Financial Economics. Lecture 6. Stephen Kinsella. Dept. Economics, University of Limerick.

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1 Financial Economics Lecture 6 Stephen Kinsella Dept. Economics, University of Limerick. stephen.kinsella@ul.ie February 10, 2010 Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

2 Agenda Last Time: 1 More on Limit orders and market making 2 profit and loss in market making This time: 1 Finish off limit orders 2 Econophysics 3 Connect to probability theory/portfolio analysis Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

3 In the news: 1 IMF: NAMA won t get banks lending 2 Markets generally up, but FED says credit tightening on the way. 3 Ireland: government tax revenues have fallen by EUR 700 million from EUR 3.7 billion in January 2009 to EUR 3 billion in January (Not sure if I mentioned this before.) 4 Euro is weakening speculation buildup? Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

4 Part I Limit Order Markets, yet again Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

5 Limit Order Markets Definition (Limit Order) A limit order is a precommitment (t, j, x, p) made on a date t to trade up to a given amount x of some asset j at a limit price p. Limit Orders very important Limit and market orders constitute the core of any order-driven continuous trading system (eg NYSE, London Stock Exchange, Euronext, Tokyo and Toronto Stock Exchanges, as well as all the ECNs) Issues with limit orders 1 Inventories/Waiting costs matter, might lead to uncertainty 2 Imposes a queuing discipline: first in, first out. That rewards first-movers providing liquidity at a given price. 3 Idealized supply and demand markets, but microstructure of actual markets really matters. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

6 Another Example. In Class exercise. Lesson Real markets need financial intermediaries to work effectively. Examples: brokers, credit rating agencies, dealers, investment banks, insurance companies, pension funds, savings banks, closed and open ended mutual funds, private banks, venture capitalists, finance houses and commercial banks. Everyone, basically :). Stephen Kinsella (University of Limerick) EC4024 February 10, / 23 Consider this limit order market. Price Limit Order Buy Limit Order Sell. = =

7 Spread Vs Drift Definition (Drift) Recall the spread is s = p b p o. The drift is the change p q = p i = p i 1 = d of the mean quote p oi + p bi /2 = p i from one quote to the next. Example Start with a spread (29.5, 30). For every buy you make, drop both quotes by 0.5. Here the drift is exactly the same as the spread. Definition (Profit) N No. transaction Profit is 2 = (spread drift) ( size of mkt), where size is the number of assets (shares, etc) they have. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

8 Example Example Say you want to buy a stock somewhere in the price range $18 $39. Trading happens in modest enough lots of 10 rounds per days for 250 trading days. Let the drift always be half the spread. MM makes profit of N = (10 250) 2 Why does drift matter? (spr = 1 dr = 1/2)size = 100rd.lots = $62, 500. Drift gives MM his buffer over a large quote range, lends liquidity. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

9 Limit orders and probability An interesting confluence It turns out price and time priority of a limit order translate directly into a probability distribution over execution timing and liquidity. We can use probability to understand these markets. But first, econophysics. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

10 Part II Econophysics Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

11 Econophysics [See: 1 Eugene Wigner: Invariance Laws, non-violable laws of nature, eg Gravity/Inertia. Base entire (empirical) theories on these invariants. 2 Basic idea: a mathematical law cannot be discovered from empirical data unless something is repeated systematically. 3 Karl Popper: you re not doing science unless you can falsify: Falsifiable models have no free parameters to tweak that would make a wrong model fit adequate data. 4 Basis for modern econ. theory: 1 The optimization principle. People try to choose the best patterns of consumption they can afford, and/or 2 The equilibrium principle: prices adjust until the amount that people demand of something is equal to the amount that is supplied. 5 Falsifiable finance models: empirically based. 6 falsifiable classes of market dynamics models deduced directly from empirical data. Apply to Money, income, wealth, and the stock market, etc. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

12 Part III Probability Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

13 Risk 1 All markets bear risk. One wouldn t gamble without it. 2 Risk is measured by the expectation of loss and the variance of the gamble. 3 People have different preferences over risk-loving, averse to some degree, etc 4 Market makers should look for volatile stocks to make $$. Why? Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

14 Forecasting & Prediction 1 Forecasting and predibction not something economists of any repute do. (but please do buy Ireland in 2050 :) 2 Prediction means, literally, to speak in the future tense. So, useless. Anyone can do that. 3 Want to profit from prediction? Need something predictable (tides/weather/sun rises/) 4 All you actually need to be is right(-er) than the other predictors though. 5 Statistically: want to gain info on the first moment of the probability distribution of price changes. If you can do this better than most people, you are sorshed, loike. 6 No-one actually cares about mean squares, vix, etc: they want to back out calculations where the profit it. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

15 Random Walks 1 Examine sequences on daily, weekly, monthly price series. 2 Data: high/low closes, and volume. 3 Hypothesis: Expected change in prices is zero. 4 OR: it is impossible to systematically exercise good judgement in the securities markets. 5 OR: The chance of a stock s future price going up is the same as it going down. A follower of random walk believes it is impossible to outperform the market without assuming additional risk. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

16 Dick and Jane Figure: Dick and Jane Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

17 Example 1 2 parameters: expected value E(X ) and variance σ(x). Dick and Jane go to school. Get from home to school via winding path. 2 pennies. 2 heads come up, if you re dick, you go 2 steps forward. 1 head, 1 tail, you go 1 step. 2 tails, you sit still. There are traps, you land in one, go back to start. Or: Prob(HH) 1/4, S = 2, Prob(HT) 1/2, S = 1, Prob(TT) 1/4 S = 0. E(s) = 1/4(2) + 1/2(1) + 1/4(0) = 1 and σ 2 s = E(s) 2 (E(s)) 2 = 1/ /2 1 1 = 0.5. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

18 Expected advance and dispersion for j steps of random walk 1 Call P(i) the position in the walk after i steps 2 Say we start at P 0, move in steps of s j size. P(i) = P 0 + i s j. (1) Expected position is the sum of expected values of each step (assuming independence) E(P i ) = P 0 + E( i s j ) = P 0 + j=1 j=1 i E(s j ) = P 0 + j=1 i h j (2) j=1 Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

19 Example Dispersion after i steps yield the classic result that the sum of i independent variables is the sum of their variances. i σ pi = E(Pi 2 ) (E(P i ) 2 ) 1/2 = ( δj 2 ) 1/2 (3) We can express the actual position of a price after i steps. First assume that each step has the same value and dispersion (you don t need to but the result is cooler this way): then j=1 σp i = iδ, E(P i ) = P 0 + ih. (4) P(i) = P ( 0) + i s j = P 0 + ih ± iδ (5) j=2 Or: the actual random walk P(i) at the ith step is equal to the starting position plus the i steps, a straight line of slope h, and an uncertainty of iδ. Brownian motion is just continuous time version of this. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

20 Examples [Mathematica notebooks] Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

21 STOP! Write down 2 things you remember from today. Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

22 Next time 1 Macro descriptions of markets with random walk properties. 2 Portfolio analysis 1: Capital Asset Pricing model. Reading: (1, Chapter 4) Stephen Kinsella (University of Limerick) EC4024 February 10, / 23

23 References [1] Keith Pilbeam. Finance and Financial Markets. Palgrave-Macmillan, 2nd edition, Stephen Kinsella (University of Limerick) EC4024 February 10, / 23