Jacky Mallett Institute of Intelligent Machines. Modeling the Textbook Fractional Reserve Banking System Modeling the Textbook Fractional Reserve Banking

Jacky Mallett Institute of Intelligent Machines.

Modeling the Textbook Fractional Reserve Banking System

Modeling the Textbook Fractional Reserve Banking System.

Jacky [email protected]



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.



Although generally referred to as monetary expansion – in reality the critical issue is Bank Deposit expansion

Physical deposits and withdrawals of physical money

Bank B

Inter-bank transfers / Customer cheques.

Bank C

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)

Deposits Loans

Liabilities Assets

Bank A



Textbook model of Fractional Reserve Banking

Bank A

Bank B

Bank C

Bank Deposit Loan ReserveA 1000 900 100

B 900 810 90

C 810 729 81

D 729

∑ 3439 2439

Bank D

Where x is the initial deposit and R is the reserve percentage



Source: Macmillan Report to the British Parliament 1931Author: John Maynard Keynes



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

0

2000

4000

6000

8000

10000

12000

Expansion from Initial Conditions for the Banking SystemInitial Deposit = 1000 Reserve Requirement = 10%

DepositsLoansReserve



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).



Euro 1998 - 2007



USA M2



China – 2006 - 2010

Reserve requirements increased to over 20% since 2006 in failed attempt to constrain growth



1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 -

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

Iceland M3(Bank Deposits + Physical Currency)

M3



UK 1999 - 2008

Note that M2 measures and higher (M3, M4) include debt instruments in several forms (money market, retail money market funds)



Japanese M2 1980 – 2010 M2 Percentage Change

December 29th 1989 Nikkei reaches peak of 38,597

Japanese Credit Bubble



Bank A

Simulation Model – Establishing a flow relationship

Each Round• Bank lends money to employees• Bank pays employees each round from interest

received on loans• Defaults are handled as delays in repayment

Loans & Salary payments

Loan repayments

Bank A: Employee/Depositors

Bank B

Bank B: Employee/Depositors



Model



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.



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



Monetary Cycles.

Money / Loan Supply

Contraction due to loan defaults, drops in loan demand, monetary flows

Time

Expansion due to Interbank lending leaks, new bank creation, equity capital expansion, etc.



Effects of Changes on Price LevelIncrease 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 moneyProductive - 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.



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.



“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

x 4 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

x 6 6 x 5,000,000 yards of cloth x $1 a yard

Quantity Theory of Money Chapter 2, Section 1:

M($5,000,000) V Q P

x 4 200,000,000 loaves of bread x $.10 a loaf

x 10 10,000,000 tons of coal x $5 a ton

x 6 30,000,000 yards of cloth x $1 a yard



UK 1999 - 2008

Note that M2 measures and higher (M3, M4) often include debt instruments in several forms (money market, retail money market funds)



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.”

http://www.econlib.org/library/YPDBooks/Fisher/fshPPM.html



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?



Background Material



1668

1800

1890

1914

1925

1929

1931

1945 -1972

1972

1988

Sveriges Riksbank – First Central Bank

European Gold and Bimetallism Period – fixed rates of exchange between gold and banknotes. American Free Banking and other experiments

Economists begin to question status of Bank Deposits in relation to money

World War 1 - British Empire suspends convertibility of banknotes (Gold standard)

Britain returns to to Gold Standard

American Stock Exchange crash, caused by speculative leveraged borrowing, triggers bank failure and massive monetary contraction.

British Parliament Report of the MacMillan Committee – contains deposit expansion explanation

Bretton Woods agreement fixes currency relationships with US dollar and gold

Nixon abandons the gold standard – floating currency regime returns

1st Basel Treaty – Shifts focus of banking regulation to risk, and capital based reserves



Total Lending sourced from Banking System - USA

Estimated 2010:

$10 trillion commercial bank assets (loans) + $7 trillion asset backed securities

Versus $10 trillion liabilities (deposits)

Situation is replicated in many major economies.

This is new



Basel Accord Framework

Money

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)

Flows of money

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



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



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?



Icelandic Inflation LinkingAccounting 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?



Iceland – Landsbanki M.Kr.Consolidated Accounts: Annual Report 2000-2007

LiabilitiesAssets(Loans)

Deposits "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



Bank A

Bank B

Bank C

Bank D



Bank A

Money is a token of Exchange – Debt is a flow of Money.

Bank Loans represent asymmetric flows of money over time.e.g.

25 year loan for $100,000

Total repaid@ 5% $175,000 @ 7.5% $222,000@ 10% $272,000



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.



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 BobBank Bob lends Eve $100,000 Eve repays $10,000 debt and deposits $90,000 at Bank AliceBank Alice lends Eve $1,000,000

Eve deposits this at Bank Bob…

Several rounds later they all retire to a sub-tropical paradise.



Modern Systems use Equity CapitalUnder 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



Economic activity is conducted as a series of flows of money within the economy:Direct transfers in exchange for goods and servicesBank originated debt and repaymentsGovernment 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.



Money

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

$100,000 received - $202,000 repaid

Loan “capital” is a varying quantity over time that represents the amount outstanding of the initial loan.

DebtLoan capital

Debt is an asymmetric flow of money

Documents

Jacky Mallett Institute of Intelligent Machines. Modeling the Textbook Fractional Reserve Banking System Modeling the Textbook Fractional Reserve Banking