Modelling Financial Markets

Transcription

1 Modelling Financial Markets -What Works -What Doesn t -What we Don t Know Laurence Irlicht Victorian Funds Management Corporation V I CT ORI AN F U N D S M A N A GE MENT C O R P ORATION

2 Disclaimer: Any relationships detailed in this presentation are based on analysis and on particular historical data. The analysis or the data may be subject to errors or inaccuracies, and the relationships estimated from the data are at best approximations and may not hold at all outside the period analysed. Regardless of whether there are or are not any errors in the data or estimated relationships, such relationships may or may not hold in the future. Any techniques, ideas, methods, relationships, algorithms, or other information in this presentation are presented only as examples and are not intended to be used in any fashion whatsoever. If any person or organisation or any other entity decides to use anything arising from this presentation they do so at their own risk. We do not suggest that any information, ideas, algorithms, relationships or anything else in this presentation are useful for any particular purpose whatsoever. Any forecasts (including but not limited to forecasts of risks or returns) in this presentation may be affected by inaccurate assumptions, changing situations, risks, unforeseen events or other things. So actual outcomes may be significantly different to predictions. The author of this presentation believes that the information provided is correct at the time of compilation but does not warrant the accuracy of that information. Performance information is historical. Performance returns may vary. Past performance is not indicative of future performance. This presentation should not be construed as offering financial advice. The author disclaims all responsibility for any loss or damage which any person, organisation or other entity may suffer from reliance on this information or any opinion, forecast, conclusion, idea, method, algorithm or recommendation or anything else in this presentation whether the loss or damage is caused by any fault or negligence on the part of the author or otherwise. 2

3 Outline: 1. Properties of Financial Markets and their Models 2. Philosophy of Financial Market Modelling 3. Types of Models Used 4. The Model versus Reality 3

4 Properties of Financial Markets 1. In any modelling you must know your domain, to know when your model will / won t work 2. Financial Markets are different because the modelling of your competitors will directly affect the behaviour of the market 3. Market Efficiency argument If it is possible to make money from a relationship then people will keep doing it till the relationship arbitrages away But If everyone believed in market efficiency then opportunities would keep arising More Reasonable: Market Efficiency is not True or False ; there is a level of Market Efficiency which is in equilibrium (cost/reward for each artefact) 4

5 Understanding Markets Example. Thought Experiment 1: Consider your personal portfolio. The market drops by (10%,20%,30%) in a day. What would you do? Cut your losses? Use this as a buying opportunity? Thought Experiment 2: You believe the market is undervalued. You are long futures. The market drops by (10%,20%,30%) in a day, providing an associated margin call. What would you do? Implication: We may be able/choose to hold our position to a certain loss, after that our decisions may be different. So markets have feedback, and we cannot know what will happen until we are there. 5

6 Property 1: Changing Relationships 100% Rolling 12Month Correlations with S&P/ASX300 50% VALUE 0% -50% May-97 May-98 May-99 May-00 May-01 May-02 May-03 May-04 Gold Property Trusts SP % Relationships can exhibit significant drift, or jump discontinuities, or just change

7 Property 2: Non Normality (or Non any other distribution) Example (S&P500) 20% S&P500 Daily Returns 10% 0% % -20% 2σ 4σ 6σ 7

8 Property 3: Things outside your domain can affect the results 1. Geopolitical 2. Environmental 3. Health 4. ANYTHING Many models try to immunise against such affects to purely capture the effect you have found. (Pairs Trading). 8

9 Property 4: Things can change Quickly and Dramatically! 9

10 What do we know about markets? (Summary) 1. Things are changing all the time Don t expect stationarity 2. Markets are not a closed system Any event noted by people can affect markets (in unexpected ways) 3. The dynamics may change within the domain / over time So - we won t know till we get there 4. Data is NOISY. 5. Perceived relationships may or may not exist Implication: All predictions will be inaccurate, and so our use of that Information must be robust to such issues. 10

11 Outline: 1. Properties of Financial Markets and their Models 2. Philosophy of Financial Market Modelling 3. Types of Models Used 4. The Model versus Reality 11

12 Old Macdonald s Conundrum If you keep betting the farm on situations where you re almost sure to make a small profit, but each time have a small probability of losing the farm, eventually you won t have a farm If you underestimate the risk of losing the farm, it may happen sooner than you think. Ed Thorpe The Distribution of Stock Price Changes, Wilmott Magazine. 12

13 Aspects which are Modelled 1. Prediction Returns, Risks, Dynamics, Relationships (if x then y) 2. Valuation Derivatives, Securities, Indices 3. Explanation Market Dynamics, Portfolio Performance, Decision Analysis 4. Optimization Portfolio/Trade design for particular dynamics or return distributions 13

14 What makes a Believable model: 1. As simple as possible and as complex as needed 2. Intuitive (matches what we know/believe) Behavioural Finance Valuation Theory Know when/why it works 4. Robust

15 Optimality is Nice Robustness is Optimal! 1. Optimality refers to performance under Assumed Conditions 2. Robustness refers to performance outside of the Assumed Conditions 0. 6 O p t i m a l R o b u s t

16 What makes a Robust Model: 1. Works across many time periods 2. Works across many market conditions 3. Not sensitive to parameter changes 4. Robust to Outliers 5. Adaptive to change 6. Diversification 7. Graceful Degradation

17 Traps - But it Back-Tested beautifully Data Mining (spurious relationship) 2. Structural Change 3. Temporary Deviation 4. Bad Data Earnings Estimates Economic Series Outliers 5. The relationship never existed...

18 Outliers... liars The importance of simply Graphing the data cannot be overstated

19 Issue: Cause and Effect 1. Over the past x years, the number of televisions in Australia has risen strongly 2. Over the past x years the Australian dollar has risen against the US Dollar Therefore the Aussie dollar is negatively correlated with the amount of TV we watch.. This is obviously not causal. Both have moved for different reasons. The problem is that statistics may show a significant relationship. Naive solution is to assume that taking the first derivative will solve this problem (removing trend component or reducing to stationary series). This may not necessarily work.

20 Sometimes Data can Lead Understanding 1. Consider an Australian company selling commodities in $USD. 2. Would you expect the stock price to drop if the $AUD rises? (Since you get less $AUD per $USD?) 3. But What if there was a relationship between the $AUD and commodity prices? (It could go the other way.) 20

21 What can we learn from this? 1. We require Understanding (Data to Outcome) What caused the 2% Increase in weight to XYZ? 2. It is useful if relationships can make sense Enables us to trust them Generalisation: Statistical Strength + Fundamental Rational 3. Sensitivity Analysis is Imperative Minimise the impact of noise on the output 21

22 Outline: 1. Properties of Financial Markets and their Models 2. Philosophy of Financial Market Modelling 3. Types of Models Used 4. The Model versus Reality 22

23 You almost need a model to choose the model to use Linear Regression - most common, but limited 2. Neural Networks - hard to attribute 3. Co-Integration - fits some market behaviour 4. Copulas - show promise 5. Chaos Theory - Do you believe it? 6. Kalman Filtering - Naturally Adaptive 7. Non-Parametric Regression - (too?) Flexible 8. Markov Models -Intuitive Logic 9. Decision Trees - Intuitive 10. Advanced Signal Processing - shows promise 11. Mixture and Regime Shift - hard to know when AND MANY MORE No model is universally best, each is suited to a particular situation... Information Theoretic Techniques (such as MML) can be a help here.

24 Outline: 1. Properties of Financial Markets and their Models 2. Philosophy of Financial Market Modelling 3. Types of Models Used 4. The Model versus Reality 24

25 The Model is Not Reality "In theory, theory and practice are the same. In practice, they are not." Lawrence Peter Berra aka Yogi Berra (American Baseball player and manager) The trick is to know when and how much to trust the model 25