“OVER” AND “UNDER” VALUED FINANCIAL INSTITUTIONS:

EVIDENCE FROM A “FAIR-VALUE” P/B ECONOMETRIC MODEL

Economic Research & Investment StrategyIlias LekkosVeni Arakelian

INTRODUCTION

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• Part of our mandate in the formulation of the investment strategy of the Bank is to be able toidentify and evaluate investment opportunities (either in the Fixed Income or in Equity space)within the financial institutions’ universe.

• In that respect, our basic analytical tool is our Financial Institutions Assessment Model, whichallows us to distill the entire universe of listed financial institutions in order to arrive at ashortlist of our preferred investment choices and sort them from the best to worst based ontheir financial strength, balance-sheet quality and finally their capital adequacy.

• The aim of the present study is to introduce the second stage of our investment strategyprocess that allows us to evaluate the relative “overvalue” or “undervalue” of the shortlistedfinancial institutions based on the distance between their market-based price-to-book ratios(hereafter P/B) and our estimated “fair-value” P/B.

WHY DO BANKS MERIT A DIFFERENT APPROACH?

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The models analysts, investment strategists or even rating agencies use to evaluate financialinstitutions stand at a sharp contrast to the equivalent models used for the evaluation of non-financial corporates. This can be attributed to a number of unique features exhibited byfinancial institutions which drive a wedge between them and non-financial corporates. Morespecifically:

a. Differences in accounting practices. Banks’ assets are by and large financial rather real. Forthat reason banks’ assets are more likely and easier to be marked to market instead ofbeing carried at amortised cost.

b. Depreciation. Following from the first point, real assets require a higher rate ofdepreciation. As a result, depreciation is a major driving force in non-financial corporatebook values. In contrast, depreciation plays a minor role in financials.

c. Regulation. Banks play a key role in the functioning of the economy and financial criseshave the ability to depress economic growth for a prolonged period of time. For thatreason, banks are tightly regulated entities and are required to maintain predefined levelsof capital adequacy and liquidity.

d. Provision for credit risk and the ability for “smoothing of earnings”. Provisioning policiesmay differ across financial institutions giving management discretion as to the timing ofrecognition and realization of losses.

WHY P/B?

4

We have chosen price-to-book, P/B, or else the ratio of the market value of equity to its bookvalue, as our preferred variable to model for a number of reasons:

a. P/B reflects markets’ view of the additional intangible value created by banks’ managementthrough the deployment of banks’ assets and liabilities.

b. P/B reflects markets’ assessment on the discrepancies between the discounted future cashflows generated by each bank and its accounting valuation of equity.

c. P/B reflects discrepancies between the markets’ view on the value of their assets and liabilitiesand their accounting treatment.

FACTORS DRIVING “FAIR-VALUE” P/B

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Assets & Asset Quality

1. Assets (in logarithm) denominated in euros.

2. Problem Loans / Gross Loans (PL2GL): The ratio is used to compare the quality of loan

portfolios among banks, as high Problem Loans / Gross Loans ratios can be interpreted as

engagement in high-risk lending policies, which can lead to financial losses and a higher

probability of bank failure.

3. Loan Loss Provisions / Gross Loans (LLP2GL): It is an indicator of how protected a bank is

against future losses. A higher ratio means the bank has an enhanced capacity to absorb

losses in an economic downturn or in the event of a recession.

FACTORS DRIVING “FAIR-VALUE” P/B

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Capital Adequacy & Liquidity

5. Tier 1 Ratio (TIER1): It is the ratio that is most strongly associated with the true amount of

capital that is being leveraged and therefore is a good way to understand a bank’s current

leverage, defining the connection between a banks adjusted total assets (average total

consolidated assets) and it’s core capital.

6. Shareholders’ Equity / Total Assets (SEq2TA): It represents the amount of assets on which

shareholders have a residual claim in the event of a company-wide liquidation.

7. Gross Loans / Total Deposits (GL2TD): The loan-to-deposit ratio is the ratio of a bank’s

total outstanding loans for a period to its total deposit balance. If the ratio is lower than

one, the bank relies on its own deposits to make loans to its customers, without any

outside financing. If on the other hand the ratio is greater than one, the bank borrows

money which it re-loans at higher rates, rather than relying entirely on its own deposits.

8. Liquid Banking Assets / Tangible Banking Assets (LBA2TB): A broad measure of the ratio

between liquid and illiquid assets on banks’ balance-sheet.

FACTORS DRIVING “FAIR-VALUE” P/B

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Efficiency & Profitability

9. Cost to Income (C2I): It is the ratio of the Operating Expenses over the Operating Income

generated. The Operating Expenses equal to the sum of Employees Cost and the Other

Operating Expenses, whereas the Operating Income equals to Net Interest Income plus

Other Income. The Cost to Income ratio gives a clear view of how efficiently the bank is

being run. The lower the ratio, the more profitable the bank is.

10. Return On Assets (ROA): The most common way to calculate ROA is by dividing the Net

Income over the Total Assets. Higher ROA indicates more asset efficiency.

11. Net Interest Margin (NIM): It measures the difference between interest paid and interest

received, adjusted relative to the amount of interest-generating assets. It is calculated by

dividing the Net Interest Income (i.e., the interest income – funding expense) over the

Average Interest Earning Assets.

METHODOLOGY

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Our approach is based on a bank valuation model emphasizing the value created by banks’ core

loan and deposit relationships (Calomiris and Nissim (2014)). In this setting, “fair-value” P/Bs

would be driven by the market value of intangibles and other drivers of future earnings (Gordon

(1962), Damodaran (2009)), to the extent that these are not already reflected in observed book

values.

In this context, we investigate the cross-sectional and time series relationship between banks’

P/Bs and the set of fundamental factors we have identified as key drivers of “fair-value” P/Bs.

We used a sample of 61* banks (spanning 23 countries) with the highest scores in our FI

Assessment Model.

Formally, our model is set up as follows:

𝑷𝑩𝒊,𝒕 = 𝜷𝟎 + 𝜷𝟏𝒍𝒐𝒈(𝑨𝒔𝒔𝒆𝒕𝒔)𝒊,𝒕 + 𝜷𝟐PL2GL𝒊,𝒕

+ 𝜷𝟑LLP2GL𝒊,𝒕 + 𝜷𝟒 TIER1𝒊,𝒕 + 𝜷𝟓SEq2TA𝒊,𝒕 + 𝜷𝟔GL2TD𝒊,𝒕

+𝜷𝟕C2I𝒊,𝒕 +𝜷𝟖 LBA2TB𝒊,𝒕 +𝜷𝟗 𝑹𝑶𝑨𝒊,𝒕 +𝜷𝟏𝟎 𝑵𝑰𝑴𝒊,𝒕 +𝜺𝒊,𝒕

where 𝑖 = 1,⋯ , 61 and 𝑡 = 2011𝑄1 − 2017𝑄4.

*In order to have a balanced panel data model, we exclude the financial institutions whose data are not available for the entire period.

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Mar

-11

Jul-

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No

v-1

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Mar

-12

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No

v-1

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-13

Jul-

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No

v-1

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-14

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No

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-15

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No

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-16

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No

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-17

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0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

25th-75th 10TH AVERAGE 90TH

All the data are obtained from Moody’s Database. The figure below shows the evolution of the

percentiles of the P/B data for the period 2011Q1-2017Q4. To save space, the descriptive statistics

and the empirical distributions of the variables are reported in the Appendix.

Figure 1: Percentiles for the P/B from 2011Q1-2014Q4

METHODOLOGY

RESULTS: ESTIMATED PARAMETERS

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Table 1: Cross-section and periods effects specification fixed

Full sample (2011Q1 - 2017Q4) 2011Q1 - 2014Q4 2015Q1 - 2017Q4

Variable Coefficient Coefficient Coefficient

C 3.133921* 4.043874* 3.048711*

LOG(ASSETS) -0.118572* -0.225224* -0.133976

PL2GL -2.999671* -2.296433* -1.334242

LLP2GL 2.150798* 0.090946 3.187381

TIER1 0.011983* 0.023173* -0.000614

SEq2TA -4.786491* -5.988295* 1.45746

GL2TD -0.153145* -0.086043 -0.261685*

LBA2TBA -0.321547* 0.284276 -0.613878*

C2I -0.065811* -0.025012 0.053531

ROA 1.872391* 3.174834* -2.383626

NIM -1.092236 2.944508 7.661704

R-squared (%) 86.0593 90.0707 93.0315

DISCUSSION OF RESULTS

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• The estimated coefficients are statistically significant (with the exception of NIM) and have in

most cases the economically expected sign.

• The model penalizes size given that the 𝑙𝑜𝑔(𝐴𝑠𝑠𝑒𝑡𝑠) enter the model with a negative sign as

well as financial institutions with low credit quality (negative coefficient on PL2GL) and rewards

high level of provisioning (positive coefficient on LLP2GL).

• High levels of profitability (ROA) and the efficiency (low C2I) are also having a positive impact

on P/Bs.

• High levels of TIER1 also push fair values of P/Bs higher but not the Seq2TA.

• Finally, liquidity variables have a somewhat contradictory impact given that high levels of

gross loans to deposits (GL2TD) are penalized but so too high levels of liquid assets to

tangible banking assets (LBA2TBA). A possible explanation for this finding is that liquid assets

improve liquidity but harm profitability given their low yielding capacity.

• As a robustness check exercise, we split the period into two subperiods. The significance of

the variables changes keeping some commonalities to the aggregate model, mainly with

respect to the ability of the model to explain the variation of the P/B. This finding is of great

importance, considering the international panel setting.

BANKS SCORES: RANKING OF FI BASED ON P/BS DEVIATION FROM FAIR-VALUE

12

We evaluate P/B deviations from “fair-values” as of 2017Q4 and we sort the banks from under-valued to over-valued.

Actual Fitted Residual z-score

BPER Banca S.p.A. - 0.460 0.714 -0.253 -1.873

Mizuho Bank, Ltd. - 0.610 0.851 -0.241 -1.852

Morgan Stanley & Co. LLC (Municipal Deriv.) - 1.883 2.130 -0.247 -1.299

Credit Suisse Group AG - 0.737 1.033 -0.297 -1.297

Komercni Banka, a.s. - 1.721 1.995 -0.274 -1.223

Commonwealth Bank of Australia - 2.140 2.463 -0.323 -1.215

Sumitomo Mitsui Banking Corporation - 0.665 0.798 -0.133 -1.170

Banco Comercial Portugues, S.A. - 0.327 0.583 -0.257 -1.143

Deutsche Bank AG - 0.433 0.593 -0.160 -1.118

Canadian Imperial Bank of Commerce - 1.883 2.061 -0.178 -1.087

Australia and New Zealand Banking Grp. Ltd. - 1.423 1.712 -0.289 -1.076

Commerzbank AG - 0.370 0.532 -0.162 -1.063

United Overseas Bank Limited - 1.223 1.402 -0.179 -1.062

UniCredit S.p.A. - 0.501 0.628 -0.128 -1.043

The Royal Bank of Scotland Group plc - 0.692 0.805 -0.113 -0.931

Barclays Plc - 0.619 0.731 -0.112 -0.837

SunTrust Bank - 1.395 1.468 -0.073 -0.693

Bank of Nova Scotia - 1.740 1.933 -0.193 -0.671

Bank of America Corporation - 0.996 1.065 -0.070 -0.586

Banco Bilbao Vizcaya Argentaria, S.A. - 0.961 1.033 -0.072 -0.465

SpareBank 1 SR-Bank ASA - 0.885 0.950 -0.066 -0.457

Standard Chartered PLC - 1.113 1.263 -0.150 -0.425

Banco Popular Espanol, S.A. - 0.707 0.768 -0.061 -0.352

Intesa Sanpaolo S.p.A. - 0.907 0.951 -0.045 -0.290

National Australia Bank Limited - 1.617 1.675 -0.058 -0.286

Raiffeisen Bank International AG - 2.122 2.186 -0.063 -0.252

Westpac Banking Corporation - 1.836 1.875 -0.038 -0.158

State Street Bank and Trust Company - 0.742 0.759 -0.017 -0.127

Natixis - 1.158 1.175 -0.018 -0.114

Royal Bank of Canada - 2.167 2.176 -0.009 -0.078

Bank of Ireland - 0.864 0.866 -0.001 -0.003

Actual Fitted Residual z-score

DNB Bank ASA - 0.873 0.838 0.035 0.149

CaixaBank, S.A. - 2.153 2.116 0.038 0.156

National Bank of Canada - 1.870 1.840 0.030 0.162

Wells Fargo & Company - 1.564 1.543 0.022 0.174

Sparebanken Sor - 0.820 0.774 0.046 0.187

Erste Group Bank AG - 1.040 1.010 0.031 0.201

Bank of Montreal - 1.628 1.603 0.025 0.239

Aktia Bank p.l.c. - 1.060 1.029 0.031 0.267

Jyske Bank A/S - 0.996 0.954 0.042 0.287

Svenska Handelsbanken AB - 1.735 1.701 0.034 0.310

Societe Generale - 0.739 0.697 0.042 0.406

Banco Sabadell, S.A. - 0.910 0.850 0.060 0.469

Lloyds Banking Group plc - 1.110 1.005 0.105 0.539

HSBC Holdings plc - 0.673 0.551 0.122 0.615

Citigroup Inc. - 0.792 0.744 0.049 0.783

Swedbank AB - 1.767 1.623 0.143 0.798

Bankia, S.A. - 0.891 0.554 0.336 0.820

Banco Santander S.A. (Spain) - 1.066 0.923 0.143 0.885

Bankinter, S.A. - 1.640 1.324 0.316 0.913

KBC Group N.V. - 1.608 1.326 0.283 0.913

SEB - 1.538 1.372 0.167 0.920

Sydbank A/S - 1.415 1.139 0.276 1.247

Macquarie Group Limited - 2.106 1.522 0.583 1.380

Danske Bank A/S - 1.444 1.163 0.281 1.503

Goldman Sachs Group, Inc. (The) - 1.234 1.002 0.233 1.532

The Bank of New York - 1.373 1.060 0.313 1.912

KeyCorp - 1.392 1.027 0.365 2.431

JPMorgan Chase & Co. - 1.354 1.087 0.267 2.488

Nordea Bank AB - 0.867 0.657 0.210 2.798

Table 2: Bank Scoring Based on the P/B

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APPENDIX

DESCRIPTIVE STATISTICS OF SELECTED VARIABLES

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Figure 2: Price-to-book (P/B) distribution from 2011Q1-2017Q4

04080120160200240

0.0 0.5 1.0 1.5 2.0 2.5 3.0 Series : PBSa mple 2011Q1 2017Q4Obs erva tions 1820Mea n 1.040677Media n 0.947434Ma ximum 2.999640Minimum 0.000000Std. Dev. 0.540893Skewnes s 0.621394Kurtos is 2.913713Ja rque-Bera 117.6911Proba bi l i ty 0.000000

Figure 3: Total Assets (Assets) in euros from 2011Q1-2017Q4

0100200300400500600700800

0.00 0.05 0.10 0.15 0.20 0.25

Series: LLP2GLSample 2011Q1 2017Q4Observations 1813Mean 0.029789Median 0.013604Maximum 0.263732Minimum 0.000000Std. Dev. 0.039011Skewness 2.834667Kurtosis 12.79444Jarque-Bera 9674.806Probabil ity 0.000000

Figure 4: Cost to Income (C2I) distribution from 2011Q1-2017Q4 Figure 5: Gross Loans / Total Deposits (GL2TD) distribution from 2011Q1-2017Q4

02004006008001,0001,2001,400

0 2 4 6 8 10 Series : C2ISa mple 2011Q1 2017Q4Obs ervati ons 1815Mea n 0.628260Media n 0.596027Ma ximum 11.36941Minimum -0.180787Std. Dev. 0.357661Skewnes s 18.36259Kurtos is 488.6539Ja rque-Bera 17938890Probabi l i ty 0.000000

Figure 6: Liquid Banking Assets/Tangible Banking Assets (LBA2TB) distribution from 2011Q1-2017Q4

Figure 7: Loan Loss Provisions / Gross Loans (LLP2GL) distribution from 2011Q1-2017Q4

0

40

80

120

160

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Series: PB

Sample 2011Q1 2017Q4

Observations 1708

Mean 1.078419

Median 0.970976

Maximum 2.999640

Minimum 0.000000

Std. Dev. 0.524951

Skewness 0.660367

Kurtosis 2.903627

Jarque-Bera 124.7998

Probabi l i ty 0.000000

0

40

80

120

160

200

240

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Series: LBA2TBA

Sample 2011Q1 2017Q4

Observations 1703

Mean 0.308486

Median 0.270032

Maximum 0.817949

Minimum 0.003771

Std. Dev. 0.154028

Skewness 0.968203

Kurtosis 4.055107

Jarque-Bera 345.0649

Probabil ity 0.000000

0

40

80

120

160

200

240

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

Series: GL2TD

Sample 2011Q1 2017Q4

Observations 1703

Mean 1.072062

Median 1.005053

Maximum 2.669171

Minimum 0.062882

Std. Dev. 0.405120

Skewness 0.525488

Kurtosis 3.968490

Jarque-Bera 144.9340

Probabil ity 0.000000

0

200

400

600

800

1,000

0 1 2 3 4 5

Series: C2I

Sample 2011Q1 2017Q4

Observations 1703

Mean 0.627020

Median 0.601326

Maximum 5.311377

Minimum -0.016802

Std. Dev. 0.258356

Skewness 9.724806

Kurtosis 156.6338

Jarque-Bera 1701696.

Probabi l i ty 0.000000

0

40

80

120

160

200

240

280

0 400000 800000 1200000 1600000 2000000 2400000

Series: ASSETS

Sample 2011Q1 2017Q4

Observations 1703

Mean 574431.9

Median 468242.4

Maximum 2399583.

Minimum 4924.251

Std. Dev. 547186.7

Skewness 1.296756

Kurtosis 3.955795

Jarque-Bera 542.1112

Probabil ity 0.000000

0

100

200

300

400

500

0.00 0.02 0.04 0.06 0.08 0.10

Series:LLP2GL

Sample 2011Q1 2017Q4

Observations 1701

Mean 0.022516

Median 0.012489

Maximum 0.108106

Minimum 0.000000

Std. Dev. 0.022824

Skewness 1.536235

Kurtosis 4.647017

Jarque-Bera 861.3249

Probabil ity 0.000000

DESCRIPTIVE STATISTICS OF SELECTED VARIABLES

For illustration reasons, the next figure shows the bank problem loans to total gross loans globally.

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Figure 10: Tier 1 Ratio (TIER1) distribution from 2011Q1-2017Q4

Figure 8: Net Interest Margin (NIM) distribution from 2011Q1-2017Q4 Figure 9: Shareholders’ Equity / Total Assets (SEq2TA) distribution from 2011Q1-2017Q4

0

40

80

120

160

200

240

280

0.00 0.01 0.02 0.03 0.04

Series: NIM

Sample 2011Q1 2017Q4

Observations 1703

Mean 0.015447

Median 0.014970

Maximum 0.038127

Minimum -0.001749

Std. Dev. 0.006554

Skewness 0.576999

Kurtosis 3.164597

Jarque-Bera 96.41833

Probabi l i ty 0.0000000

40

80

120

160

200

240

280

-0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12

Series: SEq2TA

Sample 2011Q1 2017Q4

Observations 1703

Mean 0.068197

Median 0.063864

Maximum 0.128865

Minimum -0.021452

Std. Dev. 0.021982

Skewness 0.658127

Kurtosis 3.260990

Jarque-Bera 127.7704

Probabil ity 0.000000

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Series: TIER1

Sample 2011Q1 2017Q4

Observations 1706

Mean 13.51835

Median 12.80000

Maximum 29.30000

Minimum 0.000000

Std. Dev. 3.222161

Skewness 1.098906

Kurtosis 7.102015

Jarque-Bera 1539.445

Probabi l i ty 0.000000

BANK PROBLEM LOANS TO TOTAL GROSS LOANS GLOBALLY

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Figure 11: Bank problem loans to total gross loans (%). Source: www.indexmundi.com

REFERENCES

• Calomiris, Charles W., and Doron Nissim, 2014. Crisis-related shifts in the market valuation of

banking activities, Journal of Financial Intermediation, 23, 400-435.

• Damodoran, A., 2009. Valuing Financial Service Firms, mimeo.

• Gordon, M., 1962. The Investing, Financing and Valuation of the Corporation, Homewood, IL: R D

Irwin.

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