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Modeling the Textbook Fractional Reserve Banking System
Modeling the Textbook Fractional
Reserve Banking System.
Jacky Mallett
[email protected]
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Fractional Reserve Banking
• Quantity of Loans banks make is a function of their deposits.
• Physical money is deposited at banks
• Loans create additional bank deposits (money)
• Depositors retain the rights to all money in their accounts.
• Evolved from Goldsmiths making short term loans against their
gold holdings in 1600’s
• Mutated from a system that was based on physical currency to one
that is (or soon will be) entirely based on electronic bank accounts
• Fractional reserve banking because historically Banks were
required to only to lend a fraction of their total deposits, and had
to retain a reserve.
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Although generally referred to
as monetary expansion – in
reality the critical issue is Bank
Deposit expansion
Bank B
Deposits
Loans
Liabilities
Assets
Bank A
Inter-bank transfers /
Customer cheques.
Physical deposits
and withdrawals
of physical money
System originated as a way of regulating physical money in proportion to gold
deposits, but has experienced substantial structural changes over time.
e.g. Various forms of Gold Standard Regulation (19th century)
Bretton Woods (1944 – 1971)
Basel Capital Accords (1988 – to date)
Jacky Mallett Institute of Intelligent Machines.
Bank C
Modeling the Textbook Fractional Reserve Banking System
Textbook model of Fractional Reserve Banking
Bank A
Bank B
Bank C
Bank
Deposit
Loan
Reserve
A
1000
900
100
B
900
810
90
C
810
729
81
D
729
∑
3439
2439
Bank D
x + xR + xR + xR +…
2
3
¥
1
= xå R = x
R
n =1
n
Where x is the initial deposit and R is the reserve percentage
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Source: Macmillan Report to the British Parliament 1931
Author: John Maynard Keynes
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Expansion from Initial Conditions for the Banking System
Initial Deposit = 1000 Reserve Requirement = 10%
12000
10000
8000
Deposits
6000
Loans
Reserve
4000
2000
0
Under Textbook Economics assumptions the limit on the capital amount of all outstanding
bank loans in the Banking System is 90% of total Money Supply
Model Predicts expansion to a stable state with a money multiplier of 1/Reserve
requirement
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Missing from the Textbook Model
•
•
•
•
Loan Defaults
Loan Repayments
Interbank Lending.
Capital Holdings of the banks (owner’s reserve
against defaults)
• Required reserves at the Central Bank.
• Direct Intervention by the Central Bank
(Quantitative easing, lender of last resort)
Critically there appears to be no empirical evidence
supporting the limits that are predicted by the model
(ever).
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Euro 1998 - 2007
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
USA M2
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
China – 2006 - 2010
Reserve requirements increased to over 20% since 2006 in failed attempt to
constrain growth
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Iceland M3(Bank Deposits + Physical Currency)
1,800,000
1,600,000
1,400,000
1,200,000
1,000,000
M3
800,000
600,000
400,000
200,000
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
UK 1999 - 2008
Note that M2 measures and higher (M3, M4) include debt instruments in
several forms (money market, retail money market funds)
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Japanese M2 1980 – 2010
M2 Percentage Change
December 29th 1989 Nikkei reaches peak of 38,597
Japanese Credit
Bubble
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Simulation Model – Establishing a flow relationship
Loans & Salary payments
Bank A
Bank A: Employee/Depositors
Bank B
Bank B: Employee/Depositors
Loan repayments
Each Round
• Bank lends money to employees
• Bank pays employees each round from interest
received on loans
• Defaults are handled as delays in repayment
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Model
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Results
• Textbook example cannot work as shown
• Banks cannot stay in regulation without Interbank Lending
• Lending flows between banks can cause instability
• Money Multiplier is a function of loan duration and the reserve
requirement
• Central Banks appear to be a “Feature”
• Larger banks in the system have a lending advantage over
smaller banks that increases their size over time
• Interbank lending introduces a money creating race condition
• Lack of demand for loans can cause contraction in money supply
• System exhibits multiple instabilities.
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Model is not representative of any actual Banking System
•
•
•
•
Loan Default not explicitly included
Uses Simple Interest calculations rather than Compound Interest
Doesn’t model reserves at the central bank or capital reserves.
Doesn’t model central bank role as lender of last resort.
Complete model would need:
•
•
•
•
Compound interest
Implementation of Gold Standard regulatory framework
Implementation of Basel Accord frameworks
Modeling of local variations
• index linked loans ( Iceland)
• Fixed vs variable interest rates
• Banks lending more than their deposits (Basel)
• Software validation
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Monetary Cycles.
Money /
Loan
Supply
Expansion due to Interbank
lending leaks, new bank
creation, equity capital
expansion, etc.
Contraction due to loan defaults,
drops in loan demand, monetary
flows
Time
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Effects of Changes on Price Level
Increase
Decrease
Money
Inflation
Deflation
Tradable Goods
Deflation
Inflation
People
Deflation
Inflation
Speed of Circulation (VT)
Has no effect on price level
Has no effect on price level
Two types of Price Inflation/Deflation:
Monetary – resulting from changes in the total quantity of money
Productive - resulting from changes in the total quantity of all goods purchased
with money
For any given change in prices it is not possible to determine the exact causes without
additional information.
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Quantity Theory of Money (Irving Fisher circa 1911):
Assuming a constant supply of money and a market based economy
MV = PT
where M is total quantity of money
V is velocity of circulation of money
P is the price level
T is the total number of transactions purchased with
money
But:
we know that every Transaction is purchased with units of money and there must
be at least V transactions.
i.e. M x V = P x T’ x V
Cancelling:
Mt ≈ Pt x Tt
where t is the period of measurement.
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Quantity Theory of Money Chapter 2, Section 1:
“Let us begin with the money side. If the number of dollars in a country is 5,000,000, and their
velocity of circulation is twenty times per year, then the total amount of money changing hands (for
goods) per year is 5,000,000 times twenty, or $100,000,000. This is the money side of the equation
of exchange.
Since the money side of the equation is $100,000,000, the goods side must be the same. For if
$100,000,000 has been spent for goods in the course of the year, then $100,000,000 worth of
goods must have been sold in that year.”
M($5,000,000)
V
Q
P
x4
200,000,000
loaves of bread x $.10 a loaf
x 10
10,000,000
tons of coal x $5 a ton
x6
30,000,000
yards of cloth x $1 a yard
M($5,000,000)
V
Q
P
x4
4 x 50,000,000
loaves of bread x $.10 a loaf
x 10
10 x 1,000,000
tons of coal x $5 a ton
x6
6 x 5,000,000
yards of cloth x $1 a yard
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
UK 1999 - 2008
Note that M2 measures and higher (M3, M4) often include debt instruments in
several forms (money market, retail money market funds)
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Source:
The Purchasing Power of Money: Its Determination and Relation to Credit, Interest, and
Crises Irving Fisher 1911
http://www.econlib.org/library/YPDBooks/Fisher/fshPPM.html
Chapter 2:
“But while a bank deposit transferable by check is included as circulating media, it is not
money. A bank note, on the other hand, is both circulating medium and money.”
Chapter 3:
“The study of banking operations, then, discloses two species of currency: one, bank
notes, belonging to the category of money; and the other, deposits, belonging outside of
that category, but constituting an excellent substitute. Referring these to the larger
category of goods, we have a threefold classification of goods: first, money; second,
deposit currency, or simply deposits; and third, all other goods.”
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Research Questions
• Evolution over time of different regulatory regimes.
• Full model of Basel System
• Full model of Gold Standard system
• Effects of different forms of intervention.
• Influence of new forms of financial instrument (especially debt based).
• What is the “correct” amount of debt and bounds on interest for optimal
economic activity?
• How do long term regional flows of money affect the price level within
single currencies?
• How would an economy with a constant money supply behave?
• How do we prevent accidental and deliberate exploits?
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Background Material
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
1668
Sveriges Riksbank – First Central Bank
1800
European Gold and Bimetallism Period – fixed rates of exchange between gold and
banknotes.
American Free Banking and other experiments
1890
Economists begin to question status of Bank Deposits in relation to money
1914
World War 1 - British Empire suspends convertibility of banknotes (Gold standard)
1925
Britain returns to to Gold Standard
1929
American Stock Exchange crash, caused by speculative leveraged borrowing, triggers bank
failure and massive monetary contraction.
1931
British Parliament Report of the MacMillan Committee – contains deposit expansion
explanation
1945 -1972
Bretton Woods agreement fixes currency relationships with US dollar and gold
1972
Nixon abandons the gold standard – floating currency regime returns
1988
1st Basel Treaty – Shifts focus of banking regulation to risk, and capital based reserves
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Total Lending sourced from Banking System - USA
Estimated 2010:
This is new
$10 trillion commercial bank
assets (loans)
+ $7 trillion asset backed
securities
Versus $10 trillion liabilities
(deposits)
Situation is replicated in many
major economies.
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Basel Accord Framework
Money, Things that can be bought with
money (i.e. Preferential shares), and some
flows of money – subordinate debt, hybrid
capital (Basel 2 – removed in Basel 3)
Banks can increase their lending, by increasing
their deposits and equity capital holdings
- should be simple movements around the
system, purchased with money
- one bank gains, another loses.
But, if any form of Bank issued debt is allowed into
equity capital, then this form of regulation fails.
- debt used to regulate debt
- new debt creates money
Money
Jacky Mallett Institute of Intelligent Machines.
Flows
of
money
Modeling the Textbook Fractional Reserve Banking System
Asset Backed Securities
Sale of Bank Loans to entities outside of the regulated banking system.
Fannie Mae, created in 1938 , purchases and securitises bank loans in order to
create liquidity for loans. (Loans were primarily sold to pension funds, and
individual retirement funds)
1973 Bob Dall as part of then Salomon Brothers, created Mortgage Backed
Securities (MBS)
1980’s extended to other types of loans, credit card, car loans, etc.
Use spreads internationally, in particular UK, Australia, Ireland, New Zealand,
Belgium, Holland, etc.
Late 1990’s, begins to be used within financial system to finance lending to
speculators – including Hedge funds and private equity.
Criticized for causing banks to lend irresponsibly as there was no impact on the
bank from loan defaults
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
What happened in Iceland?
• Equity Capital Manipulation – loans to Bank employees to buy shares, Glitnir
“kiddy loans”
• Asset Backed Security lending – foreign currency loans, and inflation linked
Icelandic bonds
• Inflation linked loans, especially mortgages with no recourse conditions.
• Very bad idea in the context of an unsuccessfully regulated banking system
• Increases in the loan supply cause increase in money supply, triggering
inflationary feedback loop
• How exactly is it being accounted?
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Icelandic Inflation Linking
Accounting is critical – if inflation linking causes an increase in loan capital
Basel requirement is:
Loans (Assets) = Equity Capital + Deposits (liabilities)
If inflation linking causes an increase in Assets – how is the deposit/equity capital
imbalance handled?
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Iceland – Landsbanki M.Kr.
Consolidated Accounts: Annual Report 2000-2007
Assets
(Loans)
Deposits
Liabilities
"Funding”
Loans to Bank
Equity
Capital
2000
267
82
97
16
2001
323
100
111
20
2002
323
108
108
20
2003
448
152
209
22
2004
730
218
372
37
2005
1.405
334
689
110
2006
2.172
682
1.014
144
2007
3.057
1.421
835
180
Assets > Liabilities + Equity Capital
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Bank B
Bank A
Bank C
Bank D
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Money is a token of Exchange – Debt is a flow of Money.
Bank A
Bank Loans represent asymmetric flows of
money over time.
e.g.
25 year loan for $100,000
@ 5%
@ 7.5%
@ 10%
Jacky Mallett Institute of Intelligent Machines.
Total repaid
$175,000
$222,000
$272,000
Modeling the Textbook Fractional Reserve Banking System
What is Money?
 Before the 20th century – money was gold and bank notes of deposit
representing it
 Bank deposit accounts were not recognized as money
 Gold standard regulation established a relationship between gold and bank
notes
 Bank deposits were not explicitly regulated
 Bank deposit expansion was also a feature of gold standard regulation,
but was not recognized until late 19th century
Economics: “Money is a matter of functions four, a medium, a measure, a
standard, a store”
But – this is not what money is, this is what money is used for.
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Rothbard Fallacy
“I set up a Rothbard Bank, and invest $1,000 of cash (whether gold or
government paper does not matter here). Then I “lend out” $10,000 to someone,
either for consumer spending or to invest in his business.”
Murray Rothbard, Fractional Reserve Banking,
1995
Hearing this, Computer Scientists Alice, Bob and Eve set up two banks
Bank Alice lends Eve $10,000
Eve deposits this at Bank Bob
Bank Bob lends Eve $100,000
Eve repays $10,000 debt and deposits $90,000 at Bank Alice
Bank Alice lends Eve $1,000,000
Eve deposits this at Bank Bob…
Several rounds later they all retire to a sub-tropical paradise.
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Modern Systems use Equity Capital
Under Basel Accords, loan regulation has shifted to
equity capital or capital adequacy ratio
(Tier 1+Tier 2 Equity Capital)/Assets ≥ ~10%
From USA Call Reports:
Total Assets ≤ Total Liabilities + Equity Capital
Equity capital provides a separate buffer of money
from deposits to compensate for loan loss
Introduces stability issues due to leverage effects if
equity capital is tapped to cover defaults.
Regulatory emphasis is on reducing the risk of
equity capital losses.
No longer a fractional reserve system, total
lending exceeds total deposits
Regulation of total equity capital across the system
appears to be implicit
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Economic activity is conducted as a series of flows of money within the economy:
Direct transfers in exchange for goods and services
Bank originated debt and repayments
Government and Corporate originated debt and repayments (Bonds).
Money essentially functions as a unit of information transfer
• Fixed number of units.
• In a market based economy Price is established continuously as money flows
through the economy.
Price Level is established as a function of the total Quantity of Money (M), and the
total quantity of transactions involving money. (T)
Note:
All transactions count – Inflation measures like CPI don’t include share and asset
prices, but they should.
Jacky Mallett Institute of Intelligent Machines.
Modeling the Textbook Fractional Reserve Banking System
Debt is an asymmetric flow of money
Debt
Loan capital
A loan is a commitment to provide a flow of
monetary tokens over time.
e.g. Initial Loan $100,000 @ 6.5% over 25 years
Money
$100,000 received - $202,000 repaid
Loan “capital” is a varying quantity over time that represents the
amount outstanding of the initial loan.
Jacky Mallett Institute of Intelligent Machines.