Measuring the Capital Shortfall of Large U.S. Banks

Eric Jondeau∗ and Amir Khalilzadeh†

August 2017

Abstract

We develop a new methodology to measure the capital shortfall of commercial banks

in a market downturn. The measure, which we call Stressed Expected Loss (SEL),

takes the structure of the individual banks balance sheet. The SEL is defined as

the difference between the market value of the assets under the stress scenario and

the book value of the deposits and short-term debt of the bank. We estimate the

evolution of the probability of default and the SEL of the 31 largest commercial

banks in the U.S. between 1996 and 2016. The probability of default in a downturn

has been as high as 50% on average between 2008 and 2012. It is by now much

smaller and close to 1% on average. In contrast, the SEL has been very high

(slightly below $400 billion) during the great financial crisis. However, it is still at

a relatively high level in the recent period, close to $200 billion.

Keywords: Systemic Risk, Capital Shortfall, Multi-factor Model.

JEL Classification: C32, G01,G20, G28, G32.

∗Swiss Finance Institute and University of Lausanne. Faculty of Business and Economics, CH 1015Lausanne, Switzerland. Eric.Jondeau@unil.ch.†University of Lausanne. Faculty of Business and Economics, Institute of Banking and Finance, CH

1015 Lausanne, Switzerland. Amir.Khalilzadeh@unil.ch.

1 Introduction

Since the recent financial crisis, stress testing large commercial banks has become an

imperative task for central banks and financial stability authorities in order to protect

depositors, tax-payers, and economies in general. A typical stress test consists in defining

a scenario with a stress event (e.g., an historical event or a hypothetical scenario), linking

the macroeconomic scenario to the bank’s balance sheet, assessing the impact of the

shocks on the quality of the balance sheet and finally evaluating the potential capital

shortfall in such an event. Designing a stress test model is subject to several issues,

which include the types or risks that can be covered by the test, the type of data that is

needed to measure the capital shortfall, and the definition of the stress scenario, among

others. Moreover, there is a trade-off between the ability of the model to assess different

types of risk and its complexity. For instance, it may be that the model works well to

describe real estate risk but fails to capture other types of risks that a bank may face.

We propose a simple framework in order to assess the vulnerability of commercial

banks and the amount of capital they need to survive a future market downturn. The

flexibility of our framework allows us to identify channels through which a bank could

become fragile and evaluate the bank’s ability to survive against various market condi-

tions. The main idea is that the market value of a bank’s assets may change over time in

response to certain stresses imposed by the market to the balance sheet. In severe market

conditions, such changes can force the bank to sell its assets with short notice or even

cause its default. Unlike conventional stress test models, which include the net income

and the accounting classifications of assets, we use balance sheet information and classify

assets by borrowers’ type. In particular, we recognize three potential borrowers, namely

government, households, and corporates, and further consider real estate borrowing as a

fourth asset class. One advantage of such classification is that a market exists for each

of these asset classes. Such classification allows us to evaluate the response of the bank’s

balance sheet to changes in the creditworthiness of its borrowers. We do so by assuming

2

that a change in the creditworthiness of a given type of borrowers can be measured by a

change in the market conditions of the corresponding asset class. Thus, the market value

of the bank’s assets is affected by any change in the financial markets due to the financial

standing of the borrowers or the macroeconomic conditions. We calculate the market val-

ues of the assets for the next period through simulating stress scenarios of the financial

markets. Finally, we assess the capital shortfall that a bank may face by comparing the

market value of its assets with the face value of its liabilities. We precisely define capital

shortfall as the Stressed Expected Loss (hereinafter, SEL), which corresponds to the lack

of equity of a commercial bank in a financial downturn.

Our contribution to the literature is twofold. First we describe a bank’s balance

sheet by classifying assets into a limited number of relevant groups that can be easily

related to market stress. Such classification makes the results free of any biases due to

the accounting standards across countries and the regulatory arbitrage due to the risk-

weighted assets. Moreover, all data we use throughout the paper are publicly available.

Second, our econometric methodology allows us to assess and forecast vulnerability of

the commercial banks against various market conditions.

Our sample is based on financial institutions with $50 billion or greater in total consol-

idated assets. This list broadly corresponds to the criterion adopted by the Dodd-Frank

Wall Street Reform and Consumer Protection Act and used for the Dodd-Frank Act su-

pervisory stress tests. From this list, we keep the firms whose business is predominantly

commercial banking, i.e., firms whose deposits exceed 50% of total liabilities. This cri-

terion reduces the list to 31 commercial banks. Our sample covers the period from 1996

to 2016. We define four categories of risky assets, which can be subject to a market

downturn, i.e., government, real estate, corporate, and household securities. For each

of these categories, we define a market factor index that measures the performance of a

well-diversified portfolio of such securities. We estimate the joint dynamics of the four

market factor returns using a Dynamic Conditional Correlation model. Innovations are

jointly drawn from a t copula, which allows for the occurrence of joint extreme events.

3

We use rolling windows of five years to update the estimate of the model’s parameters in

real time.

We measure the SEL by simulating a large number of market scenarios and identi-

fying scenarios that satisfy our criterion for a market downturn. In such an occurrence,

we compute the expected loss in the assets of the bank due to the market downturn.

Eventually, by averaging over all scenarios, we deduce the probability of default and the

SEL on a given bank in a given quarter. This approach allows us to analyze the capital

shortfall of large commercial banks over time, possibly under alternative scenarios.

We consider as our baseline scenario a three standard deviation market downturn for

real estate, corporate, and household securities. We find that the probability of default of

commercial banks in a market downturn is on average close to 10% around the dot.com

crisis and close to 50% during the great financial crisis. In the recent period (after 2014),

the average probability of default is close to 1%. The SEL measure reveals that the

capital shortfall of commercial banks in a market downturn is below $100 billion until

mid-2008 and then increases to $400 billion until 2013. In the recent period, the SEL

is close to $200 billion on average. We also note that on average 60% of the aggregate

SEL is due to the Top-4 commercial banks (JP Morgan Chase Bank, Wells Fargo Bank,

Bank of America, and Citibank). Last, the SEL measure is relatively close to the SRISK

measure promoted by Acharya et al. (2012b) and Brownlees and Engle (2016). However,

the timing of these measures display some interesting differences. In particular, SEL

increases before the start of the great financial crisis, whereas SRISK is close to 0 in

2007. In contrast, SEL increases less in 2008–2009 than SRISK. In the recent period,

both measures are relatively close to each other.

Relevant Literature. This paper is mainly related to the strand of literature which

aims at empirically evaluating the capital shortfall of financial institutions.1 Our paper

differs from most of the papers in this literature in that our measure of capital shortfall

1See Bisias et al. (2012) for an exhaustive survey of systemic risk analytics.

4

has a sensible economic interpretation and therefore can be used for policy analysis.

We follow the notion of SEL introduced recently by Jondeau and Khalilzadeh (2017).

They explicitly model in a general equilibrium framework the mechanisms that generate

a procyclical dynamic of the investment bank’s leverage and a countercyclical dynamic

of the commercial bank’s leverage. Specifically, they show how macroeconomic shocks

generate commercial bank’s capital shortfall through the collateralization process and

the transmission of losses. Their model-implied measure of capital shortfall is defined

as the expected loss on the deposits of commercial banks during stressed periods. This

definition is close to that of Acharya et al. (2012b), in which the externality that generates

systemic risk is a financial institution’s propensity to be undercapitalized in a crisis, i.e.,

when the financial system as a whole is undercapitalized. We compare our result with the

SRISK measure of Brownlees and Engle (2016), which provide an empirical evaluation of

this notion. Other papers relying on the SRISK measure are by Acharya et al. (2012a),

Acharya et al. (2014), and Engle et al. (2015).

An important feature of the SEL measure is that it is driven by the difference between

the market valuation of the assets and the book valuation of the liabilities. A similar point

was made by Adrian and Shin (2010, 2014). In particular, Adrian and Shin (2014) show

that the procyclicality of the leverage of investment banks is mainly explained by the

difference in valuation approaches. In a market downturn, the loss on its assets forces the

bank to reduce its debt, which results in deleveraging. In contrast, the contracyclicality

of the leverage of commercial banks is explained by He and Krishnamurthy (2014) with

a different line of argument: in a market downturn, the bank cannot compensate it loss

on its assets by a reduction in household’s deposits. Therefore, the equity reduces and

leverage increases. A default occurs if the bank cannot find additional financing to satisfy

its capital requirement.

Our paper is also related to Begenau et al. (2015), which study banks’ risk exposure

to interest rate and credit risk through factor portfolios. We share with their paper the

use of the information of the different markets corresponding to the assets of a bank.

5

However, we do not restrict our risk factors to be only interest rate and credit risk.

Instead, we identify the channels through which such risks or other types of risk can

impact the bank’s balance sheet.

Another related field is stress testing. Several countries, including the U.S. and the

euro area, impose regular stress tests to large financial institutions. Surveys presenting

stress-testing methodology before and after the great financial crisis are Sorge (2004),

Drehmann (2009), and more recently Kapinos et al. (2015). Our approach can be viewed

as a simplified tool to evaluate the sensitivity of individual commercial banks to a stress

scenario.

The SEL aims at mesuring what would be the cost of a bank failure for the government.

We assue that deposits are tuaranteed by an insurance mechanism, such as FDIC, and

that the fraction of deposits that could not be repaid by the defaulting bank should be

repaid by authorities and therefore, ultimately, by taxpayers. Clearly, this approache does

not take all potential costs that may have to be covered by the government. Some papers

have investigated the potential costs to the government from bank failures. These costs

can arise from (explicit or implicit) guarantees, which may be necessary to limit contagion

effects. In particular, Arslanalp and Liao (2015) define a banking sector contingent

liability index, which measures the cost of the implicit guarantee from the government

under an adverse scenario defined as a two-standard-deviation event.

The rest of the paper is organized as follows. In Section 2, we describe the theoretical

aspects and methodology of our approach to construct the SEL. In Section 3, we provide

details about the data that we use for the estimation of the SEL. In Section 4, we present

and comment our empirical results. Section 5 concludes.

2 Methodology

The objective of the paper is to propose a measure of capital shortfall of commercial

banks that has theoretical grounds, that is easy to compute and update and that can

6

be used to investigate various stress scenarios. Current measures of systemic risk or

capital shortfall suffer from at least one of the following issues: (1) some measures are

not driven by economic theory, (2) some cannot be easily obtained from public data, (3)

some rely on ad-hoc calibration, or (4) some are mainly driven by the accounting values

of balance sheet items. Our approach relies on accounting data and publicly available

market factors. The only calibration is the definition of the stress scenario.

2.1 Capital Shortfall

The main idea of this approach is that the value of the liabilities of a financial institution is

known in advance, whereas the value of its assets varies with financial markets conditions.

Deposits and debt (liabilities, in short) have to be repaid at their face (or accounting)

value plus an interest. In contrast, the value of the assets may be substantially reduced

in a market downturn. It may even be that the value of the assets decreases so much

that the bank cannot repay its liabilities and defaults.

We define the T -period ahead capital shortfall of a bank i as the expectation at time

t of the loss incurred by its debtors if it defaults in a market downturn between t and

t+ T (typically a quarter). The default trigger is defined as:

[A(i)MVt+T | Market downturnt:t+T ] ≤ L

(i)BVt+T , (1)

where A(i)MVt+T and L

(i)BVt+T denote the market value of the assets and the face value of the

liabilities (including interest payments), respectively. Liabilities are the sum of deposits,

short-term debt, and long-term debt, denoted by Dep(i)BVt+T , SD

(i)BVt+T , and LD

(i)BVt+T , respec-

tively. We condition on the occurrence of a market downturn because a bank’s default

in normal market conditions is unlikely and may not have severe consequences on the

financial system as a whole. More precisely, SEL is the additional amount of equity the

7

bank would need to cover its short-term liabilities in a market downturn:

SEL(i)t:t+T = (Dep

(i)BVt+T + SD

(i)BVt+T ) (2)

−Et[A(i)MVt+T | A(i)MV

t+T ≤ L(i)BVt+T in a Market downturnt:t+T ].

It is worth mentioning that the regulator should be concerned by losses incurred by

depositors but also by losses on short-term debt. The reason is that most of short-term

debt is interbank debt. Therefore, losses on short-term debt in a default could result in

a cascade of defaults from other banks. By including short-term debt, the SEL partly

takes interconnectedness into account.

Two remarks are in order regarding Equation (2): First, the book value of liabilities

L(i)BVt+T is known at date t and mostly relies on accounting data. In contrast, the market

value of assets A(i)MVt+T can be severely affected in a market downturn, in a way that is

related to the sensitivity of the assets of the bank to the market conditions. In the next

sections, we describe how we address this issue and how we measure SEL.

2.2 Structure of the Balance Sheet

We make two important assumptions to describe the bank’s balance sheet, which are

consistent with the logic of a stress test. First, we assume that on the asset side, cash

and other assets are not sensitive to a market shock. Therefore, only the return on

market-sensitive assets will be determined at the end of the period.2 Similarly, on the

liabilities side, the interest that the bank has to pay on deposits and debt is fixed at date

t, so that only the value of equity will be determined at the end of the period. Second, to

quantify the vulnerability of a bank to market shocks, we need to measure the sensitivity

of the assets of the bank to these shocks. One important issue in doing so is that the

balance sheet of a bank is reported on a quarterly basis. Within this time period, the

value of the assets can be affected by shocks but also by the possible rebalancing of the

2In fact, as we explain below, we define other assets as the part of the assets of the bank that is notcash and cannot be directly related to financial markets (such as fixed assets or leases).

8

bank’s portfolio. Therefore, in principle, the change in the value of the assets from one

quarter to the next can be due to changes in prices as well as in quantities. However,

following the strategy of stress tests, we assume that the bank does not rebalance its

portfolio between t and t+T and therefore that changes in the market value of the asset

classes are due to changes in prices only.

The structure of the balance sheet of bank i at date t is presented in Schema 1 below.

In parentheses are indicated the interest rates or rates of returns of the various assets

or liabilities. Given our assumptions, only the returns on Market-sensitive Assets and

Equity are determined at the end of the period. We use the notation Ra,t to denote the

simple return of item a and ra,t to denote the log-return, which we will use for the model.

Schema 1: Simplified balance sheet of a commercial bank

Assets Liabilities

(RF,t) Cash: Cash(i)t Deposits: Dep

(i)t (RDep,t)

(RMA,t+T ) Market-sensitive Assets: MA(i)t

(RG,t+T ) - Government: G(i)t Debt: D

(i)t (RD,t)

(RR,t+T ) - Real estate: R(i)t - Short-term debt: SD

(i)t (RSD,t)

(RC,t+T ) - Corporates: C(i)t - Long-term debt: LD

(i)t (RLD,t)

(RH,t+T ) - Households: H(i)t

(RO,t) Other Assets O(i)t Equity: N

(i)t (RN,t+T )

In the balance sheet above, Cash (Cash(i)t ) refers to any asset with maturity less than

one quarter. As we are interested in the expected loss of the bank in the next quarter,

we treat assets maturing within a quarter as safe assets, so that the risk-free rate is set

at the beginning of each quarter.

Market-sensitive Assets (MA(i)t ) are the assets of the bank that are subject to

market risks and could be affected by changes in their prices. We define four categories

of market-sensitive assets.3 In a broad sense, Government Securities (G(i)t ) include

3Chakraborty et al. (2016) define three categories of assets for a bank: real estate exposure (measuredby MBS, unsecuritized non-commercial real estate loans, and commercial mortgages), consumer loans(including all loans to individuals not secured by real estate, and Commercial and Industrial loans. Wealso include government securities as market-sensitive assets because it is also affected by interest-raterisk (see Begenau et al., 2015).

9

U.S. Treasury securities, government agency securities, government sponsored agencies

securities, and securities issued by state and political agencies. Real estate Securities

(R(i)t ) are assets related to real estate of any kind. They are either real estate loans

directly lent by the banks or securities backed by real estate loans (MBS). We consider

real estate independently from household and corporate securities because both residential

real estate borrowing by households and commercial real estate borrowing by firms share

the same underlying risk, i.e., real estate risk. Corporate Securities (C(i)t ) include

loans to individuals or enterprises with commercial and industrial purposes (C&I), which

can be secured (but not by real estate) or unsecured, and securities backed by these loans.

Last, Household Securities (H(i)t ) are either consumer loans directly lent by the bank

or securities backed by consumer loans or other asset-backed securities (ABS). In both

cases, the underlying assets are loans such as automobile loans and credit card loans.

Details on the construction of the various items are provided in Appendix A. We

have done our best to reclassify the other assets within the four market-sensitive assets

categories when it was possible.4

The structure of the balance sheet imposes that:

(1 +RF,t)Cash(i)t + (1 +R

(i)MA,t+T )MA

(i)t + (1 +R

(i)O,t)O

(i)t

= (1 +R(i)Dep,t)Dep

(i)t + (1 +R

(i)D,t)D

(i)t + (1 +R

(i)N,t+T )N

(i)t . (3)

As changes in the balance sheet items incorporate both the price effect and the quan-

tity effect (due to rebalancing), we cannot use them to measure the sensitivity of the

assets of the banks to market shocks. To avoid this pitfall, we rely on market factors

that capture the price impact only. More specifically, we assume that the price change in

a given category of bank’s market-sensitive assets is given by the corresponding market

index return: R(i)a,t+T = R

(m)a,t+T .5 The definition of the market factor indexes is discussed

in Section 3.3.

4When other assets can be viewed as part of any of the four market-sensitive categories, we havereaffected them to the corresponding category. When it was not possible, we kept them as other assets.Eventually, the other assets category includes for instance fixed and intangible assets, leases, foreign debtsecurities, and equity securities. Overall, they represent approximately 20% of total assets. We assumethat the return on other assets is independent from the market returns. In Appendix A.4, we providedetails on how we reclassified part of the other assets.

5Assuming a sensitivity equal to 1 between the market factor return and the price chage in thecorresponding bank’s market-sensitive asset is also justified by the fact that we consider large commercial

10

Eventually, we measure the market value of the market-sensitive assets at date t+ T

(excluding portfolio rebalancing) as MA(i)t+T = (1 + R

(i)MA,t+T )MA

(i)t , where we define the

risky assets return as the weighted sum of each component’s return:

R(i)MA,t+T =

1

MA(i)t

[G

(i)t R

(m)G,t+T +R

(i)t R

(m)R,t+T + C

(i)t R

(m)C,t+T +H

(i)t R

(m)H,t+T

]= w

(i)G,t R

(m)G,t+T + w

(i)R,t R

(m)R,t+T + w

(i)C,t R

(m)C,t+T + w

(i)H,t R

(m)H,t+T , (4)

where w(i)a,t is the weight of asset category a in total market-sensitive assets at the beginning

of the period. We use this relation to quantify the impact of a shock on risky assets factors

to the assets of the bank at the end of the period.

2.3 Estimation Strategy

The main question is now to determine the market value of the market-sensitive assets

in the case of a market downturn. To address this question, we need a model that

describes the joint dynamics of the market factors returns. More specifically, we need

to capture two important properties of the data: (1) the time dependence of market

factor returns, which has to describe how a stress scenario can develop through time; (2)

the contemporaneous dependence between the market factor returns, which has to allow

for joint crashes. To do so, we design a model for daily market factor returns with the

following properties: time dependence is described by a Dynamic Conditional Correlation

(DCC) model; contemporaneous dependence is described by a copula model, which allows

for co-crashes. A similar approach has been adopted by Brownlees and Engle (2016) and

Engle et al. (2015).

The model is the following: we define the vector of market factor excess log-returns,

r̃(m)t+1 =

(r̃

(m)G,t+1, r̃

(m)R,t+1, r̃

(m)C,t+1, r̃

(m)H,t+1

)′, where r̃

(m)a,t+1 = r

(m)a,t+1 − rF,t. To describe the time

dependence of the system, we define the vector that includes two consecutive daily excess

log-returns: Xt+1 = (r̃(m)t+1 , r̃

(m)t )′. Conditional on the information set at date t − 1, the

return process at t+1 has mean Et−1[Xt+1] = 0 and covariance matrix Vt−1[Xt+1] = Ht+1.

The conditional covariance matrix Ht+1 is estimated using a DCC model (Engle and

banks, which presumably hold well-diversified portfolios. We follow the approach adopted by Begenauet al. (2015).

11

Sheppard, 2001; Engle, 2001):

Ht+1 = D−1/2t+1 Γt+1D

−1/2t+1 ,

Γt+1 = (diag (Qt+1))−1/2Qt+1 (diag (Qt+1))−1/2 ,

Qt+1 = (1− δ1 − δ2)Q̄+ δ1Qt + δ2 D−1/2t−1 Xt−1X

′t−1D

−1/2t−1 ,

where diag(Qt+1) denotes a matrix with zeros, except for the diagonal that contains the

diagonal of Qt+1, and Dt+1 is the diagonal matrix with the variances of Xt+1 (conditional

on t−1) on its diagonal and zero elsewhere. Parameters δ1 and δ2 are restricted to ensure

that the conditional correlation matrix, Γt+1, is positive definite.

Using the dynamic covariance matrix Ht+1 estimated with the DCC model, we then

deduce the following Dynamic Conditional Beta (DCB) model, which describes the dy-

namics of the market factor returns (see Engle, 2012):

r̃(m)G,t+1 = β

(G)G,t+1 r̃

(m)G,t + εG,t+1 (5)

r̃(m)R,t+1 = β

(G)R,t+1 r̃

(m)G,t + β

(R)R,t+1 r̃

(m)R,t + β

(C)R,t+1 r̃

(m)C,t + β

(H)R,t+1 r̃

(m)H,t + εR,t+1

r̃(m)C,t+1 = β

(G)C,t+1 r̃

(m)G,t + β

(R)C,t+1 r̃

(m)R,t + β

(C)C,t+1 r̃

(m)C,t + β

(H)C,t+1 r̃

(m)H,t + εC,t+1

r̃(m)H,t+1 = β

(G)H,t+1 r̃

(m)G,t + β

(R)H,t+1 r̃

(m)R,t + β

(C)H,t+1 r̃

(m)C,t + β

(H)H,t+1 r̃

(m)H,t + εH,t+1.

In this model, we assume that the government factor return only depends on its own lag,

whereas the other factor returns depend on one lags of all factor returns. We use the

notation HAb,t+1 = Cov[r̃(m)A,t+1, r̃

(m)B,t ], where the upper case A means that the return is

dated t+ 1 and the lower case b means that the return is dated t. Now, we have:6

β(G)G,t+1 = H−1

gg,t+1HGg,t+1,

6We have investigated several alternative specifications of the dependence between market factors.

12

for the government factor return and

βA,t+1 = (β(G)A,t+1, ..., β

(H)A,t+1) =

Hgg,t+1 Hgr,t+1 Hgc,t+1 Hgh,t+1

Hrg,t+1 Hrr,t+1 Hrc,t+1 Hrh,t+1

Hcg,t+1 Hcr,t+1 Hcc,t+1 Hch,t+1

Hhg,t+1 Hhr,t+1 Hhc,t+1 Hhh,t+1

−1HAg,t+1

HAr,t+1

HAc,t+1

HAh,t+1

,

for the other factor returns with A = R,C,H.

As conditional information is defined two periods earlier, the error term εt+1 =

{εG,t+1, εR,t+1, εC,t+1, εH,t+1} has potentially a moving average MA(1) structure. It may

also be non-linearly dependent both in the time series (due to heteroskedasticity) and in

the cross-section (due to tail dependence). To deal with heteroskedasticity, we assume

a univariate asymmetric GARCH model (Glosten et al., 1993), where, as before, the

volatility is conditional on the information set at date t− 1:

εa,t+1 = σa,t+1 (ak,t+1 + θa za,t), (6)

where θa denotes the MA(1) parameter and

σ2a,t+1 = ωa + αaε

2a,t−1 + βaσ

2a,t + γaε

2a,t−11(εa,t−1≤0), (7)

for a ∈ {G,R,C,H}.The standardized error term za,t+1 = εa,t+1/σa,t+1 is described as skewed t ran-

dom variable za,t+1 ∼ f(za,t+1; νa, λa), where f denotes the pdf of the skewed t distri-

bution, with νa the degree of freedom and λa the asymmetry parameter. We define

ut+1 = {uG,t+1, uR,t+1, uC,t+1, uH,t+1} as the value of the marginal distribution evaluated

at the observed zt+1. Thus ua,t+1 = F (za,t+1; νa, λa), where F is the cdf of the skewed

t distribution. Then, we assume a t copula to define the dependence structure of ut+1,

denoted by C(ut+1). The t copula has been found to capture the dependence structure

of the data very well (Engle et al., 2015). It accommodates tail dependence and its el-

liptical structure provides a convenient way to deal with large-dimensional systems. The

13

cumulative distribution function (cdf) of the t copula is defined as:

CΓ,ν̄(uG,t+1, ..., uH,t+1) = tΓ,ν̄(t−1ν̄ (uG,t+1), ..., t−1

ν̄ (uH,t+1)), (8)

where tν̄ is the cdf of the univariate t distribution with degree of freedom ν̄ and tΓ,ν̄ is

the cdf of the multivariate t distribution with correlation matrix Γ and degree of freedom

ν̄. The contemporaneous dependence between the innovation terms is captured by the

matrix Γ. It is worth noting that, in simulation this model will be able to generate

co-crashes, which would not be the case with a standard DCB model with Gaussian

innovations. In addition, as the degree of freedom and the dependence matrix are likely

to vary over time, we use a rolling window approach to accommodate for changes in the

value of the parameters. See Section 4.1 for additional details on the estimation.

2.4 Forecasting Strategy

Consistently with our definition of the SEL (Equation (2)), we now forecast the market

value of the bank’s assets assuming a stress scenario in the next quarter τ + 1. For this

purpose, we simulate a large number of draws of the factor model described in Section

2.3 for the next T = 60 days following the estimation period. We select the draws that

satisfy our predifined stress scenario. Then, using Equation (4), we forecast the market

value of the market-sensitive assets under these stress scenarios. Specifically, we proceed

as follows:

Step 1. At the end of quarter τ (day t), we consider the various items of the balance

sheet of the bank for quarter τ . We determine the weights w(i)a,τ for the four categories of

market-sensitive assets. We estimate the factor model using daily data over the last five

years.

Step 2. Using the factor model, we simulate a sequence of T daily market factor returns,

from day t + 1 to day t + T corresponding to quarter τ + 1. We select the samples

corresponding to the definition of a market stress (as defined in Section 2.5). We denote

by SC,τ+1 the number of such samples. We also denote by r̃(m)sa,t+1 the excess log-return on

market factor a at day t+ 1 for simulated sample s = 1, · · · , SC,τ+1.

14

Step 3. As we assume that bank does not rebalance its portfolio during the quarter, for

a given sample s with a market downturn, we forecast the market-sensitive returns at the

end of quarter τ + 1 as:

R(i)sMA,τ+1 = w

(i)G,τ R

(m)sG,τ+1 + w

(i)R,τ R

(m)sR,τ+1 + w

(i)C,τ R

(m)sC,τ+1 + w

(i)H,τ R

(m)sH,τ+1,

where R(m)sa,τ+1 = exp

(∑t+Tk=t+1 r

(m)sa,k

)− 1 denotes the cumulated simple return of asset a

during quarter τ + 1, with r(m)sa,k = r̃

(m)sa,k + rF,k−1. We deduce the market value of the

assets at the end of quarter τ+1 as: A(i)sτ+1 = (1+R

(i)sMA,τ+1)MA

(i)sτ +(1+RF,τ+1)Cash

(i)τ +

(1 +RO,τ+1)O(i)τ . We note that the value of cash, Cash

(i)τ+1 that we observe in the balance

sheet f bank i in quarter τ + 1 does not correspond to our measure (1 + RF,τ+1)Cash(i)τ .

The reason is that we do not allow the bank to rebalance its asset portfolio during the

quarter, consistently with the stress test methodology.

Step 4. The bank is expected to default in a given sample s with a market downturn if,

at the end of quarter τ + 1, the market value of the assets is below the accounting value

of the liabilities:

A(i)sτ+1 ≤ L

(i)τ+1 = (1 +RDep,τ+1)Dep(i)

τ + (1 +RSD,τ+1)SD(i)τ + (1 +RLD,τ+1)LD(i)

τ .

We iterate Steps 2 to 4 for each sample s with a market downturn, for s = 1, · · · , SC,τ+1.

Step 5. As we simulated a large number of samples, we estikate the probability of default

of the bank in quarter τ + 1 with the proportion of simulated samples in which the bank

defaults:

Π(i)τ+1 = Pr[Bank i’s default | Market downturnτ+1] =

1

SC,τ+1

SC,τ+1∑s=1

1{A(i)sτ+1≤L

(i)τ+1}

.

The estimate of the SEL is obtained as follows :

SEL(i)τ+1 = [(1+RDep,τ+1)Dep(i)

τ +(1+RSD,τ+1)SD(i)τ ]− 1

SC,τ+1

SC,τ+1∑s=1

A(i)sτ+1 1{A(i)s

τ+1≤L(i)τ+1}

.

15

2.5 Stress Scenarios

We define a stress scenario as a set of thresholds θτ = (θG,τ , θR,τ , θC,τ , θH,τ )′ based on the

information available at the end of quarter τ . If the market factor return at the end of

quarter τ + 1 is such that R(m)a,τ+1 ≤ θa,τ , then we consider that market a is under stress

in quarter τ + 1. We design a scenario along two dimensions: (1) the list of markets that

are hit by a downturn and (2) the severity of the stress across time and markets.

In principle, any downturn in the Treasury, Real estate, Corporate, or Household

markets is a potential shock to the banks’ assets. Therefore, the stress scenarios can be

defined as a combination of markets hit by a shock. The main results we report in Section

4 are based on a scenario in which either of the three risky markets (excluding Treasuries)

crashes. More precisely, we count as a crash any downturn exceeding the given threshold

θa,τ over quarter τ + 1 in either of the three markets a = R,C,H.7

Regarding the size of the downturn, we determine the threshold θa,τ for each of the

markets, below which market a is considered to be under stress. We define this thresh-

old in a real-time way using the performance of each market in the recent past. More

precisely, we set the threshold of market a for quarter τ + 1 (θa,τ ) as (negative) three

standard deviations below the average quarterly return of market a during the previous

five years. The main advantage of this approach is that it produces crash thresholds that

are consistent with the current conditions of this market. This is a realistic assumption

as creditworthiness of the bank’s borrowers, either set by external rating agencies or by

internal evaluation, are different across loan types and over time. The dynamics of market

factors are used in Section 3.3 to define the magnitude of the stress scenarios.

In our baseline scenario, we define a crash occurrence in quarter τ + 1 in simulated

sample s when R(m)sR,τ+1 ≤ θR,τ or R

(m)sC,τ+1 ≤ θC,τ or R

(m)sH,τ+1 ≤ θH,τ . We denote by SC,τ+1

the number of simulated samples that satisfy this condition in quarter τ + 1. Therefore,

the probability of crash in τ + 1 is given by Pr[Market downturnτ+1] =SC,τ+1

S, where S

is the total number of simulated samples.

7One can also think of simultaneous crashes in the three markets, which is a more restrictive scenario.Other stress scenarios could also include a downturn in the Treasury market.

16

3 Data

3.1 Sample Selection

While our approach is applicable to any financial institution whose source of funding is

predominantly deposits, we focus on large depository institutions. To define our sample

of commercial banks, we start with the sample of 34 large financial institutions with $50

billion or greater in total consolidated assets considered by the Federal Reserve Board

in its 2017 stress test.8 The list consists of 28 banks, 4 speciality lenders, and 2 global

investment banks. All of these large firms have as subsidiaries one or more commercial

banks. Given our interest on the commercial banking activity of these firms, we further

check if the business of the firms is predominantly commercial banking or not. For in-

stance, Bank of America Corporation has several nested bank holding companies (BHCs),

with two commercial banks owned by the last nested BHC. Our criteria for the inclusion

of each commercial bank are that (1) it sufficiently represents the top-tier BHC and (2)

the deposits of the bank represent most of the liabilities of the top-tier BHC. Thirty one

commercial banks, listed in Table 1, pass these criteria.9

The balance sheet data comes from the Call Report forms FFIEC 031 and 041. FFIEC

031 is the consolidated report of condition and income for a bank with domestic and

foreign offices, and FFIEC 041 is the same form filled by banks with only domestic

offices.10 All such data are in quarterly frequency and collected from the SNL platform.

8The Dodd-Frank Wall Street Reform and Consumer Protection Act, passed by the Congress in2010, requires the Board of Governors of the Federal Reserve System to conduct an annual supervisorystress test of large financial institutions with $50 billion or greater in total consolidated assets. Theassessment, which has a quantitative and forward-looking stand, is conducted through the Dodd-FrankAct supervisory stress testing and evaluates the health of large financial institutions under stressfuleconomic and financial market conditions.

9The remaining three institutions are American Express Company, Goldman Sachs Group, and Mor-gan Stanley. American Express Company is a speciality lender with a BHC. The BHC includes acommercial bank and a saving and loan association, which together represent 54% of the total assets ofthe firm and hold deposits that represent only 42% of total liabilities of the firm. Goldman Sachs Groupand Morgan Stanley also have commercial bank subsidiaries but they represent only 18% and 16% ofthe ultimate parents, respectively, in total assets and they hold deposits that represent only 15% of totalliabilities of the ultimate parents in both cases. So given that more than half of the debt are liabilitiesother than deposits, we drop these three firms from the sample.

10This form is different from the one filled on a quarterly basis by the top-tier BHC (FR Y-9C) andfrom that of parent company itself (FR Y-9LP), if the institution holds at least $500 million of totalassets. So, even though the commercial banks in our sample are subsidiaries of a larger BHC, which itselfmight be owned by a top-tier BHC, we do not need to go through these two later forms. The balancesheet of commercial bank subsidiaries contains more detailed information such as maturities of loans and

17

Our final sample is data from 31 commercial banks over the period of 1996:Q1–2016:Q4,

that is, 2’604 bank-quarter observations, representing more than 70% of the total assets

of all commercial banks.

Table 1 reveals that the Top-4 banks of our sample (JP Morgan Bank, Wells Fargo

Bank, Bank of America, and Citabank) represent more than 60% of total assets and total

deposits and slightly less than 60% of total equity. In addition, on averabe the book

leverage (equity over assets) is equal to 12% with a minimum of 7.3% and a maximum

of 16.7%.

Table 2 presents summary statistics of some important ratios for the 31 commercial

banks in our sample. The assets of the commercial banks represent the main assets of

their ultimate parent: on average, the assets of the commercial bank represent 88% of

the assets of the ultimate parent, with a minimum of 60%. Also, on average, deposits

represent 87% of the liabilities (deposits plus debt) of these commercial banks. Finally, on

average, deposits in the commercial banks represent 77% of the liabilities of the ultimate

parent. Santander Holdings USA has the minimum deposits holding (52%) within its

commercial bank, Santander Bank.

[Insert Tables 1 and 2 here]

3.2 Evolution of the Bank’s Balance Sheet

Schema 2 provides a summary of the aggregate balance sheet of the largest commercial

banks. The four market-sensitive asset classes defined in Section 2.2 together represent

on average 63.4% of the total assets. The remaining assets correspond to interest-bearing

cash (13.3%), derivatives (3.8%), and the other assets that are not present in our classi-

fication above (20.5%).

Government securities are mostly Treasuries (44%), followed by state and politically

related securities (34%) and agency securities (22%). Real estate securities are composed

of (residential and commercial) real estate loans (68%) and mortgage-backed securities

(32%). Corporate securities are loans (92%) to firms, either co-syndicated or not, for

commercial and industrial purposes. The remaining are either such loans for the purpose

securities. However, other important information such as the market capitalization and the credit ratingare only available for the top-tier BHC.

18

of trading or structured products with the loans as collateral. Finally, household securities

are composed of consumer loans (89%) and securitized consumer loans (11%).

Schema 2: Simplified aggregate balance sheet of commercial banks

(average, in % of total assets)

Assets Liabilities

Cash: 13.3 Deposits: 66.7

Market-sensitive Assets: 63.4

- Government: 5.0 Debt: 20.9

- Real Estate: 32.3 - Short-term debt: 19.0

- Corporate: 17.1 - Long-term debt: 1.9

- Household: 9.0

Derivatives: 3.8 Derivatives: 3.5

Other Assets: 20.5 Equity: 9.0

Figure 1 shows the temporal evolution of the four categories of assets defined in Section

2.2. We note that the weight of the asset classes is relatively stable over time. The main

category, market-sensitive assets, has slightly increased, from 60% at the beginning of

the period to 65% at the end of the period. In addition, cash has also slightly increased,

whereas derivatives and other assets have decreased. These levels and trends suggest that

our decomposition of the assets and our focus on the risky assets as the main source of

stress of the bank’s balance sheet are likely to provide relevant results.

The evolution of market-sensitive assets is plotted in Figure 2. Real estate asset are

the largest category and are followed by corporate, and government securities. The figure

also reveals some interesting patterns about the portfolio of the commercial banks over the

past 21 years. By the onset of bubble dot-com crisis at the beginning of the sample, banks

reduce their holding of corporate and government securities and invest more in household

and real estate securities. However, after the great financial crisis, banks lighten their

real estate portfolio and increase their holding of government securities.

Total liabilities consist of 66.7% of deposits, 20.9% of debt (19% of short-term debt

and 1.9% of long-term debt), 3.5% of derivatives, and 9% equity capital. Figure 3 displays

the evolution of these liabilities classes over time. It clearly shows that long-term debt and

derivatives represent a negligible part of commercial bank’s financing. We also observe

that after the financial crisis, commercial banks have increases their financing through

19

deposits (from 70% of total liabilities before the crisis to 85% after the crisis) and reduced

the use of short-term debt (from 25% to 10%, respectively). Last, the figure reveals that

the reinforcement of regulation has resulted in an increase of the weight of equity after

the financial crisis (from 9% to 12%).

[Insert Figures 1 to 3 here]

3.3 Construction of the Market Factors

In this section, we provide details on the market factors that we use to measure the per-

formance of the market-sensitive asset classes defined above. As each of these categories

contains different types of loans and debt securities, we did our best to select market-

wide indexes reflecting the performance of these components. Specifically, we use total

return indexes provided by Bank of America Merrill Lynch (BofA).11 The list of these

indexes is displayed in Table 3. They track the performance of the market-sensitive asset

classes that financial institutions hold in their portfolios. In Appendix B, we provide

details on the constituents and characteristics of each index and describe our approach

for constructing the market factors based on the balance sheet information and the above

mentioned BofA indexes.

Indexes are available at daily frequency since January 1991. Table 4 reports summary

statistics on the performance of the constructed market factors indexes based on the

1996–2016 sample, which corresponds to the availability of bank accounting data. Figure

4 displays the evolution of the four factor indexes in level and returns over the sample

period. We observe that large price changes are very limited for government securities.

For other market factors, we note that they can be very volatile over some periods of

time. For instance, real estate, corporate, and household securities have suffered from

large price moves in 2007–2010. Household securities have experienced large price changes

in 1998–1999. Corporate securities also exhibit a large drawdown in 2015.

11BofA provides extensive coverage of global fixed income markets through 4’500 standard indexestracking more than $66 trillion in fixed income securities. These indexes are available across differentmarket segmentations such as sector, rating, maturity, and combinations of them. Information aboutcriteria for selecting constituent securities and weighting and rebalancing strategies are available in theBofA website and by third party data vendors.

20

Using the strategy described in Section 2.5, we compute thresholds defining market

downturns for each asset class using quarterly returns over five year subsamples. As

explained before, thresholds vary significantly over time, with large differences before and

after the financial crisis. The real estate market threshold (θR,τ ) has an average equal to

−3%, −15.8%, and −11% for the pre-crisis, crisis, and post-crisis periods, respectively.

The corporate securities threshold (θC,τ ) has an average equal to −10.9%, −15.2%, and

−12%, respectively. Finally, the average of the household securities threshold (θH,τ ) is

−5.1%, −6.3%, and −4.5%, respectively.12

[Insert Tables 3 and 4 and Figure 4 here]

4 Empirical Results

In the first step, we estimate the model desribing the dynamics of the risk factors as

explained in Section 2.3. Then, we follow the steps explained in Section 2.4 and compute

the probability of default and the SEL for the selected commercial banks.

4.1 Parameter Estimates and Betas

Table 5 reports parameter estimates of the market factor model when the complete sam-

ple (1996–2016) is used for the estimation. In the construction of the SEL measure, we

use rolling widows of five years to allow the parameters to vary over time. The parameters

driving the dynamics of the volatility process are relatively standard. We note that the

persistence of volatility is very high. The asymmetry parameter γ is barely significant,

except for corporate market index returns, for which it is large and positive. The parame-

ter estimates of the individual skewed t distributions reveal that innovation distributions

have fat tails and a negative asymmetry. Degree of freedom parameters ν are relatively

low indicating large excess kurtosis for each of the factors. The degree of freedom ν̄ of

the copula is also low, close to 4. This value suggests that the dependence between the

market returns is large in the extremes. Finally, the copula correlation matrix Γ indicates

12This approach allows us to design the stress scenario in real time. We also considered the case offixed thresholds (based on the standard deviation of market returns over the full sample), but did notfind significant differences.

21

that government, real estate, and household index returns are highly correlated, whereas

the dependence between corporate index return and the other market factors indexes is

lower.

[Insert Table 5 here]

We use five-year rolling windows to reestimate every month the parameters, in par-

ticular to capture the changes in the dependence between factor returns. Figure 5 (Panel

A) displays the evolution of the degree of freedom ν̄ through time. We observe that it

decreases during the dot.com crisis and the great financial crisis to levels below 4, sug-

gesting a stronger dependence between market factors. In the recent period, it varies in

a range between 4 and 7.

We also find that the dependence between market factor returns implied by the copula

model varies a lot over time. The dynamics of the correlation matrix Γ is presented in the

figure. On the one hand (Panel B), we note that the dependence between government and

real estate is high, between 60% and 95% over time. It reaches a maximum just before

the great financial crisis (approximately 95%). The correlation between corporate on one

side and government and real estate on the other side move in parallel. It is high at the

beginning of the sample (close to 80% − 90%) and decreases after 2000. At the end of

the sample, the dependence is between 40% and 60%. On the other hand (Panel C), the

dependence between household return and other market factors returns has been affected

by large moves. The correlation parameter is higher than 60% for the three categories

at the beginning of the sample, decreases to approximately 20% in 2000 and raises again

afterwards. However, the correlation with government and real estate reaches high levels

at the end of the sample (close to 80%), whereas the correlation with corporates remains

close to 40%.

Figure 6 displays the dynamics of the conditional betas, which reflect the time de-

pendence between factor returns. Although lagged effects are relatively limited, some

patterns emerge. First, lagged government return usually has a negative impact on other

markets. In the great financial crisis, all β(G)a,t+1 parameters are negative, for a = R,C,H.

Second, lagged corporate return has a large positive impact on current corporate return.

22

This is also the case for lagged real estate on current real estate in the recent period. The

dynamics of household return seems barely affected by lagged returns.

[Insert Figures 5 and 6 here]

4.2 Probability of default and SEL

Figure 7 displays the temporal evolution of the probability of a market downturn in the

next quarter based on S = 100′000 simulated samples. We observe that the probability

increases substantially in 1998 just before the dot-com crisis, reflecting notably the de-

crease in the degree of freedom of the t copula. It is close to 20% at the end of 1999 and

remains above 15% until 2014. The probability of a downturn increases again substan-

tially in 2007 at the eve of the great financial crisis. This increase is due to turbulence

in financial markets, which are captured by real estate, corporate, and household market

factors, even before affecting the balance sheet of the commercial banks. Interestingly,

the probability of a downturn reduces to very low level between 2011 and 2013, but has

recently surged to approximately 10% since 2014.

We now consider main results regarding the estimates of the probability of default of

commercial banks and the aggregate SEL. As Figure 8 (Panel A) shows, the average prob-

ability of default is relatively low in a market downturn at the beginning of the sample.

At the eve of the dot.com crisis (1998–1999), the probability increases to approximately

15% on average. However, afterwards, it remains at a low period (typically below 10%)

until the beginning of the great financial crisis. At the end of 2008, the probability of

default jumps to 50% and remains high until the end of 2009. After a short period of time

close to 20%, the probability increases again in 2010–2011 because of the increase in the

risk of real estate and corporate securities, as illustrated in Figure 4. At the end of 2013,

the probability of default decreases to low levels, with an average close to 1% in case

of a market downturn. There are two complementary reasons for this result. First, the

magnitude of the downturn is lower because fixed income markets are much less volatile.

Second, commercial banks have restructured their balance sheet in a safer way: they have

increased their capital ratio and therefore finance their investment with more equity. In

addition, they have substantially increased their cash holding. We notice that, even if

23

the probability of default has decreased on average in the recent period, some banks still

exhibit a relatively high probability of default.

Figure 8 (Panel B) also displays the temporal evolution of the SEL measure. It

confirms that before 2008, the capital shortfall of commercial banks was relatively small,

i.e., below $100 billion. In the great financial crisis (say between 2008 and 2013), the

SEL has consistently been above $200 billion. In the last 3 years, we notice a substantial

decrease in the SEL, reflecting the improvement in banks’ conditions.

In Figure 9, we illustrate the relative contribution of the Top-4 banks and the other

banks to the aggregate SEL. Except in a few number of short periods of time, the Top-

4 banks contribute to most of the aggregate SEL. Before the great financial crisis, the

aggregate SEL of the top-4 banks is approximately $50 billion, whereas the remaining

banks only contribute for less than $10 billion. In 2008–2013, both groups contribute

to the increase in the SEL. Top-4 banks have an aggregate SEL between $200 and $250

billion. The contribution of the other banks is lower but ranges between $100 and $150

billion.

[Insert Figures 7 to 9 here]

4.3 Comparison with SRISK

It is worth comparing the SEL with the SRISK measure proposed by Acharya et al.

(2012b) and Brownlees and Engle (2016). We denote by W(i)τ the market capitalization

of firm i in quarter τ and L(i)τ = A

(i)τ /W

(i)τ its financial quasi-leverage. SRISK in quarter

τ + 1 is defined as:

SRISK(i)τ+1 =

{θ(L(i)

τ − 1)− (1− θ)Et[1− LRMES(i)

τ+1

]}W (i)τ , (9)

where LRMES(i)τ+1 = −Et

[W

(i)τ+1/W

(i)τ − 1 | Market downturnτ+1

]denotes the long-run

marginal expected shortfall of the firm’s return in the event of a financial crisis. It is

defined as:

LRMES(i)τ+1 = −Et

[R

(i)τ+1 | R(M)

τ+1 ≤ θM,τ

], (10)

24

where θM,τ is the threshold for a downturn on the equity market.

In Brownlees and Engle (2016), the market downturn corresponds to a θM,τ = 40%

semiannual decline in the stock market index. One advantage of SRSIK is that it only

requires the computation of how the bank market capitalization would be affected in a

market downturn. In contrast, SEL requires to compute the sensitivity of all the market-

sensitive asset classes to a market downturn. However, SRISK implicitly assumes that the

shock on the market capitalization correctly reflects the impact of the market downturn

on the asset classes, an assumption that may not be always true.

We compute the SRISK by aggregating the individual measures provided by the

Volatility Laboratory on its website.13 Figure 11 both series have similar dynamics,

although they exhibit some noticeable differences. First, the SEL measure is significantly

higher than SRISK at the eve of the great financial crisis (close to $100 billion vs. $5

billion in 2007). As argued by Acharya et al. (2009), the premise of the crisis was already

visible mid 2006 with the downturn in the real estate market and the increase in credit

instrument spreads. These events were at least partly captured by the market factors

and therefore are incorporated into the SEL. In contrast, as the equity market did not

react as quickly to these events, SRISK is not affected i 2006-2007 until the downturn in

the equity market.

Second, the SEL increases less than SRISK after the start of the crisis. In 2009,

SRISK is more than twice as big as SEL ($560 billion vs. $250 billion). The difference

can be explained by some specific events that affected large BHCs. Citigroup was in

trouble as early as 2007 because of its investment in the real estate market. Its SRISK

jumped from 0 to $111 billion in 2008 whereas Citibank SEL did not vary significantly

(from 4 to 18). Also JP Morgan Chase and Bank of America have acquired in 2008

some investment banks in trouble (Bear Stearns and Merrill Lynch, respectively). These

events were perceived as risky by equity markets, so that SRISK of these institutions

increased significantly in 2008 (from 47 to 138 billion for JP Morgan Chase and from 25

to 125 billion for Bank of America in 2008, respectively). However, the commercial banks

themselves were not directly affected by these deals, so that they had limited impact on

13The website is available at https://vlab.stern.nyu.edu/. As some of the 31 banks in our list are notcovered by VLab, we aggregate the SRISK of all of the available banks.

25

the SEL measure. The increase in the SEL is only from 20 to 29 for JP Morgan Chase

and from 32 to 55 for Bank of American in 2009.

Afterwards, both measures have similar temporal evolution. At the end of 2016, SEl

and SRISK are equal to $200 billion and $80 billion, respectively. These estimates suggest

that the risk borne by commercial banks is still relatively high in the recent period.

[Insert Figure 11 here]

4.4 Individual Probability of Default and SEL

Finally, we report details on individual banks and group of banks. Table 6 reports our

estimates of the individual probability of default and SEL for all banks, averaged before,

during, and after the great financial crisis. Banks are sorted according to their total

assets as of end of 2016. As the table reveals, the probability of default jumps for most

of the banks during the great financial crisis. For instance, for five out of the six largest

banks, the probability of default in a downturn is on average larger than 20% during the

period 2008–2013. After 2013, the probability decreases substantially, to levels usually

below 1%.

We also observe that the SEL is rather low before 2008. Only two banks (Bank of

America and Citibank) suffer from an estimated SEL close to $10 billion. During the

financial crisis, the SEL exceeds $10 billion on average for 3 more banks (JPMorgan Chase

Bank, Wells Fargo Bank, and U.S. Bank). The aggregate SEL for these 5 banks exceeds

$170 billion on average between 2008 and 2013. In the recent period (2014–2016), the

SEL remains at relatively high level even if the probability of default in a downturn is

much lower. The aggregate SEL for the same 5 banks is close to $140 billion on average.

[Insert Table 6 here]

5 Conclusion

In this paper, we develop a new methodology to measure the capital shortfall of commer-

cial banks in a market downturn. The measure, which we call Stressed Expected Loss

(SEL), takes the structure of the individual banks balance sheet. The capital shortfall

26

is defined as the lack of bank’s equity in case of a market downturn. We first identify

how the various asset categories are related to market factors capturing the temporal

evolution of government, real estate corporate, and household securities. Then, we define

a market downturn scenario as a fall in some of the market factor indexes. The SEL is

then the difference between the market value of the assets under the stress scenario and

the book value of the deposits and short-term debt of the bank.

We estimate the evolution of the probability of default and the SEL of the 31 largest

commercial banks in the U.S. between 1996 and 2016. The probability of default in a

downturn has been as high as 50% on average between 2008 and 2012. It is by now much

smaller and close to 1% on average. In contrast, the SEL has been very high (slightly

below $400 billion) during the great financial crisis. However, it is still at a relatively

high level in the recent period, close to $200 billion.

Our approach has two main advantages. First, it is easy to implement because it

relies only on easily available data (individual bank’s accounting data and market factor

indexes). In particular, the bank does not to be listed as we use the market value of the

assets and not of the equity. Second, our approach can be used to investigate alternative

scenarios of a market downturn. For instance, the market downturn may specifically

come from corporates or from households.

27

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29

Table 1: List of the 31 commercial banks in our sample

Ultimate Parent Commercial Bank Assets Deposits Equity

JPMorgan Chase & Co. JPMorgan Chase Bank, National Assoc. 2’083 1’480 205Wells Fargo & Co. Wells Fargo Bank, National Assoc. 1’727 1’339 155Bank of America Corporation Bank of America, National Assoc. 1’677 1’334 206Citigroup Inc. Citibank, National Assoc. 1’350 946 144U.S. Bancorp U.S. Bank, National Assoc. 441 343 45PNC Financial Services Group, Inc. PNC Bank, National Assoc. 356 262 38Capital One Financial Corp. Capital One, National Assoc. 286 217 35TD Group US Holdings LLC TD Bank, National Assoc. 269 229 35Bank of New York Mellon Corp. Bank of New York Mellon 258 213 24State Street Corp. State Street Bank and Trust Co. 239 192 22BB&T Corp. Branch Banking and Trust Co. 214 168 28SunTrust Banks, Inc. SunTrust Bank 201 162 23HSBC North America Holdings Inc. HSBC Bank USA, National Assoc. 197 147 24Fifth Third Bancorp Fifth Third Bank 140 107 17KeyCorp KeyBank, National Assoc. 134 107 15Regions Financial Corp. Regions Bank 125 100 16Northern Trust Corp. Northern Trust Co. 124 102 9Ally Financial Inc. Ally Bank 124 79 18M&T Bank Corp. Manufacturers and Traders Trust Co. 123 97 15Citizens Financial Group, Inc. Citizens Bank, National Assoc. 117 83 16MUFG Americas Holdings Corp. MUFG Union Bank, National Assoc. 116 89 16BMO Financial Corp. BMO Harris Bank, National Assoc. 106 80 15Huntington Bancshares Incorp. Huntington, National Bank 100 78 11Discover Financial Services Discover Bank 91 54 10BancWest Corp. Bank of the West 84 62 12BBVA Compass Bancshares, Inc. Compass Bank 84 68 12Santander Holdings USA, Inc. Santander Bank, National Assoc. 83 60 13Comerica Inc. Comerica Bank 73 60 7Zions Bancorporation ZB, National Assoc. 63 54 8Deutsche Bank Trust Corp. Deutsche Bank Trust Co. Americas 54 42 9CIT Group Inc. CIT Bank, National Assoc. 42 32 5

Note: This table presents names of the 31 commercial banks in our sample sorted by

their total assets, as well as names of their ultimate parents. Numbers are billion dollar

amount of total assets, deposits, and equity of the commercial banks for 2016:Q4.

30

Table 2: Summary Statistics on Commercial Banks and their Ultimate Par-ent

Commercial Bank AssetsUltimate Parent Assets

Commercial Bank DepositsCommercial Bank Liabilities

Commercial Bank DepositsUltimate Parent Liabilities

Mean 0.88 0.87 0.77Median 0.96 0.88 0.77Std dev. 0.12 0.06 0.13Minimum 0.60 0.67 0.52Maximum 0.998 0.98 0.97

Note: This table presents summary statistics on the commercial banks in our sample and their

ultimate parent. Numbers are based on balance sheet of the 31 commercial banks and their

ultimate parent as of 2016:Q4.

31

Table 3: Selected Market Factor Indexes

Selected Index Ticker #Bonds Rating Effective EffectiveDuration Yield

Government

US Treasury Master G0Q0 259 AAA 6.03 1.91US Agencies Composite Master UAGY 447 AA-AAA 3.91 1.85National Select Municipal Securities UAMA 7897 AA-AAA 7.91 2.25

Real Estate

US GNMA MBS MGNM 116 AAA 5.38 2.92US Fixed Rate Commercial MBS CMA0 2146 A-AAA 4.66 2.96US Fixed Rate Commercial MBS CB45 372 BBB 4.71 5.27US Fixed Rate Home Equity Loan ABS R0H1 1 AAA 1.62 4.94US Fixed Rate Home Equity Loan ABS R0H2 5 BBB-AA 6.21 5.19

Corporate

US Non-Financial Corporate CF0X 5619 BBB-AAA 7.80 3.27US High Yield Corporate H0A4 1576 B-BB 4.07 4.81US High Yield Corporate H0A3 312 D-CCC 3.08 10.34

Household

US Fixed Rate Automobile ABS R0U1 616 AAA 1.24 1.62US Fixed Rate Automobile ABS R0U2 481 BBB-AA 1.83 2.64US Fixed Rate Credit Card ABS R0C1 90 AAA 1.91 1.71US Fixed Rate Credit Card ABS R0C2 19 BBB-AA 1.50 2.11US High Yield Consumer Products H0CO 29 CCC-BB 3.44 5.80

Note: This table presents details on the market factor indexes selected for our empirical analysis.

The first column shows the selected total return indexes separated by the asset classes defined

earlier. The second column shows their ticker identified by Bank of America Merrill Lynch

(BofA). The third column shows the number of constituent bonds in each index. Rating is the

average of Moody’s, S&P, and Fitch ratings. The two last columns present effective duration

and yield of each index provided by BofA as of July 2017.

32

Table 4: Descriptive Statistics of Market Factor Returns

Market index Mean Std dev. Skewness Kurtosis Minimum Maximum

Government 4.8 3.6 -0.4 5 -1.6 1.2Real estate 4.7 4.8 -2.1 159 -7.0 7.3Corporate 6.6 4.3 -1.5 23 -4.1 2.2Household 5.0 3.0 -5.4 134 -5.0 2.1

Note: This table presents summary statistics of returns of constructed market indexes. Mean,

Standard deviation, Minimum, and Maximum are in percentage. Mean and Standard deviation

are annualized. Numbers are based on daily data from January 1996 to December 2016 (5’410

observations).

33

Table 5: Parameter Estimates (Based on the 1996–2016 Sample)

Government Real estate Corporate Household

Panel A: Parameter estimates

Volatility dynamicsω (×106) 0.030 0.005 0.109 0.001

(0.001) (0.337) (0.005) (4.160)α 0.036 0.009 0.076 0.019

(0.002) (0.001) (0.007) (0.001)γ -0.004 0.029 0.078 0.021

(0.005) (0.002) (0.008) (0.003)β 0.96 0.98 0.87 0.97

(0.001) (0.001) (0.006) (0.001)

Skewed t distributionν 7.2 4.5 5.7 3.5

(0.671) (0.436) (0.460) (0.176)λ -0.092 -0.082 -0.058 -0.045

(0.016) (0.017) (0.016) (0.014)

DCC parametersδ1 0.015 (0.001)δ2 0.983 (0.001)

Copula degree of freedomν̄ 3.87 (3.61,4.13)

Correlation matrix ΓRG,t RR,t RC,t

RR,t 0.82 – –RC,t 0.61 0.62 –RH,t 0.66 0.65 0.45

Panel B: Average of conditional βs

RG,t−1 RR,t−1 RC,t−1 RH,t−1

RG,t 0.082 – – –RR,t -0.101 0.114 0.082 -0.087RC,t -0.279 0.013 0.421 -0.012RH,t -0.054 0.013 0.072 0.051

Note: This table presents parameter estimates of the DCB model with t copula innovations(Panel A). Estimates are based on the sample 1996–2016. Volatility dynamics are for the returnseries. Estimated parameters of the Skewed t distribution are for the individual innovations. thedegree of freedom ν̄ and the correlation matrix Γ correspond to the t copula of the innovationmargins. Panel B presents the average of the conditional beta parameter estimates over the fullsample.

34

Table 6: Probability of Default and SEL for Commercial Banks in our Sample

Commercial BankPre-crisis Crisis Post-crisis1996–2007 2008–2013 2014–2016ΠD SEL ΠD SEL ΠD SEL

JPMorgan Chase Bank, National Assoc. 3.8 7.9 23.7 47.9 0.2 37.6Wells Fargo Bank, National Assoc. 1.8 6.0 32.4 39.7 0.6 33.3Bank of America, National Assoc. 3.5 13.8 24.1 58.7 0.3 46.1Citibank, National Assoc. 5.2 9.7 9.0 20.7 0.3 12.4U.S. Bank, National Assoc. 4.3 0.6 35.0 11.5 0.8 9.3PNC Bank, National Assoc. 5.4 0.6 29.1 9.5 0.7 1.7Capital One, National Assoc. 4.2 0.2 5.6 6.4 0.1 5.3TD Bank, National Assoc. 7.6 0.2 9.5 6.7 0.3 7.7Bank of New York Mellon 1.9 1.8 10.4 4.5 0.2 4.9State Street Bank and Trust Co. 0.5 0.9 10.3 4.4 0.3 3.6Branch Banking and Trust Co. 5.5 0.0 36.1 6.2 0.5 1.2SunTrust Bank 3.6 0.3 28.9 6.7 0.8 4.6HSBC Bank USA, National Assoc. 5.6 1.5 15.4 5.5 0.4 5.0Fifth Third Bank 4.5 0.2 16.3 3.9 0.9 0.3KeyBank, National Assoc. 5.9 0.3 33.5 3.4 1.4 0.7Regions Bank 6.6 0.7 31.4 6.0 0.5 3.6Northern Trust Co. 3.5 0.1 11.8 1.1 1.1 0.7Ally Bank 0.0 0.0 12.4 0.0 0.7 0.0Manufacturers and Traders Trust Co. 4.6 0.3 33.1 4.0 0.6 0.9Citizens Bank, National Assoc. 0.0 0.0 17.3 5.3 0.3 2.1MUFG Union Bank, National Assoc. 4.5 1.6 35.4 2.8 0.8 2.1BMO Harris Bank, National Assoc. 4.7 0.6 14.3 2.7 0.2 2.2Huntington, National Bank 7.4 0.1 46.4 2.3 1.7 0.2Discover Bank 2.5 1.4 0.7 1.5 0.0 0.4Bank of the West 2.2 0.3 7.9 0.6 0.1 2.1Compass Bank 9.5 0.1 10.2 2.8 0.4 1.0Santander Bank, National Assoc. 0.0 0.0 0.0 0.0 0.3 0.8Comerica Bank 7.4 1.2 49.4 3.2 3.1 2.9ZB, National Assoc. 11.1 0.2 41.9 1.1 0.8 1.1Deutsche Bank Trust Co. Americas 0.3 0.1 0.0 0.0 0.0 0.0CIT Bank, National Assoc. 0.0 0.0 0.0 0.0 0.6 0.1

Note: This table reports estimates of the probability of default and SEL for all banks, averaged

before, during, and after the great financial crisis. Banks are sorted according to their total

assets as of 2016:Q4. The probability of default is in percentage. The SEL is in $ billion.

35

Figure 1: Temporal Evolution of the Main Categories of Assets

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 20170

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Cash

Risky Assets

Derivatives

Other Assets

Note: This plot displays the four main types of assets as a fraction of total assets. Dataare quarterly and obtained from Call Reports. Averages are taken across banks and areweighted by total assets of each bank.

36

Figure 2: Temporal Evolution of the Types of Market-sensitive Assets

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 20170

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Real estate

Corporate

Household

Government

Note: This plot displays the four main types of market-sensitive assets as a fractionof total market-sensitive assets. Data are quarterly and obtained from Call Reports.Averages are taken across banks and are weighted by total assets of each bank.

37

Figure 3: Temporal Evolution of the Types of Liabilities & Equity

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 20170

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Deposit

Short-Term Debt

Equity

DerivativesN

Long-Term Debt

Note: This plot displays the composition of debt of the bank as a fraction of total debt.Data are quarterly and obtained from Call Reports. Averages are taken across banks andare weighted by total assets of each bank.

38

Figure 4: Temporal Evolution of the Market Factors Prices and Returns

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17100

200

300

400Government

-5

0

3

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17100

200

300

400Real estate

-7

0

7

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17100

200

300

400Corporate

-5

0

3

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17100

200

300

400Household

-5

0

3

Note: This figure displays the levels of the constructed market factors on the left axisand their returns on the right axis for the period from January 1996 to December 2016.

39

Figure 5: Temporal Evolution of Copula Parameter Estimates

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 173

4

5

6

7

8Panel A: Degree of freedom

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

0.2

0.4

0.6

0.8

1Panel B: Correlation matrix (part 1)

Corporate and Government

Corporate and Real estate

Real estate and Government

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

0.2

0.4

0.6

0.8

1Panel C: Correlation matrix (part 2)

Government and Household

Corporate and Household

Real estate and Household

Note: This figure display the temporal evolution of the estimates of the copula degree offreedom ν̄ and correlation matrix Γ. The model is estimated using rolling windows of 5years.

40

Figure 6: Estimates of Conditional Dynamic Betas

98 01 04 06 09 12 15−0.5

0

0.5Governmentt−1 → Governmentt

98 01 04 06 09 12 15−1

0

1Governmentt−1 → Realestatet

98 01 04 06 09 12 15−0.5

0

0.5Realestatet−1 → Realestatet

98 01 04 06 09 12 15−0.5

0

0.5Corporatet−1 → Realestatet

98 01 04 06 09 12 15−1

0

1Householdt−1 → Realestatet

98 01 04 06 09 12 15−1

0

1Governmentt−1 → Corporatet

98 01 04 06 09 12 15−0.5

0

0.5Realestatet−1 → Corporatet

98 01 04 06 09 12 150

0.5

1Corporatet−1 → Corporatet

98 01 04 06 09 12 15−0.5

0

0.5Householdt−1 → Corporatet

98 01 04 06 09 12 15−0.2

0

0.2Governmentt−1 → Householdt

98 01 04 06 09 12 15−0.2

0

0.2Realestatet−1 → Householdt

98 01 04 06 09 12 15−0.5

0

0.5Corporatet−1 → Householdt

98 01 04 06 09 12 15−0.5

0

0.5Householdt−1 → Householdt

Note: This figure display the temporal evolution of the conditional beta estimates. Themodel is estimated using rolling windows of 5 years.

41

Figure 7: Probability of Crash

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

5

10

15

20

25

%

Note: This figure display the probability of crash, measured in percentage.

42

Figure 8: Aggregated Probability of Default and SEL

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

10

20

30

40

50

%

Panel A: Probability of default

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

100

200

300

400Panel B: SEL

Note: This figure display the aggregate probability of default and SEL. The probabilityof default is measured in percentage and SEL is measured in $ billion.

43

Figure 9: Probability of Default and SEL for Top-4 and Others

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

10

20

30

40

50

60

%

Panel A: Probability of default

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

50

100

150

200

250Panel B: SEL

top 4

other

Note: This figure display the aggregate probability of default and SEL for the Top-4 commercial banks and the group of the other banks. The probability of default ismeasured in percentage and SEL is measured in $ billion.

44

Figure 10: Probability of Default and SEL for Large and Complex Banksand Others

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

10

20

30

40

50

60

%

Panel A: Probability of default

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

50

100

150

200

250

300

350Panel B: SEL

Large and complex banks

Large and non-complex banks

Note: This figure display the aggregate probability of default and SEL for the largeand complex banks and the large and noncomplex banks. The probability of default ismeasured in percentage and SEL is measured in $ billion.

45

Figure 11: SEL and SRISK

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 170

100

200

300

400

500

600

SEL

SRISK

Note: This figure display the SEL and the SRISK measures for the banks for which theSRISK measure is available on the Volatility Laboratory website. The SEL and SRISKare measured in $ billion.

46

Appendices

A Bank Balance Sheet

In this appendix, we start with the standard balance sheet of commercial banks and provide

details on the main categories of assets. Banks in general hold loans and securities. Loans

are issued and held until they mature, whereas, securities might be sold before they mature.14

Banks classify loans they issue based on the borrower’s purposes. For instance, they issue loans

to borrowers who wish to buy a residential real estate property or an automobile or they issue

loans to corporate firms for commercial and industrial purposes. Our perspective however in

classifying assets is twofold as we take stand of both borrowers’ type and loans’ type. Thus,

borrowers of the loans issued by the banks are households and firms.15 For instance, household

are recipients of consumer loans, whereas firms receive commercial and industrial loans. But

borrowers’ type alone is not enough to account for all loans. In such cases, we take the view

of loans’ type. For instance, although residential (commercial) real estate loans are issued to

household (firms), we take them as real estate assets due to the important role of the real estate

value in the economy.

Securities, on the other hand, can be standard securities, such as Treasury bills, or structured

securities, such as mortgage backed securities (MBS). Here again, our stand is both borrowers’

type and securities’ type. For instance, for Treasuries the borrower is the government, whereas

for the MBS we rely on the type of the underlying asset to decide about the asset class of the

MBS.16

Throughout Sections A.1, A.2, and A.3 below, we detail the securities and loans of the banks

that fit our definition of asset classes, and in Section A.4 we explain our viewpoint about assets

(either loans or securities) that cannot be allocated into market-sensitive asset classes.

14While commercial banks are more involved in loan investments, other financial institutions investmore in securities than loans.

15An insignificant amount of loans are also issued to other financial institutions either banks or non-banks, which we classify them as other assets

16For MBS and in general asset backed securities, we can also decide based on the backing loans. Forinstance, when the backing loan is a pool of residential loans, we group the MBS into the same class asthe residential loans.

1

A.1 Standard Debt Securities

Treasury, Agency, and State, and Politically Related Securities. Treasuries are

all types of fixed income instruments issued by the U.S. government. In government agency

securities, debt obligations are fully and explicitly guaranteed by the U.S. government. The

difference between government agencies and government-sponsored agencies is that in the latter

case the debt obligations are not explicitly guaranteed by the full faith and credit of the U.S.

government. As an example, Ginnie Mae is a government agency, whereas Freddie Mac is a

government-sponsored agency. Last, states and political subdivisions also issue debt obligations.

As we explained in Section 2.2, we merge these three groups into one class of assets, i.e.,

Government securities. In our sample of commercial banks, the contribution of each of the three

categories to the total Government securities is on average 44%, 22%, and 34%, respectively.

As we explain later in this appendix, we use the time-varying weights of each category in order

to construct the corresponding market factor for the Government securities.

The holding of Treasuries and agency securities by banks kept tracking each other up to the

2008 crisis but diverged since then. The holding of Treasuries has increased up to 65% in the

recent years while holding of agency securities has dropped to 5%. The proportion of state and

politically related securities in total Government securities, while negatively correlated with the

other two categories before the crisis, remains stable around 30% afterwards.

A.2 Structured Debt Securities

Structured assets are those backed by a pool of loans. These loans, which can be of any type

(see Appendix A.3), are originated by the bank itself or other financial institutions. Another

type of structured assets are collateralized debt obligations, which are pools of risky tranches

from other structured assets further tranched and formed into a new security. In all cases of

such assets, what matter for the purpose of our classification are the final holding institution of

the asset (the bank) and pool of the loans (the underlying assets).

Mortgage Backed Securities. Bank holding of MBS consists of Residential MBS and

Commercial MBS.17 In either case, the mortgages are in the form of pass-through and non-

17In the case of an RMBS, the underlying property is a 1-4 family residential property, whereas forCMBS, the securitization is done on commercial properties. As opposed to an RMBS, commercialmortgages are often set for a fixed term and therefore are less exposed to prepayment risk.

2

pass-through mortgages.18 Both pass-through and non-pass-through mortgages (RMBS and

CMBS) can be issued and/or guaranteed by GSEs and non-GSEs.19 So, in total one can think

of eight different possible combinations. For instance, banks hold pass-through RMBS, which

are issued by GSEs, or pass-through CMBS, which are issued by non-GSEs. It can also happen

that the issuers are different for a CMO. For instance, a CMO is issued by a non-GSE but the

collateral is an MBS, which is issued by a GSE.

As we explain in Section 2.2, we add real estate loans to the MBS described above, in order

to construct the real estate asset class. We note that the underlying securities in this class

are residential or commercial real estate properties. Information on the weights of RMBS and

CMBS are not available in Call Reports prior to 2009. Since then, the majority of pass-through

RMBS are issued and guaranteed by GSEs. Other RMBS, such as CMO and REMIC, are

mainly due to GSEs. However, it is likely that the order has been reverse prior to 2009, that

is, banks tended to hold private label RMBS.

A.3 Loans

Commercial and Industrial Loans. Banks issue loans to borrowers, individuals or firms,

as long as it is for commercial and industrial purposes. Among these loans are also leveraged

loans to corporate firms. We do not have information about the exact amount of this type of

loans in the balance sheet. However, we use the market indexes that track the performance

of such loans, so that we can proxy the performance of the commercial and industrial loans.

A leveraged loan is a senior secured floating rate corporate loan to a high yield firm, which is

senior to the unsecured high yield bonds of the firm. As opposed to the standard term loans,

a syndicated loan is a loan extended by a group of financial institutions to a single borrower.

Syndicates often include both banks and non-bank financial institutions, such as collateralized

loan obligation structures (CLOs), insurance companies, pension funds, or mutual funds. Once

issued, the share of the loan can be sold to investors in the secondary market.

18Non-pass-through mortgages include all classes of collateralized mortgage obligations (CMO), realestate mortgage investment conduit (REMIC) and stripped MBS.

19Main GSEs are the Government National Mortgage Association (GNMA, Ginnie Mae), the FederalNational Mortgage Association (FNMA, Fannie Mae), and the Federal Home Loan Mortgage Corporation(FHLMC, Freddie Mac). Non-GSEs are non-U.S. government issuers such as depository institutions,insurance companies, state and local housing authorities.

3

A.4 Other Assets

Table A1 summarizes information about other assets, which are not explicitly classified as cash

or market-sensitive assets. These assets represent on average 20.5% of total assets of commercial

banks and can be divided into three groups: Securities (26.4%), Loans and Leases (32.1%), and

Other Assets (41.5%).

The largest part in Securities is Other Debt Securities (14.5%), which are trading and non-

trading securities. Only a small fraction of these debt securities are held in the domestic offices.

Additionally, given that they are for trading, they are only present in the balance sheet of the

few large banks.

In Loans and Leases, the largest part is Other Loans (17.6%), which consists of three types

of loans: loans given to non-depository financial institutions, loans given for purchasing and

carrying securities (secured and unsecured) including loans given to brokers and dealers, and

finally all other loans. Most of these loans are domestic loans.

Finally, in Other Assets, the largest part is Other Assets (24.9%). These include accrued

interest receivable, net deferred tax assets, equity securities without readily determinable fair

value, cash surrender value of life insurance assets, and other assets not classified elsewhere. We

do not report derivatives with positive fair value (with an average of $30 billion) as we assume

that they would cancel out derivatives with negative fair value.

As explained in Appendix C, except the third group of other assets, we take into account

the Securities, Loans and Leases and use their corresponding yield such that we can capture

their changes in the balance sheet.

[Insert Table A1 here]

A.5 Trading Assets

We have already discussed the asset classes of a bank in the Appendices A.1 to A.4. We now

devote this section to trading assets for two reasons: (1) they are the assets that differentiate

the commercial banking and market making activities of BHCs; (2) banks were not required to

report details about their trading assets in foreign offices before 2008. Therefore, we need to

reconstruct the balance sheet of the bank before this date in order to have a complete picture

of the dynamic of bank balance sheet.

Trading assets should be reported at their fair value by banks that have a quarterly average

of trading assets equal to $2 million or more for any of the four preceding quarterly reports.

4

However, banks with domestic offices only and with less than $100 million in total assets are

exempt to report trading assets. Also, banks that reported a quarterly average for trading

assets of $1 billion or more in any of the four preceding calendar quarters are forced to report

additional information about their trading accounts.

Trading activities of a bank usually include: (a) regularly underwriting or dealing in secu-

rities; interest rate, foreign exchange rate, commodity, equity, and credit derivative contracts;

other financial instruments; and other assets for resale, (b) acquiring or taking positions in such

items principally for the purpose of selling in the near term or otherwise with the intent to

resell in order to profit from short-term price movements, and (c) acquiring or taking positions

in such items as an accommodation to customers or for other trading purposes.

Except cash, all other types of assets can exist in the trading account of a bank. That

is, government related securities, MBSs, real estate loans, commercial and industrial loans,

consumer loans, and derivatives with positive fair value. Trading assets represent approximately

9% of total assets of commercial banks in our sample.

[Insert Figure ?? here]

Other Debt Securities. This category represents 4% of total assets in 2008 and includes

structural financial products and all other debt securities. In general, information about these

assets is very limited in the balance sheet. However, banks are required to report in a memoran-

dum the predominant type of collateral or reference assets supporting the structural financial

products.20 This enables us to group them to the appropriate class of securities. The second

group, all other debt securities, consists of asset-backed securities and other debt securities. In

the memorandum, such ABSs are detailed only for banks that reported a quarterly average for

trading assets of $1 billion or more in any of the four preceding calendar quarters.21 Thus we

use information about collateral in order to decide to which security class these assets belong,

and leave those that we cannot identify as other assets.

Other Trading Assets. These are trading assets that cannot be classified by a bank in a

certain group and are around 2% of total assets. Banks do not identify the type of these assets in

20Collateral includes: (1) trust preferred securities issued by financial institutions (2) trust preferredsecurities issued by real estate investment trusts (3) corporate and similar loans (4) 1-4 family residentialMBS issued or guaranteed by GSEs (5) 1-4 family residential MBS not issued or guaranteed by GSEs (6)diversified pools of structured financial products (such as CDOs squared and cubed) (7) other collateralor reference assets.

21Collateral for ABSs includes: (1) credit card receivables (2) home equity lines (3) automobile loans(4) other consumer loans (5) commercial and industrial loans (6) other.

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their balance sheet. But banks with sizable trading account (more than $1 billion) are required

to report in a memorandum the part of other trading assets that consists of equity securities.

We take these assets as other assets in our classification and calculate their appropriate yield.

Other Loans. These loans are way below 1% of total assets since 2008. Given their small

size, we do not include them in our security classes and let them to appear as other assets in

our classification with the appropriate yield.22

Missing Information Before 2008.

• At the bank level, not all information is available for domestic and foreign offices. Cash,

Deposits, Trading Assets, and Loans are reported for domestic offices along with the

consolidated ones. Total Assets and Liabilities and non-trading Securities are required

to be reported under the schedule RC-H. However, non-trading Securities (Government,

MBS, Other) are not reported before 2008. As a result, it is not possible to have the

full balance sheet for domestic offices before 2008 in details. Schedule for BHCs similar

to schedule RC-H for banks does not exist. So, the amount of domestic non-trading

securities is not available in their balance sheets.

• Both at the BHC and bank levels, details on Trading Assets are not reported for foreign

offices before 2008 in details. One can only find derivatives and the total trading assets.

In sum, disaggregated information about the amount of domestic non-trading securities and

foreign trading securities before 2008 is not available through the Call Report.

B BofA indices and Construction of Market Factors

Government Related Indexes. As we explained in Section A of this appendix, govern-

ment related assets are the sum of Treasuries, agency, state and politically related assets. Thus,

among the universe of BofA indexes, we select those whose performance best explains the per-

formance of such assets. The selected indexes are U.S. Treasury Master total return index,

U.S. Agencies Composite Master total return index, and National Select Municipal Securities

total return index. Treasury Master index contains 259 sovereign bonds across all maturities,

22They include loans to depository institutions and acceptances of other banks, loans to finance agri-cultural production and other loans to farmers, loans to foreign governments and official institutions,obligations (other than securities and leases) of states and political subdivisions in the United States.

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with effective duration of about 6 years. Bonds with effective duration of up to 5 years repre-

sent around 60% of the total value of the index and bonds with effective duration of 10 years

and more represent around 17%. Except few government guaranteed bonds in the Agencies

Composite Master index, the other 95.5% of 480 bonds are agency securities. The effective

duration is approximately 4 years. The third index contains U.S. Tax-Exempt Municipals,

which contains 7′759 bonds including Refunded bonds (1%), General Obligation bonds (45%),

and Revenue bonds (54%). The effective duration is approximately 7.8 years. While the first

index is available as early as 1990, the other two exist on a daily basis since 1996 and 2001,

respectively, making them absent in our construction of the government index for the periods

before. Information about these indexes and the subsequent indexes are summarized in Table

3.

To construct the final index, we calculate the weights of each of the three assets, that is,

Treasuries, agency, and municipal securities over time using aggregate data (Flow of Funds) of

the banking sector. On average, close to half of the government related assets are Treasuries

and the other half is split between agency (20%) and municipal (30%) bonds. We construct a

weighted average index using the weights of Treasuries, agency and municipal securities. Table

4 presents the summary statistics for the constructed indexes.

[Insert Tables 3 and 4 here]

Real Estate Related Indexes. For real estate securities, we choose three types of indexes.

First, Government National Mortgage Association (GNMA) represents the agency guaranteed

mortgage backed securities. It consists of 116 bonds and has an effective duration of 5.4 years.

Second, two indexes based on commercial mortgage backed securities and composed of 2′518

bonds together are used to represent investment grade rating, with an average duration of 4.7

years. Finally, there are two indexes based on six home equity loan asset backed securities, with

durations equal to from 1.6 and 6.2, respectively.

Similar to the government index, to construct the real estate risk factor, we approximate the

contribution of various real estate securities in the banking sector using the Flow of Funds data.

On average, 60% of the real estate assets are residential loans and securities and the rest are

32% commercial mortgages backed securities and finally 8% of home equity loans. We use these

weights to construct the final real estate index. The selected indexes contribute to the final

index only when they are available. For instance, the CMBS with BBB rating is only available

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since 2006, so we use the same index with bonds maturing 0-10 years, which is available since

1998.

Corporate Related Indexes. The index representing risky corporate assets (commercial

and industrial loans issued by the bank) is based on three indexes. The first index tracks the

performance of 5′619 non-financial investment grade corporate bonds, with an average duration

of 7.8 years. The other two indexes represent sum of 1888 high yield corporate bonds. The

majority of the bonds in these indexes belong to industrial sector, so that the financial sector

only represents 6% of the total number of bonds. The duration of the high yield indexes is half

the duration of the high grade index.

Household Related Indexes. We select an index such that it represents the non-residential

household assets of the banks. Most of the household assets of banks are consumer loans, which

are non-securitized. However, since the credit quality of the underlying affects the claims on

the asset, we assume that the performance of the securitized assets is a good proxy for the

performance of the underlying. Consumer loans can be divided into three groups: credit card

loans, automobile loans, and other loans issued to the households. Thus we select four indexes

that track the performance of credit card and automobile asset-backed securities across. These

indexes together include 1′206 securities with duration ranging from 1.2 to 1.9 years and corre-

spond to different ratings of the ABS. As for the third group of consumer loans, we use a high

yield consumer products index, which is based on 29 securities and has an average duration of

3.4 years.

We construct the final risk factor using the weighted average of individual indexes where

we infer the weights from the Flow of Fund data. On average consumer loans consist of 35%

automobile loans, 15% credit card loans, and 20% other loans.

C Measuring Interest Rates

For the items in the balance sheet that are not market-sensitive assets, we determine the corre-

sponding yield and cost of each item. The cost of borrowing (RD,t) can be computed for each

bank as Interest Expenses on Borrowing divided by Average Borrowing. Average Borrowing is

defined as Average Interest Bearing Liabilities minus Average Interest Bearing Deposits. The

cost of deposits (RDep,t) is obtained by dividing Interest Expenses on Deposits to Average Inter-

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est Bearing Deposits, where the latter is the average of interest bearing deposits of current and

previous calendar quarters. Return on the other assets (RO,t) is the weighted average of several

rates: the yield on loans, the yield on leases, the yield on balances in the depository institutions

and the yield on debt and equity securities. Comparing these rates obtained from the informa-

tion in the balance sheet and federal fund rate, we find that RF,t < RDep,t < RD,t < RO,t (with

average values: 1.8% < 1.9% < 3.5% < 5.6%).23

23All of these rates required some cleaning. Missing values were replaced by the value from previousquarter. For the cases where the first quarter was missing, we used the rate of the same quarter fromnext firms in the size ranking. Rates higher than 20% were replaced by the median of the sample for thesame quarter.

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Table A1: This table displays the other assets, which are not part of riskyassets. In the first column, Securities can be for trading or non-trading. Num-bers in the third column are asset weighted averages across banks from 1996to 2016.

Type Description Amount % of($ billion) total

Securities 34.6 26.4Other Loans 0.6 0.4Total Marketable Equity Securities 0.7 0.5Other Trading 14.4 11.0Other Debt Securities (SFP, ABS, etc) 18.9 14.5

Loans and Leases 42.0 32.1Agricultural Production Loans 0.8 0.6Leases 6.2 4.7Loans & Acceptances of Depository Inst. 12.1 9.2Other Loans 22.9 17.6

Other Assets 54.1 41.5Investment in Unconsolidated Subsidiaries 1.2 0.9Premises and Fixed Assets 4.0 3.1Intangible Assets 16.4 12.6Other Assets 32.5 24.9

Total 132 100

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