Lecture Eight

1
Lecture Eight

• Finance Theory
• The Capital Assets Pricing Model
• A Keynesian Critique
• A Keynesian Alternative

2
Recap

• Breakdown of Phillips curve
• Rise of neoclassicism
• Critiques of logical foundations of neoclassical
  micro
• Today
• Neoclassical foundations of finance theory
• Some problems
• An alternative view
• Fishers Debt-Deflation theory of Great
  Depressions elaborated
• Minskys Financial Instability Hypothesis
• Peters Fractal Markets Hypothesis
• Prospects for US

3
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

4
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)
5
The Capital Assets Pricing Model

• IOC reflects correlation of separate investments.
  Consider 3 investments A, B, C
• A contains investment A only
• Expected return is ERa,
• Risk is sRa
• B contains investment B only
• Expected return is ERb,
• Risk is sRb
• C some combination of a of A (1-a) of B
• ERcaERa (1-a)ERb

6
The Capital Assets Pricing Model

• If rab1, C lies on straight line between A B

7
The Capital Assets Pricing Model

• If rab1, C lies on straight line between A B

8
The Capital Assets Pricing Model

• If rab1, C lies on straight line between A B

9
The Capital Assets Pricing Model
10
The Capital Assets Pricing Model

• If rab0, C lies on curved path between A B

This is zero
Hence this is zero
11
The Capital Assets Pricing Model

• If rab0, C lies on curved path between A B

12
The Capital Assets Pricing Model

• If rab0, C lies on curved path between A B

Straight line relation
Hence lower risk for diversified portfolio (if
assets not perfectly correlated)
13
The Capital Assets Pricing Model
14
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

15
The Capital Assets Pricing Model
Efficiency maximise expected return minimise
risk given constraints
16
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...

17
The Capital Assets Pricing Model

• Defended by appeal to Friedmans
  Instrumentalism (next lecture)
• 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

18
The Capital Assets Pricing Model
19
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

20
The Capital Assets Pricing Model
Range of efficient assetcombinations after
market price adjustments more than just one
efficient portfolio
21
The Capital Assets Pricing Model

• Theory so far applies to combinations of assets
• Individual assets normally lie above capital
  market line (no diversification)
• Cant relate between ERi si
• Can relate ERi to systematic risk
• Investment i can be part of efficient combination
  g
• Can invest (additional) a in i and (1-a) in g
• a1 means invest solely in i
• a0 means some investment in i (since part of
  portfolio g)
• Some alt0 means no investment in i
• Only a0 is efficient

22
The Capital Assets Pricing Model
23
The Capital Assets Pricing Model

• Slope of IOC and igg curve at tangency can be
  used to derive relation for expected return of
  single asset

• This allows correlation of variation in ERi to
  variation in ERg (undiversifiable, or systematic,
  or trade cycle risk)
• Remaining variation is due to risk inherent in i

24
The Capital Assets Pricing Model
25
The Capital Assets Pricing Model

• Efficient portfolio enables investor to minimise
  asset specific risk
• Systematic risk (risk inherent in efficient
  portfolio) cant be diversified against
• Hence market prices adjust to degree of
  responsiveness of investments to trade cycle
• Assets which are unaffected by changes in
  economic activity will return the pure interest
  rate those which move with economic activity
  will promise appropriately higher expected rates
  of return. OREF II

26
The Capital Assets Pricing Model

• Crux/basis of model markets efficiently value
  investments on basis of expected returns/risk
  tradeoff
• Modigliani-Miller extend model to argue valuation
  of firms independent of debt structure (see OREF
  II)
• Combination the efficient markets hypothesis
• Focus on portfolio allocation across investments
  at a point in time, rather than trend of value
  over time
• Argues investors focus on fundamentals
• Expected return
• Risk
• So long as assumptions are defensible

27
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

28
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)

29
A Keynesian view

• Key issue is uncertainty, not risk
• Cannot possibly estimate expected returns far
  into future
• our basis of knowledge for estimating the yield
  ten years hence of an investment amounts to
  little... those who seriously attempt to make any
  such estimate are often so much in the minority
  that their behaviour does not govern the market.
• Instead, conventions to cope with uncertain
  future
• assume that the present is a ... serviceable
  guide to the future that the existing state of
  ... prices ... is based on a correct summing up
  of future prospects we endeavor to fall back on
  the judgment of the rest of the world which is
  perhaps better informed.

30
Keyness view

• Investors profit by picking shifts in confidence
• the professional investor and speculator are ...
  concerned, not with making superior long-term
  forecasts of the probable yield of an investment
  over its whole life, but with foreseeing changes
  in the conventional basis of valuation a short
  time ahead of the general public this
  behaviour... is an inevitable result of an
  investment market... For it is not sensible to
  pay 25 for an investment of which you believe the
  prospective yield to justify a value of 30, if
  you also believe that the market will value it at
  20 three months hence. OREF II
• Markets thus conducted by speculation on
  immediate behaviour of other speculators, rather
  than rational calculation

31
Keyness view

• Recall earlier lectures on Keynes and uncertainty
• The Stockmarket as a beauty contest and the
  third degree
• pick out the six prettiest faces the prize
  being awarded to the competitor whose choice most
  nearly corresponds to the average preferences of
  the competitors as a whole... We have reached the
  third degree where we devote our intelligences to
  anticipating what average opinion expects the
  average opinion to be.
• The practicality of rational calculation?
• Investment based on genuine long-term
  expectation is scarcely practicable. He who
  attempts it must surely run greater risks than
  he who tries to guess better than the crowd how
  the crowd will behave

32
The Price system and Asset Markets

• Normal micro theory
• Supply a positive function of price
• Demand a negative function of price
• Supply and demand independent
• If price rises
• Supply rises
• Demand falls
• Tendency towards equilibrium
• But finance markets
• Supply (of assets, shares) possibly a positive
  function of price
• Demand also a positive function of price

33
The Price system and Asset Markets

• If price of assets (shares, real estate, etc.)
  rising, demand also rises
• Buyers hope to buy and sell on a rising market
• The faster the rate of price increase (generally
  speaking) the faster the growth of demand
• Tendency to move away from equilibrium
  (fundamental value, historic price to earnings
  ratios, etc.)
• Price thus destabilises an asset market
• An alternative theory to equilibrium-oriented
  conventional finance theory needed which
  acknowledges destabilising role of asset prices
• Derived from Fisher and Keynes by Minsky

34
Fisher Keyness unlikely ally

• Conventional theory of finance an extension of
  Fishers Theory of Interest (1930)
• The rate of interest expresses a price in the
  exchange between present and future goods
• Three elements combine to determine rate of
  interest
• Subjective the marginal preference for present
  over future goods
• strong preference borrower weak preference
  lender balance determines supply of funds
• Objective investment opportunity determines
  demand for funds
• The Market equilibrium interest rate equates
  supply to demand

35
Fisher Keyness unlikely ally

• Market for loans differs from normal market
• normal market, payment made and goods exchanged
  simultaneously (in absence of credit)
• Loans goods (loaned money) exchanged now
  repayment (principal interest) occurs later
• Two special assumptions needed to eliminate this
  difference
• (A) The market must be cleared--and cleared with
  respect to every interval of time. (B) The debts
  must be paid. (Fisher 1930 495)
• Fishers book published in 1930
• In 1929, Fisher comments Stocks appear to have
  reached a permanently high plateau and then
  came October 23rd Black Wednesday

36
Alternative Finance (1) Financial Instability

• Fisher Keynes blended into alternative theory
  of finance by Minsky the Financial Instability
  Hypothesis
• partial objective to explain Great Depressions
• overall objective an alternative economics to
  neoclassical micro/macro

37
Minskys interpretation of Keynes

• Two price levels
• Commodity prices set by markup on cost of
  production
• Assets / equipment prices based on expected
  revenue
• Volatile basis for expectations essential
• Future fundamentally uncertain we simply do not
  know, so conventions developed
• Present accepted as a serviceable guide to the
  future
• Current expectations presumed correct
• Mass sentiment
• Finance demand for money
• it is ... the financial facilities which
  regulate the pace of new investment Keynes 1937

38
Minskys Hypothesis

• Economy in historical time
• Debt-induced recession in recent past
• Firms and banks conservative re debt/equity
  ratios, asset valuation
• Only conservative projects are funded
• Recovery means conservative projects succeed
• Firms and banks revise risk premiums
• Accepted debt/equity ratio rises
• Assets revalued upwards

39
The Euphoric Economy

• Self-fulfilling expectations
• Decline in risk aversion causes increase in
  investment
• Investment expansion causes economy to grow
  faster
• Asset prices rise, making speculation on assets
  profitable
• Increased willingness to lend increases money
  supply (endogenous money)
• Riskier investments enabled, asset speculation
  rises
• The emergence of Ponzi (Bondy?) financiers
• Cash flow from investments always less than
  debt servicing costs
• Profits made by selling assets on a rising market
• Interest-rate insensitive demand for finance

40
The Assets Boom and Bust

• Initial profitability of asset speculation
• reduces debt and interest rate sensitivity
• drives up supply of and demand for finance
• market interest rates rise
• But eventually
• rising interest rates make many once conservative
  projects speculative
• forces non-Ponzi investors to attempt to sell
  assets to service debts
• entry of new sellers floods asset markets
• rising trend of asset prices falters or reverses

41
Crisis

• Ponzi financiers go bankrupt
• can no longer sell assets for a profit
• debt servicing on assets far exceeds cash flows
• Asset prices collapse, drastically increasing
  debt/equity ratios
• Endogenous expansion of money supply reverses
• Investment evaporates economic growth slows or
  reverses
• Economy enters a debt-induced recession ...

42
The Aftermath

• High Inflation?
• Debts repaid by rising price level
• Economic growth remains low Stagflation
• Renewal of cycle once debt levels reduced
• Low Inflation?
• Debts cannot be repaid
• Chain of bankruptcy affects even non-speculative
  businesses
• Economic activity remains suppressed a
  Depression
• Big Government?
• Anti-cyclical spending and taxation of government
  enables debts to be repaid
• Renewal of cycle once debt levels reduced

43
Modelling Minsky

• A taste of dynamics a model of Minsky built on
  Marxs model of cyclical economy
• accumulation slackens in consequence of the rise
  in the price of labour, because the stimulus of
  gain is blunted. The rate of accumulation
  lessens but with its lessening, the primary
  cause of that lessening vanishes, i.e. the
  disproportion between capital and exploitable
  labour power The price of labor falls again to a
  level corresponding with the needs of the
  self-expansion of capital To put it
  mathematically, the rate of accumulation is the
  independent, not the dependent variable the rate
  of wages the dependent, not the independent
  variable. (Marx 1867, 1954 580-581)

44
Modelling Minsky

• Mechanism is
• high rate of growth causes high level of
  employment
• high level of employment causes increase in wage
  level
• increase in wage level reduces profit
• reduced profit reduces investment
• lower investment reduces growth rate
• lower growth rate reduces employment
• lower employment leads to falling wage level
• falling wage level restores profitability,
  restarting cycle

45
Modelling Minsky

• Minskys theory explicitly based on time and
  changes in variables over time
• Cant be modelled using simultaneous equations
  (which ignore time)
• Instead have to use
• Differential equations (rate of change of y with
  respect to time is a function of)
• Computer simulation (artificial economies with
  time-based variables)
• Differential equations (normally) show rate of
  change of one variable as a function of values of
  another.
• Much of classical economics can be described as
  verbal differential equations. An example
  Malthus on population

46
Digression Dynamics Equations

• I think I may fairly make two postulata. First,
  That food is necessary to the existence of man.
  Secondly, That the passion between the sexes is
  necessary and will remain nearly in its present
  state...
• Population, when unchecked, increases in a
  geometrical ratio. Subsistence increases only in
  an arithmetical ratio. A slight acquaintance with
  numbers will shew the immensity of the first
  power in comparison of the second.
• These can be put into verbal differential
  equations
• In the absence of food shortages, population
  grows exponentially
• Food increases linearly
• In actual differential equations, we get

47
Malthuss Population Dynamics
Births minus deaths
A small constant for high F/P ratios but rises
dramatically as F/P falls below a critical level
Percentage rate of change of population
No ceteris paribus Feedback from F to P.
Modelling this
A constant
Slope of food output
48
Malthuss Population Dynamics
Putting it all together, we get
Nonlinear negative feedback contribution from
population
Population growth in the absence of food shortages
Linear attenuating feedback from food (C is
initial level)
I dont think Malthus ever realised that this was
(roughly) the path he predicted for population...
49
Modelling Minsky

• Same type of logic needed to express Minskys
  model of finance
• Specify relationships in terms of rate of change
  of y is a function of
• Relate all elements in causal chain until it
  loops back on itself
• (Malthuss theory is incomplete here there is no
  feedback from population to food)
• No more ceteris paribus since everything
  determines everything else, but in a time
  sequence.
• So to model Minsky, we start with Marx 1867 and
  Goodwin 1967...

50
Modelling Minsky

• Causal chain
• Capital (K) determines Output (Y)
• Output determines employment (L)
• Employment determines wages (w)
• Wages (wL) determine profit (P)
• Profit determines investment (I)
• Investment I determines capital K
• chain is closed

accelerator
productivity
Phillips curve
Investment function
Depreciation
51
An Economic Model without Finance
52
A Economic Model with Finance

• Add debt
• Firms borrow when desired investment exceeds
  profits
• Debt solely used to finance investment
• Profit is now output net of wages and debt
  repayment

Debt
Interest rate
Gross Profit
Simulation again...
53
A Economic Model with Finance
54
A Economic Model with Finance
55
The Inefficient Markets Hypothesis

• Argument that investors
• react slowly to news
• over-react
• ignore reversion to the mean
• Series of good reports leads to expectation of
  more good news
• Firm valuation rises, seen as growth stock
• rise becomes self-fulfilling bandwaggon buying
• Firm cannot sustain above sector/economy
  performance indefinitely
• Initial bad news reports ignored as firm
  reverts to mean
• Finally, bear valuations set in bandwaggon
  selling
• growth stock underperforms in medium term

56
The Inefficient Markets Hypothesis

• 90 of price variability due to internal dynamics
  of speculators watching other speculators
• EMH idea of investors focusing solely upon
  expected risk/return wrong

Instead, speculators watch other speculators
57
The Fractal Markets Hypothesis

• Puzzle
• If EMH is so wrong intellectually, how come it
  almost seems right in the data?
• Solution a highly chaotic distribution is very
  hard to distinguish from a truly random
  distribution
• Chaos/Complexity
• Deterministic system (no shocks involved) which
  generates highly complex, aperiodic cycles
• Discussed in lecture on dynamics
• Applied to finance, the Fractal Markets
  Hypothesis
• Apparently random movements of stock market in
  fact mask a fractal dynamic process
• so whats a fractal?

58
The Fractal Markets Hypothesis

• A pattern produced by a highly nonlinear
  self-referential process
• Or in English
• Take an initial number
• Apply some (possibly simple but) nonlinear
  transformation to it
• Use the resulting number as the next input to be
  transformed
• Resulting time series can appear highly random,
  but at the same time
• is generated by a process with no chance (risk)
  involved
• has an underlying structure, which can however be
  very hard to discern

59
The Fractal Markets Hypothesis

• Peters applies fractal analysis to time series
  generated by asset markets
• Dow Jones, SP 500, interest rate spreads, etc.
• finds a fractal structure
• intellectually consistent with
• Inefficient Markets Hypothesis
• Financial Instability Hypothesis
• Based upon
• heterogeneous investors with different
  expectations, different time horizons
• trouble breaks out when all investors suddenly
  operate on same time horizon with same
  expectations

60
The Fractal Markets Hypothesis

• Take a typical day trader who has an investment
  horizon of five minutes and is currently long in
  the market. The average five-minute price change
  in 1992 was -0.000284 per cent it was a bear
  market, with a standard deviation of 0.05976 per
  cent. If, for technical reasons, a six standard
  deviation drop occurred for a five minute
  horizon, or 0.359 per cent, our day trader could
  be wiped out if the fall continued. However, an
  institutional investora pension fund, for
  examplewith a weekly trading horizon, would
  probably consider that drop a buying opportunity
  because weekly returns over the past ten years
  have averaged 0.22 per cent with a standard
  deviation of 2.37 per cent. In addition, the
  technical drop has not changed the outlook of the
  weekly trader, who looks at either longer
  technical or fundamental information. Thus the
  day traders six-sigma standard deviation event
  is a 0.15-sigma event to the weekly trader, or no
  big deal. The weekly trader steps in, buys, and
  creates liquidity. This liquidity in turn
  stabilises the market. (Peters 1994)

61
Conclusion

• View of finance depends on whether take
  equilibrium or dynamic view
• equilibrium
• optimum allocation of funds, rational markets
• dynamic
• speculative markets, accumulation of debt,
  possibility of crisis
• Current crises difficult, if not impossible, to
  explain in equilibrium terms
• Rapid movements in markets (e.g., sevenfold
  devaluation of Indonesian rupiah in a week by
  money markets) cant be due to similar fall in
  real productivity of Indonesian economy
• Finance and economic outcomes clearly linked
  (rather than independent as in standard theory)

62
Conclusion Asian Crisis

• Debt-deflation probable cause of Asian crisis
• Originating in Japans Bubble Economy 1987-90
• Huge bad debts carried by banks after crash of
  real estate market
• Boom in Asia partly funded by Japanese/American
  banks seeking profit after collapse of own
  markets in 90/91
• Crash in Asia amplified by free capital markets
• Currencies devalued on fear of inability to repay
  loans
• Devaluation (4-fold for Thailand, 7-fold for
  Indonesia) guarantees loans cannot be repaid
• Depression ensues
• Solution must involve repudiation of debt

63
Conclusion New York New York

• Current US economic boom (now probably over)
  underwritten by asset price boom
• Boom due to
• Euphoric expectations on Internet
• Feedback from rising prices to rising prices
• Debt Financing of share purchases
• The bust? Complicated by Mutual Funds, but
• At 351, PE ratio highest in (non-Depression)
  history
• Broad market in decline now for more than 2
  years boom focused in very narrow range of
  stocks (as in 1929)
• USA debt/output ratio 150 (vs 60 in 1929
  Fisher 1933)
• Inflation on border of deflation (as in 1929)
• one major difference Big Government
• impact discussed in Week 11