Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
Expected Loan Loss Provisioning: An Empirical Model*
Yao Lu The University of Chicago Booth School of Business
Valeri Nikolaev The University of Chicago Booth School of Business
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 historical 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+1𝐵𝐵𝑡𝑡
�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+ 𝐿𝐿𝑡𝑡
𝑡𝑡+3
(1+𝑟𝑟𝑡𝑡)3+ ⋯+ 𝐿𝐿𝑡𝑡
𝑡𝑡+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−𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑡𝑡
𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑖𝑖𝑡𝑡−1, where 𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝐼𝐼𝑡𝑡𝐼𝐼𝑖𝑖𝑡𝑡 =
𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑟𝑟𝑁𝑁𝑜𝑜𝑡𝑡 𝑟𝑟𝑁𝑁𝑟𝑟𝑁𝑁𝐿𝐿𝑟𝑟𝑁𝑁𝑖𝑖𝑡𝑡𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑖𝑖𝑡𝑡−1
,
𝑁𝑁𝐴𝐴𝐸𝐸𝑖𝑖𝑡𝑡 =𝑁𝑁𝑜𝑜𝐿𝐿−𝑎𝑎𝑎𝑎𝑎𝑎𝑟𝑟𝑟𝑟𝑎𝑎𝑎𝑎 𝑎𝑎𝑜𝑜𝑎𝑎𝐿𝐿𝑜𝑜𝑖𝑖𝑡𝑡
𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑖𝑖𝑡𝑡−1, 𝐿𝐿𝐼𝐼𝑃𝑃𝑡𝑡𝑃𝑃𝑃𝑃𝐼𝐼90𝑖𝑖𝑡𝑡 =
𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑜𝑜 𝑝𝑝𝑎𝑎𝑜𝑜𝑡𝑡 𝑑𝑑𝑟𝑟𝑁𝑁 90 𝑑𝑑𝑎𝑎𝑑𝑑𝑜𝑜𝑖𝑖𝑡𝑡𝐿𝐿𝑜𝑜𝑎𝑎𝐿𝐿𝑖𝑖𝑡𝑡−1
, 𝑈𝑈𝐼𝐼𝐼𝐼𝑈𝑈𝑝𝑝𝑈𝑈𝑈𝑈𝑦𝑦𝑈𝑈𝐼𝐼𝐼𝐼𝑡𝑡𝑡𝑡 is the
unemployment rate, 𝑁𝑁𝐶𝐶𝐼𝐼𝐼𝐼𝑡𝑡𝑡𝑡 =𝑁𝑁𝐶𝐶𝐼𝐼𝐿𝐿𝑑𝑑𝑁𝑁𝐶𝐶𝑡𝑡−𝑁𝑁𝐶𝐶𝐼𝐼𝐿𝐿𝑑𝑑𝑁𝑁𝐶𝐶𝑡𝑡−1
𝑁𝑁𝐶𝐶𝐼𝐼𝐿𝐿𝑑𝑑𝑁𝑁𝐶𝐶𝑡𝑡−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).
http://www.occ.treas.gov/ftp/release/2009-16a.pdf
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
T