Basic material

What is a stock?• Fundamentals; prices and value; • Nature of stock data• Price, returns & volatility

Empirical indicators used by ‘professionals’

Investors Fundamental investors

• Value investors

• The Zulu Principle, Making Extraordinary- Profits from Ordinary Shares, Jim Slater, Orion

Technical analysts• Noise traders, chartists

• Investors Chronicle Guide to Charting, Alistair Blair, FT Pitman

Fundamental Analysts ask

Is the economy heading up or down? Is the sector likely to follow a different path from

the economy as a whole? What profits has the firm made over the past few

years? What do I think about future trading prospects? Based on the profit forecast, what will future

earnings be? From the earnings, what is the PE? What is the PE likely to be in future? On the basis of expected earnings, dividends and

PE, are the shares cheap or expensive? Is the firm financially sound?

Read the accounts

Technical analysts

Follow the charts rely on price

history and trends Assess

‘momentum’ Look for relative

strength, support and resistance levels

• Heads, shoulders, necklines, tops, spikes, islands….!

Analyst

http://www.digitallook.com/

Giga amounts of financial data are now available

• Since 19th century data recorded on daily basis• Since 1984 sampling rate of <1minute• Since 1993 ‘tick-by-tick’ or transaction by

transaction• In 1963 Cotton price study, Mandelbrot used 2000 points• In 1995 S&P study he used 500,000 points• In 1999 NYSE+1000 companies Stanley et al used 40,000,000

points

• Statistical analysis is essential for• fundamental understanding of market dynamics• Applied studies of option pricing and portfolio

management

Intra-day price changes

Intraday volatility

Scales and reference units• In physics:

• reference units maintained and improved by selected laboratories – metrology

• In finance: • Units (currencies) fluctuate • Events (transactions) occur at random times

with random intensity!• Need to consider both price and time scales….? • tick time?

Time Scales• Physical time

• Well defined

• Trading time: is it similar..?• Global markets now active 24 hours for major stocks and

currencies• Remain closed weekends and holidays so how do we model:

• closed markets • arrival of news over weekend• Closure-closure studies show variance between successive

days is ~20% lower than similar values across weekend

• Different investor time horizons• Different strategies for trading

• Market activity implicitly assumed to be uniform during trading hours but both volume and no. of contracts varies

Tick time

• *I-1, *I, *I+1, *I+2, *I+3,…….• Transactions recorded ‘tic-by-tic’. • Maybe define time in terms of transactions and

time between transaction eliminated.• Or define probability distribution associated with

waiting times• Sabatelli et al Eur J Phys 19th century Irish data and

Montroll CTRW

• Volume of transactions remains as random variable

• In general, care should always be taken when comparing different results

Price Formation at the Stock Exchange

Determined by supply and demand Price quoted as bid and ask

• Bid: price at which trader is willing to buy• Ask: price at which trader is willing to sell• Bid-ask spread depends on liquidity (ease

with which stocks are traded)

Market order Executed when a matching order

arrives But price may change during time

investor takes investment decision and execution of order• Market order is ‘unlimited’

Limit order Executed only when market price is

above (or below) a specified threshold

Order only executed when market price is such that it can be executed

Kept in order book until this time or until expiry

Stop order Triggered when market price reaches

predetermined threshold Stop-loss issues unlimited sell order when

price falls below threshold Protection against unlimited losses NB No guarantee, order will be executed AT or

even close to the threshold set (problem during crashes)

Stop-buy issues unlimited buy order when… …..

Price formation at auction

Orders received Buy, Sell,

volume and limit price Market order

• Limit price infinity for buy

• Limit price zero for sell

,1 ,

1

2

, ,2 ,

,

....... buy o

....... sell orders

rders

L L

L L m

L

L

mS

S S S

S S

1

1

( ) ( ), 1,..

( ) ( ), 1,....

..k

k b ii

k

k s ii

O

D S V S k

S V S

m

k m

Price allows execution of maximum volume of orders with minimal residue left unexecuted consistent with order limits

Order Book

Cumulative Order Volumes

0

200

400

600

800

1000

1200

1400

1600

159 160 161 162 163 164 165

Price

Cu

mu

lati

ve v

olu

mes

All sell orders up to 162 executedBuy order at 162 executed only in part ie 200 out of 300Sold.Remainder lapses or new price is negotiated

162.2

Order Book with market buy order

0

200

400

600

800

1000

1200

1400

1600

1800

2000

158 160 162 164 166

Price

Ord

er

Vo

lum

es Demand

Supply

Demand includingmarket order

Now all demand with limit of 163 executed

162.5

100 out of 300 soldOrder completed in part

Market maker seeks to damp out demand Continuous trading

Pretrading• Closed to traders

Matching• How to deal with new orders?• How to deal with crashes. Booms?

Closing auction

Examine Fluctuations: S(t, ) = ln[P(t+ )/P(t)]

Price P(t)

Time t

~8% pa

~15% pa

FTSE Closing Price

0

1000

2000

3000

4000

5000

6000

7000

8000

1990-05-07

1993-01-31

1995-10-28

1998-07-24

2001-04-19

2004-01-14

2006-10-10

Date

FT All share index 1800-2001

FTA Index

0

500

1000

1500

2000

2500

3000

3500

1750 1800 1850 1900 1950 2000 2050

Thomas Robert Malthus 1766-1834

• dP/dt P• P ~ exp(t)

• Could Log P =A t +B be a useful first approximation?

• Maybe… but we are still left with fluctuations.

Ln FTA: 1800-1950;1950-2001

Ln(FTA) = 0.0043T - 4.7942

R2 = 0.426

1.7

2.2

2.7

3.2

3.7

4.2

4.7

1750 1800 1850 1900 1950 2000

Ln

FTA

Ln FTA = 0.0767t - 145.66

R2 = 0.955

0

1

2

3

4

5

6

7

8

9

1930 1950 1970 1990 2010

Ln

FTA

Dow Jones 1896-2001Dow Jones 1896-2001

0

2000

4000

6000

8000

10000

12000

14000

1880 1900 1920 1940 1960 1980 2000 2020

Ln FTA 1800-2001 Ln DJ 1896-2001

Ln DJ~ 0.061t - 114

R2 = 0.93

Ln FTA = 0.065t - 122.3

R2 = 0.92

Ln FTA = 0.004t - 4.5

R2 = 0.33

2

3

4

5

6

7

8

9

10

1780 1830 1880 1930 1980

What is an appropriate stochastic variable for fluctuations of financial time series?

• Simple difference?• Z(t) = P(t+Δ) – P(t)

• Use of discount factor?• ZD(t) = {P(t+Δ) – P(t)}D(t)

• What to choose for D?

• Rate of return?• R(t) = {P(t+Δ) – P(t)}/P(t)

• Most widely used is• S(t) = Ln P(t+Δ) –Ln P(t) • = Ln{P(t+Δ)/P(t)}• Deals with discounting in an

approximate sense

Z,R,S If P(t+Δ)~P(t) or Δ« t then S(t) = Ln[P(t+Δ)/ P(t)] ~R(t)

-1

-0.5

0

0.5

1

1.5

1780 1880 1980

R(t)

S(t)

-600

-400

-200

0

200

400

600

800

1780 1880 1980

Z(t)

R(t)

S(t)

Z(t) v S(t)

If Δ « t then S(t) = Ln[P(t+Δ)/ P(t)] ~R(t)

• The graphs below illustrate the two functions for the FTSE over the period 1992 - 99

FTA (Annual Z Return-mean)

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1800 1850 1900 1950 2000

FTA Annual volatility

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1800 1850 1900 1950 2000

Average 0.024

Return fluctuations Cumulative Distribution

-0.5

0

0.5

-1.00 -0.50 0.00 0.50 1.00

Volatility Cumulative Distribution

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8