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Basic material
What is a stock?• Fundamentals; prices and value; • Nature of stock data• Price, returns & volatility
Empirical indicators used by ‘professionals’
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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
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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?
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Read the accounts
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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….!
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Analyst
http://www.digitallook.com/
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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
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Intra-day price changes
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Intraday volatility
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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?
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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
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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
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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)
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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’
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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
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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… …..
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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
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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
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Order Book with market buy order
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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
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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
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Examine Fluctuations: S(t, ) = ln[P(t+ )/P(t)]
Price P(t)
Time t
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~8% pa
~15% pa
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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
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FT All share index 1800-2001
FTA Index
0
500
1000
1500
2000
2500
3000
3500
1750 1800 1850 1900 1950 2000 2050
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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.
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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
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Dow Jones 1896-2001Dow Jones 1896-2001
0
2000
4000
6000
8000
10000
12000
14000
1880 1900 1920 1940 1960 1980 2000 2020
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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
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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
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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)
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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
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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
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Return fluctuations Cumulative Distribution
-0.5
0
0.5
-1.00 -0.50 0.00 0.50 1.00
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Volatility Cumulative Distribution
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8