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Honours Finance Advanced Topics in Finance: Nonlinear Analysis

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Title: 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
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