Honours Finance Advanced Topics in Finance: Nonlinear Analysis

1
Honours Finance (Advanced Topics in Finance
Nonlinear Analysis)

• Lecture 1 Introduction
• The Dual Price Level Analysis

2
What is Finance?

• The branch of economics concerned with the
  behaviour of money and the markets for claims on
  physical assets
• 2 approaches
• money and financial assets are no different to
  other commodities except that time preference is
  involved
• they are stable equilibrium systems subject to
  external shocks
• money and financial assets are fundamentally
  different to standard commodities
• they are unstable far from equilibrium systems
  (also subject to external shocks)

3
What is Finance?

• First approach (Modern Portfolio Theory MPT or
  Modern Finance) dominates finance literature
  but...
• Is acknowledged by almost all finance
  professionals to be clearly wrong
• If true
• asset prices should follow a random walk
• The numbers generated by any finance market
  should be independently and identically
  distributed (iid)
• Both conditions are manifestly falsified by the
  data
• So second approach has at least prima facie
  grounds for being correct, but
• sporadically developed by tiny minority of
  profession
• theoretical linkages not well known

4
Subject Overview

• Broadly this subject covers
• (1) Foundations of endogenous instability
  approach to analysing finance markets
• (2) Essential mathematical techniques for
  analysing endogenous instability, covering topics
• taught in Maths 1.3 but not put into economic
  context (polynomial series expansions of
  functions, matrix algebra)
• taught by maths department in 3rd year (ordinary
  differential equations ODEs)
• not taught at all at this University (systems of
  ODEs, introductory chaos theory)
• (3) Behavioural approach to Finance

5
Subject Overview

• Critique of Efficient Markets Hypothesis
• The Dual Price Level theory of Finance
• Techniques for analysis of deterministic
  nonlinear systems
• Ordinary Differential Equations
• Block Diagram Techniques
• A non-standard quantitative approach to Portfolio
  Analysis
• Nonlinear computer approaches to Portfolio
  Analysis
• Neural networks
• Genetic Algorithms
• Recent advances
• Econophysics nonextensive statistical mechanics

6
Subject Overview

• Necessarily technical mathematical approach, but
• attempt to keep focused on purpose behind
  techniques
• material learnt will help understand basis of
  different approaches to finance
• Dual Price level theory
• never collated before
• necessarily more macro in flavour because
• unlike MPT, argues finance does have
  macroeconomic impact
• developed by leading critical macroeconomists
  Marx, Fisher, Keynes, Kalecki, Minsky
• has both philosophic and mathematical aspects
• But first, recap on CAPM

7
The Capital Assets Pricing Model

• Problem How to predict the behaviour of capital
  markets
• Solution extension of economic theories of
  investment under certainty...
• to investment under conditions of risk
• Based on neoclassical utility theory
• Investor maximises utility subject to (s.t.)
  constraints
• Utility is a
• Positive function(ive fn) of expected return ER
• -ive fn of risk (standard deviation) sR
• Constraints are available spectrum of investment
  opportunities

8
The Capital Assets Pricing Model
Investment opportunities
Z inferior to C (lower ER) and B (higher sR)
Indifference curves
Border (AFBDCX) is Investment Opportunity Curve
(IOC)
9
The Capital Assets Pricing Model

• Sharpe assumes riskless asset P with ERPpure
  interest rate, sRP0.
• Investor can form portfolio of P with any other
  combination of assets
• One asset combination will initially dominate all
  others

10
The Capital Assets Pricing Model
Efficiency maximise expected return minimise
risk given constraints
11
The Capital Assets Pricing Model

• Assume limitless borrowing/lending at riskless
  interest rate return on asset P
• Investor can move to anywhere along PfZ line by
  borrowing/lending
• Problem
• P the same for all investors (simplifying
  assumption)
• But investor perceptions of expected return,
  risk, investment correlation will differ
• Solution
• assume homogeneity of investor expectations
  OREF II
• utterly unrealistic assumption, as is assumption
  of limitless borrowing by all borrowers at
  riskless interest rate. So...

12
The Capital Assets Pricing Model

• Defended by appeal to Friedmans
  Instrumentalism
• the proper test of a theory is not the realism
  of its assumptions but the acceptability of its
  implications
• Consequence of assumptions
• spectrum of available investments/IOC identical
  for all investors
• P same for all investors
• PfZ line same for all investors
• Investors distribute along line by
  borrowing/lending according to own risk
  preferences

13
The Capital Assets Pricing Model
14
The Capital Assets Pricing Model

• Next, the (perfect) market mechanism
• Price of assets in f will rise
• Price of assets not in f will fall
• Price changes shift expected returns
• Causes new pattern of efficient investments
  aligned with PfZ line

15
The Capital Assets Pricing Model
Range of efficient assetcombinations after
market price adjustments more than just one
efficient portfolio
16
The Capital Assets Pricing Model

• In order to derive conditions for equilibrium in
  the capital market we invoke two assumptions.
  First, we assume a common pure rate of interest,
  with all investors able to borrow or lend funds
  on equal terms. Second, we assume homogeneity of
  investor expectations investors are assumed to
  agree on the prospects of various investmentsthe
  expected values, standard deviations and
  correlation coefficients described in Part II.
  Needless to say, these are highly restrictive and
  undoubtedly unrealistic assumptions. However,
  since the proper test of a theory is not the
  realism of its assumptions but the acceptability
  of its implications, and since these assumptions
  imply equilibrium conditions which form a major
  part of classical financial doctrine, it is far
  from clear that this formulation should be
  rejectedespecially in view of the dearth of
  alternative models leading to similar results.
  (Sharpe 1964 1991 emphasis added)
• But Sharpe later admits to some qualms with this

17
The CAPM Reservations

• People often hold passionately to beliefs that
  are far from universal. The seller of a share of
  IBM stock may be convinced that it is worth
  considerably less than the sales price. The buyer
  may be convinced that it is worth considerably
  more. (Sharpe 1970)
• However, if we try to be more realistic
• The consequence of accommodating such aspects of
  reality are likely to be disastrous in terms of
  the usefulness of the resulting theory... The
  capital market line no longer exists. Instead,
  there is a capital market curvelinear over some
  ranges, perhaps, but becoming flatter as risk
  increases over other ranges. Moreover, there is
  no single optimal combination of risky
  securities the preferred combination depends
  upon the investors preferences... The demise of
  the capital market line is followed immediately
  by that of the security market line. The theory
  is in a shambles. (Sharpe 1970 emphasis added)

18
Within Economics Instrumentalism

• Logical consistency of assumptions has been
  challenged (Sraffa), not just realism
• Sciences do attempt to build theories which are
  essentially descriptions of reality
• Musgrave (1981) argues Friedmans significant
  theory, unrealistic assumptions position invalid
• Classifies assumptions into 3 classes
• Negligibility assumptions
• Domain Assumptions
• Heuristic Assumptions

19
Within Economics Instrumentalism

• Negligibility Assumptions
• Assert that some factor is of little or no
  importance in a given situation
• e.g., Galileos experiment to prove that weight
  does not affect speed at which objects fall
• dropped two different size lead balls from
  Leaning Tower of Pisa
• assumed (correctly) air resistance negligible
  at that altitude for dense objects, therefore
  ignored air resistance
• Domain assumptions
• Assert that theory is relevant if some assumed
  condition applies, irrelevant if condition does
  not apply

20
Within Economics Instrumentalism

• e.g., Newtons theory of planetary motion
  assumed there was only one planet
• if true, planet follows elliptical orbit around
  sun.
• if false planets relatively massive, motion
  unpredictable. Poincare (1899) showed
• there was no formula to describe paths
• paths were in fact chaotic
• planets in multiple planet solar systems
  therefore have collisions
• present planets evolved from collisions between
  proto-planets
• evolutionary explanation for present-day
  roughly elliptical orbits

21
Classes of assumptions

• Heuristic
• assumption known to be false, but used as
  stepping stone to more valid theory
• e.g., in developing theory of relativity,
  Einstein assumes that distance covered by person
  walking across a train carriage equals
  trigonometric sum of
• forward movement of train
• sideways movement of passenger

Then says We shall see later that this result
cannot be maintained in other words, the law
that we have just written down does not hold in
reality. For the time being, however, we shall
assume its correctness. (Einstein 1916)
passenger
0.9 c
train
0.9 c
lt 1.0 c
sum
22
Just where are markets efficient?

• The Efficient Markets Hypothesis assume
• All investors have identical accurate
  expectations of future
• All investors have equal access to limitless
  credit
• Negligible, Domain or Heuristic assumptions?
• Negligible? No if drop them, then according to
  Sharpe The theory is in a shambles (see last
  lecture)
• Heuristic? No, EMH was end of the line for
  Sharpes logic no subsequent theory developed
  which
• replaced risk with uncertainty, or
• took account of differing inaccurate assumptions,
  different access to credit, etc.
• Basis of eventual empirical failure of CAPM

23
The CAPM Evidence

• Sharpes qualms ignored CAPM takes over
  economic theory of finance
• Initial evidence seemed to favour CAPM
• Essential ideas
• Price of shares accurately reflects future
  earnings
• With some error/volatility
• Shares with higher returns more strongly
  correlated to economic cycle
• Higher return necessarily paired with higher
  volatility
• Investors simply chose risk/return trade-off that
  suited their preferences
• Initial research found expected (positive)
  relation between return and degree of volatility
• But were these results a fluke?

24
The CAPM Evidence

• Volatile but superficially exponential trend
• As it should be if economy growing smoothly

But looking more closely...
25
The CAPM Evidence

• Sharpes CAPM paper published 1964
• Initial CAPM empirical research on period
  1950-1960s
• Period of financial tranquility by Minskys
  theory
• Low debt to equity ratios, low levels of
  speculation
• But rising as memory of Depression recedes
• Steady growth, high employment, low inflation
• Dow Jones advance steadily from 1949-1965
• July 19 1949 DJIA cracks 175
• Feb 9 1966 DJIA sits on verge of 1000 (995.15)
• 467 increase over 17 years
• Continued for 2 years after Sharpes paper
• Then period of near stagnant stock prices

26
The CAPM Evidence

• Dow Jones treads water from 1965-1982
• Jan 27 1965 Dow Jones cracks 900 for 1st time
• Jan 27 1972 DJIA still below 900! (close 899.83)
• Seven years for zero appreciation in nominal
  terms
• Falling stock values in real terms
• Nov. 17 1972 DJIA cracks 1000 for 1st time
• Then all hell breaks loose
• Index peaks at 1052 in Jan. 73
• falls 45 in 23 months to low of 578 in Dec. 74
• Another 7 years of stagnation
• And then liftoff

27
The CAPM Evidence
21 years ahead of trend...

• Fit shows average exponential growth 1915-1999
• index well above or below except for 1955-1973

Crash of 73 45 fall in 23 months
Sharpes paper published
Jan 11 73 Peaks at 1052
Dec 12 1974 bottoms at 578
Bubble takes off in 82
CAPM fit doesnt look so hot any more
Steady above trend growth 1949-1966 Minskys
financial tranquility
CAPM fit to this data looks pretty good!
28
The CAPM Evidence According to Fama 1969

• Evidence supports the CAPM
• This paper reviews the theoretical and empirical
  literature on the efficient markets model We
  shall conclude that, with but a few exceptions,
  the efficient markets model stands up well.
  (383)
• Assumptions unrealistic but that doesnt matter
• the results of tests based on this assumption
  depend to some extent on its validity as well as
  on the efficiency of the market. But some such
  assumption is the unavoidable price one must pay
  to give the theory of efficient markets empirical
  content. (384)

29
The CAPM Evidence According to Fama 1969

• CAPM good guide to market behaviour
• For the purposes of most investors the efficient
  markets model seems a good first (and second)
  approximation to reality. (416)
• Results conclusive
• In short, the evidence in support of the
  efficient markets model is extensive, and
  (somewhat uniquely in economics) contradictory
  evidence is sparse. (416)
• Just one anomaly admitted to
• Large movements one day often followed by large
  movements the nextvolatility clustering

30
The CAPM Evidence According to Fama 1969

• one departure from the pure independence
  assumption of the random walk model has been
  noted large daily price changes tend to be
  followed by large daily changes. The signs of the
  successor changes are apparently random, however,
  which indicates that the phenomenon represents a
  denial of the random walk model but not of the
  market efficiency hypothesis But since the
  evidence indicates that the price changes on days
  follow ing the initial large change are random in
  sign, the initial large change at least
  represents an unbiased adjustment to the ultimate
  price effects of the information, and this is
  sufficient for the expected return efficient
  markets model. (396)
• 35 years later, picture somewhat different

31
The CAPM Evidence According to Fama 2004

• The attraction of the CAPM is that it offers
  powerful and intuitively pleasing predictions
  about how to measure risk and the relation
  between expected return and risk.
• Unfortunately, the empirical record of the model
  is poorpoor enough to invalidate the way it is
  used in applications.
• The CAPM's empirical problems may reflect
  theoretical failings, the result of many
  simplifying assumptions
• In the end, we argue that whether the model's
  problems reflect weaknesses in the theory or in
  its empirical implementation, the failure of the
  CAPM in empirical tests implies that most
  applications of the model are invalid. (Fama
  French 2004 25)

32
The CAPM Evidence According to FF 2004

• Clearly admits assumptions dangerously
  unrealistic
• The first assumption is complete agreement given
  market clearing asset prices at t-1, investors
  agree on the joint distribution of asset returns
  from t-1 to t. And this distribution is the true
  onethat is, it is the distribution from which
  the returns we use to test the model are drawn.
  The second assumption is that there is borrowing
  and lending at a risk free rate, which is the
  same for all investors and does not depend on the
  amount borrowed or lent. (26)
• Bold emphasis model assumes all investors know
  the future
• Assumptions, which once didnt matter (see
  Sharpe earlier) are now crucial

33
The CAPM Evidence According to FF 2004

• The assumption that short selling is
  unrestricted is as unrealistic as unrestricted
  risk-free borrowing and lending But when there
  is no short selling of risky assets and no
  risk-free asset, the algebra of portfolio
  efficiency says that portfolios made up of
  efficient portfolios are not typically efficient.
  This means that the market portfolio, which is a
  portfolio of the efficient portfolios chosen by
  investors, is not typically efficient. And the
  CAPM relation between expected return and market
  beta is lost. (32)
• Still some hope that, despite lack of realism,
  data might save the model

34
The CAPM Evidence According to FF 2004

• The efficiency of the market portfolio is based
  on many unrealistic assumptions, including
  complete agreement and either unrestricted
  risk-free borrowing and lending or unrestricted
  short selling of risky assets. But all
  interesting models involve unrealistic
  simplifications, which is why they must be tested
  against data. (32)
• Unfortunately, no such luck
• 40 years of data strongly contradict all versions
  of CAPM
• Returns not related to betas
• Other variables (book to market ratios etc.)
  matter
• Linear regressions on data differ strongly from
  risk free rate (intercept) beta (slope)
  calculations from CAPM

35
The CAPM Evidence According to FF 2004

• Tests of the CAPM are based on three
  implications
• First, expected returns on all assets are
  linearly related to their betas, and no other
  variable has marginal explanatory power.
• Second, the beta premium is positive, meaning
  that the expected return on the market portfolio
  exceeds the expected return on assets whose
  returns are uncorrelated with the market return.
• Third, assets uncorrelated with the market have
  expected returns equal to the risk-free interest
  rate, and the beta premium is the expected market
  return minus the risk-free rate. (32)

36
The CAPM Evidence According to FF 2004

• There is a positive relation between beta and
  average return, but it is too "flat." the
  Sharpe-Lintner model predicts that
• the intercept is the risk free rate and
• the coefficient on beta is the expected market
  return in excess of the risk-free rate, E(RM) -
  R.
• The regressions consistently find that the
  intercept is greater than the average risk-free
  rate, and the coefficient on beta is less than
  the average excess market return (32)

37
The CAPM Evidence According to FF 2004

• Average Annualized Monthly Return versus Beta for
  Value Weight Portfolios Formed on Prior Beta,
  1928-2003

• the predicted return on the portfolio with the
  lowest beta is 8.3 percent per year the actual
  return is 11.1 percent. The predicted return on
  the portfolio with the highest beta is 16.8
  percent per year the actual is 13.7 percent.
  (33)

38
The CAPM Evidence According to FF 2004

• The hypothesis that market betas completely
  explain expected returns
• Starting in the late 1970s evidence mounts that
  much of the variation in expected return is
  unrelated to market beta (34)
• Fama and French (1992) update and synthesize the
  evidence on the empirical failures of the CAPM
  they confirm that size, earnings-price, debt
  equity and book-to-market ratios add to the
  explanation of expected stock returns provided by
  market beta. (36)
• Best example of failure of CAPM as guide to
  building investment portfolios Book to Market
  (B/M) ratios provide far better guide than Beta

39
The CAPM Evidence According to FF 2004

• Average returns on the B/M portfolios increase
  almost monotonically, from 10.1 percent per year
  for the lowest B/M group to an impressive 16.7
  percent for the highest.
• But the positive relation between beta and
  average return predicted by the CAPM is notably
  absent the portfolio with the lowest
  book-to-market ratio has the highest beta but the
  lowest average return.
• The estimated beta for the portfolio with the
  highest book-tomarket ratio and the highest
  average return is only 0.98. With an average
  annualized value of the riskfree interest rate,
  Rf, of 5.8 percent and an average annualized
  market premium, Rm - Rf, of 11.3 percent, the
  Sharpe-Lintner CAPM predicts an average return of
  11.8 percent for the lowest B/M portfolio and
  11.2 percent for the highest, far from the
  observed values, 10.1 and 16.7 percent.

40
The CAPM Evidence According to FF 2004

• Average Annualized Monthly Return versus Beta for
  Value Weight Portfolios Formed on B/M, 1963-2003

• Simple regression gives opposite relationship to
  CAPM return rises as beta falls! High returns
  with low volatility

41
The CAPM Evidence According to FF 2004

• End result CAPM should not be used.
• The CAPM has never been an empirical
  success The problems are serious enough to
  invalidate most applications of the CAPM.
• For example, finance textbooks often recommend
  using the CAPM risk-return relation to estimate
  the cost of equity capital But CAPM estimates
  of the cost of equity for high beta stocks are
  too high and estimates for low beta stocks are
  too low
• The CAPM is nevertheless a theoretical tour de
  force. We continue to teach the CAPM as an
  introduction to the fundamental concepts of
  portfolio theory and asset pricing
• But we also warn students that despite its
  seductive simplicity, the CAPM's empirical
  problems probably invalidate its use in
  applications. (FF 2004 46-47)

42
The Dual Price Level theory of Finance

• If even the true believers have abandoned CAPM,
  a new theory is needed
• However everything old is new again
• Many contributions to economics finance
  neglected because of CAPM dominance
• These contributions provide philosphical/theoretic
  al basis for emerging nonlinear theories of
  finance
• Smith, Fisher, Keynes, Schumpeter, Kalecki,
  Minsky, Marx
• First some preliminary visual statistics

43
The archetypal financial series the DJIA
Superficially lognormal, a random walk...
44
The cyclical DJIA? Deflate by CPI and
Is there an underlying dynamic?

• Similar cyclical patterns evident in interest
  rates, inflation

45
USA Interbank Lending Rate
GreatDepression
Post-WarRecovery
WWII
46
Pre-capitalist perspective on money

• Contrary to majority opinion, capitalism has not
  existed forever
• Capitalist economy evolved out of feudal systems
  of Europe
• Feudal systems based on social hierarchy
  determined by birth
• King at top ruled kingdom
• Lords beneath controlled fiefs (large estates)
• effective owners of land, but title legally with
  king
• paid tribute to king, provided knights for
  armies, etc.
• Serfs worked the land
• bonded to land
• system of mutual obligation between serfs and lord

47
Pre-capitalist perspective on money

• Disparate systems of artisans constituted
  industry
• normally organised in guilds
• No formal financial system
• wealth in physical terms (goods, gold) rather
  than money
• Dominant ideology of feudal system religious
• social order ordained by God
• The rich man at his castle, the poor man at his
  gate God made one high, one lowly, and ordered
  their estate
• Main religion Catholicism
• Major minority Jewish, tiny minority Muslim
• Religious attitude to moneylending censorious an
  evil

48
From Usury to Utility

• During pre-capitalist era, money regarded as
  fundamentally different to normal commodities
  because
• barren Normal commodity sold at profit by
  tradesman
• profit represents labour of tradesman a man may
  ... seek gain, not as an end, but as payment for
  his labor (Aquinas)
• No labour involved in money exchange To take
  interest for money lent is unjust in itself,
  because this is to sell what does not exist, and
  this evidently leads to inequality which is
  contrary to justice. (Aquinas)
• Intended only for circulation, not accumulation
• Usury (lending of money at secured rate of
  return) banned

49
From Usury to Utility

• In practice usury undertaken
• not prohibited from one religion to another (in
  Christian/Jewish religions), so fictional chains
  (see HET lectures) used to lend from Christian to
  Christian
• But legislative prohibitions until 1624
• UK Act Against Usury of 1571 prohibited usury
  absolutely, but penalties depended on rate of
  interest charged
• If less than ten per cent, the usurer forfeited
  the interest
• If greater, usurer forfeited the interest plus
  three times the principal (half going to the
  Crown, half to the informer) (Jones 1989 62-64,
  92).

50
From Usury to Utility

• Religion basis of anti-usury ideology
• 1571 Act prohibited usury absolutely on the basis
  that the role of Parliament was to apply the
  word of God to an issue on which God had
  expressed Himself (Jones 1989 1)
• theoretical prohibition dominant until late 17th
  century but absolute prohibition repealed in 1624
• Usury still a sin but practice now an issue for
  usurer and God, not the Law
• Legal Usury now defined in terms of the interest
  rate greater than 8 per cent was usurious

51
From Usury to Utility

• Pre-1571, rates of interest
• varied between 12 and 500 per cent per annum
• majority between 15 and 50 per cent, but quite
  unsystematic sample from time of Elizabeth I

Littlewonderthatusurerwas adirty word!
52
From Usury to Utility

• Pre-capitalist rates clearly unsustainable
• Little wonder that religions protected borrower
• And if the debtor is in straitened
  circumstances, then (let there be) postponement
  to (the time of) ease and that ye remit the debt
  as almsgiving would be better for you if ye did
  but know. (Quran , Al-Baqara 2.280)
• As capitalist era commences, legislative pressure
  reduces maximum rate of interest
• Post 1571, 10 per cent 1624, 8 per cent 6 per
  cent during 17th century
• 5 per cent in late 18th century

53
From Usury to Utility

• Actual rate tended to be just below legal maximum
• 3 to 4.5 per cent versus 5 per cent ceiling
  (Smith 1776 Book 1, Ch 9)
• Lending of money at interest common commercial
  practice by dawn of capitalist era, but still
  prohibited by religious ideology. Alternative
  theory needed to justify it
• Utilitarianism the eventual alternative theory,
  but not the first perspective of economists
• Instead, Smith
• criticised prohibitions on usury but
• supported legal limits to the rate of interest

54
From Usury to Utility

• The complete prohibition of interest taking like
  all others of the same kind, is said to have
  produced no effect, and probably rather increased
  than diminished the evil of usury (Smith, 1776
  Book I, Ch. 9).
• Laws prohibiting lending increase the evil of
  usury the debtor being obliged to pay, not only
  for the use of the money, but for the risk which
  his creditor runs by accepting a compensation for
  that use. He is obliged, if one may say so, to
  insure his creditor from the penalties of usury.
  (Smith, 1776 Book II, Ch. 4)
• But control over the rate of interest a good
  thing

55
From Usury to Utility

• In countries where interest is permitted, the
  law, in order to prevent the extortion of usury,
  generally fixes the highest rate which can be
  taken without incurring a penalty. This rate
  ought always to be somewhat above the lowest
  market price... In a country, such as Great
  Britain, where money is lent to government at
  three per cent and to private people upon a good
  security at four and four and a half, the present
  legal rate, five per cent, is perhaps as proper
  as any. (Smith, 1776 Book II, Ch. 4)
• The reasons?
• Better control of allocation of finance
• Higher rate of productive investment
• Prevention of exploitation

56
From Usury to Utility

• The legal rate ... ought not to be much above
  the lowest market rate. If the legal rate is
  much higher, the greater part of the money which
  was to be lent would be lent to prodigals and
  projectors, who alone would be willing to give
  this high interest...
• A great part of the capital of the country would
  thus be kept out of the hands which were most
  likely to make a profitable and advantageous use
  of it, and thrown into those which were most
  likely to waste and destroy it.
• Where the legal rate of interest, on the
  contrary, is fixed but a very little above the
  lowest market rate, sober people are universally
  preferred, as borrowers, to prodigals and
  projectors. The person who lends money gets
  nearly as much interest from the former as he
  dares to take from the latter, and his money is
  much safer in the hands of the one set of people
  than in those of the other.

57
From Usury to Utility

• A great part of the capital of the country is
  thus thrown into the hands in which it is most
  likely to be employed with advantage. (Smith,
  1776 Book II, Ch. 4)
• Thus according to Smith, credit controls
  improve allocation of finance
• Willingness to pay higher rates correlated with
  reduced quality of lender
• Acknowledgement of speculative and wasteful
  employment of credit, possibility of
  bankruptcy/default by borrowers, and
  macroeconomic consequences (lower rate of growth)
• Distinction between normal goods, where market
  can set the price, and money where a maximum
  should be set
• But Smiths realism defeated by Benthams
  utilitarianism

58
From Usury to Utility

• no man of ripe years and of sound mind, acting
  freely, and with his eyes open, ought to be
  hindered, with a view to his advantage, from
  making such bargain, in the way of obtaining
  money, as he thinks fit... This proposition, were
  it to be received, would level ... all the
  barriers which law, either statute or common,
  have in their united wisdom set up, ... against
  the crying sin of Usury. (Bentham 1787, In
  Defence of Usury)
• Benthams starting point was libertarianism
• You, who fetter contracts you, who lay
  restraints on the liberty of man, it is for you
  (I should say) to assign a reason for your doing
  so.

59
From Usury to Utility

• Benthams target was not prohibition, but
  controls on the maximum rate (as accepted by
  Smith)
• To say then that usury is a thing that ought to
  be prevented, is saying ... that the utmost rate
  of interest which shall be taken ought to be
  fixed... A law punishing usury supposes,
  therefore, a law fixing the allowed legal rate of
  interest.
• As a leading proponent of the removal of all
  restraints to trade, Bentham starts by asking
  why a policy, which, as applied to exchanges in
  general, would be generally deemed absurd and
  mischievous, should be deemed necessary in the
  instance of this particular kind of exchange .

60
From Usury to Utility

• Bentham considers and dismisses each perceived
  argument in favour of controls on the maximum
  rate of interest
• Money exchange vs commodity exchange why the
  difference?
• Much has not been done, ... in the way of fixing
  the price of other commodities and, in what
  little has been done, the probity of the
  intention has, I believe, in general, been rather
  more unquestionable than the rectitude of the
  principle, or the felicity of the result. Putting
  money out at interest, is exchanging present
  money for future but why a policy, which, as
  applied to exchanges in general, would be
  generally deemed absurd and mischievous, should
  be deemed necessary in the instance of this
  particular kind of exchange, mankind are as yet
  to learn.

One of the earliest statements of this concept
61
From Usury to Utility

• Money exchange vs commodity exchange why the
  difference?
• For him who takes as much as he can get for the
  use of any other sort of thing, an house for
  instance, there is no particular appellation, nor
  any mark of disrepute nobody is ashamed of doing
  so, nor is it usual so much as to profess to do
  otherwise. Why a man who takes as much as he can
  get, be it six, or seven, or eight, or ten per
  cent for the use of a sum of money should be
  called usurer, should be loaded with an
  opprobrious name, any more than if he had bought
  an house with it, and made a proportionable
  profit by the house, is more than I can see.

62
From Usury to Utility

• Money exchange vs commodity exchange why a
  maximum?
• Another thing I would also wish to learn, is,
  why the legislator should be more anxious to
  limit the rate of interest one way, than the
  other? why he should set his face against the
  owners of that species of property more than of
  any other? why he should make it his business to
  prevent their getting more than a certain price
  for the use of it, rather than to prevent their
  getting less? why, in short, he should not take
  means for making it penal to offer less, for
  example, than 5 per cent as well as to accept
  more?

63
From Usury to Utility

• Protection of prodigals
• Admits prevention of prodigality of some merit
• That prodigality is a bad thing, and that the
  prevention of it is a proper object for the
  legislator to propose to himself, so long as he
  confines himself to, what I look upon as, proper
  measures, I have no objection to allow
• But argues that a prodigal will not, in fact, be
  charged an excessive rate of interest
• In the first place, no man, ..., ever thinks of
  borrowing money to spend, so long as he has ready
  money of his own, or effects which he can turn
  into ready money without loss.
• Prodigal with money and/or liquid assets
  therefore wont borrow

64
From Usury to Utility

• Protection of prodigals
• Exceptions to above (no money) but with requisite
  collateral can get a loan at the usual rate
• Those that do not have security will only be lent
  to by those who like them, and these friendly
  persons will naturally offer them the standard
  rate
• Persons who either feel, or find reasons for
  pretending to feel, a friendship for the
  borrower, can not take of him more than the
  ordinary rate of interest persons, who have no
  such motive for lending him, will not lend him at
  all.
• So Shylock died with Shakespeare in the 16th
  century?

65
From Usury to Utility

• Protection of the mentally unsound
• No idiot is likely to be less accurate than a
  legislator
• I am by this time entitled to observe, that no
  simplicity, short of absolute idiotism, can cause
  the individual to make a more groundless
  judgment, than the legislator, who, in the
  circumstances above stated, should pretend to
  confine him to any given rate of interest, would
  have made for him.
• Supremacy of individual judgment, however
  hampered, over legislative.

66
From Usury to Utility

• Protection of the mentally unsound
• Mentally unsound more in need of protection from
  high prices of normal commodities than of money
• Buying goods with money, or upon credit, is the
  business of everyday. borrowing money is the
  business, only, of some particular exigency,
  which, in comparison, can occur but seldom.
  Regulating the prices of goods in general would
  be an endless task, and no legislator has ever
  been weak enough to think of attempting it. ...
  But in what degree soever a man's weakness may
  expose him to imposition, he stands much more
  exposed to it, in the way of buying goods, than
  in the way of borrowing money.

67
From Usury to Utility

• Benthams justification of a total free market
  for loans
• based on individual liberty and individual
  utility maximisation
• asserts commonality of contracts for money with
  all other commodity contracts
• introduces concept of a loan as exchanging
  present money for future
• makes some rather questionable assumptions (only
  friends lend to prodigals)
• does not address Smiths macroeconomic arguments
  (more productive investment, higher rate of
  growth if maximum interest rate set by law)

68
From Usury to Utility

• Despite weaknesses, Benthams utilitarian
  approach becomes basis of modern theory of
  finance via Fisher Mark I
• The rate of interest expresses a price in the
  exchange between present and future goods.
  (Fisher 1930 61),
• This price is the product of three forces
• the subjective preferences of individuals for
  present goods over future goods
• the objective possibilities for profitable
  investment
• and a market mechanism for loanable funds which
  brings these two forces into equilibrium.

69
From Usury to Utility

• the subjective preferences of individuals for
  present goods over future goods determines supply
  of funds
• a low time preference
• most likely a lender
• high time preference (prefers to consume now
  rather than later)
• most likely a borrower.
• Borrowing thus means by which those with a high
  preference for present goods acquire the funds
  they need now, at the expense of later income.

70
From Usury to Utility

• The objective side of the equation
• the marginal productivity of investment or
  marginal return over cost (1930 182).
• willingness to borrow/lend not enough
• must also be possible for borrowed money to be
  invested and earn a rate of return.

71
From Usury to Utility

• Market mechanism brings subjective and objective
  forces into harmony
• Supply
• A high rate of interest
• even those with a very high time preference will
  lend
• supply of funds will be quite high
• Low rate of interest
• only those with a very low time preference will
  lend
• very small supply of funds

72
From Usury to Utility

• Demand
• High rate of interest
• most investments will be unviable
• demand for funds will be low
• Low rate of interest
• most investments have positive net present value
• demand for funds will be high
• Market mechanism
• Forces of supply and demand determine equilibrium
  interest rate at which the funds demanded and the
  funds supplied are equal.

73
From Usury to Utility

• Fishers analysis supports zero rate of interest
  during medieval/feudal times
• Average rate of accumulation zero (all surplus
  consumed by royal class)
• Average rate of return on investment therefore
  zero
• Rate of subjective time preference must therefore
  also become zero
• Since, as we have seen, this rate must equal the
  rates of preference, or impatience, and also the
  rate of interest, all these rates must be zero
  also. (1930 186)
• Modern Finance thus supports prohibition on
  interest laws reflected subjective rate of time
  preference of medieval society.

74
From Usury to Utility

• More on utility theory of finance later in course
• Now to Fisher and the alternative Dual Price
  Level theory
• Two conditions needed for market to perform in
  Fishers equilibrium model
• (A) The market must be clearedand cleared with
  respect to every interval of time.
• (B) The debts must be paid. (1930 495)
• i.e.
• No disequilibrium
• No bankruptcy/default
• As unrealistic as Bentham on prodigals, but...

75
From Usury to Utility

• Fisher cognisant of
• social basis to time preference
• the smaller the income, the higher the
  preference for present over future income (71)
• If a person has only one loaf of bread he would
  not set it aside for next year even if the rate
  of interest were 1000 per cent for if he did so,
  he would starve in the meantime (71-72)
• the effect of poverty is often to relax
  foresight and self-control and to tempt us to
  trust to luck for the future, if only the
  all-engrossing need of present necessities can be
  satisfied (72)

76
From Usury to Utility

• affect of time pattern and expectations on time
  preference
• A man who is now enjoying an income of only
  5000 a year, but who expects in ten years to be
  enjoying one of 10,000 a year, will today prize
  a dollar in hand far more than the prospect of a
  dollar due ten years hence. His great
  expectations make him impatient to realize on
  them in advance. He may, in fact, borrow money to
  eke out this year's income and promise repayments
  out of his supposedly more abundant income ten
  years later (73)
• Akin to lending to poor/lending to prodigals in
  Smiths reasons to restrain the rate of interest
• Both reasons why preconditions (A) and (B) may
  not be met in the real world

77
From Utility to Depression

• As well as one of worlds most prominent
  economists, Fisher was also a newspaper columnist
  (a risky business...)
• On Wednesday, October 15, 1929, Fisher
  commentsStock prices have reached what looks
  like a permanently high plateau. I do not feel
  that there will soon, if ever, be a fifty or
  sixty point break below present levels, such as
  Mr. Babson has predicted. I expect to see the
  stock market a good deal higher than it is today
  within a few months.
• On October 23rd, 1929, Black Wednesday Dow Jones
  loses almost 10 in a single day
• 4 years later, the broad market was 1/6th of its
  peak, and Irving Fisher had lost over 10 million.

78
The Wall Street Crash
From 32 at its zenith
To below 5at its nadir
in less than 3 years
79
From Utility to Depression

• Fishers reputation destroyed by above
  prediction, but turned to developing theory to
  explain the crash
• The Debt Deflation Theory of Great Depressions
• based on rejection of conditions (A) and (B)
  above
• Previous theory assumed equilibrium but real
  world equilibrium short-lived since New
  disturbances are, humanly speaking, sure to
  occur, so that, in actual fact, any variable is
  almost always above or below the ideal
  equilibrium (1933 339)
• As a result, any real world variable is likely to
  be over or under its equilibrium level--including
  confidence speculation

80
Debt Deflation Theory of Great Depressions

• Key problems debt and prices
• The two dominant factors which cause
  depressions are over-indebtedness to start with
  and deflation following soon after
• Thus over-investment and over-speculation are
  often important but they would have far less
  serious results were they not conducted with
  borrowed money. That is, over-indebtedness may
  lend importance to over-investment or to
  over-speculation. The same is true as to
  over-confidence. I fancy that over-confidence
  seldom does any great harm except when, as, and
  if, it beguiles its victims into debt. (Fisher
  1933 341)
• When overconfidence leads to overindebtedness, a
  chain reaction ensues

81
Debt Deflation Theory of Great Depressions

• (1) Debt liquidation leads to distress selling
  and to
• (2) Contraction of deposit currency, as bank
  loans are paid off, and to a slowing down of
  velocity of circulation. This contraction of
  deposits and of their velocity, precipitated by
  distress selling, causes
• (3) A fall in the level of prices, in other
  words, a swelling of the dollar. Assuming, as
  above stated, that this fall of prices is not
  interfered with by reflation or otherwise, there
  must be
• (4) A still greater fall in the net worths of
  business, precipitating bankruptcies and

82
Debt Deflation Theory of Great Depressions

• (5) A like fall in profits, which in a
  "capitalistic," that is, a private-profit
  society, leads the concerns which are running at
  a loss to make
• (6) A reduction in output, in trade and in
  employment of labor. These losses, bankruptcies,
  and unemployment, lead to
• (7) Pessimism and loss of confidence, which in
  turn lead to
• (8) Hoarding and slowing down still more the
  velocity of circulation. The above eight changes
  cause
• (9) Complicated disturbances in the rates of
  interest, in particular, a fall in the nominal,
  or money, rates and a rise in the real, or
  commodity, rates of interest. (1933 342)

83
Debt Deflation Theory of Great Depressions

• Fisher thus concurs with ancient charge against
  usury, that it maketh many bankrotts (Jones
  1989 55)
• While such a fate largely individual in a feudal
  system, in a capitalist economy a chain reaction
  ensues which leads the entire populace into
  crisis
• Theory nonequilibrium in nature
• argues that we may tentatively assume that,
  ordinarily and within wide limits, all, or almost
  all, economic variables tend, in a general way,
  towards a stable equilibrium
• but though stable, equilibrium is so delicately
  poised that, after departure from it beyond
  certain limits, instability ensues (Fisher 1933
  339).

84
Debt Deflation Theory of Great Depressions

• Two classes of far from equilibrium events
  explained
• Great Depression, when overindebtedness coincides
  with deflation
• with deflation on top of excessive debt, the
  more debtors pay, the more they owe. The more the
  economic boat tips, the more it tends to tip. It
  is not tending to right itself, but is capsizing
  (Fisher 1933 344).
• Cycles, when one occurs without the other
• with only overindebtedness or deflation, economic
  growth eventually corrects situation it
• is then more analogous to stable equilibrium
  the more the boat rocks the more it will tend to
  right itself. In that case, we have a truer
  example of a cycle (Fisher 1933 344-345)

85
Debt Deflation Theory of Great Depressions

• Fishers new theory ignored
• Old theory made basis of modern finance theory
• Debt deflation theory revived in modern form by
  Minsky
• Fishers macroeconomic contribution (which
  emphasised the need for reflation and 100
  money during the Depression) overshadowed by
  Keyness General Theory
• Many similarities and synergies in Keynes and
  Fisher, but different countries meant one largely
  unaware of others work

86
Keynes and Debt-deflation

• Some consideration of debt-deflation in General
  Theory when discussing reduction in money wages
  (neoclassical proposal)
• Since a special reduction of money-wages is
  always advantageous to an individual entrepreneur
  ... a general reduction may break through a
  vicious circle of unduly pessimistic estimates of
  the marginal efficiency of capital On the other
  hand, the depressing influence on entrepreneurs
  of their greater burden of debt may partially
  offset any cheerful reactions from the reductions
  of wages. Indeed if the fall of wages and prices
  goes far, the embarrassment of those
  entrepreneurs who are heavily indebted may soon
  reach the point of insolvencywith severe adverse
  effects on investment. (Keynes 1936 264)

87
Keynes and Debt-deflation

• The method of increasing the quantity of money
  in terms of wage-units by decreasing the
  wage-unit increases proportionately the burden of
  debt whereas the method of producing the same
  result by increasing the quantity of money whilst
  leaving the wage-unit unchanged has the opposite
  effect. Having regard to the excessive burden of
  many types of debt, it can only be an
  inexperienced person who would prefer the
  former. (1936 268-69)
• Keyness focus here more physical and macro
  (impact on investment) than Fisher Keyness main
  contributions on finance relate to
• Dual Price Level hypothesis
• Analysis of expectations and behaviour of finance
  markets

88
Keynes and the Dual Price Level Hypothesis

• In most of General Theory, Keynes argued that
  investment motivated by relationship between
  marginal efficiency of investment schedule (MEI)
  and the rate of interest
• In Chapter 17 of General Theory, The General
  Theory of Employment and Alternative theories
  of the rate of interest (1937), instead spoke
  in terms of two price levels
• investment motivated by the desire to produce
  those assets of which the normal supply-price is
  less than the demand price (Keynes 1936 228)
• Demand price determined by prospective yields,
  depreciation and liquidity preference.
• Supply price determined by costs of production

89
Keynes and the Dual Price Level Hypothesis

• Two price level analysis becomes more dominant
  subsequent to General Theory
• The scale of production of capital assets
  depends, of course, on the relation between
  their costs of production and the prices which
  they are expected to realise in the market.
  (Keynes 1937a 217)
• MEI analysis akin to view that uncertainty can be
  reduced to the same calculable status as that of
  certainty itself via a Benthamite calculus,
  whereas the kind of uncertainty that matters in
  investment is that about which there is no
  scientific basis on which to form any calculable
  probability whatever. We simply do not know.
  (Keynes 1937a 213, 214)

90
Keynes and the Dual Price Level Hypothesis

• In the midst of incalculable uncertainty,
  investors form fragile expectations about the
  future
• These are crystallised in the prices they place
  upon capital asset
• These prices are therefore subject to sudden and
  violent change
• with equally sudden and violent consequences for
  the propensity to invest
• Seen in this light, the marginal efficiency of
  capital is simply the ratio of the yield from an
  asset to its current demand price, and therefore
  there i