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Managerial Economics

- Lecture Eleven
- Alternative theories of finance

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

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

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)

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

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

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)

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

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)

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

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

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)

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

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

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

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)

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)

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

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

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

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

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

Fractal Finance

- Example NASDAQ over two time periods which one

is longer?

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

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)

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

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

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

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?

Fractal Finance

- Power law fits stock market data

- Gaussian fit hopeless
- Far more extreme events than random change

predicts

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

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

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?

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

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?

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?

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

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

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

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

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

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

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

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/

Inefficient Markets Hypothesis

- Haugens plot of Fama-French B/M ratios and

future returns

Value

Growth

Inefficient Markets Hypothesis

- Cumulative effect of Value vs growth investment

30-64

Inefficient Markets Hypothesis

- Mean reversion todays excellent companies do

badly

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

Inefficient Markets Hypothesis

- Investing in Low P/E companies far better than

Index

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

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

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

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

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

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.

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?

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

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

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

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

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

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

System dynamics of Stock Market

- Generates cycle in P/E ratios

- Add random shocks panics pattern looks like

actual stock market data

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

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

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)

Whew! Next week

- Overview of conventional trade theory
- Final week critique of comparative advantage

outline of competitive advantage

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

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

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?

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.

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

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?

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

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

The Payback Period

CAPM variance matters

Uncertainty downside matters

High odds of disaster

Low odds of disaster

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)

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)

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

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

The Payback Period

Discount reduces value to 60 nominal after 10

years

Disaster reduces value to 8 nominal after 10

years

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

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

The Payback Period

- On NPV grounds, A is much better than B

- But when the possibility of disaster is

considered

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

The Payback Period

Using these discrete formulas

A is the hands-down winner

B now preferred, as with continuous case

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!

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

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?

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

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?

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

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

The Payback Period

Discrete form

- This function far more sophisticated than simple

NPV term - In uncertain world, payback rules!

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