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?

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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….!

Analyst

Giga amounts of financial data are now available Since 19 th 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 19 th 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 Price allows execution of maximum volume of orders with minimal residue left unexecuted consistent with order limits

Order Book All sell orders up to 162 executed Buy order at 162 executed only in part ie 200 out of 300 Sold.Remainder lapses or new price is negotiated 162.2

Order Book with market buy order

Now all demand with limit of 163 executed out of 300 sold Order 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

FT All share index

Thomas Robert Malthus 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: ;

Dow Jones

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? Z D (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)

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

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