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How have Global Financial Institutions Responded to the

Challenges of the Post-Crisis Era?

December 6, 2015

Michael S. Pagano, Ph.D., CFA

Professor of Finance

The Robert J. and Mary Ellen Darretta Endowed Chair in Finance,

Villanova University, 800 Lancaster Ave., PA. 610-519-4389

The study examines the largely unexplored effect of changes in the

competitive landscape for large, global financial institutions on their

ability to take risks, as well as deploy capital and labor in an

efficient manner based on a novel measure of inefficiency. The

analysis shows during 2001-2013 that inefficiency peaked during

the 2008 crisis period and has fallen back to levels close to pre-crisis

periods. The model also performs well in out-of-sample forecasts of

the financial firms’ future market values. These results suggest that

large financial firms have been adjusting to the “new normal” of the

post-crisis period and thus are able to use capital and labor more

efficiently within the constraints of current market conditions. In

addition, a nonlinear pattern between inefficiency and a firm’s asset

size suggests that there might be an optimal scale for such firms in

the $450-$650 billion range.

Without question, the first part of the 21st century has been a

challenging one for business in general but most notably for large financial

institutions (FIs) that operate on a global basis. These key providers of

liquidity, credit, and other important financial services to corporations,

consumers, portfolio managers, investment analysts, and other institutional

investors have been buffeted by a seemingly endless array of economic,

political, and regulatory challenges. For example, the 2001-2014 period has

experienced two U.S. recessions (including a “Great” one), the 9/11/2001

terrorist attacks, major boom/bust cycles within the real estate markets of the

U.S. and Europe, a 2008 global stock market crash triggered by the Lehman

Bros. failure in September (and presaged by the Bear Stearns takeover by JP

Morgan in March of that same year), the TARP bail-out program of U.S.

financial institutions, the enactment of the 2010 Dodd-Frank Act and its

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associated “Volcker Rule,” a multi-country sovereign debt crisis in Europe

(2010-present), new Basel III capital standards and bank stress-testing

requirements, along with conflicts in the Ukraine, Iraq, Syria, Afghanistan, and

several other nations.

Given all these events / changes, industry observers such as Moody’s

note that these “developments have triggered a series of strategic repositioning

initiatives that are fundamentally reshaping several of the global investment

banks with the objective of improving return on equity and increasing

shareholder value.”1 Thus, my main research question is: how efficient have

global, systemically important financial institutions (G-SIFIs) been in adjusting

to these post-crisis events and regulatory changes?2 Many of these firms were

at the epicenter of the 2008-2009 U.S. financial crisis and thus have been

under greater regulatory and media scrutiny.3

“Efficiency” can be defined in several ways and I employ a relatively

unexplored definition of this term which uses a classic “production function”

approach to see how well a firm’s managers can convert key inputs such as

financial capital and labor into a “final output” which, for shareholders, is the

market value of the firm’s equity. This concept relies on the principles and

techniques typically used in the economics literature. In particular, this novel

approach is based most closely on earlier research on the efficiency of financial

institutions found in Hughes, Lang, Mester, Moon, and Pagano (2003) which

1 See Moody’s Investor Services’ Special Comment dated May 14, 2014.

2 Pagano and Sedunov (2014), among others, describes a systemically important financial institution as one that has

strong inter-relations not only between firms within its home country but also with financial firms in other nations

which, in the event of a crisis, can lead to international risk spillover effects.

3 For the classification of G-SIFIs, we rely on the Financial Stability Board (FSB) and its recent report which

identifies 30 such institutions (along with 2 other firms that were identified on earlier G-SIFI lists). We also include

14 North American-focused firms which are viewed as systemically important within the North American region.

Appendix A lists the 46 firms that are considered to be systemically important financial institutions and are used in

the empirical tests.

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they refer to as “market value shortfall.”4 In the following analysis, we estimate

how efficient the managers of 32 G-SIFIs and 14 North American SIFIs have

been during 2001-2013 by computing the difference between a “best-practice”

market value for each firm (given the firm’s investment in capital / labor) and

the firm’s actual market value of equity. The basic idea is that SIFIs which

have a larger difference between the best-practice value and the observed

market value will, by definition, have a larger market value shortfall and are

therefore considered to be more “inefficient” in managing their resources than

firms with smaller differences. I then use this model to test its out-of-sample

performance in forecasting the market values of equity for large SIFIs in 2014.

The results suggest there are large cross-sectional and times-series

variations in these inefficiency measures and that the U.S. financial crisis in

2008 had a strong but mostly temporary impact on the efficient management of

G-SIFIs. I also examine what factors are the key drivers of these fluctuations

and find a nonlinear pattern between a firm’s level of inefficiency and its overall

size (as measured by the book value of total assets), after controlling for firm-

specific levels of profitability, productivity, and risk-taking. Inefficiency is

greater with the smallest and largest FIs and thus firms in the middle range of

the sample were found to be the most efficient, thus suggesting there might be

an “optimal” size for FIs once they reach a certain size ($450-$650 billion in

assets). Thus, an intermediate-sized firm could benefit from the inherent

economies of scale related to the financial services industry but this firm is also

not too large so that these benefits are outweighed by the costs associated with

managing a more complex organization. The model developed here is also

useful for describing future market values of equity for large FIs on an out-of-

sample basis, as this attribute is particularly important for investors, analysts,

and regulators. For example, the model explains over 90% of the variation in

large SIFI’s market values over the subsequent year.

4 This concept of market value-based “inefficiency” is the focus of analysis in Hughes et al. (2003) and is also

applied to other FI-related research in Hughes, Lang, Mester, and Moon (1999) and Hughes, Mester, and Moon

(2001).

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Recent Trends in G-SIFIs’ Profitability, Growth, and Risk-

Taking

Due to the economic, political, and regulatory headwinds described

earlier, it is important to see how G-SIFIs and regional SIFIs have been affected

by these developments in terms of profitability, productivity, employment, and

risk-taking. Panels A-D of Figure 1 illustrate the time-series trends for equally

weighted industry averages of: a) annual sales productivity (Revenue Per

Employee), b) firm-level employment (Average Annual Employment per Firm), c)

a proxy for risk-taking (Cash & Marketable Securities / Total Assets ratio), and

d) equity market reactions to these trends (as measured by the firm-level

average of the Market-to-Book Equity ratio).

Figure 1, Panel A shows that sales productivity rose during 2001-2007

and then dropped sharply in 2008 before rebounding and leveling off again

near the pre-crisis peak level of 2007. Panel B reveals an increase in average

firm Employment that is similar to the 2001-2007 increase in Revenue per

Employee but rather than dropping in 2008, average employment has

essentially remained flat during 2008-2013.5 In contrast, Panel C highlights a

large jump in cash and marketable securities in SIFI portfolios during the post-

crisis period. One can view this increase in liquid securities (and shift away

from riskier, less-liquid assets) as a proxy for decreased risk-taking by SIFIs.

This drop in risk-taking is also reinforced by declining financial leverage due to

regulators’ requirements for larger capital buffers during the post-crisis

period.6 Lastly, Panel D of Figure 1 reports a sharp downtrend in the average

market-to-book equity ratio (MBE) for these firms (from over 2.5 to below 1.0)

5 The plateau in Employment shows that the average net change in employees is around zero since 2008 even though

the composition of staff might have changed (e.g., increased hiring in compliance and risk management might have

been offset by layoffs in the front and back offices).

6 To conserve space, recent trends in financial leverage for SIFIs are not reported here but have been widely reported

in other outlets (e.g., see Wright, 2015).

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and this ratio has remained depressed during the entire post-crisis period.

This final panel indicates that equity investors are still concerned about the

effects of pre-crisis behavior on future cash flows.7 However, as Hughes et al.

(2003) noted, the market-to-book ratio may not be a good metric to evaluate

management’s efficiency because this ratio measures “achieved market value”

rather than “potential market value” and thus leads to a biased measure of

inefficiency. This point will be discussed in greater detail in the following

section. Overall, the graphs reported in Figure 1 confirm the view that the

SIFIs continue to face a difficult operating environment during the post-crisis

period (although sales productivity and employment appear to have adjusted in

recent years).

Our Approach to Estimating the Efficiency of SIFIs

To estimate the efficiency of a FI (or its converse, inefficiency), we rely on

the method developed by Hughes et al. (2003). As noted above, Hughes et al.

(2003) and others have taken a “production function” approach where the key

inputs are an equity investor’s capital and physical labor (e.g., number of

employees at a specific FI). The process leads to producing a primary “output”

which is what financial theorists typically refer to as the main goal of the firm:

i.e., the production function of the firm ultimately attempts to maximize

shareholder value (the output). One can view a firm’s risky free cash flow (and

its related growth rate) as “intermediate goods” which ultimately affect the

“final output,” which is the market value of the equity investors’ investment. A

stylized version of this production function model of equity value can be

described as follows:8

7 For example, the U.S. Justice Department recently announced that current investigations of fixing LIBOR rates

might also mean that prior legal settlements/agreements between the Justice Department and several large FIs might

have been violated and thus could create even more legal liabilities for these firms (see McLaughlin and

Schoenberg, 2015).

8 Note that the valuation model is specified in general terms and thus can accommodate both constant growth and

abnormal growth assumptions, as well as any type of asset pricing approach because the firm’s cash flows, their

riskiness, and their required discount rate are viewed as “intermediate” goods and thus do not need to be explicitly

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Ve = f(FCFe, g, R) = g(K, L, T) (1)

where, FCFe is the free cash flow available to shareholders and g and R are the

expected growth rates and discount rates related to these cash flows. In

Equation (1), the second equality indicates that the cash flow is itself a

function of the firm’s key inputs (where K = financial and physical capital

investments, L = labor, and T = time, which serves as a proxy for technological

change). Thus, in this stylized model, management’s choices in terms of the

types and quantities of capital and labor will produce financial services which,

in turn, generate revenues, costs, and free cash flows which can then be

returned to shareholders or reinvested in the firm. These choices and their

outcomes will, in turn, affect the firm’s market value of equity.9

The production approach can be estimated by stochastic frontier analysis

(SFA), as first described in Jondrow et al. (1982). In this method, we can

measure the firm’s efficiency (or its converse, inefficiency) by first controlling

for any effects on our main output (the market value of a firm’s equity) that

might be due to luck / random chance. It is important to adjust for this

randomness in observed output in order to get a cleaner estimate of how

management’s production choices affect firm value. The main reason why one

needs to control for random effects can be seen when one tries to measure the

efficiency of two corn farmers (X and Y) which own two similar-sized fields. If

we were to simply measure the two farmers’ choices of capital and labor, as

well as the resulting output, then we would conclude that farmer X is the more

efficient farmer since he grew the most corn over, say, the past 6 months

(assuming the levels of capital and labor were the same across the two

farmers). However, it could be that farmer X’s high level of output is due to the

(good) luck of receiving a great deal of rainfall on his land whereas farmer Y’s

plot did not receive as much rain. Thus, after adjusting for the statistical

stated in Equation (1). In this way, we can directly equate the firm’s market value of equity to management’s initial

choices related to investments in capital and labor (as specified by the second equality in Equation (1)).

9 Although this study focuses on SIFIs, the approach outlined in Eq. (1) can also be applied to non-financial firms.

However, an analysis of this broader set of companies is left for future research.

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“noise” caused by the differences in rainfall, we might find that farmer Y is

actually more efficient. That is, farmer X’s output may have been inflated by

things out of his control while former Y’s output was depressed due to her bad

luck in terms of rainfall. So, to produce a fair and accurate assessment of a

firm’s level of efficiency, these random factors need to be accounted for in the

estimation technique.

In our context, we can use the SFA methodology to adjust for these

random effects, as well as explicitly model the firm’s conscious choices related

to capital (measured by the book value of equity) and labor (measured by the

number of employees). After accounting for the above factors, we define the

remainder as “inefficiency” and it represents the difference between the “best-

practice” market value for a firm (given its capital-labor choices) and a firm’s

actual market value. That is, the SFA method compares the firm’s noise-

adjusted market value relative to a best-practice “frontier” value based on the

production possibilities for the entire industry. The difference between the

firm’s value and the frontier’s value (controlling for the firm’s level of inputs) is

a measure of the firm’s inefficiency (expressed as a percentage of the frontier’s

value).

More formally, the SFA approach (based on a half-normal error

distribution) can be employed to estimate the following production model:

Ve = g(K, L, T) = (2)

ln(MVEi,t) = β0 + β1 ln(BVEi,t) + β2 ln(Employeesi,t) + ∑+2

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(Time Effectst) + εi,t

where, MVEi,t is the market value of equity for firm-i at the end of year-t and

BVEi,t is the book value for this firm-year, Employeesi,t is the total number of

employees for this firm-year, Time Effectst represent annual fixed effects factors

to control for changes in technology and the macroeconomy over time. In

addition, εi,t is a composite error term that equals (υi,t – µi,t) and distinguishes

between the FI’s inefficiency (µi,t) and random statistical noise (υi,t). Thus,

Equation (2) can be estimated with a pooled sample of annual observations for

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all 46 SIFIs during 2001-2013 to obtain scaled inefficiency estimates. Thus, the

inefficiency ratio equals the estimate of µi,t divided by the firm’s potential

market value of equity for each firm-year observation.

Equation (2) can be viewed as a form of the classic Cobb-Douglas

production function model and thus uses natural logarithms of the market and

book values of equity, as well as the natural logarithm of the number of

employees.10 Although the Cobb-Douglas function is used here for specific

firms within one industry, this function has also been used at the country level

to analyze and forecast macroeconomic growth as well as estimate stock

market valuations at the national level (e.g., see McMillan, Pinto, Pirie, and Van

de Venter, 2011).

To make the above points about the SFA methodology more concrete, an

example might be helpful. Assume, for example, that a firm has $80 worth of

equity book value, its noise-adjusted market value is $90, and the frontier’s

best-practice market value is estimated to be $100 for any firm with $80 of

book value. In other words, $100 is the maximum potential market value for a

firm with $80 of historic (book value) investment capital. In this case, the

firm’s inefficiency ratio is 10%, as the firm’s actual market value is only $90,

which is 10% less than the maximum value of $100 (computed as follows:

($100 - $90) / $100 = .10). Figure 2 shows this numerical example in

graphical form where the vertical distance between point A (the maximum

value) and point B (the actual value) measures the dollar amount of market

value shortfall, or inefficiency. It should also be noted that this inefficiency

estimate controls for random effects (good / bad luck) whereas a simple

market-to-book ratio does not. In this example, the market-to-book equity

10 The Cobb-Douglas (1928) production function defines output (Y) as a function of capital (K) and labor (L) inputs:

Y = AKαLβ. In logarithmic form, this function becomes: ln(Y) = A + α ln(K) + β ln(L) where A is a factor that can

be viewed as a measure of a firm’s level of technology. As can be seen above in Equation (2), one can interpret the

sum of annual time fixed effects as equal to A in the Cobb-Douglas framework. Thus, the model used here is very

close to the format of a classical Cobb-Douglas production function. In addition, a more complex model (i.e., the

translog production function) includes the squared terms as well as an interaction term for K and L. In tests not

reported here, the main results described in this study are robust to the use of this more complex translog function.

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ratio (MBE) is 1.125 because the $90 market value is greater than the $80

book value. Interestingly, some analysts who focus solely on MBE would

therefore conclude the firm’s managers are doing a good job when, in fact, the

firm is under-achieving based on the inefficiency ratio.

One of the key advantages of a metric such as the inefficiency measure

employed here is that it gives a clearer picture of management’s choices and

their effect on equity value than a more conventional MBE ratio because the

latter does not account for random, temporary factors that can influence

market value (but are out of the control of current management). In the

context of G-SIFIs, a good example of these random effects on market value

could be some of the shareholder and government lawsuits against these firms

for prior misconduct related to abuses in the areas of subprime mortgage

lending, LIBOR fixings, foreign exchange trading, etc. Each of these areas of

misconduct clearly affected the market values of G-SIFIs that were involved in

these cases when the cases were first disclosed but now, years later, the MBE

ratios of many of these firms remain depressed (as shown earlier in Panel D of

Figure 1). In the post-crisis period, the negative effects of these cases on G-

SIFIs’ market values can be viewed by current senior management of these

firms as “bad luck” that is out of their control since it happened several years

in the past and by a former set of managers. Also, it could be that a firm might

be based in a region that is experiencing strong economic growth. Just like the

farmer/rainfall example, the management of this firm’s market value might be

increased soley by the good fortune of being in a high growth region that is not

due to any conscious choice of management. Thus, as noted earlier, to more

accurately assess current management’s production choices, one must remove

these random effects (both positive and negative) using the SFA methodology.

In addition to controlling for random influences in our inefficiency

estimates, another possible confounding effect is self-selection bias because the

G-SIFIs have attracted greater attention from regulators and the media due to

the size and scope of these firms’ operations (as well as all the negative events

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described above). Thus, this is a set of firms that is likely to exhibit a

Heckman-type self-selection bias (see Heckman, 1979) because large FIs are

more likely to be deemed G-SIFIs just by virtue of their asset size and global

scope of operations.

Accordingly, a three-step process is used to answer the paper’s main

research question:

1. Estimate a Heckman selection model to account for possible self-

selection bias associated with the likelihood of being designated a G-SIFI due to

the firm’s size / investor base. This model is specified as follows:

SIFIi,t = α0 + α1 (BVAi,t) + ϕi,t (3)

ln(MVEi,t) = β0 + β1 ln(BVEi,t) + β2 (Employeesi,t) + ∑+2

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(Time Effectst) + εi,t (4)

where, SIFIi,t = a dummy variable equal to 1 if the firm is classified as a G-SIFI

and 0 otherwise; and BVAi,t = the firm’s book value of total assets. The

Heckman model first estimates a probit model based on Equation (3) where the

likelihood of a firm being categorized as a G-SIFI is a function of the firm’s total

scope of operations (proxied by BVAi,t). The method then estimates Equation

(4) to see if the parameter estimates of this production function-type regression

are influenced by the results of Equation (3).

2. If evidence of selection bias is found in the initial step, then the

Inverse Mills Ratio (IMR) from the first stage Heckman model is included in the

second step as a way to control for any selection bias. In this second stage, I

estimate the SFA production model and control for size-related selection bias

(via the IMR), as well as the key inputs noted earlier (capital and labor) and

technological change (via time fixed effects). These variables are commonly

used in production functions (see Greene, 2008, for further discussion of the

econometric issues related to estimating production functions).

3. After estimating the SFA’s production frontier, I can compute the

inefficiency measures for each firm (and for each year since we have annual

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data) as described earlier in Equation (2). These inefficiency estimates (ranging

from 0, perfectly efficient, to 1.00, completely inefficient) are then used in our

third step as the dependent variable in a pooled OLS regression. In this last

stage, a firm’s annual inefficiency estimates (IEi,t) are pooled together with all

other firms’ inefficiency estimates (both G-SIFIs and regional SIFIs for 2001-

2013) and then regressed against factors that are most likely to influence a

SIFI’s level of inefficiency (namely, the firm’s overall size, as measured by its

book value of total assets (BVA); sales productivity, as proxied by Revenue Per

Employee (RevPerEmp); operating profitability, as measured by Operating

Margin, (OperMargin) and risk-taking (or lack thereof, as proxied by Cash

Ratio—cash and marketable securities as a percentage of total assets).11 I also

include BVA2 to see if firm size has a nonlinear effect on inefficiency. Time-

and firm-level fixed effects are included to control for any other unobservable

market-wide and company-specific factors that are not explicitly included in

the model. This third-stage model is described as follows:

IEi,t = δ0 + δ1 (BVAi,t) + δ2 (BVA2i,t) + δ3 (RevPerEmpi,t) + δ4 (OperMargini,t) +

δ5 (CashRatioi,t) + ∑+5

12

=1 (Time Effectst) + ∑+17

45

=1 (Firm Effectsi) + ωi,t (5)

where, IEi,t = the firm- and year-specific inefficiency estimate which measures

the market value shortfall between the “best-practice” market value and the

firm’s actual market value (IEi,t = µi,t divided by the frontier value for the i-th

firm at time-t).12

11 Total Assets per Employee was also found to be a statistically significant alternative to Revenue per Employee

and thus the model’s productivity control variable is robust to the choice of using an asset-based or revenue-based

metric.

12 Note that in Equation (5) the independent variables are contemporaneous with the dependent variable. To test for

possible endogeneity effects between the dependent and independent variables, I also lag all independent variables

and re-estimate (5). The results (not reported here to conserve space) are qualitatively and quantitatively similar to

those reported later in Table 4 although the statistical significance of

δ

1 weakens moderately (from a p-value of .03

to .16). Thus, for the remainder of this analysis, the contemporaneous form of the model specified above in

Equation (5) is utilized.

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The Impact of the U.S. Financial Crisis on G-SIFI Behavior and

Efficiency

To estimate the models described in the prior section, we collect calendar

year-end annual data during 2001-2013 for equity market capitalization, as

well as various balance sheet and income statement items, for 46 SIFIs from

Bloomberg.13 Annual data were used rather than relatively “noisy” quarterly

information in order to obtain more reliable efficiency estimates. Table 1

reports the summary statistics for our main variables of interest. In particular,

one can see that the average Inefficiency Ratio is .2342 with a standard

deviation of .0828 (i.e., the market value shortfall as a percentage of the best-

practice market value, conditioned on the firm’s size). The standard deviation,

as well as the range of this measure (.0656 to .5625), shows that there is

considerable variation in efficiency across firms and over time. Other variables

such as ROA, Operating Margin, and Market-to-Book ratio (MBE) also exhibit

relatively large standard deviations. This is not surprising given the turbulent

period under study (2001-2013) and the global scope of the SIFIs (e.g., the

firms in the sample are headquartered in 15 different nations spanning Asia,

Europe, South America, and North America).

Figure 3 displays some of this variation for the Inefficiency Ratio,

Operating Margin, and ROA using equally weighted annual averages of all firms

in the sample. As Figure 3 illustrates, average inefficiency spiked to .254

during the 2008 crisis period but has nearly returned in 2013 to its pre-crisis

low of .223. Another interesting pattern can be seen in Figure 4, which plots

the equally weighted average of all firms’ Inefficiency Ratio against the average

book value of Total Assets. As can be seen in Figure 4, a nonlinear relationship

exists between inefficiency and firm size, with average inefficiency achieving its

minimum within the range of $450 to $650 billion in assets. Thus, large SIFIs

(but not the very largest) seem to enjoy the benefits of increased scale without

13 For firm-level employment, we obtained data primarily from Bloomberg but supplemented this data source by

obtaining information directly from firm’s financial disclosures whenever the data were not reported via Bloomberg.

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incurring as many of the costs associated with larger size (e.g., difficulty in

managing the enterprise, agency conflicts, and increased regulatory scrutiny).

As shown below in Table 4, this nonlinear relationship holds even after

controlling for other possible confounding effects in a multivariate regression

framework.

Our main results for 46 SIFI’s during 2001-2013 are sixfold. First, as

suggested in the previous section, selection bias exists within our pooled

sample of G-SIFIs and North American SIFIs. The first stage Heckman model

in Table 2 shows that the likelihood of being identified as a G-SIFI is strongly

(positively) related to the FI’s book value of assets (a typical measure of a firm’s

scale of operations). In turn, as shown by the significant “rho” term in the

third column of Table 2, this selection bias can affect the parameter estimates

for the SFA production model in the second step. Thus, we include the Inverse

Mills Ratio (IMR) from the Heckman model in the SFA production function to

account for these selection issues.

Second, the SFA production model is a statistically valid way to analyze

changes in the market value of these firms. For example, Table 3 shows that

all three key factors (capital, labor, and the IMR) have a significant impact on

the firm’s main output for shareholders (i.e., the market value of equity). These

results hold even after controlling for time-varying fixed effects which take

account of annual shifts in the industry’s production frontier due to changes in

technology and/or the macroeconomy. Also, the statistically significant

parameter estimate for the σµ variable confirms that the SFA methodology is a

more suitable approach than other econometric methods which do not attempt

to control for random chance when estimating a firm’s level of inefficiency.

Third, a nonlinear relationship between firm size and inefficiency

suggests that financial firms are more efficient when they are neither too small

nor too large. In Table 4, column 1, the final stage’s pooled OLS model of the

full sample’s inefficiency estimates (with time and firm fixed effects as well as

firm-clustered standard errors) shows a clear nonlinear relationship between

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firm size and inefficiency. This can be seen by the negative coefficient on the

linear form of firm size (BVA) and the positive parameter estimate for the

nonlinear term (BVA2).

The negative coefficient on the linear form of BVA and the positive

coefficient on the squared form of BVA indicates that, at first, inefficiency

decreases (or, conversely, the firm’s efficiency increases), as firm size grows.

However, at some point, the pattern switches and thus further increases in

firm size beyond this point lead to greater inefficiency. This nonlinearity

suggests that the costs of becoming extremely large (e.g., over $1 trillion in

assets) could outweigh the benefits and thus FIs of intermediate size (albeit still

very large at around $450 - $650 billion) might be more efficient in terms of

employing capital and labor to maximize shareholder value. Overall, these

results confirm that Figure 3’s graphical display of this relationship between

size and inefficiency is robust to the inclusion of other potential factors such as

the firm’s productivity (RevPerEmp), profitability (OperMargin), and risk-taking

behavior (CashRatio).14

Fourth, the results of several robustness tests show that the initial

inefficiency findings of Table 4 (column 1) are supported when the control

variables are lagged by one year (to control for possible simultaneity issues).15

Also, the original pattern persists when we split the sample into pre-/post-

crisis periods (i.e., 2001-2007 vs. 2008-2013), although the linear term for BVA

is less significant for the latter period (see columns 2 and 3 of Table 4).

Interestingly, the nonlinear pattern appears to be driven by the smaller,

regional firms because BVA and BVA2 are highly significant for these North

American firms but are both insignificant for the G-SIFIs (see columns 4-5 of

14 Note that the parameter estimates of all three of these additional control variables are negative and two of these

three variables are statistically significant. This suggests that increases in productivity and profitability are

important determinants in reducing a firm’s market value shortfall. However, the proxy for risk-taking (CashRatio)

reports a statistically weak negative sign (i.e., higher levels of CashRatio mean less risk-taking which corresponds,

weakly, to greater efficiency during this turbulent sample period).

15 As noted earlier, these results are not reported here to conserve space.

15

Table 4). For the G-SIFIs, size is not as much of a differentiator (since they are

all very large in size) and thus productivity and profitability are the key drivers

of inefficiency. A dummy variable for the introduction of the Dodd-Frank Act

during 2010-2011 was not statistically significant and thus, contrary to some

observers’ beliefs, this regulation does not appear to have been an important

driver of an FI’s level of efficiency / inefficiency during the sample period

although more time may need to pass before one can make a definitive

conclusion.16

Fifth, an alternative measure for the dependent variable was employed to

see if a simpler, more conventional measure such as the market-to-book equity

ratio (MBE) can capture the same forces that are summarized in our

inefficiency measure. However, as these additional tests confirmed in column

6 of Table 4, MBE does not show similar levels of significance and / or

nonlinear effects of firm size. Thus, the inefficiency estimates based on a

classic production model of firm are more highly correlated with firm

fundamentals such as productivity and profitability than the market-to-book

ratio. As suggested earlier, this divergence between inefficiency and MBE could

be due to the fact that inefficiency isolates those factors under management’s

control while MBE includes both permanent and random / temporary effects

on firm value.

Lastly, I test the out-of-sample performance of Equation (4) by using the

coefficients from Table 3 based on 2001-2013 to estimate the sample’s market

values of equity for 2014. Figure 5 plots the actual market values against the

model’s fitted values for our sample of FI’s (both G-SIFIs and North American

SIFIs). The model shows a relatively tight fit with the actual values. For

example, the R-square of a regression of the actual values on the fitted values

is 0.91 and confirms that Equation (4) is a useful description of the key factors

driving a SIFI’s market value of equity. However, the model’s parameters also

16 Due to the lack of significance of this effect, these results are not reported here to conserve space.

16

suggest that Equation (4) tends to over-estimate the actual market values

because the slope parameter is less than 1.0 and the intercept is significantly

different than zero. Overall, the model is a good descriptor of future market

values that portfolio managers, investors, and regulators can use to assess an

FI’s return prospects and overall capital adequacy.

Conclusion

Due to the importance of G-SIFIs for investors in the global economy and

the major regulatory and operating challenges facing these firms, it is

important to understand how well they are responding to this changing

financial environment. I apply a classic production model to assess the

efficiency of these SIFIs in a novel manner during 2001-2013. Although there

has been wide variation over time and across firms, I find that these SIFIs

appear to be moving in the right direction in terms of altering their strategies

and business operations to become more efficient and ultimately enhance

shareholder value.

For example, inefficiency peaked during the 2008 crisis period and has

fallen back to levels similar to pre-crisis periods. So, even though traditional

financial measures such as MBE, ROA, and Operating Margin have not

returned to pre-crisis levels, the inefficiency metric reported here indicates that

G-SIFIs and other large FIs in North America are adjusting to the “new normal”

of the post-crisis period and thus are able to use capital and labor more

efficiently within the constraints of current market conditions. In addition, a

nonlinear pattern between inefficiency and a firm’s asset size suggests that

there might be an optimal scale for such G-SIFIs in the $450-$650 billion

range. A test of the out-of-sample performance of the model’s ability to

describe future movements in large FIs’ market value of equity also shows the

usefulness of the model beyond the 2001-2013 estimation period. In sum, if

current managers of G-SIFIs continue on the current path towards greater

efficiency and do not revert to overly risky pre-crisis behaviors, then both

17

creditors and shareholders in these firms can benefit from a safer (albeit slower

growing) financial system.

Acknowledgments

I thank Austin Ryback and Liang Yu for their research assistance and comments,

as well as comments from Tina Yang.

Keywords: Financial Institutions, Regulation, Efficiency, Financial Intermediation,

International Finance, Equity Investments

18

References

Bongini, Paola, Nieri, Laura, & Pelagatti, Matteo. 2015. “The importance of

being systemically important financial institutions.” Journal of Banking and

Finance 50: 562-574.

Cobb, C.W., and Paul H. Douglas. 1928. “Theory of Production.” American

Economic Review 18, 139-165.

Greene, William H. 2008. Econometric Analysis. Upper Saddle River, NJ:

Prentice Hall, 90-92.

Heckman, J. 1979. “Sample Selection Bias as a Specification Error.”

Econometrica, vol. 47: 153-161.

Hughes, Joseph P., Lang, William, Mester, Loretta J., Moon, Choon-Geol. 1999.

“The dollars and sense of bank consolidation.” Journal of Banking and Finance

23: 291–324.

Hughes, Joseph P., Mester, Loretta J., Moon, Choon-Geol. 2001. “Are scale

economies in banking elusive or illusive? Incorporating capital structure and

risk into models of bank production.” Journal of Banking and Finance 25:

2169–2208.

Hughes, Joseph P., Lang, William, Mester, Loretta J., Moon, Choon-Geol,

Pagano, Michael S. 2003. “Do bankers sacrifice value to build empires?

Managerial incentives, industry consolidation, and financial performance.”

Journal of Banking and Finance 23: 291–324.

Jondrow, J., Lovell, C.A.K., Materov, I.S., Schmidt, P., 1982. On the estimation

of technical efficiency in the stochastic frontier production function model.

Journal of Econometrics 19: 233–238.

McLaughlin, David, and Schoenberg, Tom. 2015. “Banks Said to Risk Old Libor

Charges in U.S. Currency Probes,” Bloomberg News: March 17.

19

McMillan, Michael G., Pinto, J.E., Pirie, Wendy L., and Van de Venter, Gerhard.

2011. Investments: Principles of Portfolio and Equity Analysis. Hoboken, NJ: J.

Wiley & Sons, 469-484.

Moody’s Investor Service. 2014. “Global Investment Banks: Competing

Demands of Regulators and Shareholders Force Strategic Repositioning that

may further Differentiate Credit Profiles.” Special Comment: May 15.

Pagano, Michael S., Sedunov, John. 2014. “A Comprehensive Approach to

Measuring the Relation Between Systemic Risk Exposure and Sovereign Debt.”

Villanova U. working paper.

Wright, David. 2015. “Dodd-Frank Four Years Later.” Deloitte CFO Journal:

March 27.

20

Table 1. Summary Statistics for the Full Sample (2001 – 2013)

This table reports descriptive statistics based on calendar year-end values for 32 Global SIFIs

and 14 North American SIFIs. SIFI Dummy equals one for the Global SIFIs and is zero for the

North American SIFIs. Inefficiency Ratio measures the firm’s market value shortfall divided by

the maximum potential market value, given a firm’s book value of equity, as defined in

Equation (5).

Variable

N

Mean

Median

Standard

Deviation

Market Value of Equity ($Bil)

(MVE)

Book Value of Equity ($Bil)

(BVE)

Book Value of Assets ($Bil)

(BVA)

Market to Book Equity Ratio

(MBE)

Revenue Per Employee ($000)

(RevPerEmp)

Operating Margin (OperMargin)

Cash to Asset Ratio (CashRatio)

Net Income Margin (NIMar)

Return on Assets

(ROA)

Return on Equity

(ROE)

Global-SIFI

(SIFI Dummy)

Inefficiency Ratio

552

567

568

552

536

562

549

561

567

570

570

529

55.449

45.884

702.318

1.521

304.720

0.2888

0.1739

0.1847

0.0185

0.0926

0.7035

0.2342

39.458

28.272

439.912

1.383

269.835

0.2982

0.1278

0.1995

0.0087

0.1096

1.0000

0.2230

54.525

51.483

793.183

0.916

188.328

0.2247

0.1576

0.1973

0.0227

0.1157

0.4571

0.0828

21

Table 2. Heckman 2-Stage Selection Model

This table reports the estimates of probit and regression models for SIFI Dummy and ln(MVE), respectively, based

on annual data for 46 large U.S. and international financial institutions. t-statistics are reported in parentheses.

SIFI Dummy

t-statistic

Market Value of

Equity: ln(MVE)

t-statistic

Constant

-0.774908

***

(-8.40)

-0.12441

(-0.98)

Book Value of Assets

(BVA)

0.004306

***

(10.42)

Book Value of Equity

ln(BVE)

0.85597

***

(23.49)

Number of Employees

ln(Employee)

0.11577

***

(3.20)

Time Effect – 2001

0.756403

***

(7.50)

Time Effect – 2002

0.389360

***

(3.93)

Time Effect – 2003

0.732799

***

(7.45)

Time Effect – 2004

0.695031

***

(7.24)

Time Effect – 2005

0.768988

***

(8.16)

Time Effect – 2006

0.782388

***

(8.47)

Time Effect – 2007

0.549122

***

(5.96)

Time Effect – 2008

-0.168430

**

(-1.80)

Time Effect – 2009

0.086954

(0.94)

Time Effect – 2010

-0.012901

(-0.14)

Time Effect – 2011

-0.387462

***

(-4.20)

Time Effect – 2012

-0.165100

**

(-1.84)

Rho

0.8401810

***

(17.14)

No. of Observations

539

Schwarz Criterion

753.4

***: 0.01 Confidence Level

**: 0.05 Confidence Level

*: 0.10 Confidence Level

22

Table 3. Stochastic Frontier Analysis (SFA) for Full Sample

This table reports the estimates of a Cobb-Douglas production function of equity market value using stochastic

frontier analysis (SFA) for 46 SIFIs during 2001-2013. t-statistics are reported in parentheses.

***: 0.01 Confidence Level

**: 0.05 Confidence Level

*: 0.10 Confidence Level

Market Value of

Equity: ln(MVE)

t-statistic

Intercept

0.032342

(0.21)

ln(BVE)

0.841981

***

(20.50)

ln(Employees)

0.175411

***

(4.44)

Inverse Mills Ratio (IMR)

0.167354

***

(3.66)

Time Effect – 2001

0.724976

***

(7.66)

Time Effect – 2002

0.420598

***

(4.56)

Time Effect – 2003

0.666954

***

(7.39)

Time Effect – 2004

0.624960

***

(7.17)

Time Effect – 2005

0.659458

***

(7.65)

Time Effect – 2006

0.672551

***

(7.91)

Time Effect – 2007

0.393247

***

(4.70)

Time Effect – 2008

-0.284430

***

(-3.22)

Time Effect – 2009

-0.079778

(-0.95)

Time Effect – 2010

-0.075058

(-0.93)

Time Effect – 2011

-0.383271

***

(-4.63)

Time Effect – 2012

-0.202757

**

(-2.53)

Noise:

σ

υ

i,t

0.321804

***

(11.03)

Inefficiency:

σ

µ

i,t

0.343370

***

(4.52)

Number of Observations

529

Schwarz Criterion

595.6

23

Table 4. Determinants of Inefficiency Ratio Estimates for Full Sample

This table reports in columns 1-5 the estimates of Equation (5)’s panel regression models of inefficiency ratios (the dependent variable) on annual data

for 46 large U.S. and international financial institutions. Column 6 reports the results based on alternative dependent variable, the market-to-book

equity ratio (MBE). Time- and firm-specific fixed effects are included but not reported here to conserve space. t-statistics are reported in parentheses.

Variable

(1)

Full Sample

(2)

2001-

2007

Sub-Period

(3)

2008-

2013

Sub-Period

(4)

N.A. SIFI

(5)

Global SIFI

(6)

Alternate D.V.

MBE ratio

Constant

0.320022

***

0.336341

***

0.306284

***

0.387772

***

0.290357

***

0.54787

***

(35.28)

(27.64)

(19.11)

(23.16)

(21.04)

(3.88)

BVA

-0.00003

**

-0.00004

**

-0.00003

-0.00056

***

0.000008

-0.00007921

(-2.23)

(-2.55)

(-1.43)

(-5.21)

(0.47)

(-0.66)

BVA2

0.00016

***

0.000179

***

0.000175

**

0.005074

***

0.000048

-0.00011907

(3.31)

(3.01)

(2.22)

(3.36)

(0.83)

(-0.25)

RevPerEmp

-0.00009

***

-0.00008

***

-0.00009

**

-0.00015

**

-0.00010

***

0.00055075

***

(-5.08)

(-4.18)

(-2.60)

(-2.50)

(-5.26)

(3.28)

OperMargin

-0.17884

***

-0.19969

***

-0.18268

***

-0.29497

***

-0.14015

***

1.02055

***

(-12.72)

(-8.77)

(-8.77)

(-11.63)

(-8.51)

(7.17)

CashRatio

-0.0216

-0.03982

0.030011

-0.01118

-0.00350

0.25606

(-1.02)

(-1.53)

(0.77)

(-0.35)

(-0.13)

(1.27)

Number of Observations

504

268

236

156

348

501

Adjusted R2

0.3086

0.3178

0.3081

0.5698

0.2947

0.5052

***: 0.01 Confidence Level

**: 0.05 Confidence Level

*: 0.10 Confidence Level

24

Figure 1. Trends in Systemically Important Financial Institutions (Panels A – D)

Panel A. Panel B.

Panel C. Panel D.

25

BVE

Figure 2. Diagram of Stochastic Frontier Method

。

。 。 。

。 。 。 。

。 。 。

。

MVE

Inefficiency

80

90

100

B

A

26

Figure 3.

27

Figure 4.

28

Figure 5.

y = 0.919x - 0.9771

R² = 0.9103

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

12345678

Actual ln(MVE)

Fitted ln(MVE)

Fitted vs. Actual 2014 Market Value of Equity (MVE)

29

Appendix A. Systemically Important Financial Institutions

Table A1 provides a list of G-SIFIs based on the latest classification by

the Financial Stability Board (November 2014), as well as 14 North American-

focused SIFIs.

Table A1. List of SIFIs used in the analysis

Company

Global SIFI?

Agricultural Bank of China

Yes

Bank of America

Yes

Banco Santander

Yes

Bank of China

Yes

Banque Populaire

Yes

Barclays

Yes

BB&T

No

Banco Bilbao Vizcaya Argentaria

Yes

Bank of New York Mellon

Yes

Bank of Montreal

No

BNP Paribas

Yes

Citigroup

Yes

Comerica Incorporated

No

Commerzbank

Yes

Credit Agricole

Yes

Credit Suisse

Yes

Deutsche Bank

Yes

Dexia

Yes

Fifth Third Bancorp

No

Goldman Sachs

Yes

Huntington Bancshares Incorporated

No

HSBC Holdings PLC

Yes

Industrial & Commercial Bank of China

Yes

The ING Group

Yes

J.P. Morgan

Yes

Key Bancorp

No

Lloyds Banking Group PLC

Yes

Mitsubishi UFG Financial Group

Yes

Mizuho Financial

Yes

Morgan Stanley

Yes

M&T Bank

No

Nordea

Yes

PNC Bank

No

Regions Financial Corp

No

Royal Bank of Scotland

Yes

Societe Generale

Yes

Standard Chartered

Yes

State Street Corp.

No

SunTrust Banks Inc.

Yes

Sumitomo Mitsui Financial Goup

Yes

Toronto Dominion Bank

No

UBS Group AG

Yes

Unicredit

Yes

U.S. Bancorp

No

Wells Fargo Corporation

Yes

Zions Bancorporation

No