Managerial Economics

1
Managerial Economics

• Lecture Eleven
• Alternative theories of finance

2
Recap

• Conventional CAPM finance theory
• Derived by applying conventional economic theory
  to finance
• Utility maximising individual, budget line of
  available investments
• BUT it neatly separates finance theory
• (Modigliani-Miller dividend irrelevance theorem
  etc.)
• Firms value independent of how finances
  investment
• Finance therefore doesnt affect the economy
• Empirical data manifestly refutes CAPM
• We need a really new theory of finance
• For complete coverage, do Behavioural Finance
  with me and Craig Ellis next semester
• But for an overview

3
The really new finance

• Two key aspects
• Economics Finance not separable
• How firm finances its investments does affect
  value
• How investment financed affects economic outcomes
• Finance does affect the economy.
• Back to Schumpeter
• Behaviour of finance markets
• Not random walk and fundamental value but
• Fractal walk speculators speculating on
  speculators
• First, Schumpeters finance-real economy link
• Entrepreneurs must borrow to finance innovations
• Credit thus plays essential role in economys
  boom/bust cycle

4
Schumpeters model money has real effects

• In Schumpeters model, entrepreneurs start new
  firms
• No retained earnings, capital, workers
• the carrying out of new combinations takes
  place through the withdrawal of services of labor
  and land from their previous employments
• this again leads us to the heresy that money,
  and other means of payment, perform an
  essential function,
• hence that processes in terms of means of payment
  are not merely reflexes of processes in terms of
  goods.
• In every possible strain, with rare unanimity,
  even with impatience and moral and intellectual
  indignation, a very long line of theorists have
  assured us of the opposite. (Schumpeter p. 95)

5
Schumpeters model money has real effects

• Conventional interpretation of money emphasises
• Money simply a veil over barter
• Money plays no essential role
• Double all prices incomes, no-one better or
  worse off
• Schumpeter accepts above as true for existing
  products, production techniques, etc., in general
  equilibrium
• But new products, new methods, disturb the
  circular flow. Money plays essential role in
  this disequilibrium phenomenon
• Affects the price level and output
• Doubling all prices incomes would make some
  better off, some worse
• Those with debts would be better off
• Including entrepreneurs

6
Schumpeters model money has real effects

• Conventional theory suffers from barter
  illusion
• Existing producers using existing production
  methods exchanging existing products
• Walras Law applies
• Major role of finance is initiating new products
  / production methods etc.
• For these equilibrium-disturbing events, classic
  money a veil over barter concept cannot apply.
• From this it follows, therefore, that in real
  life total credit must be greater than it could
  be if there were only fully covered credit. The
  credit structure projects not only beyond the
  existing gold basis, but also beyond the existing
  commodity basis. (101)
• Walras Law therefore false for growing economy

7
Schumpeters model credit has real effects

• The entrepreneur needs credit
• This purchasing power does not flow towards him
  automatically, as to the producer in the circular
  flow, by the sale of what he produced in
  preceding periods.
• If he does not happen to possess it he must
  borrow it He can only become an entrepreneur by
  previously becoming a debtor
• his becoming a debtor arises from the necessity
  of the case and is not something abnormal, an
  accidental event to be explained by particular
  circumstances. What he first wants is credit.
  Before he requires any goods whatever, he
  requires purchasing power. He is the typical
  debtor in capitalist society. (102)

8
Schumpeters model credit has real effects

• In normal productive cycle, income from
  production finances purchases credit can be
  used, but not essential
• The decisive point is that we can, without
  overlooking anything essential, represent the
  process within the circular flow as if production
  were currently financed by receipts. (104)
• Effectively, Says Law applies supply creates
  its own demand
• Aggregate demand equals aggregate supply (with
  maybe some sectors above, some sectors below)
• But credit-financed entrepreneurs very different
• Expenditure (demand) not financed by current
  receipts (supply) but by credit
• Aggregate Demand exceeds Aggregate Supply

9
Schumpeters model credit has real effects

• Credit finance for entrepreneurs thus endogenous
  not deposits create loans but loans create
  deposits
• In so far as credit cannot be given out of the
  results of past enterprise it can only consist
  of credit means of payment created ad hoc, which
  can be backed neither by money in the strict
  sense nor by products already in existence...
• It provides us with the connection between
  lending and credit means of payment, and leads us
  to what I regard as the nature of the credit
  phenomenon. (106)

10
Schumpeters model credit has real effects

• Giving credit involves creating purchasing
  power, and newly created purchasing power is of
  use only in giving credit to the entrepreneur,
  credit is essentially the creation of purchasing
  power for the purpose of transferring it to the
  entrepreneur, but not simply the transfer of
  existing purchasing power.
• The creation of purchasing power characterises,
  in principle, the method by which development is
  carried out in a system with private property and
  division of labor.
• By credit, entrepreneurs are given access to the
  social stream of goods before they have acquired
  the normal claim to it. (106-107)
• Credit irrelevant to equilibrium economics, but
  essential to disequilibrium process of economic
  development

11
Schumpeters model credit has real effects

• credit is not essential in the normal circular
  flow, because it can be assumed there that all
  purchases of production goods by producers are
  cash transactions or that in general whoever is a
  buyer previously sold goods of the same money
  value
• However it is certain that there is such a gap
  to bridge in the carrying out of new
  combinations. To bridge it is the function of the
  lender, and he fulfils it by placing purchasing
  power created ad hoc at the disposal of the
  entrepreneur.
• Then those who supply production goods need not
  "wait" and yet the entrepreneur need advance them
  neither goods nor existing money. Thus the gap is
  closed which would otherwise make development
  extraordinarily difficult, if not impossible in
  an exchange economy where private property
  prevails. (107)
• So process of innovation change breaches Says
  Law in growing, changing economy
• Demand exceeds receipts from current sales
• Difference financed by credit (debt) to
  entrepreneurs

12
Schumpeters model credit has real effects

• Says Law Walras Law apply in circular flow,
  but not entrepreneurial credit-financed activity
• In the circular flow, from which we always
  start, the same products are produced every year
  in the same way. For every supply there waits
  somewhere in the economic system a corresponding
  demand, for every demand the corresponding
  supply. All goods are dealt in at determined
  prices with only insignificant oscillations, so
  that every unit of money may be considered as
  going the same way in every period. A given
  quantity of purchasing power is available at any
  moment to purchase the existing quantity of
  original productive services, in order then to
  pass into the hands of their owners and then
  again to be spent on consumption goods. (108)

13
Aside Marx with different adjectives

• Schumpeters thinking here very similar to Marx
• Marx argued there were two Circuits of Capital
• CommodityMoneyCommodity
• Equivalent to Schumpeters circular flow
• Essentially Says Law applies
• Sellers only sell in order to buy
• MoneyCommodityMoney
• Equivalent to Schumpeters entrepreneurial
  function
• Says Law doesnt apply The capitalist throws
  less value in the form of money into the
  circulation than he draws out of it... Since he
  functions ... as an industrial capitalist, his
  supply of commodity-value is always greater than
  his demand for it. If his supply and demand in
  this respect covered each other it would mean
  that his capital had not produced any
  surplus-value... His aim is not to equalize his
  supply and demand, but to make the inequality
  between them ... as great as possible. (Marx
  1885 120-121)

• Schumpeters point
• Capitalist throws in borrowed money
• Succeeds if can repay debt and pocket some of the
  gap

14
Schumpeters model credit has real effects

• If now credit means of payment are created and
  placed at the entrepreneur's disposal, then his
  purchasing power takes its place beside the
  total previously existing.
• Obviously this does not increase the quantity of
  productive services existing in the economic
  system. Yet "new demand" becomes possible in a
  very obvious sense.
• It causes a rise in the prices of productive
  services. From this ensues the "withdrawal of
  goods" from their previous use (108)
• Aggregate Demand exceeds Aggregate Supply Says
  Law violated in move from stationary state
• Sum of excess demands negative (not zero as in
  Walras Law)
• Credit-financed demand a source of price
  inflation

15
Schumpeters model credit has real effects

• Just as when additional gas streams into a
  vessel the share of the space occupied by each
  molecule of the previously existing gas is
  diminished by compression, so the inflow of new
  purchasing power into the economic system will
  compress the old purchasing power.
• When the price changes which thus become
  necessary are completed, any given commodities
  exchange for the new units of purchasing power on
  the same terms as for the old, only the units of
  purchasing power now existing are all smaller
  than those existing before and their distribution
  among individuals has been shifted. (109)
• This inflation
• Isnt necessarily a bad thing
• Can be reversed by dynamics of economic
  development

16
Schumpeters model credit has real effects

• credit inflation .. is distinguished from
  inflation for consumptive purposes by a very
  essential element
• The entrepreneur must not only legally repay
  money to his banker, but he must also
  economically repay commodities to the reservoir
  of goods
• after a period at the end of which his products
  are on the market and his productive goods used
  up - he has, if everything has gone according to
  expectations, enriched the social stream with
  goods whose total price is greater than the
  credit received and than the total price of the
  goods directly and indirectly used up by him.
• Hence the equivalence between the money and
  commodity streams is more than restored, the
  credit inflation more than eliminated, the effect
  upon prices more than compensated for. (110)

17
Schumpeters model credit has real effects

• Furthermore, the entrepreneur can now repay his
  debt (amount credited plus interest) at his bank,
  and normally still retain a credit balance (
  entrepreneurial profit) that is withdrawn from
  the purchasing-power fund of the circular flow.
  (111)
• So dynamic view of economy
• Overturns money doesnt have real effects bias
  of neoclassicals/monetarists
• Breaches supply creates its own demand Says
  Law view of self-equilibrating economy
• Breaches Walras Law if n-1 markets in
  equilibrium, nth also in equilibrium general
  equilibrium analysis
• Links finance and economics without finance
  there would not be economic growth, but
• Finance can affect economic growth negatively as
  well as positively (if entrepreneurial
  expectations fail)

18
The really new finance

• Dynamic vision of economics overturns equilibrium
  truths
• Ditto realistic view of finance markets not
  equilibrium but disequilibrium dynamics
• Three highly unrealistic assumptions essential to
  CAPM
• Investors agree on values of all shares
• Perceptions of values are correct
• All investors have limitless access to risk free
  finance
• Outcome shares follow random walk
• Really new finance rejects all these assumptions
• Investors disagree on values of shares
• Future uncertain perceptions of future wrong
• Differing access to finance
• Outcome shares follow fractal walk

19
The really new finance

• Several as yet not integrated aspects
• Behavioural Finance
• Investors dont make rational utility
  maximising decisions when confronted with risky
  financial choices
• Inefficient Finance
• Finance markets themselves not efficient
• Minority Game
• Financial Markets as game in which you win by
  being in the minority
• Fractal Finance
• Statistical properties of markets fractal and
  power law, not random
• Last (empirical) aspect first

20
Fractal Finance

• Remember last week Fama (1969)when still
  believer in CAPMnoted large daily price changes
  tend to be followed by large daily changes. The
  signs of the successor changes are apparently
  random?
• A characteristic of fractal distributions
• Many elements interact with each other and
• Interactions nonlinear small movements cause
  large ones
• Example earthquakes
• Caused by movement of tectonic plates
• Movement of one plate against another builds up
  tension
• Earthquake releases tension in one spot
• Makes other releases elsewhere more likely
• One big movementfollowed by others
• Eventually settles down then cycle renews

21
Fractal Finance

• Results
• Earthquakes cluster
• Long period of small quakes then
• Sudden large quake
• Lots of large aftershocks
• Eventually calm returns
• Then tension builds up again before next release
• No average size earthquake
• Quakes of all scales occur
• Big quake just a small quake that does not stop
• Self-similarity
• Close up, small-scale quake effects look like big
  quakes on larger scale
• Same phenomena found in stock market data

22
Fractal Finance

• Volatility clustering
• Periods of high volatility not randomly
  distributed but clustered together
• No average size daily/weekly/yearly movement
• Averages standard deviations can be calculated
• But data does not fit means, deviations etc.
• Highly skewed
• Many more large events than predicted
• Self-similarity
• Intra-day pattern in a day looks like
• Daily pattern in a month
• Monthly pattern in a decade

23
Fractal Finance

• Example NASDAQ over two time periods which one
  is longer?

24
Fractal Finance

• Whats the point?
• Randomly generated pattern would have decreasing
  volatility as time scale increased
• Variance of random distribution scales to square
  root of time scale
• Variance of actual financial time series scales
  linearly with time
• No average scale of movement at any time scale
• Random distribution huge movements can be ruled
  out
• Actual financial time series huge movements can
  and do occur
• 10 fall of DJIA on Black Friday in 1929
• 25 fall of ASX on Black Tuesday in 1987
• 14 fall of NASDAQ in April 2000

25
Fractal Finance

• If we take a graph of the SP 500 index , and
  place it above a graph of an uncorrelated biased
  random walk with the same overall bias, at first
  glance they seem almost identical.
• When we look closer, however, we notice the graph
  of the SP 500 has occasional large fluctuations
  (e.g. the huge drop that took place on Black
  Monday in October, 1987 (when most world markets
  lost 20-30 of their value over a period of 1-2
  days).
• We do not see this kind of large fluctuation in
  the biased random walk graph because the
  probability of taking a very large number of
  random steps in the same direction (which would
  be necessary for a large fluctuation) is
  exponentially small. (Stanley, Physica A 2000 9)

26
Fractal Finance

• If market obeyed CAPM, prices would follow
  random walk along upward trend
• Deviations from trend would fit within normal
  distribution
• Defined average
• Dispersion described by standard deviation
• If market fractal, prices follow power law
• Number of movements of some size related to size
  raised to some power

27
Fractal Finance

• Basic model the sandpile (Per Bak)
• Tip sand onto ground forms a sandpile
• Lots of little local avalanches all the time
• But generally sandpile grows uniformly
• Until slope reaches some critical level
• Next sandgrain causes pile-wide avalanche
• Pile collapses to well below critical shape
• Additional sand reforms shape till critical point
• Big avalanche is a small avalanche that doesnt
  stop
• Number of avalanches of given size roughly equals
  size raised to a power

28
Fractal Finance

• Same idea in markets
• Generally rising price level
• Small crashes all the time
• Systemic critical level approached
• Next small crash sets of systemic crash
• Number of crashes (or bubbles) of given size
  roughly equals size raised to some power
• Size measure daily percentage movement of index
• Fractal market prediction number per century of
  daily crashes of (e.g.) 10 roughly equals 0.1
  raised to some power
• Take logs

29
Fractal Finance

• Power law fit Dow Jones

Power law predicts6 10 daily movementsper
century
Actual number was 8
1 means 10110events per century
-1 means 10-110 daily change

• Does this tell us anything the EMH doesnt?

30
Fractal Finance

• Power law fits stock market data

• Gaussian fit hopeless
• Far more extreme events than random change
  predicts

31
Fractal Finance

• Random walk prediction OK for small movements
• /-3 780 reality v 718 random prob.
• Hopeless for large
• /-6 57 v 1
• /- 8 11 v 1 in a million chance

-2 means 10-2 onesuch event predictedevery
century
11 lastcentury
10-6 1 event predictedevery 1 million centuries
Actual number 57
10-1.18 change
-1.2 means 10-1.26 daily change
32
Fractal Finance

• Other statistical properties found
• Tsalliss q
• Sornettes Log-periodic crashes
• Most research done by physicists
  (econophysicists)
• Characterise how the market behaves
• Large movements
• Clearly interactions between agents
• Like interactions between grains of sand in
  sandpileone grain pushes several others that
  push others chain reaction to avalanche
• Doesnt explain why market behaves this way
• Over to behavioural finance

33
Behavioural Finance

• CAPM based on rational utility maximising
  behaviour
• Expected utility hypothesis
• Given two risky outcomes, agent chooses one that
  maximises expected value

• Problem 1 You have to choose between two
  alternatives
• A 50 chance of 100 and 50 chance of nothing
• B 75 chance of 200 and 25 chance of -100
• Which would you choose?...
• Write your choice down
• A or B?

34
Behavioural Finance

• According to economic theory you should choose B
• EVA . 5 x 100 . 5 x 0 50
• EVB .75 x 200 .25 x -100 150-25 125
• Unfortunately, in experiments, most choose A over
  B
• Theory modified to take into account risk
  averse behaviour
• People seek to maximise not EV, but subjective
  utility of EV, taking risk preference into
  account
• Same basic relation applies can break down
  utility of gamble into odds times utility of
  components

• Modified theory describes people who choose A
  over B as risk averse B over A as risk
  seeking
• But still theory doesnt work experiments show
  people choose risk averse bundle some times,
  risk seeking others

35
Behavioural Finance

• Problem 2 You have to choose between two
  alternatives
• A do nothing
• B accept gamble with outcome either X or Y
• X a 50 per cent chance to win 150, and
• Y a 50 per cent chance to lose 100.
• What would you choose option A or option B?
• Would your choice change if your overall wealth
  were lower by 100?
• Write your choice down
• A or B?
• Would your choice change?

36
Behavioural Finance

• Problem 3 You have to choose between two
  alternatives
• A Lose 100 with certainty
• B accept gamble with outcome either X or Y
• X a 50 per cent chance to win 50, and
• Y a 50 per cent chance to lose 200
• What would you choose option A or option B?
• Would your choice change if your overall wealth
  were higher by 100?
• Write your choice down
• A or B?
• Would your choice change?

37
Behavioural Finance

• Majority of experimental subjects choose
• Problem 2 Adont gamble
• Problem 3 Baccept gamble
• Pattern contradicts expected utility theory
• 2A is risk-averse choice
• U(0) gt U( 0.5 x 150 0.5 x -100)U(EV75-50)
• U(0) gt U(EV25)
• 3B is risk-seeking!
• U(-100) lt U(0.5 x 50 0.5 x -200)U(EV25-100)
• U(-100) lt U(EV-75)
• 100 addition to wealth question allows next
  step
• U(0) lt U(EV25)
• Preference reversal most experimental subjects
  dont behave rationally (as economists define
  rational)
• Another example at end of lecture

38
Behavioural Finance

• Behavioural finance theorists interpretation
• People arent rational as economists define it
• Economists
• linear trade-off losses and gains weighted
  equally
• Absolute wealth position all that matters
• Economic thought involves rational non-emotional
  calculation
• Behavioural finance
• Nonlinear tradeoff losses weighted more than
  gains
• Relative wealth position matters
• Economic thought involves emotional intuition as
  well as rationality
• Intuition much faster but can sometimes be
  incorrect

39
Behavioural Finance

• Psychologist Kahneman won 2003 Nobel Prize for
  Economics
• Argues for two reasoning systems in humans
• Intuition
• Reason

• Neoclassical economics models behaviour as if
  only rational system exists, but both exist are
  used in economic financial decisions

40
Behavioural Finance

• Intuitive, emotional, relative judgments lie
  behind standard choices by experimental subjects
• the very abrupt switch from risk aversion to
  risk seeking could not plausibly be explained by
  a utility function for wealth. Preferences
  appeared to be determined by attitudes to gains
  and losses, defined relative to a reference
  point We therefore proposed an alternative
  theory of risk, in which the carriers of utility
  are gains and losseschanges of wealth rather
  than states (Kahneman Nobel Prize lecture 1456)
• In prospect theory, people react more to losses
  than gains pain of loss weighted more heavily
  than pleasure of gain

41
Behavioural Finance

• The value function is defined on gains and
  losses and is characterized by three features
• (1) it is concave in the domain of gains,
  favoring risk aversion
• (2) it is convex in the domain of losses,
  favoring risk seeking
• (3) most important, the function is sharply
  kinked at the reference point, and
  loss-aversesteeper for losses than for gains by
  a factor of about 22.5. (1456)

• Rational choice model that dominates
  conventional economics finance thus unsuitable
  for real people

42
Behavioural Finance

• The rational agent of economic theory would be
  described, in the language of the present
  treatment, as endowed with a single cognitive
  system that has the logical ability of a flawless
  System 2 and the low computing costs of System 1
• The behavioural finance model of the agent
  has a different architecture The core ideas are
• the two-system structure, intuition reason
• the large role of System 1 intuition
• and extreme context-dependence
• The central characteristic of agents is not that
  they reason poorly but that they often act
  intuitively (1469)
• Applied to stock market Haugens Inefficient
  Markets Hypothesis

43
Inefficient Markets Hypothesis

• Emphasises emotional component of investor
  decision-making
• Fad (or Schumpeterian innovation) makes some
  industry sector or firm growth stocks
• Valued above average Price to Book value (P/B)
• Other unpopular value stocks ignored
• Valued below average P/B ratio
• Growth stocks inevitably disappoint
• Value stocks often surprise
• Repeated on scale of individual firms
• Poor performing firm undervalued good one
  overvalued
• Reversion to mean causes star to disappoint,
  dog to outperform
• Series of reports needed before trend spotted

44
Inefficient Markets Hypothesis

• Institutional investors forced by need to match
  index to purchase broad portfolio
• Non-institutional investors can profit by
• Buying value stocks Low P/B ratio low earnings
  volatility
• Timing entrance/exit from market
• Many structural anomalies in stock market
  returns
• The incredible January effect
• Rise of market almost every January
• 95 of gains in December-April
• Selective buy-in sell-out works
• Some sample data from Bob Haugen (main proponent
  IMH) http//www.bobhaugen.com/

45
Inefficient Markets Hypothesis

• Haugens plot of Fama-French B/M ratios and
  future returns

Value
Growth
46
Inefficient Markets Hypothesis

• Cumulative effect of Value vs growth investment
  30-64

47
Inefficient Markets Hypothesis

• Mean reversion todays excellent companies do
  badly

48
Inefficient Markets Hypothesis

• If you invested 100 in each group of companies
  in 1981

Unexcellent Companies
297.5
181.6
Excellent Companies

• Unexcellent companies portfolio far better
• Reversion to the mean poorer companies had more
  room to improve

49
Inefficient Markets Hypothesis

• Investing in Low P/E companies far better than
  Index

50
Behavioural Finance

• Behavioural economics emphasises emotional,
  non-rational aspects of human decision making
• But 2nd explanation of behavioural economics
  results
• Economics falsely applies risk theory to
  uncertainty
• What economists call rational isnt rational in
  uncertain world
• Expected value theory originally developed to
  interpret gambling behaviour in risky games
  (roulette, cards,)
• Applied to economics after work on Games
  Economic Behaviour by mathematician John von
  Neumann economist Oskar Morgenstern
• BUT
• von Neumann Morgenstern used risk to build
  numerical theory of consumer choice

51
Behavioural Finance

• Mapping consumer preferences to arbitrary scale
  of utils using risk as guide to valuation
• Choice between
• one banana for certain or
• gamble between no banana or 2 bananas
• What odds of success needed before take gamble
  rather than sure thing?
• Say consumer accepts 70 odds of success
• Then 1 banana gives 70 of utility of 2 bananas
• Set U(0)0 U(1)1
• Then U(1)/U(2) 0.7
• U(2) 1/0.7 1.43
• Numerical measure of utility intended to be
  complete replacement for indifference curve
  analysis

52
Behavioural Finance

• It can be shown that under the conditions on
  which the indifference curve analysis is based
  very little extra effort is needed to reach a
  numerical utility. (von Neumann Morgenstern
  1944 17)
• if the preferences of the individual are not
  at all comparable, then the indifference curves
  do not exist. If the individuals preferences are
  all comparable, then we can even obtain a
  (uniquely defined) numerical utility which
  renders the indifference curves superfluous.
  (19-20)
• Cautioned their concept of risk could not be
  subjective

53
Behavioural Finance

• Probability has often been visualized as a
  subjective concept more or less in the nature of
  estimation. Since we propose to use it in
  constructing an individual, numerical estimation
  of utility, the above view of probability would
  not serve our purpose. The simplest procedure is,
  therefore, to insist upon the alternative,
  perfectly well founded interpretation of
  probability as frequency in long runs. (von
  Neumann Morgenstern 1944 19)
• i.e., risk of receiving banana had to mean
  average outcome of lots of gambles
• Banana a day for rest of your life vs
• 70 chance of 2 bananas vs zero for rest of your
  life
• Reconsider first example this way

54
Behavioural Finance

• Problem 1 You have to choose between two
  alternatives
• A 50 chance of 100 and 50 chance of nothing
• B 75 chance of 200 and 25 chance of -100
• Whatever you choose will be repeated 1000 times
• Youd have to be stupid to choose A over B
• A Win 100 500 times Nothing 500 times
• Total winnings over 1000 games 50,000
• B Win 200 750 times lose 100 250 times
• Total winnings over 1000 games 125,000
• Ditto for other problem

55
Behavioural Finance

• Problem 2 You have to choose between two
  alternatives
• A do nothing
• B accept gamble with outcome either X or Y
• X a 50 per cent chance to win 150, and
• Y a 50 per cent chance to lose 100
• A get nothing
• B 500 x 150 500 x -100 25,000
• Definitely choose B.
• Problem 3 A lose 100 for certain vs B 50 odds
  of 50 and 50 odds of -200
• A lose 100,000
• B 500 x 50 500 x -200 lose 150,000
• Definitely choose A.

56
Behavioural Finance

• Expected value calculations work when gamble
  repeated
• Dont work when only one off
• Reason? one-off gamble involves uncertainty
• With multiple gamble, you get expected value of
  gamble
• Repeat gamble 1000 times
• If true odds 7525, youll get roughly 750 of A
  and 250 of B
• With one-off gamble, you DONT get expected
  value of gamble
• You get EITHER one alternative OR the other
• Cant predict which one will actually happen not
  risky but uncertain
• Expected value of gamble irrelevant what
  matters is impact of one-off outcome
• Which is most like investing gamble repeated
  1000 times or one-off uncertain outcome?

57
Behavioural Finance

• Investment decisions subject to uncertainty, not
  risk
• Keynes emphatic about this in General Theory
• factors which determine the rate of investment
  are most unreliable, since it is they which are
  influenced by our views of the future about which
  we know so little.
• no solid basis exists for a reasonable
  calculation (154)
• So how do we decide how to invest?
• we form conventions (see Lecture 9)
• We try to minimise uncertainty
• One method payback period
• Normally derided by economists

58
Investment under uncertainty

• Economists (and some accountants!) recommend Net
  Present Value calculations instead
• Estimate future income stream
• Discount future income by rate of interest
• Undertake projects when discounted value of
  expected future income exceeds investment cost
• Basis of
• Marginal Efficiency of Investment ideas in
  macroeconomics
• Finance advice about personal corporate
  investment decision making
• Payback period derided as unsophisticated
• Not taking account of time value of money

59
Investment under uncertainty

• E.g., Gitman Financial Management text
• Although popular, the payback period is
  generally viewed as an unsophisticated capital
  budgeting technique, since it does not explicitly
  consider the time value of money by discounting
  cash flows to find present value. (Gitman 353)
• In fact payback more sophisticated because takes
  some account of uncertainty
• Immediate future much like present
• Further into future, present much less effective
  guide
• Simple rule discount far future cash flows more
  than near future
• Rather than

we need something like
Click here for more
60
Back to the Stock Market

• However unrealistic, CAPM gives model of stock
  market
• Economists need models
• In economic literature, good verbal model loses
  to lousy mathematical one every time
• Can we build realistic mathematical model of
  stock market?
• Two examples
• Trond Andresens systems engineering model
• Fundamental traders, trend traders, mood
• Physicists Minority Game
• Game won by being in minority

61
System dynamics of Stock Market

• Two main types of traders
• Fundamental value traders
• Buy shares if believe price below fundamental
  value
• Basically, long-term price to earnings ratio
• Trend traders
• Buy if share is increasing in value sell if
  falling
• Two systemic variable
• Mood of market influenced by
• short term trend optimistic if rising,
  pessimistic if falling
• Divergence from long-term trend pessimistic if
  well above trend, optimistic if well below
• Panic when random downswing causes sudden
  collapse of optimistic mood

62
System dynamics of Stock Market

• Basic mechanics of model
• Starts in some state (say below long-term value)
• Fundamental traders buy shares
• Trend traders jump on the bandwaggon also buy
• Combined demand drives price/earnings ratio up
• Upward trend causes rising optimism
• Share price rises to above long-term value
  keeps rising
• But eventually
• Fundamental traders sell in increasing volumes
• Mood sours as divergence above long term P/E
  grows
• Weight of fundamental sales plus declining mood
  sales starts downswing
• P/E ratio starts to fall system runs in reverse
• Random shocks Panic response causes crashes

63
System dynamics of Stock Market

• Generates cycle in P/E ratios

• Add random shocks panics pattern looks like
  actual stock market data

64
System dynamics of Stock Market

• Model implemented as numerical flowchart (like
  Minsky model in Vissim)

• Knowledge of differential equations nonlinear
  dynamics needed to develop this sort of model

65
Minority Game

• Computing-based model
• Basic idea model stock market as multi-player
  game
• Players bet whether market will go up or down
• Those gambling on up bid to buy
• Those gambling on down bid to sell
• Sum of buy sell positions determines actual
  movement
• If majority bids up, price rises, sellers make a
  profitminority wins
• If majority bids down, price falls, buyers get
  bargainsminority wins again
• No equilibrium strategy possible if winning
  strategy emerges, majority adopts it turns it
  into losing strategy

66
Minority Game

• Mathematics of model dynamics largely solved
• Fokker-Planck-Einstein (from quantum
  mechanics!) equation captures gt 90 of model
  dynamics
• Far too complex to understand (PhD in theoretical
  physics needed)
• Dynamics of model mimic some but not all aspects
  of real market
• often it is convenient to join the majority
  trend
• During the Internet stock follies, it was
  possible to reap considerable profits by going
  along with the explosive boom, provided one got
  off in time
• But majority situations may actually have
  minority elements embedded in them
• being different from the crowd at the right time
  is the key to success. In a booming trend, it is
  the minority of those who get off first who win,
  while others lose. (Challet et al. pp. 12-13)

67
Whew! Next week

• Overview of conventional trade theory
• Final week critique of comparative advantage
  outline of competitive advantage

68
Behavioural Finance

• Problem 4 You have to choose between two
  alternatives
• A Lose 45 with certainty
• B 5050 chance of losing either 100 or 0
• What would you choose option A or option B?
• Problem 5 You have to choose between two
  alternatives
• A 10 chance of losing 45 and a 90 chance of
  0
• B 5 chance of losing 100 and a 95 chance of
  0
• What would you choose option A or option B?
• Write your choices down
• 4 A or B
• 5 A or B

69
Behavioural Finance

• Most experimental subjects choose 4B and 5A
• Preference reversal again
• Choice of 4B implies
• U(-45)lt U(EV0.5 x -100 0.5 x 0)
  U(EV-500)
• U(-45)lt U(EV-50)
• Choice of 5A implies
• U(EV0.1 x -45 0.9 x 0) gt U(EV0.05 x -100
  0.95 x 0)
• U(EV-4.5) gt U(EV-5)
• Multiply by ten (double all prices incomes)
• U(EV-45) gt U(EV-50)
• Repeating 1000 times makes 4A 5B only sensible
  choices
• 4A 45,000 loss vs 4B 50,000 loss
• 5B 2,500 loss vs 5A 4,500 loss

70
The Payback Period

• Risk Outcome has a known chance of being one of
  a finite number of known outcomes
• Roll dice how many outcomes, what are chances of
  a 6?
• Bet on a football game?
• Recent form a passable guide
• Win/lose/draw the only possible outcomes
• Uncertainty Outcome has an unknown chance of
  being one of a possibly infinite number of
  unknown outcomes
• Odds rival firms beats you to an invention?
• Odds of discovering a cure for cancer?
• Odds new technology making your products
  obsolete?
• Odds that Wall Street will crash in October?

71
The Payback Period

• Well-developed techniques to understand and cope
  with risk
• Odds, Probability, Statistics, all based on
• Known distribution of outcomes
• Ability to repeat experiment time and time
  again
• How to understand, cope with uncertainty?
• Cant understand what we dont even know, but we
  have to cope. Investment involves the future, and
  the future is uncertain. Keynes 1937

• The game of roulette is not subject to
  uncertainty the prospect of a European war is
  uncertain, or the rate of interest twenty years
  hence, or the obsolescence of a new invention,
  About these matters there is no scientific basis
  on which to form any calculable probability
  whatever. We simply do not know.

72
The Payback Period

• Can adjusting the discount rate for riskthe
  Risk Adjusted Discount Rate (RADR)do it?
• Example Investing in drilling for oil in the
  East Timor Sea
• Risk-free discount rate 7
• Main risk (really uncertainty) military action
  in Indonesia disrupts operations
• Can we just double discount rate, say?
• Consider example cash flows
• Initial investment 1,000 million
• Expected cash flows 200 million p.a. for ten
  years

73
The Payback Period

• NPV using risk-free and risk-adjusted discount
  rates

• NPV using risk-adjusted discount rates still
  positive, so youd go ahead
• But what if disaster strikes oil rig blown up in
  military conflict in year 5?

74
The Payback Period

• Cash flows stop in Year 5

• Both methods give negative NPV
• Higher discount rate doesnt really help when
  uncertainty really affects HOW LONG you expect
  cash flows to last.

• Is there any technique which can cope with this
  aspect of uncertainty?
• The Payback Period
• Focus on making a profit and avoiding disaster

75
The Payback Period

• Focus not on risk
• Variance in returns matters
• Low variance, low risk
• High variance, High Risk
• Higher returns associated with higher risk
  (variance)
• But on uncertainty and avoidance of disaster
• Variance comparatively irrelevant
• Area below zero matters
• High return may mean low risk

76
The Payback Period
CAPM variance matters
Uncertainty downside matters
High odds of disaster
Low odds of disaster
77
The Payback Period

• NPV calculated using constant discount rate
• But possibility of disaster an increasing
  function of time
• more time for competitor to invent rival product
• greater likelihood of downturn in business cycle
  etc.
• More distant cashflows should be discounted more
  heavily than more immediate cash flows
• Simplest method
• possibility of disaster rises linearly with time
• so discount term on cash flows rises linearly
• with NPV, discount rate risk free rate (r) for
  all time
• as well, disaster discount rate needed with (b x
  t) term (b a constant) chance of disaster grows
  with time (approximation only actual situation
  more complex still)

78
The Payback Period

• NPV formula in discrete form is

Expected value
Inflow in year i
Discount rate

• In continuous time form this is

Cash flows as a function of time

• If disaster strikes at time s, then the NPV of
  cash flows only will be

• Since all cash flows after time s are zero
  (ignoring disaster related negativese.g., Exxon
  Valdize cleanup costs)

79
The Payback Period

• s can vary between t0 (disaster immediately) and
  tinfinity (no disaster ever).
• Have to sum this over all possible values
• If disaster at time s is a rising function of
  time

• Sum of all possible values up to time t is
  integral of this over time

• This gives us a new factor by which NPV can be
  multiplied to take account of possibility of
  disaster at any time in the future

Complicated integration actually needed to get to
this point
80
The Payback Period

• Multiplied by a probability of disaster factor
  which rises very sharply as time goes on

• Expected value of cash flows when disaster
  explicitly allowed for

• Normal NPV term

• Disaster term has little effect early on
• But eventually totally dominates discount term

81
The Payback Period
Discount reduces value to 60 nominal after 10
years
Disaster reduces value to 8 nominal after 10
years
82
The Payback Period

• An example
• Two projects A and B
• Same Initial investment cost of 100 million
• A has expected cash flows which
• Start in year 1 at zero and rise to 25 million
  by the years end
• Rise at 25 p.a. till year 8, then stop
  completely
• B has expected constant cash flows of 50 million
  p.a.
• Compare projects using
• NPV with discount rate of 5
• NPV with discount rate of 5 AND disaster
  probability of 5

83
The Payback Period

• Formula for continuous time discounting is

• For A, start is 1, end is 8, C(t) is?

• Equals zero in year 1, 25 m at end of year 2
• Start date of 1 gets round -25 m value for
  beginning of year 0

• B is much simpler

84
The Payback Period

• On NPV grounds, A is much better than B

• But when the possibility of disaster is
  considered

85
The Payback Period

• Values drastically lower than NPV levels
• strong impact of uncertainty
• Priority reversed
• more immediate cash flows of B preferred to
  higher but delayed cash flows of A
• Almost the same result for less accurate discrete
  formulas
• As with discount, discrete disaster term
  approximates continuous term

86
The Payback Period
Using these discrete formulas
A is the hands-down winner
B now preferred, as with continuous case
87
The Payback Period

• Taking stock
• NPV formula is

Discounts, but ignores issue of uncertainty
or

• Uncertainty-aware formula is

or
Discounts and makes some allowance for uncertainty
Which is more sophisticated? No contest!
88
The Payback Period

• Do businessmen use anything so complicated?
• Of course not
• (but might expect their financial advisers to do
  so!)
• Is there anything businesses commonly use that
  approximates to this?
• Yes The Payback Period
• Payback period
• Puts maximum time M allowed for project to cover
  initial costs
• Ranks projects within time limit on basis of
  expected revenues
• We can relate M to previous formulas and idea of
  probability of disaster D striking before payback
  period M

89
The Payback Period

• Take the disaster weight at M as indicator of
  possibility of disaster-free operation up until M

• Subjective possibility of a disaster D before M
  is thus

• This lets us derive b from D and M

Using logs

• How to interpret D?

90
The Payback Period

• Firm willing to accept a very high acceptable
  risk of disaster applies a very low uncertainty
  discount to future cash flows
• So high acceptable level of D (say, acceptance of
  95 chance that disaster will occur before
  payback period M)
• translates as very low level of D actually
  applied to future cash flows (5 for acceptable
  level of 95)

Acceptable level of disaster (failure to payback
within M years) to firm
Uncertainty discount applied to expected future
cash flows
91
The Payback Period

• An example
• Firm has WACC of 10, payback period of 4 years,
  accepts projects with 95 chance of succeeding
  within payback period
• Same as accepting projects with 5 or less chance
  of disaster
• Therefore

• So we have derived b (argument in
  uncertainty/possibility of disaster function)
  from
• maximum acceptable payback period M
• Possibility D of disaster (not paying back
  investment) before M
• Disaster odds function thus incorporates
  uncertainty
• How to interpret b?

92
The Payback Period

• b an argument in expression

• Expression returns a number
• M is dimensioned by time and is squared
• Thus b must be dimensioned by time-2

Define T

• Dimensions cancel out so that T is a period of
  time
• using previous example

In general
93
The Payback Period

• Interpreting T
• Something like the horizon of uncertainty
• Time so far in the future (subjectively for given
  firm) that all bets are off credence given to
  hypothetical cash flows after time T drops off
  rapidly.
• Putting this all together
• M shows maximum acceptable payback period
• D shows maximum acceptable risk of disaster
  before M
• Together these yield T, horizon of uncertainty
  for this firm
• These determine uncertainty-aware discounting
  function

94
The Payback Period
Discrete form

• This function far more sophisticated than simple
  NPV term
• In uncertain world, payback rules!

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