Discourses on financial markets: Mainstream models, Chaos, Panic

and Mania

Markets, Cycles and Risk

Models of market analysis, risk and forecasting

• The Fundamentalists• The Chartists• The Efficient Market

modelers • The Chaos theorists• The Historians

The fundamentalists• Oldest way to handle “risk” and understand

how markets operate• If a stock is rising or falling seek the cause in

a study of the company or the economy behind it.

• Postulate: the price of a stock , bond, derivative or currency moves because of some endogenous (or most of the time exogenous) event.

• Implicit assumption: if one knows the cause, one can forecast and manage risk

Problems with the models of the fundamentalists

– In reality causes are often obscure and not predictable

– Information can be concealed or misrapresented (internet bubble, Enron, Parmalat)

– The market mechanisms that links news to price (cause to effect) is often inconsistent (threat of war => some times dollar rises or some time dollar falls. Ex post link is clear, but ex ante there are arguments for both ways)

– Investment strategy based on fundamental is grounded on dubious principle “I know more than everybody else”.

Enter the Chartists

• Second oldest form of analysis, also called “technical”. Back in favour in the 1990s and thriving in currency markets

• Chartists are technicians who look for trend indicators in graphical charts, usually depicting price as a function of time, but often including information on intraday highs & lows as well as closing price.

• A chartist typically will want to buy into an uptrend, sell into a downtrend and stay out of the market for a sideways trend ("momentum investing").

Problems with the chartists

• Thay are all doing it• Everybody knows that

everybody else know about this or that technical aspect of the chart (“support points”, “trading range” etc.)

• Hence bets are placed accordingly• Financial astrology is not a basis for understanding financial markets

Enter the efficient market modellers

• What business schools call “modern finance”. • It emerged from maths of chance and stats• Basic concept:

– Prices are not predictable,HOWEVER– their fluctuations can be described by the

mathematical laws of chance– HENCE: their risk is measurable, and

manageable.

Some names• Harry Markowitz

– the prospect of every stock depends on two number, the reward (mean) and risk (variance of what you expect the stock will pay)

• William F. Sharpe and Capital Asset Pricing Model– Look at relation between individual stock and market. – Constructs portfolios based on stock’s β (‘beta’), the amount by

which the stock reacts to the market

– It says that the more you risk, the more you expect to be paid

– It says that the most important risk investor face is the general state of the economy reflected in how markets are doing.

the Efficient Market Hypothesis (EMH)

• stock prices follow a random walk

• percentage price deviations (returns) follow the Normal distribution, with stable mean

and finite variance

Are stock returns Normally-distributed? FTSE100: closing prices, 1985–2005.

0

1000

2000

3000

4000

5000

6000

7000

8000

31/1

2/19

85

31/1

2/19

86

31/1

2/19

87

31/1

2/19

88

31/1

2/19

89

31/1

2/19

90

31/1

2/19

91

31/1

2/19

92

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2/19

93

31/1

2/19

94

31/1

2/19

95

31/1

2/19

96

31/1

2/19

97

31/1

2/19

98

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99

31/1

2/20

00

31/1

2/20

01

31/1

2/20

02

31/1

2/20

03

31/1

2/20

04

Are stock returns Normally-distributed?FTSE100: daily price deviations, 1985–2005.

-10

-5

0

5

10

31/1

2/85

31/1

2/86

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Dai

ly d

evia

tions

, %

are stock returns Normally-distributed?

FTSE100: daily price deviations, 1985–2005.

-4 -2 0 2 4

deviation

0

200

400

600

800

1,000

1,200F

req

ue

nc

y

Mean = 0.0306Std. Dev. = 1.03986N = 5,078

Are stock returns Normally-distributed?

• Normal distribution:•• 0.0063% of observations lie more than 4 std. deviations • from the mean – approx. 1 in 16,000

• 0.000057% of observations lie more than 5 std. deviations from the mean – approx. 1 in

1,750,000

•

Are stock returns Normally-distributed?FTSE100: daily price deviations, 1985–2005, plus std. deviation bands

-10

-5

0

5

10

31/1

2/85

31/1

2/86

31/1

2/87

31/1

2/88

31/1

2/89

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Dai

ly d

evia

tions

, %

5s4s

-4s-5s

Compare for example

• Mean height for adult male is 174cm with std dev of 9.6cm.

• 4 std dev is 212cm or 7 feet

• 5 std dev is 222cm or 7 feet, 4 inches

Problems with EMM: shaky assumptions 1 . . .

• People are rational and aim only to get rich– People are not always rational and self-interested

• All investors are alike– Investors but stock sfor different reasons and different length of

time

• Price change is practically continuous– Price changes are not smooth, but they do jump.

This not only for chaotic rationales (see later) but also because 80% of quotes end in 0 or a 5, skipping intermediate digits.

. . . Shaky assumptions 2

• Price changes follow a Brownian motion– Browniam motion is a term describing the motion

of molecule in a uniformly warm medium and believed by EMM to apply to price changes. Based on:

– Independence (price changes last year or yesterday do not influence today’s price change) => wrong

– Statistical stationarity (the process generating price changes stays the same over time) => wrong

– Normal distribution (price changes follow the proportions of the bell curve) => wrong

Which chart is real?Plotting changes in stock prices

• Real

• EMH generated

• Real

• Fractal Model– (Mandelbrot)

If it is wrong, why it is used?

• “it is the benchmark to which everyone in the market refers, much the way, say, people talk abut the temperature in winter even though whether they actually feel cold also depend on the wind, the snow, the clouds, their clothing, and their health. Citigroup’s options analysts have their Black-Scholes formula in front of them all the time, in spreadsheets” (Mandelbrot 2005: 81)

Turbulant Markets

• Turbulence prima facie: erratic peaks and troughs which tend to cluster together (as in wind turbulence)

• The study of this turbulence => fractal geometry, a new branch of mathematics widely applied to a number of fields http://classes.yale.edu/fractals/Panorama/welcome.html)

• This may describe patterns (without predicting), but cannot provide explanation.

the fractal market hypothesisvs EMM

• stochastic process• vs. • non-linear (‘chaotic’) deterministic process

• ),(~ 2Nxt

)1( 11 ttt xxx

Manias and Panic: Hyman Minsky model