Essays on Money, Banking, and Finance A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at George Mason University By Thomas L. Hogan Master of Business Administration The University of Texas at Austin, 2007 Bachelor of Business Administration The University of Texas at Austin, 2000 Director: Lawrence H. White, Professor Department of Economics Spring Semester 2011 George Mason University Fairfax, VA
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Essays on Money, Banking, and Finance
A dissertation submitted in partial fulfillment of the requirements for the degree ofDoctor of Philosophy at George Mason University
By
Thomas L. HoganMaster of Business Administration
The University of Texas at Austin, 2007Bachelor of Business Administration
The University of Texas at Austin, 2000
Director: Lawrence H. White, ProfessorDepartment of Economics
I dedicate this dissertation to my parents. Thank you for your love, your integrity, and yourunending patience. You made me the man I am today. I love you both.
I would also like to make a special dedication to Douglas B. Rogers. Doug was a greatfriend and innovative economist whose time with us ended far too soon.
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Acknowledgments
I would like to thank my dissertation committee chaired by Lawrence H. White joined byTyler Cowen and Gerald A. Hanweck. Dr. White, thank you for your invaluable guidanceboth through the dissertation process and in my efforts to become a scholar. I aspire toyour example in teaching, writing, and research. Dr. Hanweck, I am privileged to havehad the opportunity to work with you on your research and appreciate your assistance andencouragement in my own research. Dr. Cowen, thank you for your insightful commentson my dissertation and other projects.
While at George Mason, I have had the great privilege to study with several gifted and in-spiring faculty members. Peter J. Boettke eats, sleeps, and breathes economics and infuseshis students with a passion for learning. Peter T. Leeson is a simply brilliant economist anda model that all Mason students would be proud to emulate. My other amazing instructorsinclude Bryan D. Caplan, Garett B. Jones, John V. C. Nye, Richard E. Wagner, and WalterE. Williams whose classes continue to permeate my understanding of economics. Virgil H.Storr, Chris J. Coyne, and Omar Al-Ubaydli greatly helped to further my understandingof economics and my career in the field. Thanks also to Peter Lipsey, Lane Conaway, andMary Jackson who provided invaluable assistance in my dissertation and throughout thePh.D. process.
Outside of George Mason I have been privileged to work with Andy Young of West VirginiaUniversity who has guided me in my writing and research. Thanks to Travis Wisemanof West Virginia University who has been a valuable co-author. Thanks also to professorsMichael W. Brandl, Eric Hirst, Greg F. Hallman, and Stephen P. Magee of the University ofTexas who encouraged me to pursue my dream of becoming a college professor and helpedmake that dream a reality.
Thank you to my friends in the graduate economics program at George Mason University.Daniel J. Smith and Alexander Fink are already great economists and will soon be joinedby Nicholas A. Curott, Stewart Dompe, Tom K. Duncan, David J. Hebert, Kyle Jackson,William Luther, and Nicholas A. Snow. Thanks to the students who preceded me in theGMU graduate economics program and helped guide my way, especially Dan J. D’Amico,Adam G. Martin, Jeremy M. Horpedahl, David Skarbek, Emily C. Skarbek, Adam C. Smith,Diana W. Thomas, Michael D. Thomas, and Tyler Watts.
One name that deserves to be on the list of great economists is Douglas B. Rogers. Dougwas an innovative economist, a gifted writer, an exciting teacher, an amazing athlete, anda loving friend. Doug challenged me, encouraged me, corrected me, and inspired me. Dougis dearly missed and will always be lovingly remembered by his friends, family, and all whoknew him.
For financial support, I would like to thank the Mercatus Center at George Mason Univer-sity, the Richard E. Fox Foundation Fellowship, the Lynde and Harry Bradley Foundation
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Fellowship, the Charles G. Koch Charitable Foundation, and the Institute for HumaneStudies. Their support made this dissertation possible. These papers also benefited fromcomments and criticisms in presentations at the 2011 Association of Private Enterprise Ed-ucation international conference and the GMU Monetary Research Cluster.
Thanks to my friends back home in Texas, across the country, and around the world. Mostof all, let me thank my best friends James Gill, Bill McMains, Phillip Olcese, Matt Steven-son, and Leo Welder. You have each been an inspiration to me. Thank you for putting upwith my stubbornness through all the years and with my lack of communication over therecent few. The many other people deserving of recognition are too numerous to name, solet me simply give one big “Thank you” to all the friends I grew up with in Corpus Christior made along the way at the University of Texas, the McCombs MBA program, GeorgeMason University, and in Vienna, Frankfurt, and London.
My family too deserves thanks and praise. My father Roland Hogan has always been myhero and a model for me in my hopes, goals, and dreams. My mother Kathy Hogan keptme grounded so that my goals and dreams could actually be accomplished. My sister LauraBrady has, despite my efforts to hide it, always been a role model to me in her academic,professional, and personal endeavors. My brother Kevin Hogan, who is now pursuing doc-torate of his own, is smarter than he knows and more creative and kind than I could hopeto be. Thanks to my bother-in-law Corbin who I feel is like a brother to me. Thanks tomy loving and wonderful grandmother Margaret Greene and her children, grandchildren,sisters, and cousins. I must fail here to thank my extended family by name since doingso would require adding a further appendix to this paper, but I love you all and appreci-ate your help and support. However, I would like to specifically thank my uncles ThomasGreene, Mark Hulings, and John Greene who kept me interested in business, politics, andeconomics and who in many ways inspired me to pursue my Ph.D. in economics.
My greatest thanks go to Jesica Tomlinson. Thank you, Jesica. You most of all deserve myappreciation. You most of all bore the burden of my overloaded schedule and frantic lifestyleover the past two years. You put up with my stressed-out phases and absent-minded antics.I appreciate everything you have given me and all you have done for me. I love you so much.
This dissertation will address three significant topics in money, banking, and finance.
The first chapter contributes to the current debate over is Gresham’s Law. This “law” had
long been considered a basic principle of monetary economics, yet over the last few decades
it has become commonly criticized as a failure. I clarify the theory of Gresham’s Law as a
description of price controls on the exchange of currencies and provide historical evidence
of the influence of Gresham’s Law on English coinage from 1344 to 1815.
The second chapter presents a generalized version of the Diamond-Dybvig model. The
recent literature on bank runs, following Diamond and Dybvig (1983), studies the banking
sector in isolation from the greater economy. Here I model an economy that includes not only
DD type bank depositors but also producers of goods. When consumers can exchange goods
for deposits, trade provides a welfare improvement, and bank runs are not an equilibrium
unless the bank is fundamentally insolvent.
The final chapter examines the influences of capital and risk-based capital (RBC) on
the stock prices and bond yield spreads of US bank holding companies from 2000 to 2010.
Both capital and RBC are significantly related to these risk indicators in several quarters.
However, there does not appear to be a significant difference between the influences of
capital and RBC in any quarter, indicating that RBC does not improve upon the standard
capital ratio.
Chapter 1: Introduction
This dissertation will address three significant topics in money, banking, and finance. Sev-
eral contemporary works have revived the debate over Gresham’s Law. The next chapter
on Gresham’s Law seeks to quell that discussion. Chapter 3 addresses the Diamond-Dybvig
model of deposit banking. I propose a previously unknown equilibrium in the famous model
of Diamond and Dybvig (1983). The final chapter analyzes the influence of capital and risk-
based capital (RBC) on perceptions of bank risk. I find that bank risk is related to RBC
but that RBC provides no new information compared to the standard capital ratio.
In chapter 2, I address the recent debate over Gresham’s Law. Gresham’s Law states
that bad (legally overvalued) money drives out good (legally undervalued) money. This
“law” had long been considered a basic principle of monetary economics, yet over the last
few decades it has become commonly criticized as a failure. This paper clarifies the theory of
Gresham’s Law as a description of price controls on the exchange of currencies. It provides
historical evidence of the influence of Gresham’s Law on English coinage from 1344 to 1815.
Chapter 3 presents a generalized version of the Diamond-Dybvig model of banking. The
recent literature on bank runs, following Diamond and Dybvig (1983), studies the banking
sector in isolation from the greater economy. Here I model an economy that includes not only
DD type bank depositors but also producers of goods. When consumers can exchange goods
for deposits, trade provides a welfare improvement, and bank runs are not an equilibrium
unless the bank is fundamentally insolvent. Instability is, thus, not inherent to banking but
results from restrictions on information and exchange. I show that this is consistent with
historical evidence from the US banking system.
Chapter 4 examines RBC as a measure of bank risk. Recent changes in US banking
regulation have emphasized RBC as a buffer against bank insolvency. This paper compares
RBC to the standard capital ratio of equity over assets. For each quarter from 2000 to
2010, I regress both capital and RBC against three indicators of risk: the absolute value
of stock returns, standard deviation of stock returns, and bond yield spreads. Both capital
1
and RBC are significantly related to these indicators in several quarters. However, I am
unable to find a significant difference between the influences of capital and RBC in any
quarter, indicating that RBC does not improve upon the standard capital ratio.
2
Chapter 2: Gresham’s Law Revisited
2.1 Introduction
Gresham’s Law was once considered a “verified fact” of monetary economics (Fisher 1894,
p.527 n.2). Yet over the last few decades, this “law” has come under dispute. This paper
seeks to clarify Gresham’s Law and respond to its critics. It provides evidence of the
influence of Gresham’s Law during England’s bimetallic period from 1344 to 1815.
A number of contemporary economists dispute Gresham’s Law. Rolnick and Weber
(1986) declares Gresham’s Law a failure and a “fallacy.” Velde, Weber, and Wright (1999,
p.1) states that “Despite it being one of the most generally accepted and frequently cited
propositions in economics, we think that existing theoretical analyses of Gresham’s Law
are lacking” and “its empirical validity is questionable, or at least seems to depend on
circumstances.” Sargent and Smith (1997, p.199), Velde and Weber (2000), and Li (2002) all
contend that Gresham’s Law sometimes holds but other times fails. Even Friedman (1990b,
p.1162 n.4) confesses that “For precision, the “law” must be stated far more specifically, as
Rolnick and Weber (1986) point out.” This paper attempts to restore Gresham’s Law by
providing the specificity which Friedman requested.
After clarifying the theory behind Gresham’s Law, its empirical validity is tested. The
history of English coinage provides strong evidence in favor of Gresham’s Law. From 1344
to 1815 the Royal Mint in London minted currencies from both silver and gold.1 The
metal content of each currency when combined with the legal tender rate that relates the
currencies creates an implied price ratio of silver to gold. Gresham’s Law predicts that
when the implied ratio between the prices of gold and silver in England overvalues gold
relative to international prices, then gold will be imported and minted while silver will be
exported. When silver is overvalued, the opposite occurs. Regression analysis on English
1Although England left the bimetallic standard in 1815 and moved to a mono-metallic gold standard,both gold and silver continued to be coined until 1917 (Craig 1953, p.422).
3
coinage shows that overvaluation significantly influence mint production at the 1% level.
This paper contends that Gresham’s Law is both logically sound and empirically ob-
servable. The next section outlines the theory of Gresham’s Law and the claims against it.
Section 2.3 describes the effects of Gresham’s Law with the historical example of English
coinage from 1344 to 1815 and verifies the strength of this relationship using regression
analysis. Section 2.4 concludes.
2.2 Gresham’s Law
Gresham’s Law is often summarized as the tendency for bad (legally overvalued) money to
drive good (legally undervalued) money out of circulation. When two monies have different
intrinsic or international values but may only be exchanged at equal value, traders benefit
by paying out the less valuable coins and hoarding, melting, or exporting the more valuable
ones. Over time, more of the good money leaves circulation until only the bad money
remains in use.
Hayek concisely explains, “The essential condition for Gresham’s Law to operate is that
there must be two (or more) kinds of money which are of equivalent value for some purposes
and of different value for others” (Hayek 1967, p.318). A disparity between prices of the
two monies persists only when subject to some non-market restriction such as a legal tender
law. As White (2000, p.xxx ) describes, “When a legal tender law sets a fixed exchange rate
between two monies of unequal market value, the legally overvalued currency drives the
legally undervalued currency out of circulation.”
A legal tender law is a price control on the exchange of currency. The law may be
imposed as either a price ceiling or a floor or both. For example, in 1696 the local exchange
rate in England of silver shillings to gold guineas shot up from 22 to 30. The Crown
responded by instituting a ceiling price of 22 shillings per gold guinea in all market exchange
of shillings and guineas (Jenkinson 1805, p.161-162). What would an economist predict as
the result of this imposition?
Figure 1 illustrates the price ceiling and its effects. The price is drawn as gold in terms
of silver, and the quantity is the amount of gold exchanged. If suppliers can only sell
gold guineas at the price of 22 shillings or below, then the quantity of gold supplied will
Figure 2.1: Short and long-term effects of a price ceiling.
fall. Additionally, the suppliers of silver (demanders of gold) will find the price to their
advantage and the quantity of silver supplied will rise (and the quantity of gold demanded).
The short-term effect will be a shortage of gold and a surplus of silver as in figure 1.a. But
if the international price ratio of gold to silver is above the price ceiling, then traders can
benefit by importing gold and exporting silver. The long-term effect will be an increase in
the supply of gold and a decrease in the supply of silver as in figure 1.b. These predictable
results are exactly what occurred following the imposition of the English price ceiling in
1696 (Fay 1935; Breckinridge 1969[1903], p.45).
Suppose instead that the legal tender law had been created as a price floor on the price
of gold. Then when the international price fell below the price floor, silver would have been
imported and coined and gold would have been melted and exported. Since a price floor on
gold is equivalent to a price ceiling on silver, any price control generally creates a shortage
of one metal currency and a surplus of the other. The relative magnitudes of these effects
will be determined by the elasticities of each currency.
When the government dictates that currencies may only be exchanged at the legal rate,
the ratio acts as both a ceiling and a floor. The market price of the currencies will converge
to the legal rate and create a shortage or surplus in the quantity. Figure 2.2 illustrates
the effects of price controls on the supply and demand of silver and gold currencies. When
the market rate of gold rises above the legal rate as in figure 2.2.a, the legal rate acts as a
price ceiling. To return the market to the legal rate, the supply of gold must increase, or
the supply of silver must decrease, or both. When the market rate of gold falls below the
5
(a) Price ceiling. (b) Price floor.
Figure 2.2: Legal tender laws as a price floor or ceiling.
legal rate as in figure 2.2.b, the legal rate acts as a price floor. To return the market to the
legal rate, the supply of silver must increase, or the supply of gold must decrease, or both.
This is the essence of Gresham’s Law, that a legal tender law will act as a price control and
create a surplus or shortage.
When legal tender laws equate coins of two different metals such as gold and silver,
Gresham’s Law takes the form of arbitrage through the import and export of precious
metal. If the local exchange rate between gold and silver deviates from the international
rate, arbitragers can profit by importing the overvalued metal and minting it into coins while
melting and exporting coins made from the undervalued currency. Thus, bad (overvalued)
money drives out good (undervalued) money as described by Gresham’s Law. Alternatively,
legal tender laws can also create a fixed rate of exchange between two currencies of the same
metal, such as when a government debases a currency by lowering its weight. In this case, the
more valuable, full-bodied coins are usually hoarded while the less valuable, underweight
coins are passed on through exchange. Again, bad (overvalued) money drives out good
(undervalued) money as described by Gresham’s Law.2
The formulation of Gresham’s Law in terms of price controls on currency is consis-
tent with historical descriptions. Thomas Gresham was the founder of the London Royal
Exchange and opposed its regulation (Fetter 1932, p.481-483). Buckley (1924, p.593-4)
describes Gresham’s opinion that “The Rate of Exchange... is fixed on the market by the
plenty of Deliverers and Takers (i.e. by Supply and Demand).” When it was suggested that
2This paper deals mainly with the operation of Gresham’s Law through international channels. Forexamples of hoarding, see Craig (1946, p.7) and Li (1963, p.47), and Kelly (1991, p.45).
6
the Crown might stabilize English currency by regulating or even closing the market for
currency exchange, “Sir Thomas Gresham... discredited all idea of direct interference with
the exchange.” Mcleod (1855) was the first to interpret Gresham’s ideas as a singular law.3
’When two sorts of coin are current in the same nation of like value by denom-
ination, but not intrinsically, that which has the least value will be current,
and the other as much as possible will be hoarded,’ or exported, we may add.
(Mcleod (1903[1855], pp.119-120) quoted in Fetter (1932, p.488))
Through the twentieth century, economists described the shortage (Fetter 1933, p.821) or
surplus (Giffen 1891, p.304) created whenever the implied ratio of gold to silver in England
was over- or undervalued relative to international rates. These descriptions are consistent
with more modern terminologies of price ceiling and price floor.
Gresham’s Law has long been considered a true and fundamental law of monetary eco-
nomics. Academic works on Gresham’s Law include older articles such as Giffen (1891),
Fisher (1894), Daniels (1895), Buckley(1924), and Fetter (1932, 1933). Contemporary works
such as Selgin (1996) and Oppers (1996, 2000) buttress the theoretical foundations of Gre-
sham’s Law, while others such as Greenfield and Rockoff (1995), Mundell (1998), and Fried-
man (1990b) provide empirical support. Friedman (1990a) and Flandreau (2002) describe
how bad money drives out good without specific reference to Gresham. Historical works
which refer to Gresham’s Law including Giffen (1891), Farrer (1968[1898]), Spooner (1972),
Friedman and Schwartz (1963), Hayek (1967, 1976), Galbraith (1975), and Selgin (2008).
Yet despite the ample historical evidence, many contemporary works proclaim the failure
of Gresham’s Law. These criticisms fall into three categories. Most common is the empirical
conjecture that Gresham’s Law sometimes works and sometimes fails. Second is the claim
that legal tender laws were often unenforceable, so Gresham’s Law could not have operated.
As will be discussed, these first two critiques are compatible with the characterization of
Gresham’s Law describing a price control on currency exchange. Last, a few critics make
the extreme case that legal tender laws have no effect on commodity money, and therefore,
Gresham’s Law always fails. It is only this final claim, that Gresham’s Law always fails,
3Giffen (1891) and (Daniels 1895) challenge whether this phrasing is consistent Thomas Gresham’s orig-inal description.
7
which this paper seeks to rebut.
Several works dispute Gresham’s Law by providing empirical cases where the law appears
to have failed. Rolnick and Weber (1986, p.193) provides examples of times when bad
money did not appear to drive out good money.4 Sargent and Smith (1997) creates a
theoretical model of commodity money and cites empirical examples from Cipolla (1956,
p.17) and Rolnick and Weber (1986) of times when the Gresham’s Law appears to have
failed. Li (2002) describes theoretical cases which “violate Gresham’s Law,” again referring
to Rolnick and Weber (1986) for specific examples. Redish (2000) examines Gresham’s Law
but finds the evidence ambiguous.
However, these historical cases are not inconsistent with Gresham’s Law as a description
of price controls. As previously described, Gresham’s Law simply asserts that a price ceiling
on the exchange of currencies creates a shortage of the undervalued currency. A case where
bad money fails to drive out the good should hardly be cited as a failure of Gresham’s
Law. It is simply an instance in which the legal tender rate was not a binding constraint,
and therefore, Gresham’s Law did not apply. If some authors chose to describe the non-
application of a law as a “failure” of that law, then the distinction is purely semantic.
Other critics of Gresham’s Law accept the influence of legal tender laws but argue
that such laws were not enforceable. Velde, Weber, and Wright (1999, p.293) cite Miskimin
(1963, p.84) that “[Gresham’s Law] assumes that the government possesses enough political
force to insist upon the legal tender value of the coinage and to decree circulation at par.
There is, however, substantial evidence that neither the French nor the English monarchies
gained this power until the end of the middle age”. Sargent and Velde (2002, p.31) claims
that “During shortages, the laws were often disobeyed.”
Clearly the critics are correct that enforcement of legal tender restrictions was not
consistent through time. During some periods of English monetary history the exchange
rates of gold and silver currencies floated freely in the market (Jenkinson 1805, p.180),
while at other times the Crown attempted to control the rate by assigning values for tax
collection (Craig 1953, p.185) or enforcing a price ceiling or floor on the exchange of currency
(Jenkinson 1805, p.161-162; Shirras and Craig 1946, p.228). Yet, this line of argument
4Most of these examples have since been disputed by Greenfield and Rockoff (1997).
8
confuses the causes and effects of Gresham’s Law. If legal tender laws fail to create a
shortage of currency, then one possibility is that the laws were not effectively enforced.
However, if coinage of a currency is found to be dependent on its legal tender laws despite
the fact that legal tender restrictions were not fully enforced, then the evidence is in favor
of Gresham’s Law, not against it.
A few works go so far as to deny the influence of legal tender laws entirely. Rolnick
and Weber (1986, p.193) states that “legal tender laws provide no reason for good money
to disappear from circulation.” The authors “propose a more feasible qualification to the
popular version of Gresham’s Law, one that depends on fixed transaction costs rather than
a fixed rate of exchange.” They find that “History seems to support our new version of
Gresham’s Law” (p.186). Sargent and Velde (1999, 2002) proposes another transaction cost
model intended to solve the “big problem of small change.” The authors dismiss Gresham’s
Law, asserting that “In our model, there is no need to appeal to that ambiguous law”
(Sargent and Velde 2002, p.31). Neither of the models from Rolnick and Weber (1986) and
Sargent and Velde (1999, 2002) contain reference to the legal tender rates since they assume
that transaction costs will trump the influence of Gresham’s Law.
Yet the success of these transaction cost models do not preclude the operation of Gre-
sham’s Law. Selgin (1996) proposes that “Rolnick and Weber’s Law” is a complement to
Gresham’s Law rather than a substitute. The same can be said of “Sargent and Velde’s
Law” of small change. Evidence in favor of these models is not evidence against Gresham’s
Law since both forces may have operated simultaneously. For this reason, the effects of
Gresham’s must be tested independently. The next section analyzes the history of En-
glish coinage, a period discussed by both Rolnick and Weber (1986) and Sargent and Velde
(2002). This analysis indicates that coin production is indeed influenced by the legal ratio
as predicted by Gresham’s Law.5
5This evidence does not contradict the models of Rolnick and Weber (1986) and Sargent and Velde (1999,
2002) since the phenomena they describe are not mutually exclusive with Gresham’s Law. Indeed, it seemslikely that both price controls and transaction costs affected the rates of gold and silver coinage.
9
2.3 English Coinage, 1344-1815
This section analyzes influence of Gresham’s Law on the history of English coinage. Gre-
sham’s Law predicts that the government’s assignment of the relative values of the currencies
(which money is good and which is bad) will determine which is minted and which is driven
out. Therefore, the implied price ratio in England relative to the world price ratio should
influence the amounts of gold and silver that are coined each year. This prediction will be
tested using historical data on English and international prices and coinage records from
the Royal Mint in London.
The history of English coinage is replete with examples of Gresham’s Law. Since ancient
times, England employed the silver penny or shilling as the medium of exchange.6 In 1344
the mint began producing gold coins in addition to silver, and England employed a bimetallic
system until 1816.7 It was during this bimetallic period that Gresham’s Law had its greatest
effect.
Throughout the bimetallic period, England experienced successive waves of change in
its monetary base which oscillated between mostly gold and mostly silver. The Crown and
agents of the mint attempted to stabilize the monetary base by legally assigning the relative
values of gold and silver currencies. However, monetary authorities of the time were often
unaware that the stability of English currency was highly dependent on the price ratios of
gold and silver in Europe and the rest of the world (Shaw 1967[1896], pp.48-49; Sargent
and Velde 2002, p.5). When the legal values of gold and silver coins implied a price ratio
between gold and silver that overvalued gold, gold was imported and coined while silver was
exported. When the implied price ratio overvalued silver, silver was imported and coined
while gold was exported.
The implied price ratio of silver to gold in England can be calculated from the legal
tender ratio and the amount of precious metal used to produce each coin. For example, in
1699 the Royal Mint in London specified the guinea’s weight at 44.5 guineas per pound of
6The shilling was “First issued in 1504,” and was “Always proportional to the penny except during thedebasement period” (Feavearyear 1931, p.349).
7In 1816 England moved to a mono-metallic gold standard, but coins of both metals continued to beminted. The nation reverted to a silver standard during the first World War, and minting of gold coinsceased in 1917 (Challis 1992, p.557).
10
gold and coined shillings at 62 shillings per pound of silver.8 While Master of the Royal
Mint, Sir Isaac Newton described how the legal tender rate of 21.5 shillings per guinea
created an implied value of just over 15.5 pounds of silver per troy pound of gold:
A pound weight Troy of Gold, eleven ounces fine & one ounce allay, is cut into
4412 Guineas, & a pound weight of silver, 11 ounces, 2 pennyweight fine, &
eighteen pennyweight allay is cut into 62 shillings, & according to this rate, a
pound weight of fine gold is worth fifteen pounds weight six ounces seventeen
pennyweight & five grains of fine silver, recconing a Guinea at 1£, 1s. 6d. in
silver money. (Newton 1717, p.166)
Newton’s calculation of 15 pounds 6 ounces 17 pennyweight and 5 grains of silver per
pound of gold is a ratio of 15.58 in decimal terms. An international trader with access to
prices above this ratio could earn an arbitrage profit by importing and coining silver while
melting and exporting gold. If international prices fell below the implied ratio, the trader
could profit by importing and coining gold and exporting silver.9
An ideal test of Gresham’s Law would be to analyze the stocks of gold and silver currency
in England to see if they behave as predicted when the implied English ratio of gold to silver
differs from international rates. Although the quantities of currency in circulation are almost
impossible to measure, comprehensive records on the annual production of gold and silver
coins are available from the Royal Mint. If Gresham’s Law is correct, then coinage rates
of gold and silver should be largely determined by the international price ratio of gold and
silver. This hypothesis will be tested using English mint production from 1344 to 1815.10
Data for this analysis will be taken from 4 sources. The implied price ratio of gold to
silver in England is calculated from the official coinage weights and legal tender ratios in
Redish (2000, p.89-92). For the international price ratio of gold to silver, data for years
8English coinage was denominated in terms of pounds sterling (£), shillings (s), and pennies or pence
(d) where £1=20s and 1s=12d.9For an example, consider the market prices as of January 1697 of £4, 1.6s. per troy pound of gold, 5s.
2d. per pound of silver, and 22s. per guinea (Li 1963, p.10). Suppose a merchant begins with 100 shillingsand can exchange pure gold and silver at an international rate of 15 to 1. The merchant trades his shillingsfor 1.61 troy pounds of silver, then exchanges them for 0.11 troy pounds of gold, and then takes his gold tothe mint where it is coined into 4.78 guineas. He can now trade his guineas for 102.88 shillings.
10Another possibile approach would be to analyze the imports, exports, and coinage of each metal. Un-fortunately, records on the import and export of gold and silver are sparse and unreliable.
11
1344 to 1499 are taken as the European average from Shaw (1967[1896], p.40), and years
1500 to 1815 are from Farrer (1898, Appendix II). Mint production of gold and silver coins
is taken from Craig (1953, pp.408-422). These data sets can be found in tables 1 through
4 respectively.
Two measures of mint production will be used for the dependent variable. Since the
dependent variable is meant to capture the amount of mint production of gold coins relative
to silver, each measure is based on the annual percentage of gold coins produced out of the
total coinage of gold and silver in that year. Equation 2.3.1 specifies this relationship where
γt is the percentage of gold coined in year t calculated form annual gold coinage gt (by tale
value) and annual silver coinage st (by tale value).
γt = gt/(gt + st) (2.3.1)
For the second measure, the dependent variable is calculated as a lagging five-year moving
average γa as calculated in equation 2.3.2.
γt =
( t+4∑i=t
gi
)/
( t+4∑i=t
(gi + si)
)(2.3.2)
The lag is intended to account for the time required for any changes in the ratio to take
effect. The purchase and transportation of foreign metals was not instantaneous, and the
minting process alone often required several months.
Figure 2.3 shows the price ratios of gold to silver over the entire period. The solid line
represents the world price. The dotted line represents the English price ratio implied by
mint weights and the legal tender ratio. The background is shaded gray in time periods
when the English implied price ratio exceeds the international ratio. This indicates that
gold is likely to be imported and minted according to Gresham’s Law.
Figure 2.4 shows the relative annual amounts of gold and silver coinage. The solid line
is a five-year moving average of annual gold coinage as a percentage of total coinage. The
shaded areas, taken from figure 2.3, indicate that the English ratio exceeds the international
ratio, so gold was overvalued in England compared to international standards. Gresham’s
12
Figure 2.3: Price ratio of gold to silver, 1344-1815.
Law predicts that when the English ratio exceeds the international ratio, gold will be
imported and minted. Silver will be minted when the English ratio is below the international
ratio. Figure 2.4 shows this correspondence to be generally accurate.
The influence of Gresham’s Law on English coinage will be tested with regression anal-
ysis. The dependent variable is the annual percentage of gold coinage as described in
equations 2.3.1 and 2.3.2. The annual over- or undervaluation in England is calculated as δt
in equation 2.3.3 where Et is the gold to silver ratio in England, and Wt is the international
ratio.
δt = Et −Wt (2.3.3)
Therefore, the regression equation is given in terms of γt and δt.
γt = α+ βδt + ε (2.3.4)
Figure 2.4: Coinage of gold vs. silver when gold is overvalued, 1344-1815.
13
The regression results are shown in figure 2.5. The first column shows that the difference
between the local and international ratios of gold to silver does significantly affect annual
mint production at a significance level of 1% with an adjusted R-squared of 6.2%. The
second column shows the results for the lagging five-year average. The result is again
significant at the 1% level but with an adjusted R-squared of 15.7%. Since the regression uses
a five-year average, the first 4 years were excluded leaving the sample with 467 obseervations
from 1344 to 1811.
Annual coinage Five-year average
Overvaluation of gold 0.084∗∗∗ 0.659∗∗∗
(0.015) (0.013)
Constant 0.131∗∗∗ 0.668∗∗∗
(0.014) (0.012)
Observations 471 467Adj. R-squared 6.2% 15.7%
* Statistically significant the 1% level.
Figure 2.5: Regression of gold coinage on the overvaluation of gold.
The results of the regression analysis show that even a basic model can detect the effects
of Gresham’s Law. Of course, there are many factors omitted from the model which might
influence mint production. Most of these effects would either decrease the actual effect of
Gresham’s Law or make its influence less detectable in the data. If accounted for, they
would likely increase the significance of the regression.
For example, the model does not consider the transportation costs of importing and
exporting precious metal. These costs slowed the transmission of bullion between countries
and dulled the “knife’s edge” created by Gresham’s Law as described by Friedman (1990a)
and formalized by Flandreau (2002). Quinn (1996, p.475) uses an estimated transportation
cost of 3% based on Jones (1988, p.123). Transaction costs can be included by adding a
dummy variable with a value of 1 in any years where the difference between the implied
price ratio in England and the international price ratio differ by less than 1.5% indicating
that arbitrage may not have been profitable during these periods. The dummy has a value
of 1 in 85 of the 472 years.
14
Several historical events affected the normal process of mint production. For example,
there were several times when the English government interfered with minting such as the
recoinages of 1414-1417, 1559, and 1696-99 (Shaw 1967[1896], pp.55,129,225). Additionally,
the implied market ratio is based on the official mint weight of each coin and does not
account for underweight coins being traded in the market. Carlile (1901, p.14) describes
how Gresham’s Law may not operate when overvalued coins are heavily worn or depreciated.
There were clearly period of English history when clipping became so bad that they inhibited
local trade and therefore could not have feasibly been exported for profit. These include the
crises of the 1540’s (Feavearyear 1931, p.56) and 1694-1696 (Craig 1953, p.184). Separate
dummy variables are added to the regression for periods of forced recoinage and depreciated
coinage.
The results of regressions which include these dummy variables are presented in figure
2.6. Accounting for transaction costs increases the adjusted R-squared to 17.2% at a sig-
nificance level of 1%. Adjusting for forced recoinages and periods of depreciated coinage
increases the adjusted R-squared to 16.2% and maintains a significance level of 1%. Us-
ing all three dummies for transaction costs, recoinage, and underweight coins increases the
adjusted R-squared to 18.6% at the same level of significance.11
As with most empirical analysis, there are limitations to the data sets used for this
examination. As noted earlier, the world price of gold is a combined price series from Shaw
(1967[1896]) and Farrer (1898). Prices from Shaw are the simple average of mint prices from
France, Germany, Spain, and the Netherlands. Farrer is a single series but does not begin
until 1500. These data sets were combined for the main regressions but were also tested
separately. The results of are given in Appendix A. The implied English price ratio from
Reddish (2000) is also imperfect since it contains minting fees for both silver and gold. A
more accurate measure would include minting fees for either gold or silver but not both. As
an alternative, the implied ratio is calculated from Feavearyear (1931, pp.348-349) which
does not include minting fees. Results from the regressions on all data sets are given in
Appendix A. The overvaluation of gold was found to significantly influence mint production
at the 1% level in 21 of the 24 variatations.
11The dummy for underweignt coins is not significant in the regressions shown in figure 2.6 but is significantin many regressions shown in Appendix A.
and c22 < R. Therefore, there is room for improvement on the competitive outcome.”
3.2.3 The All-Banking Economy
In the DD model, it is sometimes possible to improve upon the competitive equilibrium
through collective action.4 At T = 0, each agent can increase his expected future utility by
trading off some potential consumption at T = 2 for increased consumption at T = 1.
Suppose that all agents agree to pool their capital investments as a form of insurance
against the lower utility that comes with being impatient. Each agent receives a deposit
contract which he may redeem at t = 1 for an amount r1 ≥ 1. Any goods not withdrawn
at T = 1 will be used to produce consumption goods which will be divided equally among
the remaining agents at T = 2. Return r2 at time 2 is, therefore, a function of t.
r2(t) =(1− tr1)R
1− r1. (3.2.8)
To optimize expected utility as of T = 0, the group sets r1 = c1 from equation 3.2.6.
Expected time 2 consumption will be the optimal value r2(t) = c2 from equation 3.2.7.
This consumption set increases social welfare above the level achieved in the all-production
economy.
3.2.4 Bank Runs
The optimal levels of consumption described in the previous section will only result if
information about agent types is publicly observable. Banks can ensure optimal risk sharing
by verifying individual agent type Θ. Alternatively, they may use other mechanisms such as
4It is not always possible to improve upon the no-trade equilibrium since in some cases the potential forruns may preclude any gains, so no bank will be established. This possibility is acknowledged by DD (1983,
p.409), expanded by Huo and Yu (1994), and will be discussed further in section 3.2.6.
29
suspension clauses based on the portion t of type 1 agents (DD 1983, p.411). However, when
neither individual agent type nor the proportion of type 1 agents is observable, consumption
may be suboptimal since some type 2 agents may choose to consume at T = 1. When
this information is lacking, “No bank contract can attain the full-information optimal risk
sharing” (p.412).
Suppose now that t is random and stochastic. Agents have only some expectation t
which they use to calculate optimal consumption. If t 6= t, consumption is suboptimal. For
all t < t, first period consumption will be too low, and when t > t period 1 consumption
will be too high and consumption in period 2 too low. In fact, consumption in time T = 1
may be so high that there are no goods are left for consumption in T = 2. In this case, the
bank becomes insolvent before the second period. The threshold for insolvency is given in
equation 3.2.9.
r1(t+ c21) > 1. (3.2.9)
When period 1 consumption is expected to be above the threshold, all agents have the
incentive to redeem their deposits at T = 1 which constitutes a bank run.
When a run occurs, all agents attempt to redeem their deposits at T = 1, however,
not all will be successful. We follow DD (1983, p.408) in assuming a sequential service
constraint. All agents who choose to redeem at T = 1 form a line at the bank, and each
agent’s place in line is assigned at random. The line progresses with each agent redeeming
his deposit for r1 units until the bank is devoid of capital. Thus, each of the first 1/r1
redeemers will receive r1 units of consumption goods from the of 1 total unit of invested
capital (representing 100% of the capital in the economy). The remaining 1 − 1/r1 agents
are left with nothing. Therefore, each agent’s welfare in the case of a run is a probabilstic
outcome shown in equation 3.2.10.
WRun = (1/r1)u(r1) + (1− 1/r1)u(0) (3.2.10)
Welfare in the bank run equilibrium is clearly lower than the no-run equilibrium and even
lower than in the all-production economy. Total social welfare in the all-bank economy
can be calculated as the weighted expected value of run and no-run equilibria given some
30
(a) Fundamental values. (b) Expected values.
Figure 3.2: Value of deposits at T=1 in the all-bank model.
expected probability δ that a run will occur.
WBank = (1− δ)WNoRun + δWRun (3.2.11)
The incentive to run on the bank can be described in terms of the period 1 value V (c1)
of deposits to each type of depositor as illustrated in figure 3.2. These graphs show the
deposit value on the y-axis as a function of time 1 redemptions c1 = c11 + c2
1 on the x-
axis. Figure 3.2a. depicts the “fundamental” value of the deposit earned if the deposit is
redeemed in the period which matched the agent’s type. Type 1 depositors always redeem
in t = 1. They earn c11 = r1 up to the point where there c1 = 1 − t redemptions, at which
time the bank defaults. After the point of default, all agents have an expected payoff of r1
with probability 1/r1 and a payoff of 0 with probability 1− 1/r1. This probabilistic default
payoff, denoted here as r0, can range anywhere from −∞ < r0 < 1/r1 depending on the
values of ρ and γ but for convenience is shown in the range 0 < r0 < 1.
The fundamental value of deposits to type 2 agents r2 is a function of c1 given in equation
3.2.8. This is shown in figure 3.2a. as a line declining from R at c1 = 0 to 1 at c1 = 1−t, the
point where the bank defaults. When the bank goes into default, even type 2 agents choose
to redeem their deposits since nothing will be left at T = 2. All deposits will be worth r0
regardless of agent type. However, type 2 agents may decide to redeem their deposits at
T = 1 even before c1 = 1− t. Figure 3.2a. shows that after the point c1 = 1/r1− t, the time
T = 2 redemption value falls below the value at T = 1 to r2 < r1. Since type 2 agents value
31
c21 and c2
2 equally, they will choose to redeem their deposits early at T = 1. Since all agents
decide to redeem at T = 1, there is a run on the bank, and the value of deposits falls to r0.
This scenario is depicted in figure 3.2b. Whenever the expected value of c1 > 1/r1 − t, all
agents redeem at T = 1 causing a run on the bank, and the expected value of all deposits
falls to r0.
Runs can occur for two reasons. First, as previously described, the number of types 1
agents may be higher than expected to the point that they consume all goods at T = 1,
and none are left for consumption at T = 2. This will be referred to as a “fundamental
run” since the bank has more legitimate claims than it can pay out. The second type occurs
when type 2 agents choose to consume at T = 1. This “sunspot run” can occur if the agents
fear that the number of type 1 agents may be higher than previously expected (that t > t).
This differs from the fundamental run since it is only the expected difference between t and
t that causes the run.
What causes this shift in expectations? DD do not specifically say. It may be any
economy-wide signal or event and need not be economic in nature. As described by DD
(1983, p.410), it “need not be anything fundamental about the bank’s condition” but could
be any “commonly observed random variable in the economy... even sunspots.” In this
case, even a solvent bank will experience a run and default. In fact, any widely observable
signal may cause all banks in the economy to be run upon simultaneously.
Although the information which can signal the run is not specifically included in the
DD model, other works have provided explicit mechanisms. Green and Lin (2000) assumes
that information is revealed by the agent’s order in line at the bank. Alonso (1993) uses
a signal from each agent that may or may not be truthful, while Andolatto, Nosal, and
Wallace (2007) assumes that agents reveal their true types when redeeming deposits. In
Samartin (2003), agents observe their return on investment from which they can deduct
the portion of impatient agents. Because this paper attempts to replicate DD (1983) as
originally written, we continue on the assumption that agents receive some new information
at T = 1 which is not included in the model.
32
3.2.5 Actual Consumption
We can study actual consumption (as opposed to ex ante expected consumption) by analyz-
ing agents’ consumption opportunities at T = 1. Because type 1 agents only get utility from
consumption at time 1, we assume that all t agents will maximize period 1 consumption
c11 = r1 with c1
2 = 0. Therefore, type 2 agents will receive all of the remaining 1− tr1 capital
which they will divide between c21 and c2
2 consumption at times 1 and 2.
The actual consumption in period 2 is a non-linear function of consumption in period
1. In equation 3.2.8, r2 is dependent on period 1 consumption by type 1 agents. However,
since some type 2 agents may also consume in period 1, actual period 2 consumption by
type 2 agents c22 is dependent on t+ c2
1 as shown in equation 3.2.12.
c22 =
R(1− r1(t+ c21))
1− t− c21
(3.2.12)
The more agents who redeem their deposits at T = 1, the lower the payoff to patient
depositors who withdraw at T = 2. The number of early redeemers can increase until the
point c21 = 1/r1 − t where all resources are consumed, the bank becomes bankrupt, and a
run occurs. Since deposits will be worth nothing at T = 2, all type 2 agents will choose to
redeem their deposits at T = 1. Again, c21 need not actually reach the level of c2
1 = 1/r1− t.
Merely the expectation that this will occur is sufficient to create a bank run.
We can optimize social welfare according to the bank’s resource constraint. The welfare
function in equation 3.2.3 includes only type 2 depositors. Type 1 agents care only for
consumption at T = 1 and uniformly choose c11 = r1. Therefore, the social welfare function
given in equation 3.2.13 depends solely on consumption by type 2 agents.
WBank = tu(r1) + (1− t)ρu(c21 + c2
2) (3.2.13)
Unlike consumption in the all-production economy shown in figure 3.1, the resource con-
straint is not a straight line. While total period 1 consumption is less than c1 = 1/r1 − t,
individual period 2 consumption is a function of c1 = t+c21. Once total period 1 consumption
33
(a) Type 1 agents. (b) Type 2 agents.
Figure 3.3: Consumption in the all-bank model.
reaches c1 = 1/r1 − t, the bank defaults, and c2 = 0 as shown in 3.2.14.
c22 =
R(1−r1(t+c21))
1−t−c21for c2
1 < 1/r1 − t
0 for c21 ≥ 1/r1 − t
(3.2.14)
Figure 3.3 shows the resource constraints between c21 and c2
2 and utility functions for
agent types 1 and 2. This analysis matches the proof in DD (1983) that banks are subject
to non-fundamental runs, however, it deviates from their analysis in another respect. DD
(1983) analyzes ex ante expected consumption as of T = 0. It is assumed that actual
consumption in the non-run equilibrium will match the optimal levels predicted at that
time. However, that prediction does not match the agents’ ex post decisions analyzed
here as of T = 1. As shown in figure 3.3, type 2 agents do not optimize consumption by
redeeming only at T = 2. Rather, they consume some combination of c21 and c2
2. This is
due to the nonlinear nature of r2 as a function of c1. By redeeming a small amount of their
deposits at T = 1 for r1, they reduce the number of depositors waiting to redeem at T = 2.
In the second period, goods are divided among as smaller group, so each agent gets a larger
share. The optimal consumption for type 2 agents is show below.5
c21 = 1− t−
√R(r1 − 1) (3.2.15)
5These calculations are shown in Appendix B.2.
34
c22 =
1− r(
1 +√R(r1 − 1)
)r − 1
(3.2.16)
At this consumption set, period 1 consumption is always below the bank run threshold
c21 < 1/r1 − t. (3.2.17)
Thus, there exists one stable non-run equilibrium. However, as described in section 3.2.4,
any informational shock which causes the expectation of a bank run can push c21 above the
threshold and into the bank run equilibrium.
3.2.6 Do Banks Exist?
Given that runs can occur at any time for any reason, one might wonder whether a bank will
ever be formed at all. As described in section 3.2.4, a run leaves a portion 1/r1 agents with
r1 units each and the remaining portion of 1− 1/r1 agents with 0 units each. This point is
especially pertinent since the DD model assumes relative risk aversion. Zero consumption
can lead to infinitely negative utility as discussed by Huo and Yu (1994) which shows that
for some combinations of γ, t, and R it may be impossible to establish a bank. The converse
is that in some cases banks are optimal despite positive probability of a run.
Let us compare social welfare of the all-production economy WProd given in equation
3.2.3 to that of the all-bank economy WBank in equation 3.2.11. As before, WBank is given
in terms of weighted expected value given some expected probability δ that a run will occur
as shown in 3.2.18.
WBank = (1− δ)WNoRun + δWRun
= (1− δ)[tu(c11) + (1− t)ρu(c2
1 + c22)] + δ[(1/r1)u(r1) + (1− 1/r1)u(0)]
≥ tu(c11) + (1− t)ρu(c2
1 + c22) = WProd (3.2.18)
Since a bank will only be formed if welfare for an all-bank economy is expected to be greater
than or equal to that of the all-production economy, there must be some value δ low enough
35
such that WBank > WProd in order for agents to invest in the bank. We can use this
inequality in equation 3.2.11 to solve for the threshold probability δ for which a bank will
be formed.
δ =WNoRun −WProd
WNoRun −WRun(3.2.19)
For all δ ≤ δ, forming a bank creates an ex ante improvement in social welfare. However,
this all-bank economy is only a special case of a more general model.
3.3 The Multi-Sector Model
DD (1983, p.405-410) describes a model which includes both banking and production sec-
tors. However, DD (1983) and all subsequent models have focused on the banking sector
alone. This section discusses a DD model with both banking and production. Allowing
multiple sectors creates a welfare improvement since agents can hedge their risk by invest-
ing in multiple sectors. Exchange between producers and bank depositors further increases
welfare and helps prevent bank runs since risky bank notes can be traded at a discount for
real goods.
The next section describes how allowing investment in multiple sectors creates a Pareto
improvement in social welfare. Section 3.3.2 discusses exchange in the DD model. Con-
sumption decisions are discussed in section 3.3.4. Section 3.3.3 explains the lack of bank
runs in equilibrium.
3.3.1 Welfare in the Multi-Sector Model
Optimal investment in the DD model occurs when capital is divided between production
and deposits. DD (1983) note that under an optimal investment strategy, “agents will invest
at least some of their wealth in banks even if they anticipate a positive probability of a run”
(p.409, emphasis added). This clearly implies that some capital will remain outside of banks
as well. However, DD (1983) does not discuss this scenario in detail. The article begins
with the all-production economy to demonstrate the risk diversification benefits provided
by banks. It then describes an all-banking economy stating that “for now we will assume
36
all agents are required to deposit initially” (p.409, emphasis added). The language implies
that the authors will also discuss the case in which not all agents are depositors, however
they never return to this scenario.
In the multi-sector model, capital is divided between banking and production. Each
agent invests a portion φ of his goods invested in the bank and (1−φ) in production. Payoffs
for each sector are the same as previously described, c1 = 1 and c2 = R for production and
c1 = r1 and c2 = r2(c1) for banking. In the case of a bank run, payoffs to the banking sector
are c1 = r1 with probability 1/r1 and c1 = 0 with probability 1− 1/r1.
Agent utility (WMS)
No run(1− δ)
Type 1(t)
φr1 + (1− φ)(1)
Type 2(1− t)
φr2 + (1− φ)R
Run(δ)
Deposit redeemed(1/r1)
Type 1(t)
φr1 + (1− φ)(1)
Type 2(1− t)
φr1 + (1− φ)R
Deposit not redeemed(1− 1/r1)
Type 1(t)
φ(0) + (1− φ)(1)
Type 2(1− t)
φ(0) + (1− φ)R
Figure 3.4: Probability-weighted expected value of social welfare.
We calculate ex ante social welfare as the weighted sum of expected utilities for each
agent type in three potential states. These are shown in figure 3.4 along with the probability
for each state. When there is no bank run, type 1 agents receive the expected value of
c11 = φr1+(1−φ)(1), and type 2 agents receives c2
2 = φr2+(1−φ)R. In the case of a bank run,
type 1 agents have probability 1/r1 chance of receiving c11 = φr1 +(1−φ)(1) and probability
(1−1/r1) of receiving c11 = φ(0)+(1−φ)(1). Type 2 agents have probability 1/r1 chance of
receiving c21 = φr1 + (1− φ)R and probability (1− 1/r1) of receiving c2
1 = φ(0) + (1− φ)R.
37
Social welfare is the weighted sum of the potential states as calculated in equation 3.3.1.
We then repeat these regressions using standard deviation of equity prices σi as the depen-
dent variable and then again using bond yield spreads δi as the dependent variable.
These regression give us a series of quarterly cross-sectional beta estimates representing
the influence of capital and RBC on the riskiness of a BHC’s debt and equity. These
quarterly data are used to evaluate three testable hypotheses for each of our quarterly
cross-sections (absolute value of return on stocks, standard deviation of return on stocks,
and bond yield spreads). H1: Bank capital has no influence on stock returns or bond yields
(βcap = 0). H2: Bank risk-based capital has no influence on stock returns or bond yields
(βrisk = 0). H3: Bank capital and risk-based capital have the same influence on stock
returns and bond yields (βcap = βrisk).
53
The use of quarterly cross-sections has two advantages. First, we can test the significance
of βcap and βrisk in each quarter to find out not only when each β was significant but also how
their significance has changed over time. Second, using quarterly cross-sections excludes
time-dependent factors which may have affected the entire banking industry such as changes
in Fed policy or trends in the composition of bank balance sheets.
4.4 Data
The data for this analysis are taken from multiple sources. A list of BHC ID numbers
and corresponding CUSIPs as of 2008 is available from the Federal Reserve Bank of New
York (FRBNY).2 For this list of banks, we obtain stock prices from Wharton Research
Data Services (WRDS)3 and bond yield data from Thomson Reuters Datastream4 which
are matched with treasury yields to calculate the spread on each bond. These data sets are
then combined with quarterly balance sheet data from the Federal Reserve.
Daily stock prices for each bank holding company are downloaded from WRDS. Banks
are selected by PERMCO according to the bank list from the FRBNY. The fields selected
are date, PERCMO, CUSIP, and daily closing price for the period January 1, 1999 to
December 31, 2010. Any entries with characters or missing data in the price field are
dropped. A list of distinct CUSIP numbers is created from this data set to be used for
downloading bond data.
Daily bond yields for each bank holding company are downloaded from Datastream.
Bonds are selected if their CUSIP matches any CUSIP from the stocks data set. Fields
selected are date, CUSIP, book value, yield, and bond life (years to maturity) for the period
January 1, 1999 to December 31, 2010. Firms with less than one year of data are dropped.
For each firm, we calculate a daily average yield of all bonds outstanding weighted by book
value. This weighted average yield is used as the single bond yield for the firm. Each
bond is then matched to a constant-maturity index of US treasuries or similar maturity as
described in section 4.3.2. Treasury index data are downloaded from the Federal Reserve
2Available at http://www.newyorkfed.org/research/banking research/datasets.html.3Available at https://wrds-web.wharton.upenn.edu/wrds/.4Available at http://online.thomsonreuters.com/datastream/.
54
Bank of St. Louis.5
Data on the balance sheets and capital is obtained from the Federal Reserve Bank of
Chicago (FRBC) in their Consolidated Financial Statements for Bank Holding Companies
(Y-9C) reports.6 These quarterly reports contain full financial statements from all large
BHCs.7 The fields taken from these reports are report date, BHC ID number, total equity,
holdings of real estate assets, MBS, and risk-based capital ratio. New fields are calculated
for the ratios of capital, real estate, and MBS as percentages of total equity.
These three data sets are then matched using the FRBNY bank list. Stock prices are
joined to bond yield spreads using one-to-many mapping using date and CUSIP as the key
fields (for each firm, dates with a stock price but not bond spread are kept while dates with
a bonds spread but no stock price are dropped). For these daily yields and prices, a new
field is created to identify the year and quarter. This set of stock prices and bond yield
spreads is then matched to the balance sheet data using the quarter and BHC ID number
as the key fields. Daily yields and prices are matched to the firm’s balance sheet from the
beginning of the quarter (the end of the previous quarter).
Summary statistics for the final combined data set are given in appendix C.2. Table
C.2.1 contains means of balance sheet data and daily returns for the entire sample. There
are an average of 301 stock prices and 23 bond yields per quarter. Figure C.2.1 shows a
scatter plot of all quarterly BHC capital and risk-based capital ratios. Quarterly averages
for capital and RBC ratios are shown in figures C.2.2. Figure C.2.3 shows the quarterly
average yield on treasury indexes of 1, 5, and 10 year maturities along with the average BHC
bond yield in each quarter. Figure C.2.4 calculates the average yield spread per quarter.
C.2.5 shows quarterly standard deviation of stock prices and C.2.6 lists the number of stock
price observations per quarter. The number of observations per quarter declines slightly
over the sample period, likely due to the industry trend towards consolidation during this
time. Figures C.2.7 and C.2.8 show quarterly standard deviations of bond yields and the
number of bond yield observations per quarter. The number of observations is low in early
5Available at http://research.stlouisfed.org/fred2/categories/115.6Available at http://www.chicagofed.org/webpages/banking/financial institution reports/bhc data.cfm.7Until 2006, BHCs were required to complete the quarterly Y-9C report if their total assets exceeded
$150 million. Since 2006, the limit has been raised to $500 million, but some firms below this level continueto report.
55
years due to the fewer number of banks issuing bonds at that time but also due to the
difficulty of matching bond data to banks in those years, many of which are no longer in
existence. The year 2000 is not included in bond yield analysis since there were too few
observations to conduct the regression analysis.
4.5 Results
The results from these regressions show that both capital and RBC are related to bank risk
measured by bond yields and stock price volatility. Capital and RBC are most significantly
related to bond yields around the recession of 2001 and to stock returns since 2008. The
coefficients of capital and RBC are very similar in most regressions.
As described in section 4.3, our intent is to analyze the significance of βcap and βrisk
representing the influence of capital or RBC in each quarter and examine their changes
over time. We display the results of this analysis in a series of charts which plot time in
terms of quarters on the x-axis, and β coefficient on the y-axis. The solid line in each figure
represents the quarterly β estimate while the thin dotted lines represent upper and lower
confidence intervals at the 10% level. When the lower CI is above zero or the higher line
below zero, β is significant at the 10% level. These periods of significanct are shaded grey
in each figure. As mentioned in the previous section, analysis on bond yields does not begin
until 2001 due to the low number of observations before that time.
Several alternative specifications were used to test the robustness of these regressions
on leverage and capital. The bank asset categories of real estate assets and MBS were
included in regression equations because they were found to be significantly related to price
volatility. Coefficient estimates and standard errors for real estate assets and MBS are given
in appendix C.3. Other asset categories tested were subordinate debt, treasuries, trading
assets, and cash, all as percentages of equity. Most of these asset categories did have some
periods of significance but less often than real estate or MBS. All regressions yielded similar
overall results.
56
Figure 4.1: Absolute value of stock returns
Figure 4.1.a. Beta of absolute stock returns on capital
Figure 4.1.b. Beta of absolute stock returns on risk-based capital
Figure 4.1.c. Betas of absolute stock returns on capital and risk-based capital
2000
-03
2000
-06
2000
-09
2000
-12
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
-06
2002
-09
2002
-12
2003
-03
2003
-06
2003
-09
2003
-12
2004
-03
2004
-06
2004
-09
2004
-12
2005
-03
2005
-06
2005
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2005
-12
2006
-03
2006
-06
2006
-09
2006
-12
2007
-03
2007
-06
2007
-09
2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-8-6-4-202468
Signifhighb(cap)lowZero
2000
-03
2000
-06
2000
-09
2000
-12
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
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2002
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2002
-12
2003
-03
2003
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2003
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2003
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2004
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2004
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2004
-09
2004
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2005
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2005
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2005
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2005
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2006
-03
2006
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2006
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2006
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2007
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2007
-06
2007
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2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-8-6-4-202468
SignifCI_highb(risk)CI_lowZero
2000
-03
2000
-06
2000
-09
2000
-12
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
-06
2002
-09
2002
-12
2003
-03
2003
-06
2003
-09
2003
-12
2004
-03
2004
-06
2004
-09
2004
-12
2005
-03
2005
-06
2005
-09
2005
-12
2006
-03
2006
-06
2006
-09
2006
-12
2007
-03
2007
-06
2007
-09
2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-8
-6
-4
-2
0
2
4
6
8
Signifb(cap)b(risk)Zero
57
4.5.1 Absolute Value of Stock Returns
Figure 1 shows the results of the quarterly regressions of the absolute values of stock returns
on capital and RBC. Figure 1.a shows the quarterly estimates of βcap which are used to test
H1. The chart is shaded gray in 10 of the 43 quarters indicating that the βcap coefficient
is significant in these periods. We find significance for 2 quarters in 2001 and all quarters
since Q4 of 2008. Figure 1.b tests H2 with quarterly estimates of βrisk which are significant
in 8 of 43 quarters. These are Q3 of 2001 and since Q1 of 2009, all of which were also
significant
Figure 1.c tests H3 that βcap = βrisk. Quarterly estimates of βcap are shown as a dotted
black line while estimates of βrisk are shown in solid black. We can see that the patterns
of these coefficients are quite similar. Periods where these coefficients are significantly
different at the 10% level would be shaded grey except that there are no such periods. In
every quarter we fail to reject the null hypothesis that βcap = βrisk.
4.5.2 Standard Deviation of Stock Returns
Figure 2 shows the results of quarterly regressions of the standard deviation of stock returns
on capital and RBC. Figure 2.a shows the quarterly estimates of βcap. Grey shading indi-
cates that we reject the null hypothesis H1 at the 10% level. The coefficient is significant in
10 of 43 quarters: Q4 of 2001, Q2 of 2004, and since Q4 of 2008. Figure 2.b gives the βrisk
estimates which are used to test H2. We find that βrisk is significant in 8 of 43 quarters.
These are Q3 of 2005 and all quarters since Q1 of 2009.
Figure 2.c tests hypothesis H3 that βcap = βrisk. It shows the estimates of βcap as
a dotted line and βrisk as a solid line. The trends are again similar. Periods when the
estimates are significantly different would be shaded gray, but again there are none. In all
43 quarters we fail to reject the null hypothesis.
4.5.3 Bond Yield Spreads
Figure 2 shows the results of quarterly regressions of bond yield spreads on capital and
RBC. H1 is tested in figure 2.a which shows the quarterly estimates of βcap. We can reject
H1 in 6 quarters in which the coefficient is found to be significant: Q2 of 2002 and Q4 of
58
Figure 4.2: Standard deviation of stock returns
Figure 4.2.a. Beta of standard deviation of stock returns on capital
Figure 4.2.b. Beta of standard deviation of stock returns on risk-based capital
Figure 4.2.c. Beta of standard deviation of stock returns on capital and risk-based capital
2000
-03
2000
-06
2000
-09
2000
-12
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
-06
2002
-09
2002
-12
2003
-03
2003
-06
2003
-09
2003
-12
2004
-03
2004
-06
2004
-09
2004
-12
2005
-03
2005
-06
2005
-09
2005
-12
2006
-03
2006
-06
2006
-09
2006
-12
2007
-03
2007
-06
2007
-09
2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-20
-15
-10
-5
0
5
10
15
20
SignifCI_lowb(cap)CI_highZero
2000
-03
2000
-06
2000
-09
2000
-12
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
-06
2002
-09
2002
-12
2003
-03
2003
-06
2003
-09
2003
-12
2004
-03
2004
-06
2004
-09
2004
-12
2005
-03
2005
-06
2005
-09
2005
-12
2006
-03
2006
-06
2006
-09
2006
-12
2007
-03
2007
-06
2007
-09
2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-20
-15
-10
-5
0
5
10
15
20
SignifCI_highb(risk)CI_lowZero
2000
-03
2000
-06
2000
-09
2000
-12
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
-06
2002
-09
2002
-12
2003
-03
2003
-06
2003
-09
2003
-12
2004
-03
2004
-06
2004
-09
2004
-12
2005
-03
2005
-06
2005
-09
2005
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2006
-03
2006
-06
2006
-09
2006
-12
2007
-03
2007
-06
2007
-09
2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-20
-15
-10
-5
0
5
10
15
20
Signifb(cap)b(risk)Zero
59
2005 to Q4 of 2006. Figure 2.b gives the βrisk estimates in each quarter which are used to
test H2. The coefficient is significant in 7 quarters from Q2 of 2001 to Q2 of 2002, Q4 of
2002, and Q2 of 2003.
Figure 3.c compares the quarterly coefficient estimates of βcap and βrisk. Like figures
1.c and 2.c, βcap is shown as a dotted black line, and βrisk is shown in solid black. However,
unlike 1.c and 2.c, there appears to be more variation between these estimates. Both begin
below 0 and decline in 2001, although βrisk reaches a minimum in Q4 of 2001 while βcap
declines until Q2 of 2002. βcap then becomes positive in 2003 and stays mostly positive
until 2005, while βrisk remains negative over the period. Despite these modest variations,
the trends of βcap and βrisk are generally similar. They both start off negative, first decline,
then begin to rise. Both are close to 0 from 2005 through 2008 and become slightly negative
in 2009. The lack of shading in figure 3.c indicates that in every quarter we fail to reject
the null hypothesis H3 that βcap = βrisk.
Overall, the results from figures 1-3 are very similar. Estimates of the β coefficients tend
to be significant around the recessions of 2001, especially for bonds, and of 2008-2009 for
stocks. One unusual period is the significance of βcap for bond yields in 2005 and 2006 as
shown in figure 3.a. However the coefficient is small and is not significantly different from
βrisk. The trends of βcap and βrisk are remarkably similar in figures 1.c, 2.c, and 3.c, and
these coefficient estimates are not found to be significantly different from each other in any
quarter. Capital and RBC are found to be significantly related to bank risk but are not
significantly different from each other.
4.6 Conclusion
This paper compares the influences of capital and risk-based capital on bank default risk. We
analyze the correlations of capital and RBC to three indicators of bank risk: the absolute
value of stock returns, the standard deviation of stock returns, and bond yield spreads.
Both capital and RBC are found to be significantly related to all three measures of risk in
several quarters, especially around the recessions of 2001 and 2008-2009. However, the β
coefficients of capital and RBC are not found to be significantly different from each other
in any quarter.
60
Figure 4.3: Bond yield spreads
Figure 4.3.a. Beta of bond yield spreads on capital
Figure 4.3.b. Beta of bond yield spreads on risk-based capital
Figure 4.3.c. Beta of bond yield spreads on capital and risk-based capital
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
-06
2002
-09
2002
-12
2003
-03
2003
-06
2003
-09
2003
-12
2004
-03
2004
-06
2004
-09
2004
-12
2005
-03
2005
-06
2005
-09
2005
-12
2006
-03
2006
-06
2006
-09
2006
-12
2007
-03
2007
-06
2007
-09
2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-300
-200
-100
0
100
200
300
SignifCI_lowBetaCI_highZero
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
-06
2002
-09
2002
-12
2003
-03
2003
-06
2003
-09
2003
-12
2004
-03
2004
-06
2004
-09
2004
-12
2005
-03
2005
-06
2005
-09
2005
-12
2006
-03
2006
-06
2006
-09
2006
-12
2007
-03
2007
-06
2007
-09
2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-300
-200
-100
0
100
200
300
SignifhighBetalowZero
2001
-03
2001
-06
2001
-09
2001
-12
2002
-03
2002
-06
2002
-09
2002
-12
2003
-03
2003
-06
2003
-09
2003
-12
2004
-03
2004
-06
2004
-09
2004
-12
2005
-03
2005
-06
2005
-09
2005
-12
2006
-03
2006
-06
2006
-09
2006
-12
2007
-03
2007
-06
2007
-09
2007
-12
2008
-03
2008
-06
2008
-09
2008
-12
2009
-03
2009
-06
2009
-09
2009
-12
2010
-03
2010
-06
2010
-09
-300
-200
-100
0
100
200
300
SignifBetaZeroBeta
61
Appendix A: Gresham’s Law Alternative Data
England World Over Trans Recoinage Weight const N R2Reddish Shaw/Farrer 0.084∗∗∗ 0.659∗∗∗ 445 6.2%
This section will calculate the actual ex post incentives and consumption as of period T = 1
as described in section 3.3. We assume that preferences described in appendix B.1 and that
resource constraints are a combination of the regular technological constraint from equation
B.1 in section B.1 and the banking constraint from equation B.3 of section B.2. These
72
constraints are combined according to the portions of capital invested in the production
and banking sectors as shown in equation B.1.
c2 = (1− φ)R[1− (1− φ)c21] + φ
R(1− r1(t+ c21))
1− t− φc21
(B.1)
We assume that each type 1 depositors consume c11 = r1 and type 2 depositors divide
consumption between c21 and c2
2. The social utility function is the same as before.
WBank = tu(r1) + (1− t)ρu(c21 + c2
2) (B.2)
To optimize c21 and c2
2, we use the Lagrangian function in B.3.
L = tu(r1)+(1−t)ρu(c21 +c2
2)+λ
((1−φ)R[1−(1−φ)c2
1]+φR(1− r1(t+ c2
1))
1− t− φc21
−c22
)(B.3)
First order conditions are:
∂L
∂c21= (1− t)ρu′(c2
1 + c22) + λφR
(−r1(1− t− c2
1) + (1− r1(t− c21))
(1− t− c21)2
)+ λ(1− φ)R
−1
1− t= 0
(B.4)
∂L
∂c22= (1− t)ρu′(c2
1 + c22)− λ = 0 (B.5)
∂L
∂λ= (1− φ)R[1− (1− φ)c2
1] + φR(1− r1(t+ c2
1))
1− t− φc21
− c22 = 0 (B.6)
Equations B.4 and B.6 can then be combined into B.7.
−λ = λφR−(r − 1)
(1− t− c21)2
+ λ(1− φ)R−1
1− t(B.7)
Dividing both sides by −λ, we get B.8.
1 = φRr − 1
(1− t− c21)2
+R1− φ1− t
(B.8)
73
Re-arranging and multiplying by (1− t− c21)2, we get B.9
(1−R1− φ
1− t)(1− t− c2
1)2 = φR(r − 1) (B.9)
Then dividing both sides by (1−R 1−φ1−t ), we get equation B.10.
(1− t− c21)2 =
φR(r − 1)(1− t)1−R(1− φ)
(B.10)
We take the square root of both sides to get B.11 and re-arranged into B.12.
1− t− c21 =
√φR(r − 1)(1− t)
1−R(1− φ)(B.11)
c21 = 1− t±
√φR(r − 1)(1− t)
1−R(1− φ)(B.12)
We know from equation B.18 that in order to satisfy our prior assumptions the square root
in equation B.12 must be subtracted rather than added. We can therefore conclude that
the optimal levels of consumption c21 andc2
2 are given in equations B.13 and B.14.
c21 = 1− t−
√φR(r − 1)(1− t)
1−R(1− φ)(B.13)
c22 =
R−Rr(
1 +√
φR(r−1)(1−t)1−R(1−φ)
)√
φR(r−1)(1−t)1−R(1−φ)
(B.14)
74
Appendix C: Leverage and Capital Data
C.1 Federal Reserve Y9-C Regulatory Capital Schedule
Tier 1 capital 1. Total bank holding company equity capital (from Schedule HC, item 27.a) ....................................... 1. 2. LESS: Net unrealized gains (losses) on available-for-sale securities1 (if a gain, report as a
positive value; if a loss, report as a negative value)........................................................................... 2. 3. LESS: Net unrealized loss on available-for-sale equity securities1 (report loss as a positive value) .. 3. 4. LESS: Accumulated net gains (losses) on cash flow hedges1 (if a gain, report as a positive value;
if a loss, report as a negative value) .................................................................................................. 4. 5. LESS: Nonqualifying perpetual preferred stock ................................................................................. 5. 6. a. Qualifying Class A noncontrolling (minority) interests in consolidated subsidiaries ...................... 6.a.
b. Qualifying restricted core capital elements (other than cumulative perpetual preferred stock)2 ... 6.b. c. Qualifying mandatory convertible preferred securities of internationally active bank holding
companies .................................................................................................................................... 6.c. 7. a. LESS: Disallowed goodwill and other disallowed intangible assets .............................................. 7.a.
b. LESS: Cumulative change in fair value of all financial liabilities accounted for under a fair value option that is included in retained earnings and is attributable to changes in the bank holding company's own creditworthiness (if a net gain, report as a positive value; if a net loss, report as a negative value) ............................................................................................................ 7.b.
8. Subtotal (sum of items 1, 6.a., 6.b., and 6.c., less items 2, 3, 4, 5, 7.a, and 7.b) .............................. 8. 9. a. LESS: Disallowed servicing assets and purchased credit card relationships ............................... 9.a.
b. LESS: Disallowed deferred tax assets .......................................................................................... 9.b.10. Other additions to (deductions from) Tier 1 capital ............................................................................ 10.11. Tier 1 capital (sum of items 8 and 10, less items 9.a and 9.b) ........................................................... 11.
Tier 2 capital12. Qualifying subordinated debt, redeemable preferred stock, and restricted core capital elements2
(except Class B noncontrolling (minority) interest) not includible in items 6.b. or 6.c. ..................... . 12.13. Cumulative perpetual preferred stock included in item 5 and Class B noncontrolling (minority)
interest not included in 6.b., but includible in Tier 2 capital ................................................................ 13.14. Allowance for loan and lease losses includible in Tier 2 capital ......................................................... 14.15. Unrealized gains on available-for-sale equity securities includible in Tier 2 capital ........................... 15.16. Other Tier 2 capital components ........................................................................................................ 16.17. Tier 2 capital (sum of items 12 through 16) ........................................................................................ 17.18. Allowable Tier 2 capital (lesser of item 11 or 17) ................................................................................ 18.
19. Tier 3 capital allocated for market risk ............................................................................................... 19.20. LESS: Deductions for total risk-based capital .................................................................................... 20.21. Total risk-based capital (sum of items 11, 18, and 19, less item 20) .................................................. 21.
Total assets for leverage ratio22. Average total assets (from Schedule HC-K, item 5) .......................................................................... 22.23. LESS: Disallowed goodwill and other disallowed intangible assets (from item 7.a above) ............... 23.24. LESS: Disallowed servicing assets and purchased credit card relationships (from item 9.a above) . 24.25. LESS: Disallowed deferred tax assets (from item 9.b above) ............................................................ 25.
26. LESS: Other deductions from assets for leverage capital purposes .................................................. 26.27. Average total assets for leverage capital purposes (item 22 less items 23 through 26) .................... 27.28.–30. Not applicable
This schedule is to be submitted on a consolidated basis. For Federal Reserve Bank Use Only
C.I.
Dollar Amounts in Thousands
BHCX Bil Mil Thou
3/09
1. Report amount included in Schedule HC, item 26.b, "Accumulated other comprehensive income."2. Includes subordinated notes payable to unconsolidated trusts issuing trust preferred securities net of the bank holding company's investment
in the trust, trust preferred securities issued by consolidated special purpose entities, and Class B and Class C noncontrolling (minority) interests that qualify as Tier 1 capital.
7204 7206 7205
BHCK Percentage
. % . % . %
Capital ratios31. Tier 1 leverage ratio (item 11 divided by item 27) .................................................................... 31.32. Tier 1 risk-based capital ratio (item 11 divided by item 62) ...................................................... 32.33. Total risk-based capital ratio (item 21 divided by item 62) ....................................................... 33.
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Curriculum Vitae
Thomas Hogan holds bachelors and masters degrees in business administration from theUniversity of Texas at Austin. He is an adjunct instructor in the Department of Financeat George Mason University and has taught classes on financial management and moneyand banking. Thomas has worked for Merrill Lynch’s commodity trading group and as aderivatives trader for hedge funds in the U.S. and Europe. He is also a former consultantto the World Bank.