 + 𝛽𝛽1𝐴𝐴𝑈𝑈𝑈𝑈𝑈𝑈𝑤𝑤𝐼𝐼𝐼𝐼𝐴𝐴𝐼𝐼𝑖𝑖,𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑡𝑡,

where Allowance is either ALLE (allowance for expected losses) or ALLR (reported allowance).

Since ALLE incorporates forward-looking information, we expect it to be a significantly better

predictor of loan losses than is ALLR.

Table 3 presents the results of this comparison. Columns 1 and 2 show that the coefficient

(t-statistic) on ALLE is more than twice (three times) as large as on ALLR. Importantly, while

both allowance measures are significant predictors of future loan losses, the explanatory power

of ALLE is an order of magnitude higher than that of ALLR. When we include both ALLE and

ALLR in the regression (column 3), both the coefficient and t-statistics on ALLR drop

significantly, whereas the coefficient on ALLE and its level of statistical significance remain

unchanged; R-squared also remains largely unchanged. As we control for the level of past

realized losses (NCO) in columns 4-6, the coefficients and t-statistics on reported allowance,

ALLR, deteriorate further, whereas those on the allowance for estimated losses remain largely

unchanged. Unlike in the case of reported allowances, adding NCO as a control does not add

much incremental information to that contained in our measure of expected loan losses. Overall,

the ability of the reported allowance to predict future losses over a medium term horizon is

strikingly low.

These findings indicate that reported loan loss provisioning is mainly driven by historic

loss experience and not by forward-looking information. In contrast, the allowance for expected

losses contains a large amount of relevant forward-looking information not reflected in the

17

reported numbers or in the historical loss experience. These results suggest that our model is

effective at estimating a more forward-looking measure of expected loan losses.

4.2.2 Value relevance tests.

We next evaluate the value relevance of the allowance and provision for expected losses

based on our model. If ALLE is better at anticipating future losses than is ALLR, it should also be

more value relevant with respect to contemporaneous banks’ stock prices. To test value

relevance, we use the following model on a subsample of publically traded banks:

𝐿𝐿𝑟𝑟𝐷𝐷𝐴𝐴𝐼𝐼𝑖𝑖,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝐴𝐴𝑈𝑈𝑈𝑈𝑈𝑈𝑤𝑤𝐼𝐼𝐼𝐼𝐴𝐴𝐼𝐼𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑡𝑡,

where Price is the closing stock price at the end of April of the following year scaled by lagged

loan per share (total loans scaled by the number of shares outstanding in April of the current

year).4 This ensures that the dependent and independent variables are both scaled by the same

deflator. Allowance is either ALLE or ALLR, and 𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃 is capital ratio, CapR, and the natural

log of total assets, Size.

The results are presented in columns 1 and 2 of Table 4. In line with our expectations, we

find that the estimated allowance ALLE has a negative and statistically significant (at the less

than 1% level) association with Price. In contrast, ALLR is negatively associated with Price, but

the effect is not significant. In columns 3 and 4, we run the return-based version of the analysis

above, using stock returns as the dependent variable and replacing the allowances with

provisions:

𝐼𝐼𝐼𝐼𝑡𝑡𝑖𝑖,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝐿𝐿𝑟𝑟𝑈𝑈𝑃𝑃𝐷𝐷𝑃𝑃𝐷𝐷𝑈𝑈𝐼𝐼𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑡𝑡,

where Ret is the current year buy-and-hold stock return measured over the period starting in the

end of April of the current year to the end of April of the following year. In this specification,

4 We assume that a bank’s annual accounting information with a December fiscal year-end is publically available by the end of April of the following year.

18

Provision is either LLPE or LLPR, and 𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃 is net income scaled by lagged total loans, NI,

and the natural log of total assets, Size.

The results, reported in columns 3 and 4, are analogous to those in the levels-based

specifications (columns 1 and 2). We find that expected loan loss provision LLPE exhibits a

statistically significant negative association with Ret at the 5% level. While LLPR also exhibits a

negative relation with returns, it is no longer statistically significant.

As in the predictive ability tests, the results here indicate that the estimated allowances

and provisions based on our model contain significantly more information about the performance

of a bank’s loan portfolios than the reported numbers.

5. Pro-cyclicality of expected vs. reported loan loss provisioning.

A key criticism to the incurred loss approach to loan loss provisioning is its pro-

cyclicality (Laeven and Majnoni 2003, Dugan 2009, FSF Report 2009). Laeven and Majnoni

(2003) provide evidence that many banks around the world delay provisioning until too late,

thereby amplifying the impact of the economic cycle on banks’ earnings and capital. The pro-

cyclicality of loan loss provisioning arguably leads to lending pro-cyclicality and thus the

banking system’s vulnerability to the financial crisis (Beatty and Liao 2011; Bushman and

Williams 2012, 2015; GAO 2013).

While the adoption of the expected loan loss approach aims to address the pro-cyclicality

in loan loss provisioning, whether and to what extent this will be the case is not well understood

(Acharya and Ryan 2016). In fact, it is possible to envision scenarios under which the expected

loss approach will lead to greater provision pro-cyclicality. For example, it is possible that

expected losses are even smaller in periods of economic booms and greater in periods of

economic downturns as compared to reported losses, suggesting increased pro-cyclicality.

19

To provide preliminary evidence on this, we use our model to explore the pro-cyclicality

of the expected loan losses and compare it to the reported numbers. As argued by Laeven and

Majnoni (2003), pro-cyclicality of loan loss provisioning is manifested in (1) a negative

association of provisions and GDP growth, (2) a negative association between provisions and

loan growth, and (3) a negative association of loan loss provisions and bank’s earnings before

provisions.5 We start by exploring the association between provisioning and GDP growth by

running the following regression:

𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟𝑖𝑖,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝛥𝛥𝐺𝐺𝐺𝐺𝐿𝐿𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝛽𝛽3𝐹𝐹𝐸𝐸𝑖𝑖,𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑡𝑡,

where the dependent variable, 𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟, is either the reported allowance (provision), ALLR

(LLPR), or the allowance (provision) for expected loan losses, ALLE (LLPE). ΔGDP is the real

GDP growth. Controls is the natural log of total assets, Size, and FE represents bank fixed effects.

The results are presented in Table 5, Panel A. In line with the increased pro-cyclicality of

loan loss provisioning under the incurred loss approach, columns 1 and 3 indicate a pronounced

negative association of the reported loan loss provisions and allowances with changes in GDP. In

contrast, columns 2 and 4 indicate that estimated provisions and allowances based on the

expected loss approach exhibit a significant positive association with GDP growth. In other

words, the allowances for expected losses, absent earnings manipulations, behave in a counter-

cyclical ways. This evidence supports the intended effect on the new provisioning standard.

Next, we investigate pro-cyclicality by examining loan growth:

𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟𝑖𝑖,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝛥𝛥𝐸𝐸𝑈𝑈𝐼𝐼𝐼𝐼𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝛽𝛽3𝐹𝐹𝐸𝐸𝑖𝑖,𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑡𝑡,

where the dependent variable, 𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟, is either the reported allowance (provision), ALLR

(LLPR), or the allowance (provision) for expected loan losses, ALLE (LLPE). ΔLoans is the

5 Laeven and Majnoni (2003) find evidence in support pro-cyclicality based on predictions (1) and (2) but not prediction (3). The latter is consistent with earnings management to smooth earnings over time.

20

annual change in total loans. Controls is the natural log of total assets, Size, and FE represents

bank fixed effects.

The results are presented in Table 5, Panel B. Similar to the case of GDP growth,

columns 1 and 3 indicate a significant pro-cyclical behavior of the reported loan loss provisions

and allowances, i.e., they exhibit negative associations with loan growth. In contrast, columns 2

and 4 indicate that estimated provisions and allowances based on the expected loss approach

switch to counter-cyclical behavior and exhibit a positive association with loan growth, also in

line with the intended effect on the new standard.

5.1. Income smoothing

Another way to investigate the pro-cyclicality of loan loss provisioning on banks’

financials is to examine the income smoothing of expected vs. reported provisions for loan losses

(Laeven and Majnoni 2003). Income smoothing is measured by regressing provisions for loan

losses on earnings before provisions (Collins, Shackelford, and Wahlen 1995; Beatty,

Chamberlain, and Magliolo 1995). Under the incurred loss approach, because losses are not

recognized in a sufficiently timely manner, companies have incentives to smooth earnings by

over- (under-) provisioning during periods of high (low) revenues in order to protect themselves

against adverse economic shocks to future earnings (Liu and Ryan 2006). This, however, need

not be a manifestation of timely provisioning for future losses, but can be explained by general

earnings management practice. In line with this idea, Bushman and Williams (2012) find that

income smoothing dampens discipline over risk-taking. We investigate whether accounting for

expected loan losses will also generate income smoothing by running the following regression:

𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟𝑖𝑖,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝐸𝐸𝐵𝐵𝐿𝐿𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝛽𝛽3𝐹𝐹𝐸𝐸𝑖𝑖,𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑡𝑡,

21

where 𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟 is either the reported provision, LLPR, or the provision for expected losses, LLPE.

EBP is earnings before provision scaled by lagged total loans. Controls includes NCO, Size,

ΔGDP, CapR, and last-period EBP; FE represents bank fixed effects.

Table 6 reports the estimates from this model. Columns 1 and 2, which do not include

any controls, indicate that the coefficient on EBP is higher in the case of the expected provision,

LLPE, as compared to reported losses, LLPR. Note that, by design, LLPE is not subject to

earnings management. When we add NCO as the control variable in columns 3 and 4 and the

other controls in Models 5 and 6, the result remains largely the same, although the coefficient

magnitudes change after the controls are included. The evidence here suggests that, in the

absence of earnings management, provisioning for expected loan losses generates an income

smoothing property of loan loss provisions. This result is similar to what one would expect under

matching higher revenues with higher expenses. Overall, the evidence is in line with counter-

cyclical behavior of expected loan losses.

6. Firm-year proxy for under-reserving.

While prior research shows that forward-looking provisioning benefits capital markets

and improves the stability of the financial sector (Beatty and Liao 2011; Bushman and Williams

2012, 2013; Acharya and Ryan 2016), the models used to measure forward looking provisioning

cannot be used to answer a number of questions of interest. First, reported provisions have a

relatively limited amount of forward-looking information, as is also suggested by our analysis in

the prior section, and only can speak to the forward-looking nature of provisioning with respect

to short run (probable) losses. Provisions for incurred losses are likely to differ substantially

from the provisions for expected loan losses at a given point in time, and need not be positively

correlated. Thus, we still do not have a full understanding of the implications of provisioning for

22

expected losses for bank behavior. Second, most of the measures are estimated at a bank or even

country (region) level and thus do not allow answering questions related to a specific point in

time, e.g., the lack of sufficient provisioning right before the financial crisis.

To make progress with respect to these challenges, we evaluate loan loss provisioning by

assessing the degree of under-reserving for loan losses at a given point in time. We use the

estimated allowance for expected losses, ALLE, as a benchmark against which the adequacy of

the reported reserves is measured:

𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑖𝑖,𝑡𝑡 = 𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸𝑖𝑖,𝑡𝑡 − 𝐴𝐴𝐸𝐸𝐸𝐸𝐼𝐼𝑖𝑖,𝑡𝑡.

Higher (lower) UNDERR indicates a higher (lower) degree of under-reserving, i.e., less

timely reporting of loan losses at a given point in time. We validate this measure in several ways.

First, we investigate whether banks’ future performance and capital is predictable based on the

current degree of under-reserving. Second, we examine whether under-provisioning explains the

amplitude of the effect of financial crisis on banks’ stock prices and lending behavior.

6.1 Under-reserving and future accounting performance.

We first investigate whether our proxy for under-reserving in the current period is

informative about future accounting indicators: reported provisions, net income, and capital ratio.

Under-reserving for future losses today implies higher provisions, lower earnings, and lower

capital in the future. To show this, we run the following regressions:

𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟𝑖𝑖,𝑡𝑡+𝑜𝑜 = 𝛽𝛽0 + 𝛽𝛽1𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃𝑖𝑖,𝑡𝑡 + 𝛽𝛽3𝐹𝐹𝐸𝐸𝑖𝑖,𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑡𝑡,

where Depvar is either LLPR, NI, or CapR; and s=1,2,3. Controls are NCO, CapR, ΔGDP, and

Size. FE represents bank fixed effects.

Table 7 reports the results of this analysis. Columns 1-3 show that UNDERR is

significantly, positively associated with reported loan loss provisions in the following year, and

23

significantly, negatively associated with the following year’s net income and capital ratio.

Furthermore, columns 4-6 and 7-9 demonstrate that these results persist and extend to years t+2

and t+3, respectively, in the future. Overall, under-reserving banks exhibit predictable changes in

future performance and capital ratios under the current reporting practice. This indicates that our

measure of under-reserving is indeed measuring untimely reporting of accounting earnings and

capital ratios.

6.2 Under-reserving and the effect of the financial crisis of 2008.

We expect that financial markets are able to see through a lack of reserves for expected

losses.6 However, under-provisioning is expected to explain a bank’s reaction to an

unanticipated financial sector shock. Bushman and Williams (2012) provide evidence that less

forward-looking reporting of loan losses increases the risk of contraction in the bank’s assets. To

test this idea based on a measure of under-reserving for expected losses, we use the financial

crisis of 2008 as a shock and examine how banks’ stock returns and lending behavior change in

response to this shock depending on their level of under-reserving:

𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟2008 = 𝛽𝛽0 + 𝛽𝛽1𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼2007 + 𝛽𝛽2𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃2007 + 𝜀𝜀𝑖𝑖,𝑡𝑡,

where Depvar2008 is either buy-and-hold return over a 12-month period from the end of April of

2008 to the end of April of 2009, Return2008, or the change in total loans over the year 2008,

∆Loans2008; Controls include ALLR, Size, and CapR.

Table 8, Panel A reports the results. Banks that have a higher degree of under-reserving

as of the end of 2007 show significantly lower stock market returns and loan growth during the

year in which the crisis unfolded. As a placebo test, in Panel B of Table 8, we run the same test

using the year prior to the financial crisis by regressing stock returns and loan growth in 2007 on

6 We test and confirm this prediction in the Appendix Table A2.

24

the UNDERR of 2006 and the 2006 controls. In the absence of an unanticipated financial shock,

the coefficient of UNDERR is insignificant or has the opposite sign. Our results indicate that the

severity of financial crisis affected under-reserving banks more significantly.

In sum, our results in this section validate our proxy of under-reserving for expected loan

losses, which behaves in a way that a valid proxy for under-reserving should.

7. The real effects of under-reserving.

In this section, we take a step towards a better understanding of the real effects of the

current reporting practice vs. the expected loan loss provisioning. Can under-provisioning for

expected losses explain banks’ real investment and financing decisions? We take the perspective

that bank managers understand expected loan losses, even if they are not required to report them.

In a world with no agency problems (and hence no capital requirements), banks’ investment and

financing decisions should depend on the amount of losses the managers expect, not just a

portion of losses that have been incurred, i.e., on the level of real economic capital. Therefore,

holding expected losses constant, under-reporting of such losses should not significantly

influence banks’ decisions. In contrast, in a world where capital requirements written on

accounting numbers aim to control banks’ risk taking behavior, the measurement of loan losses

will affect bank decisions (Bertomeu et al. 2017). Specifically, when reported capital understates

banks’ real capital and hence relaxes banks’ capital constraint, banks have increased incentive to

continue expanding their balance sheets by issuing more loans and levering up.

In the next subsections, we explore the association between under-reserving and the

following key decisions: loan growth, leverage, liability growth, and dividend payouts.

7.1. Under-reserving and banks’ investment and financing decisions.

As a first step, we examine the prediction that for a given amount of expected loan losses

25

to which a bank is subject, the degree of under-reserving for such losses is positively associated

with increased loan growth, bank’s leverage and liabilities growth, and dividend payments in the

subsequent year. To accomplish this, we run the following regression:

𝐺𝐺𝐼𝐼𝑝𝑝𝑃𝑃𝐼𝐼𝑟𝑟𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑡𝑡−1 + 𝛽𝛽2𝐴𝐴𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡−1 + 𝛽𝛽3𝑁𝑁𝑡𝑡ℎ𝐼𝐼𝑟𝑟𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃 + 𝛽𝛽4𝐹𝐹𝐸𝐸𝑖𝑖 + 𝜀𝜀𝑡𝑡,

where Depvar are ΔLoan, ΔLeverage, ΔLiability, and Dividends measured over year t;

OtherControls is ΔGDPt, CapRt-1, and Sizet-1; FE is bank fixed effects.

Table 9, Panel A reports the results of this analysis. The coefficients on the proxy for

expected losses, ALLE, are negative for ΔLoan, ΔLiability, and Dividends, which is in line with

the expectation that higher expected losses should lead to more conservative lending policies.

We find, however, that under-reserving measured as of the end of the previous year has a

significantly positive association with loan growth, leverage and liability growth, as well as with

dividend payout decisions. By design, UNDERR’s positive contribution to balance sheet

expansion cannot be attributed to higher expected losses, and hence appears to come from the

‘slack’ in the bank’s capital introduced by the current incurred loss-based approach.

7.2. Under-reserving and the effect of economic shocks on bank decisions.

As a next step, we investigate the extent to which under-reserving may interfere with

banks’ responses to economic shocks. For a given level of expected loan losses, under-reserving

banks have more ‘slack’ in their capital and hence more room to continue with their credit policy

without making speedy adjustments in response to changes in economic conditions. Thus, we

expect the higher degree of under-reserving to lead to slower and more muted reactions to

changes in economic conditions: banks are less likely to cut back on lending and lower leverage

when the economy slows down. They are also less likely to expand lending or take on additional

leverage in response to more favorable market conditions (because they are already levered up).

26

To test this, we run regressions analogous to those in Panel A, but add the interaction

term ΔGDPt *UNDERRt-1. Table 9, Panel B reports the results of this test. As in Panel A, GDP

growth is positively associated with loan and leverage growth, consistent with banks increasing

lending and leverage during market expansions. However, the coefficient on the interaction term

ΔGDPt*UNDERRt-1 is significantly negative both for new loan issuance and for changes in

leverage. This result is in line with our expectation that under-reserving banks are slower to react

to economic shocks, consistent with under-reserving distorting banks’ decisions.

7.3. Under-reserving and the capital crunch effect.

Finally, prior research finds that banks’ lending is sensitive to their levels of capital

during recessionary periods (Bernanke and Lown 1991, Kishan and Opiela 2000). The

explanation for these findings is that banks are experiencing a “capital crunch” caused by the

pressure from regulatory capital requirements and so they reduce lending (Bernanke and Lown

1991). Given that the timelines of loan loss provisions directly affects the levels of regulatory

capital, Beatty and Liao (2011) find that banks with less timely provisioning exhibit a more

pronounced positive association between loan issuance and regulatory capital during recessions,

i.e., a greater capital crunch effect.

While Beatty and Liao (2011) measure the timeliness of provisioning with respect to

incurred losses reported under FAS 5 and measured at the bank level, we examine whether the

capital crunch effect is a function of firm-year under-reserving for expected losses. We examine

whether banks with a higher degree of under-reserving for loan losses face a greater capital

crunch effect in recessionary periods.

We run the following regression for the subsamples with low and high under-reserving:

the “low UNDERRt-1” and “high UNDERR t-1” subsamples:

27

𝛥𝛥𝐸𝐸𝑈𝑈𝐼𝐼𝐼𝐼𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝑁𝑁𝐼𝐼𝑝𝑝𝐼𝐼𝑡𝑡−1 + 𝛽𝛽2𝐶𝐶𝑈𝑈𝑈𝑈𝑤𝑤𝑃𝑃𝑈𝑈𝑤𝑤𝐼𝐼𝑡𝑡 + 𝛽𝛽3𝑁𝑁𝐼𝐼𝑝𝑝𝐼𝐼𝑡𝑡−1 ∗ 𝐶𝐶𝑈𝑈𝑈𝑈𝑤𝑤𝑃𝑃𝑈𝑈𝑤𝑤𝐼𝐼𝑡𝑡 + 𝛽𝛽4𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃

+ 𝛽𝛽5𝐹𝐹𝐸𝐸𝑡𝑡 + 𝜀𝜀𝑡𝑡,

where the “low UNDERR t-1” subsample includes observations with a bottom quintile of

UNDERR in year t-1, and “high UNDERR t-1” includes observations with a top quintile of

UNDERR in year t-1.7 Controls is Sizet-1 and ALLE t-1. The coefficient of interest is the

coefficient on the interaction 𝑁𝑁𝐼𝐼𝑝𝑝𝐼𝐼𝑡𝑡−1 ∗ 𝐶𝐶𝑈𝑈𝑈𝑈𝑤𝑤𝑃𝑃𝑈𝑈𝑤𝑤𝐼𝐼𝑡𝑡.

Table 9, Panel C reports the results of this analysis. As a benchmark, column 1 presents

the full sample analysis. In line with the capital crunch effect documented in prior studies, the

interaction CapRt-1* Slowdownt is positive and statistically significant. Column 2 is based on the

subsample of well-reserved banks. For this subsample, the coefficient of the interaction CapRt-1*

Slowdownt is positive but not statistically significant. However, when we use the high degree of

under-reserving subsample, presented in column 3, the interaction term becomes positive and

significant at the 5% level. Its coefficient is also considerably higher in terms of economic

magnitude. These results suggest that lending by under-reserving banks is more sensitive to the

level of capital during recessionary periods compared to that of well-reserved banks. This is

consistent with the notion that capital requirement pressure is a mechanism through which under-

reserving affects lending, and it reconciles our findings in Panels A and B of Table 9. Our results

are consistent with Beatty and Liao (2011), who find that banks with less timely provisioning

experience a greater capital crunch than do those with timelier provisioning. Our evidence is also

in line with Jayaraman et al. (2017), who find that pre-emptive provisioning for loan losses

reduces contraction in banks’ lending during financial downturns.

7.4. Under-reserving and bank failure.

In our final set of tests, we investigate whether banks that under-reserve for expected 7 The results are qualitatively the same if we use the top/bottom quartile or decile.

28

losses exhibit a higher probability of failure in subsequent years. If under-reserving distorts

banks’ decisions (leading to excessive loan issuance and leverage) and makes them more

exposed to the effects of an economic downturn, one should expect under-reserved banks to be

more likely to fail in the future.

We test whether under-reserving is associated with a higher probability of bank failure in

the subsequent three years by running the following probit regression model:

𝐹𝐹𝐼𝐼𝐷𝐷𝑈𝑈𝑃𝑃𝑟𝑟𝐼𝐼𝑡𝑡+𝑜𝑜 = 𝛽𝛽0 + 𝛽𝛽1𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑡𝑡 + 𝛽𝛽2𝑁𝑁𝑈𝑈𝐼𝐼𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑃𝑃𝑡𝑡 + 𝜀𝜀𝑡𝑡,

where 𝐹𝐹𝐼𝐼𝐷𝐷𝑈𝑈𝑃𝑃𝑟𝑟𝐼𝐼𝑡𝑡+𝑜𝑜 is the bank failure indicator for the next three years (s = 0, 1, 2); 𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑡𝑡 is

our measure of past under-reserving; and Controls is Size, ALLR, and CapR. Given that our data

is at the bank holding company level and that bank failures happen primarily at the commercial

bank level, we measure bank failure as a dummy variable that equals 1 if the bank holding

company is the top holder of a commercial bank that failed in a given year, 0 otherwise.8

Table 10 reports the result of these tests. We find that the coefficients on UNDERR are all

positive and significant at the 1% level across the three different lags of UNDERR. That is,

columns 1-3 indicate that present-day under-reserving is positively associated with the likelihood

of bank failure in subsequent years. As expected, the magnitude of the coefficients on 𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑡𝑡

decreases with the prediction horizon as we move across columns 1-3, but it remains highly

significant statistically. Column 4 reports a specification in which we include all three lags of the

under-reserving proxies simultaneously. In this specification, only the most recent lag is (highly)

significant. This result is expected if 𝑈𝑈𝑁𝑁𝐺𝐺𝐸𝐸𝐼𝐼𝐼𝐼𝑡𝑡 has more up-to-date information about expected

losses. Overall, the evidence indicates that under-reserving banks have a higher probability of

failure. 8 We do not use commercial bank-level data because some commercial banks are backed by BHC. During a crisis, they are likely to receive financing from their parent BHC, while other commercial banks are stand-alone and are consequently more vulnerable at such times. Comparing banks at the commercial bank level is therefore unfair.

29

In sum, our results in this section are consistent with the measurement of loan loss

provisioning having real effects with respect to banks’ decisions and stability during economic

downturns.

8. Conclusion.

Loan loss provisioning has been the subject of long-standing debate among academics

and regulators. The lack of timely provisioning for loan losses overstates banks’ capital and has

been argued to have a detrimental effect on the stability of financial sector. Recently, FASB

implemented major changes to the accounting for loan losses. The new standard introduces the

expected loan loss approach under which banks must account for expected losses when

determining loan loss provisions and allowances. This approach contrasts with the incurred-loss

reporting practice (FAS 5) currently in place. Despite the importance of timely provisioning to

banks’ regulators and accounting standard setters, the literature has made limited progress in

understanding the economic implications of expected loan loss provisioning. We argue that the

existing approach to measuring the timeliness (forward-looking nature) of loan loss provisioning

under the incurred loss framework is not suitable for understanding the timeliness of expected

loan loss provisioning. Given this, and given the unobservable nature of expected losses, it is

useful to develop a model of expected loan loss provisioning.

We propose, implement, and validate an empirical model of expected loan loss

provisioning as a function of concurrent forward-looking information about bank and macro-

economic conditions. While our model relies on several strong assumptions, it considerably

outperforms the current reporting practice at anticipating future loan losses and also exhibits

significant value-relevant information not reflected in their reported numbers. Our evidence

provides new insights into the pro-cyclicality of loan loss provisioning. While reported

30

provisions under the incurred loss approach exhibit pro-cyclical behavior, the estimated

provisions and allowances for expected loan losses are counter-cyclical.

We also provide and validate a measure of under-provisioning for loan losses for a given

bank-year. This measure is a direct proxy for the untimely reporting of banks’ profitability and

capital and is predictably associated with the adverse effect of the financial crisis on under-

reserved banks. We use the measure of under-reserving to shed some light on the real effects of

loan loss provisioning. We predict and find that, holding the amount of expected loan losses

constant, slack in real capital gives banks incentives (and opportunities) to expand their balance

sheets by issuing loans and increasing leverage, as well as to increase dividend distributions. We

further show that under-reserving banks’ are slower to respond to changes in current economic

conditions. At the same time, these banks exhibit increased probability of future failure.

Our study should be of interest to accounting standard setters and bank regulators. It

suggests that expected loan losses can be successfully measured in a way that is superior to the

current reporting practice. Our evidence suggests that expected loan loss provisioning has

important implications for the pro-cyclicality of banks’ capital and for banks’ investment and

financing decisions that ultimately affect their viability.

31

References Acharya, Viral V., and Stephen G. Ryan. "Banks’ financial reporting and financial system stability." Journal of Accounting Research 54, no. 2 (2016): 277-340. Beatty, Anne, Sandra L. Chamberlain, and Joseph Magliolo. "Managing financial reports of commercial banks: The influence of taxes, regulatory capital, and earnings." Journal of Accounting Research 33, no. 2 (1995): 231-261. Beatty, Anne, and Scott Liao. "Do delays in expected loss recognition affect banks' willingness to lend?" Journal of Accounting and Economics 52, no. 1 (2011): 1-20. Beatty, Anne, and Scott Liao. "Financial accounting in the banking industry: A review of the empirical literature." Journal of Accounting and Economics 58, no. 2 (2014): 339-383. Benston, George J., and Larry D. Wall. "How should banks account for loan losses." Journal of Accounting and Public Policy 24, no. 2 (2005): 81-100.

Bernanke, Ben S., Cara S. Lown, and Benjamin M. Friedman. "The credit crunch." Brookings Papers on Economic Activity 2 (1991): 205-247. Bertomeu, Jeremy, Lucas Mahieux, and Haresh Sapra. Accounting versus Prudential Regulation. Working paper (2017). Bushman, Robert M. "Transparency, accounting discretion, and bank stability." Working paper (2016).

Bushman, Robert M., and Christopher D. Williams. "Accounting discretion, loan loss provisioning, and discipline of banks’ risk-taking." Journal of Accounting and Economics 54, no. 1 (2012): 1-18. Bushman, Robert M., and Christopher D. Williams. "Delayed expected loss recognition and the risk profile of banks." Journal of Accounting Research 53, no. 3 (2015): 511-553. Collins, Julie H., Douglas A. Shackelford, and James M. Wahlen. "Bank differences in the coordination of regulatory capital, earnings, and taxes." Journal of Accounting Research (1995): 263-291. Dugan, J.,2009.Loan loss provisioning and pro-cyclicality. Remarks by John C. Dugan Comptroller of the Currency before the Institute of International Bankers http://www.occ.treas.gov/ftp/release/2009-16a.pdf. Financial Stability Forum. "Report of the Financial Stability Forum on addressing pro-cyclicality in the financial system." (2009). US Government Accountability Office (GAO). Financial Institutions: Causes and Consequences of Recent Bank Failures. (2013). GAO-13-71. Harris, Trevor S., Urooj Khan, and Doron Nissim. "The Expected Rate of Credit Losses on Banks' Loan Portfolios." The Accounting Review (2018).

Jayaraman, Sudarshan, Bryce Schonberger, and Joanna Shuang Wu. Good Buffer, Bad Buffer. Working paper (2017).

32

Kishan, Ruby P., and Timothy P. Opiela. "Bank size, bank capital, and the bank lending channel." Journal of Money, Credit and Banking 32, no. 1 (2000): 121-141. Laeven, Luc, and Giovanni Majnoni. "Loan loss provisioning and economic slowdowns: too much, too late?." Journal of financial intermediation 12, no. 2 (2003): 178-197.

Laux, Christian, and Thomas Rauter. "Procyclicality of US bank leverage." Journal of Accounting Research 55, no. 2 (2017): 237-273. Liu, Chi-Chun, and Stephen G. Ryan. "Income smoothing over the business cycle: Changes in banks' coordinated management of provisions for loan losses and loan charge-offs from the pre-1990 bust to the 1990s boom." The Accounting Review 81, no. 2 (2006): 421-441. Ryan, Stephen G., and Jessica H. Keeley. "Discussion of “Did the SEC impact banks’ loan loss reserve policies and their informativeness?”." Journal of Accounting and Economics 56, no. 2-3 (2013): 66-78.

33

Figure 1. Distributions of reported vs. expected allowance and provisions. ALLR (ALLE) is the reported (estimated) allowance of loan losses scaled by lagged total loans. LLPR (LLPE) is the reported (estimated) provision of loan losses scaled by lagged total loans. The sample covers annual US bank holding companies’ observations for the period from 1986 to 2017 that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website.

34

Table 1: Descriptive statistics This table reports descriptive statistics for the sample. 𝑁𝑁𝑁𝑁𝑁𝑁 is net charge-offs scaled by lagged total loans. 𝐸𝐸𝐵𝐵𝐿𝐿 is net income plus loan loss provision. 𝑁𝑁𝐼𝐼 is net income. 𝑁𝑁𝐼𝐼𝑝𝑝𝐼𝐼 is the ratio of total equity to total assets. ∆𝐸𝐸𝐼𝐼𝑃𝑃𝐼𝐼𝑟𝑟𝐼𝐼𝐿𝐿𝐼𝐼 is the absolute change in leverage, where leverage is the ratio of total assets to total equity. ∆𝐸𝐸𝑈𝑈𝐼𝐼𝐼𝐼 is the percentage change in total loans outstanding. ∆𝐸𝐸𝐷𝐷𝐼𝐼𝐿𝐿𝐷𝐷𝑈𝑈𝐷𝐷𝑡𝑡𝑦𝑦 is the percentage change in total liability outstanding. 𝐴𝐴𝐸𝐸𝐸𝐸𝐼𝐼 is the reported allowance of loan losses scaled by lagged total loans. 𝐸𝐸𝐸𝐸𝐿𝐿𝐼𝐼 is the reported loan loss provision scaled by lagged total loans. 𝑁𝑁𝐴𝐴𝐸𝐸 is the non-accrual loans scaled by lagged total loans. 𝐸𝐸𝑈𝑈𝐼𝐼𝐼𝐼 is total loans outstanding (billion US$). 𝐴𝐴𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡 is total assets (billion US$). IntRate is total interest income scaled by lagged total loans. The sample covers all annual US bank holding companies’ observations for the period from 1986 to 2017 that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated for all the variables constructed based on banks’ financial reports that appear in our regressions. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. count mean sd p25 p50 p75 NCO 28803 0.004 0.006 0.001 0.002 0.005 EBP 28832 0.023 0.011 0.016 0.021 0.027 NI 28867 0.017 0.012 0.012 0.017 0.023 CapR 31702 0.088 0.026 0.071 0.086 0.102 ΔLeverage 28927 -0.107 1.644 -0.767 -0.163 0.465 ΔLoan 28843 0.097 0.130 0.022 0.081 0.152 ΔLiability 28839 0.087 0.118 0.018 0.064 0.126 ALLR 28909 0.016 0.006 0.012 0.015 0.019 LLPR 28849 0.005 0.007 0.002 0.003 0.006 NAL 27293 0.011 0.013 0.003 0.006 0.013 Loan 32131 3.984 36.246 0.135 0.287 0.753 Asset 32131 7.698 82.866 0.220 0.460 1.148 IntRate 28814 0.111 0.043 0.079 0.105 0.134

35

Table 2: Descriptive statistics of the reported vs. estimated variables This table presents percentiles of the distribution of the estimated loan loss allowances and provisions as well as their reported counterparts. ALLR (ALLE) is the reported (estimated) allowance of loan losses scaled by lagged total loans. LLPR (LLPE) is the reported (estimated) provision of loan losses scaled by lagged total loans. UNDERR equals ALLE minus ALLR and is a measure of under-reserving for loan losses in a given bank-year. The sample covers annual US bank holding companies’ observations for the period from 1986 to 2017 that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. count mean sd p1 p10 p25 p50 p75 p90 p99 ALLR 28909 0.016 0.006 0.006 0.010 0.012 0.015 0.019 0.024 0.040 ALLE 19564 0.019 0.008 0.008 0.011 0.014 0.017 0.023 0.030 0.049 LLPR 28849 0.005 0.007 -0.001 0.001 0.002 0.003 0.006 0.012 0.035 LLPE 16883 0.004 0.008 -0.016 -0.004 -0.000 0.003 0.008 0.013 0.031 UNDERR 19476 0.004 0.009 -0.017 -0.007 -0.002 0.003 0.008 0.016 0.031

36

Table 3. Predictive power of the reported vs. estimated allowance This table reports the estimates from the OLS regressions of cumulative future charge-offs on the reported and estimated allowances for the period from 1986 to 2017. The sample covers all US bank holding companies that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated for the dependent and independent variables. Future losses is the sum of net charge-offs in the next three years scaled by lagged total loans. ALLR (ALLE) is the reported (estimated) allowance of loan losses scaled by lagged total loans. NCO is net charge-offs scaled by lagged total loans. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Standard errors are clustered by bank. Robust t-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. (1) (2) (3) (4) (5) (6) VARIABLES Future losses Future losses Future losses Future losses Future losses Future losses ALLR 0.473*** 0.304*** 0.142*** 0.164*** (9.494) (7.134) (3.282) (3.971) ALLE 1.039*** 1.019*** 0.927*** 0.929*** (39.92) (40.05) (33.11) (33.29) NCO 1.126*** 0.594*** 0.528*** (22.66) (10.68) (9.318) Observations 14,332 14,332 14,332 14,332 14,332 14,332 R-squared 0.023 0.278 0.288 0.109 0.302 0.305 Clustering Level Bank Bank Bank Bank Bank Bank

37

Table 4. Value relevance of the reported vs. estimated allowances and provisions for loan losses This table reports the average Fama and MacBeth (1973) regression estimates from cross sectional regressions of prices and returns on the reported and estimated allowances and provision. The regressions are estimated annually using data from 1986 to 2017. The sample covers all listed US bank holding companies that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated for the dependent and independent variables. Price is the closing price at the end of April of the next year and is scaled by loan per share. Loan per share is the lagged total loans divided by the number of shares for the month in which the stock price is measured. Ret is the buy-and-hold return over the period from the end of April of the current year to the end of April of the next year. ALLR (ALLE) is the reported (estimated) allowance of loan losses scaled by lagged total loans. LLPR (LLPE) is the reported (estimated) provision of loan losses scaled by lagged total loans. CapR is the ratio of total equity to total assets. NI is net income scaled by lagged total loans. Size is the natural log of total assets. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Monthly stock returns for listed bank holding corporations are obtained from the Center for Research in Security Prices (CRSP). Standard errors are based on the Fama-MacBeth procedure; t-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. (1) (2) (3) (4) VARIABLES Price Price Ret Ret ALLR 0.854 (0.961) ALLE -1.707*** (-2.933) LLPR -1.222 (-0.839) LLPE -1.014** (-2.158) CapR 1.891*** 1.876*** (12.83) (11.70) NI 2.699*** 2.944*** (3.384) (3.185) Size 0.0262*** 0.0283*** 0.00155 0.000655 (11.62) (11.03) (0.186) (0.0748) Observations 5,365 5,365 4,875 4,875 R-squared 0.195 0.205 0.112 0.103 Number of groups 22 22 21 21

38

Table 5. Pro-cyclicality of the reported vs. estimated allowances and provisions for loan losses This table reports the estimates from the OLS regressions of the reported and estimated allowances and provision on macroeconomic conditions for the period from 1986 to 2017. The sample covers all US bank holding companies that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated for the dependent and independent variables (except the macroeconomic variables). ALLR (ALLE) is the reported (estimated) allowance of loan losses scaled by lagged total loans. LLPR (LLPE) is the reported (estimated) provision of loan losses scaled by lagged total loans. ΔGDP is the real GDP growth rate over the current year. ΔLoan is the percentage change in total loans outstanding over the current year. Size is the natural log of total assets. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Standard errors are clustered by bank. Robust t-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. Panel A: Response to GDP growth (1) (2) (3) (4) VARIABLES ALLR ALLE LLPR LLPE ΔGDP -0.0338*** 0.0507*** -0.106*** 0.109*** (-15.23) (13.88) (-27.98) (22.94) Size -0.000390** 0.00319*** -0.000619*** 0.00256*** (-2.344) (18.36) (-5.511) (16.29) Constant 0.0223*** -0.0266*** 0.0178*** -0.0360*** (9.857) (-11.14) (11.18) (-16.20) Observations 19,288 19,288 16,632 16,632 R-squared 0.524 0.299 0.399 0.162 Bank Fixed Effect YES YES YES YES Clustering Level Bank Bank Bank Bank Panel B: Response to loan growth (1) (2) (3) (4) VARIABLES ALLR ALLE LLPR LLPE ΔLoan -0.00142*** 0.0232*** -0.00853*** 0.0229*** (-2.681) (34.10) (-16.32) (29.42) Size -4.17e-06 0.00351*** 0.000622*** 0.00184*** (-0.0252) (19.37) (5.509) (11.54) Constant 0.0156*** -0.0307*** -0.00334** -0.0232*** (6.950) (-12.47) (-2.169) (-10.64) Observations 19,288 19,288 16,632 16,632 R-squared 0.515 0.377 0.313 0.201 Bank Fixed Effect YES YES YES YES Clustering Level Bank Bank Bank Bank

39

Table 6. Income smoothing of the reported vs. estimated provisions for loan losses This table reports the estimates from the OLS regressions of the reported and estimated provision on earnings before provisions for the period from 1986 to 2017. The sample covers all US bank holding companies that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated for the dependent and independent variables (except the macroeconomic variables). LLPR (LLPE) is the reported (estimated) provision of loan losses scaled by lagged total loans. EBP is net income plus loan loss provision scaled by lagged total loans. NCO is net charge-offs scaled by lagged total loans. Size is the natural log of total assets. ΔGDP is the real GDP growth rate over the current year. CapR is the ratio of total equity to total assets. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Standard errors are clustered by bank. Robust t-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. (1) (2) (3) (4) (5) (6) VARIABLES LLPR LLPE LLPR LLPE LLPR LLPE EBP 0.0571*** 0.0731*** 0.0716*** 0.0841*** 0.0942*** 0.133*** (4.352) (5.057) (10.30) (6.789) (10.84) (7.530) NCO 0.967*** 0.731*** 0.893*** 1.017*** (85.39) (30.17) (76.00) (42.30) Size -0.000290*** 0.00251*** (-4.179) (19.09) ΔGDP -0.0402*** 0.189*** (-20.58) (47.88) CapR -0.0315*** 0.00249 (-11.65) (0.531) EBPt-1 -0.00382 -0.158*** (-0.549) (-8.956) Constant 0.00309*** 0.00250*** -0.000536*** -0.000241 0.00809*** -0.0421*** (10.70) (7.862) (-3.379) (-0.841) (8.112) (-22.22) Observations 16,689 16,689 16,689 16,689 16,386 16,386 R-squared 0.279 0.114 0.762 0.225 0.780 0.356 Bank Fixed Effect YES YES YES YES YES YES Clustering Level Bank Bank Bank Bank Bank Bank

40

Table 7. Predictive power of under-reserving This table reports the estimates from the OLS regressions of banks’ future performance on the level of under-reserving for the period from 1986 to 2017. The sample covers all US bank holding companies that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated for the dependent and independent variables (except the macroeconomic variables). NI is net income scaled by lagged total loans. CapR is the ratio of total equity to total assets. UNDERR is ALLE minus ALLR, where ALLR (ALLE) is the reported (estimated) allowance of loan losses scaled by lagged total loans. NCO is net charge-offs scaled by lagged total loans. CapR is the ratio of total equity to total assets. ΔGDP is the real GDP growth rate. Size is the natural log of total assets. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Standard errors are clustered by bank. Robust t-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. (1) (2) (3) (4) (5) (6) (7) (8) (9) VARIABLES LLPRt+1 NIt+1 CapRt+1 LLPRt+2 NIt+2 CapRt+2 LLPRt+3 NIt+3 CapRt+3 UNDERRt 0.213*** -0.293*** -0.113*** 0.292*** -0.326*** -0.149*** 0.247*** -0.270*** -0.125*** (23.30) (-21.84) (-8.811) (26.89) (-22.27) (-7.077) (26.14) (-18.72) (-4.981) NCOt 0.233*** -0.328*** 0.105*** -0.147*** 0.0412 0.225*** -0.366*** 0.243*** 0.264*** (11.87) (-11.61) (4.053) (-7.176) (1.383) (5.400) (-18.50) (7.817) (4.975) CapRt -0.00729 0.0401*** 0.731*** -0.000445 0.00922 0.500*** 0.00220 -0.0154 0.315*** (-1.643) (3.912) (60.52) (-0.0798) (0.824) (27.65) (0.335) (-1.357) (13.91) ΔGDPt -0.000987*** 0.000854*** -1.18e-05 -0.000642*** 0.000467*** -7.61e-05 2.36e-05 -0.000277*** -0.000139 (-25.66) (17.40) (-0.248) (-17.89) (8.987) (-0.993) (0.708) (-5.645) (-1.548) Sizet -0.000525*** -0.00356*** 0.00299*** 0.000765*** -0.00510*** 0.00521*** 0.00244*** -0.00689*** 0.00711***

(-4.347) (-14.02) (11.63) (4.776) (-16.77) (11.44) (11.77) (-18.29) (11.66) Constant 0.0155*** 0.0598*** -0.0156*** -0.00300 0.0838*** -0.0245*** -0.0282*** 0.113*** -0.0332*** (9.348) (16.63) (-4.591) (-1.354) (19.66) (-3.932) (-9.624) (21.27) (-3.887) Observations 16,638 16,638 16,638 14,834 14,834 14,834 13,244 13,244 13,244 R-squared 0.450 0.640 0.881 0.399 0.606 0.810 0.395 0.595 0.770 Bank Fixed Effect YES YES YES YES YES YES YES YES YES Clustering Level Bank Bank Bank Bank Bank Bank Bank Bank Bank

Table 8. Under-reserving banks’ performance during the financial crisis of 2008 This table reports the estimates from the OLS regressions of bank returns and loan growth in 2008/2007 on the level of under-reserving in 2007/2006. The sample covers all listed US bank holding companies that have at least 15 years of available data during the full sample period of 1986-2017. The top and bottom 1% observations are truncated for the dependent and independent variables. Returnt+1 is the buy-and-hold return over the period from the end of April of year t+1 to the end of April of year t+2. ∆𝐸𝐸𝑈𝑈𝐼𝐼𝐼𝐼 is the percentage change in total loans outstanding over the year 2008. UNDERRt is ALLEt minus ALLRt, where ALLRt (ALLEt) is the reported (estimated) allowance of loan losses at the end of year t scaled by total loans at the end of year t-1. Sizet is the natural log of total assets at the end of year t. CapRt is the ratio of total equity to total assets at the end of year t. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Monthly stock returns for listed bank holding corporations are obtained from the Center for Research in Security Prices (CRSP). T-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. Panel A: Crisis period (1) (2) VARIABLES Return2008 ΔLoan2008 UNDERR2007 -7.777*** -1.321** (-2.831) (-2.164) Size2007 0.0134 0.00384 (0.868) (0.981) CapR2007 1.513* 0.125 (1.709) (0.808) ALLR2007 -21.58*** -5.096*** (-4.677) (-4.807) Constant -0.233 0.111** (-0.986) (2.002) Observations 260 702 R-squared 0.098 0.033 Panel B: Placebo period (1) (2) VARIABLES Return2007 ΔLoan2007 UNDERR2006 -2.884 1.446** (-1.594) (2.217) Size2006 0.0105 0.00570 (1.090) (1.550) CapR2006 0.180 -0.0951 (0.319) (-0.617) ALLR2006 -9.140*** 2.423** (-2.618) (2.009) Constant -0.172 -0.0218 (-1.073) (-0.391) Observations 298 755 R-squared 0.031 0.013

42

Table 9. Real effects of the current provisioning rule: Under-reserving distorts bank decisions This table reports the estimates from the OLS regressions of the changes in loan, leverage and liability, and the level of dividend on the level of under-reserving (and its interaction with real GDP growth in some ) for the period from 1986 to 2017. The sample covers all US bank holding companies that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated for the dependent and independent variables (except the macroeconomic variables). ΔLoan is the percentage change in total loans outstanding. ΔLeverage is the absolute change in leverage and leverage is the ratio of total assets to total equity. Δliability is the percentage change in total bank liabilities. Dividends is cash dividends declared on common stock scaled by lagged total loans. UNDERR is ALLE minus ALLR, where ALLR (ALLE) is the reported (estimated) allowance of loan losses scaled by lagged total loans. ΔGDP is the real GDP growth rate. CapR is the ratio of total equity to total assets. Size is the natural log of total assets. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Standard errors are clustered by bank. Robust t-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. Panel A: The impact of under-reserving on the changes of loan, leverage, liability, and the level of dividend. (1) (2) (3) (4) VARIABLES ΔLoant ΔLeveraget ΔLiabilityt Dividendst UNDERRt-1 4.220*** 11.24** 3.148*** 0.121*** (12.80) (2.522) (10.82) (7.849) ΔGDPt 1.115*** 2.059** 0.301*** 0.0192*** (18.22) (2.412) (5.322) (9.052) CapRt-1 0.536*** 26.43*** 1.033*** 0.0387*** (5.936) (14.25) (12.07) (7.836) Sizet-1 -0.0552*** -0.355*** -0.0717*** -6.91e-05 (-15.97) (-11.52) (-22.38) (-0.506) ALLEt-1 -4.824*** 6.395 -2.882*** -0.151*** (-13.00) (1.244) (-9.051) (-9.424) Constant 0.822*** 2.106*** 0.996*** 0.00497*** (17.12) (4.922) (22.63) (2.608) Observations 17,551 17,604 17,533 17,550 R-squared 0.312 0.166 0.310 0.661 Bank Fixed Effect YES YES YES YES Clustering Level Bank Bank Bank Bank

43

Panel B. The impact of under-reserving on the reactions to GDP shocks (1) (2) (3) VARIABLES ΔLoant ΔLeveraget ΔLiabilityt ΔGDPt 1.340*** 2.767** 0.102 (15.51) (2.400) (1.323) UNDERRt-1 5.024*** 15.69*** 2.629*** (13.50) (2.764) (7.876) ΔGDPt*UNDERRt-1 -20.17*** -165.1** 12.09*** (-4.286) (-1.968) (2.788) Sizet-1 -0.0507*** -0.220*** -0.0684*** (-14.57) (-7.651) (-21.40) ALLEt-1 -5.172*** -1.770 -3.099*** (-13.83) (-0.362) (-9.640) Constant 0.806*** 2.843*** 1.061*** (16.40) (6.575) (23.56) Observations 17,551 17,604 17,533 R-squared 0.309 0.103 0.294 Bank Fixed Effect YES YES YES Clustering Level Bank Bank Bank

Panel C. The capital crunch of low UNDERR vs. high UNDERR banks

(1) (2) (3) ΔLoant ΔLoant ΔLoant VARIABLES Full sample low UNDERRt-1 high UNDERRt-1 CapRt-1 0.314*** 0.183 0.704*** (3.166) (0.862) (2.756) Slowdownt -0.0709*** -0.0524*** -0.0737*** (-8.833) (-2.698) (-3.246) CapRt-1*Slowdownt 0.415*** 0.243 0.508** (4.865) (1.371) (1.977) Sizet-1 -0.0582*** -0.0577*** -0.0572*** (-16.64) (-5.539) (-5.976) ALLEt-1 -1.352*** -1.065* -1.800*** (-8.795) (-1.849) (-5.017) Constant 0.896*** 0.859*** 0.895*** (19.26) (6.195) (6.828) Observations 17,617 3,424 3,571 R-squared 0.291 0.439 0.490 Bank Fixed Effect YES YES YES Clustering Level Bank Bank Bank

44

Table 10. Probability of failure for under-reserving banks This table reports the estimates from the probit regressions of future bank failures on previous levels of under-reserving for the period from 1986 to 2017. The sample covers all US bank holding companies that have at least 15 years of available data during the sample period and those bank holding companies that do not have 15 years of available data, but that are the primary holder of a commercial bank that failed in the sample period. The top and bottom 1% observations of the independent variables are truncated. Failure equals 1 if the bank holding company is the primary holder of a commercial bank that failed in given year, 0 otherwise. UNDERR is ALLE minus ALLR, where ALLR (ALLE) is the reported (estimated) allowance of loan losses scaled by lagged total loans. Size is the natural log of total assets. CapR is the ratio of total equity to total assets. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Commercial bank failure data comes from the Federal Deposit Insurance Corporation (FDIC) website. Standard errors are clustered by bank. Robust t-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. (1) (2) (3) (4) VARIABLES Failuret+1 Failuret+3 Failuret+3 Failuret+3 UNDERRt+2 54.53*** (3.506) UNDERRt+1 -7.307 (-0.460) UNDERRt 49.07*** 42.34*** 38.08*** 31.21** (4.631) (10.43) (10.10) (2.078) Sizet 0.161 52.39*** 23.64*** (1.384) (6.753) (2.677) ALLRt 73.50*** 0.0569 0.0402 (3.639) (1.364) (1.206) CapRt -31.38*** -11.28*** -4.207* (-4.216) (-3.946) (-1.754) Sizet+2 0.176 (1.205) ALLRt+2 72.33** (2.330) CapRt+2 -33.15*** (-3.172) Observations 19,380 19,166 18,405 14,100 Clustering Level Bank Bank Bank Bank

45

Appendix

Table A1: Regressions that predict loan default probability This table reports results of regression (5) that predicts default probability in the next five years. The regressions are estimated separately on the smallest 67% firms and largest 33% of firms, sorted into these two groups in the beginning of each year. The sample covers all US bank holding companies that have at least 15 years of available data during the sample period of 1986-2017. The top and bottom 1% observations of the dependent and independent variables (except the macroeconomic variables) are truncated. The dependent variables are the default rates over the next five years 𝑝𝑝𝑡𝑡+1… 𝑝𝑝𝑡𝑡+5, where 𝑝𝑝 is net charge-offs scaled by lagged total loans. 𝑁𝑁𝐴𝐴𝐸𝐸 is non-accrual loans scaled by lagged total loans. Pastdue90 is loans past due 90 days or more scaled by lagged total loans. Loan is total loans outstanding (billion US$). 𝑈𝑈𝐼𝐼𝐼𝐼𝑈𝑈𝑝𝑝𝑈𝑈𝑈𝑈𝑦𝑦𝑈𝑈𝐼𝐼𝐼𝐼𝑡𝑡 is the unemployment rate. 𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼 is total interest income scaled by lagged total loans. ΔGDP is the real GDP growth rate. 𝑁𝑁𝐶𝐶𝐼𝐼𝐼𝐼𝑡𝑡 is the return of the Case-Shiller Home Price Index. ∆ is the difference operator where ∆𝐶𝐶𝑡𝑡 = 𝐶𝐶𝑡𝑡 − 𝐶𝐶𝑡𝑡−1. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Standard errors are clustered by bank. Robust t-statistics are in parentheses, and significance is indicated by: ∗∗∗ < 0.01, ∗∗ < 0.05, ∗ < 0.10. Panel A: Smallest 67% firms (1) (2) (3) (4) (5) pt+1 pt+2 pt+3 pt+4 pt+5 Constant -5.212*** -4.715*** -4.033*** -3.932*** -4.248*** (-46.15) (-39.59) (-28.22) (-23.09) (-22.16) NALt 12.43*** 10.89*** 8.935*** 9.705*** 8.938** (11.79) (8.62) (5.24) (4.47) (2.90) Pastdue90t 14.36*** 5.620 7.035*** 4.809 3.506 (7.84) (1.89) (4.16) (1.23) (0.80) ΔLoant 0.0548 0.675*** 1.187*** 1.636*** 1.724*** (0.36) (4.43) (7.56) (9.95) (8.05) Unemploymentt -0.0919*** -0.178*** -0.269*** -0.267*** -0.163*** (-7.88) (-13.36) (-18.03) (-14.72) (-7.80) ΔUnemploymentt 0.132*** 0.278*** 0.334*** 0.362*** 0.190*** (3.57) (6.40) (7.31) (7.20) (3.66) ΔIntRatet -2.367* 2.529 7.216*** 13.32*** 10.33*** (-2.36) (1.91) (4.32) (7.16) (5.30) IntRatet -0.931 -3.821*** -9.508*** -16.35*** -17.43*** (-1.50) (-5.50) (-11.05) (-16.01) (-14.55) pt 43.02*** 38.74*** 35.70*** 28.85*** 24.99*** (12.27) (9.72) (7.75) (4.64) (3.48) Δpt -5.688 -6.642 -8.022 -0.839 -7.627 (-1.91) (-1.72) (-1.89) (-0.15) (-1.39) ΔGDPt 0.606 9.624*** 19.74*** 30.80*** 24.19*** (0.27) (3.94) (7.62) (11.99) (8.69) CSRett -4.902*** -6.357*** -6.680*** -4.654*** 0.172 (-19.00) (-25.67) (-23.30) (-13.40) (0.36) Observations 15717 13277 11247 9645 8385 R-squared 0.594 0.499 0.441 0.417 0.430

46

Panel B: Largest 33% firms (1) (2) (3) (4) (5) pt+1 pt+2 pt+3 pt+4 pt+5 Constant -4.581*** -3.505*** -3.109*** -3.817*** -7.639*** (-35.71) (-22.20) (-14.14) (-15.47) (-20.05) NALt 5.810*** 2.886 -2.311 -5.864 -11.53** (4.63) (1.80) (-0.89) (-1.91) (-3.04) Pastdue90t 3.493*** 4.775*** 6.649 0.178 -5.694 (3.69) (3.56) (1.73) (0.03) (-0.68) ΔLoant 0.106 0.367** 0.696*** 0.945*** 0.792*** (0.73) (2.66) (5.19) (6.30) (4.57) Unemploymentt -0.178*** -0.313*** -0.385*** -0.261*** 0.173*** (-13.32) (-16.46) (-14.65) (-10.21) (4.39) ΔUnemploymentt 0.174*** 0.103* -0.0101 0.0919 -0.00528 (4.70) (2.24) (-0.15) (1.50) (-0.09) ΔIntRatet -2.324** 1.260 3.461** 8.003*** 3.054* (-2.69) (1.33) (2.80) (6.00) (2.39) IntRatet -0.498 -2.521** -6.051*** -12.55*** -3.778* (-0.77) (-2.93) (-4.21) (-5.90) (-2.43) pt 59.88*** 61.75*** 62.16*** 61.51*** 65.54*** (21.67) (23.70) (16.95) (11.75) (14.53) Δpt -15.65*** -21.25*** -22.84*** -19.10*** -18.17*** (-5.81) (-6.53) (-4.89) (-4.28) (-3.75) ΔGDPt 1.897 0.933 9.025** 21.95*** 17.64*** (1.03) (0.41) (2.64) (6.46) (6.87) CSRett -5.427*** -6.594*** -7.204*** -3.355*** 9.450*** (-22.38) (-23.63) (-20.68) (-7.59) (12.21) Observations 9825 9068 8312 7595 6984 R-squared 0.704 0.611 0.520 0.466 0.499

47

Table A2. Under-reserving and future stock performance This table reports the average Fama and MacBeth (1973) estimates from cross sectional predictive regressions of future returns on the reported and estimated provisions and the level of under-reserving. The regressions are estimated monthly using data from 1986 to 2017. The sample covers all listed US bank holding companies that have at least 15 years of available data during the sample period. The top and bottom 1% observations are truncated for the dependent and independent variables. Ret stands for the monthly stock returns measured over the window between May to April. Bank-level annual variables are measured as of the end of the the previous year. LLPR (LLPE) is the reported (estimated) provision of loan losses scaled by lagged total loans. ALLR is the reported allowance of loan losses scaled by lagged total loans. Size is the natural log of total assets. Bank fundamentals are obtained from FR Y-9C reports available on the Federal Reserve Bank of Chicago’s website. Monthly stock returns for listed bank holding corporations are obtained from the Center for Research in Security Prices (CRSP). Standard errors are based on the Fama-MacBeth procedure; t-statistics are in parentheses. ***, **, * indicate statistical significance at less than 1, 5, and 10%, respectively. (1) (2) (3) (4) (5) VARIABLES Rett+15 Rett+15 Rett+15 Rett+15 Rett+15 LLPR -0.178 -0.131 (-1.434) (-0.929) LLPE -0.0606 -0.0511 (-1.262) (-0.974) ALLR -0.0596 (-0.585) UNDERR -0.0923 -0.0767 (-1.636) (-1.176) Size 0.000417 0.000354 0.000409 0.000453 0.000407 (0.488) (0.413) (0.480) (0.542) (0.492) Observations 55,393 55,393 55,393 62,198 62,198 R-squared 0.063 0.059 0.069 0.058 0.065 Number of groups 252 252 252 264 264