OPTIMIZATION AND FORECASTING WITH FINANCIAL TIME SERIES

Transcription

1 OPTIMIZATION AND FORECASTING WITH FINANCIAL TIME SERIES Allan Din Geneva Research Collaboration Notes from seminar at CERN, June 25, 2002

2 General scope of GRC research activities Econophysics paradigm Research areas Applications Mathematics/Physics Statistics Economic data Risk management Financial forecasting Data analysis Models Software Patents CERN Technology Transfer General know-how Intellectual property Patents/Start-ups

3 The investment problem Experimental evidence Decision process Actions Databases & real time Fundamental analysis Historical time series Theory Models Software Buy/Sell Portfolio selection Risk assessment

4 Using financial time series Optimization USD/EUR ABB Statistical analysis Modelling Portfolio selection Asset allocation Risk management Forecasting SP500 Buying Selling Rebalancing

5 Return and risk Discrete time series of prices for one asset: P i at time T i, i = 1 to N Returns: R i = P i / P i-1-1 Expected return: R = Σ i R i / N Risk as variance: V = Σ i (R i - R) 2 / N Construct portfolio of M assets with weights: W j, j = 1 to M and Σ j W j = 1 Portfolio return R' = Σ j W j * R j and variance V' Maximize function F over W for each risk averseness parameter λ: F(W) = λ * R' - (1 - λ) * V' Efficient frontier 1.80% 1.60% Return 1.40% 1.20% 1.00% 0.80% 1.70% 1.80% 1.90% 2.00% 2.10% Risk

6 Default asymmetric risk measure Downside Risk Measure 2.50% 2.00% Downside risk 1.50% 1.00% 0.50% 0.00% -5.00% -3.00% -1.00% 1.00% 3.00% 5.00% Excess return

7 Reduce problem to linear-quadratic programming without or with constraints Alternative Monte-Carlo evaluation Case of inexact input data: Robust optimization instead of sensitivity analysis stochastic programming Ellipsoidal uncertainty set leads to tractable problem

8 Excess return distribution with low downside risk Sub-optimal asset allocation Excess return distribution 25% 20% Probability 15% 10% 5% 0% -9% -7% -5% -3% -1% 1% 3% 5% 7% 9% Excess return

9 Sub-optimal asset allocation Efficient frontier with test portfolio 2.70% 2.50% 2.30% Return 2.10% 1.90% 1.70% 1.50% 1.50% 1.70% 1.90% 2.10% 2.30% 2.50% Risk

10 Performance testing of allocation strategies Performance of test portfolio 140% 130% 120% Benchmark performance 110% 100% Portfolio performance 90% 80% 12/ / / / / / /2000 Date

11 Forecasting Univariate time series Multivariate time series Multiple linear regression Indicators of technical analysis Non-linear parametric techniques Non-linear non-parametric techniques Neural networks Genetic algorithms

12 Bond forecasting with neural network model Bond yield forecasting Yield (%) 7.1% 6.9% 6.7% 6.5% 6.3% 6.1% 5.9% 5.7% 5.5% Actual yield Forecasted yield Month

13 Answers to common neural network questions What are the benefits of using neural networks? Neural network performance is at least as good as classical statistical modeling, and better on most problems. Neural networks build models that are more reflective of the structure of the data in significantly less time. Neural networks develop models through learning rather than programming. Programming is very time-consuming, and requires you to specify the exact behavior of the model. Neural networks teach themselves the patterns in the data, freeing you for more interesting work. Neural networks can build models when more conventional approaches fail. Because neural networks learn to recognize patterns in the dataset they can easily model data which is too complex for traditional approaches, such as inferential statistics or programming, logic. Neural networks are flexible in a changing environment. Rule-based systems or programmed systems are limited to the situation for which they were designed. When analysis conditions change, they are no longer valid. Although neural networks may take some time to learn a sudden change, they are excellent at adapting, to constantly changing information. Neural networks now operate well with desktop computer hardware. Although neural networks are computationally intensive, the routines have been optimized so they can now run well on personal computers. How do neural networks differ from statistics? Neural networks analyze data differently than traditional statistical methods. When applied to your data, neural networks learn from experience to recognize patterns that exist within the dataset. If you have an idea of the underlying relationships in the data, it is in some ways easier to build a model with statistical methods than with neural networks. The problem is that you often don t know the structure of the model. So you assume a model form, test its accuracy and repeat until the best model is found. Neural networks give better models faster than statistical methods when the form of the data is unknown, when the problem is complex or when the data are nonlinear. Neural networks are more flexible than statistical methods. Which are the typical areas of applications? Stock market forecasting Forex forecasting Bond yield forecasting Fund ranking Credit risk classification Real estate estimation How much data do I need to train my model? It depends on your specific application, but a guideline for the minimum amount of data required for training is 10*(M+N) where M equals the number of predictors and N equals the number of predictions What are the practical steps in model construction? Data collection Data filtering Model training Testing Validation Sensitivity analysis Interpretation How do neural networks work? There are many types of neural networks. The most basic approach is built of many nodes. Each node takes many inputs simultaneously and sums them, then produces a response dependent on the level of inputs received. If the sum of the inputs is high, the node has a strong response; if the sum of the inputs is low, the response is The response triggers an activation function which adds weight to high-value pattems and ignores the low-values. How may I use neural networks in daily work? The most user friendly implementation applies the model in an Excel spreadsheet as a new function operating on the columns of input variables.

14 Summary Different levels of difficulty in forecasting with financial time series: Aggregate statistical indicators: Expected return Volatility/Risk measures Optimization problems Primary time series: Random walks Efficient markets Behavioural finance Models Statistically significant predictions

15 Suggested reading Theory of financial risks - From statistical physics to risk management J.-P. Bouchaud, M. Potters (2000) An introduction to econophysics - Correlations and complexity in finance R. Mantegna, H. Stanley (2000) Applied stochastic models and control for finance and insurance C. Tapiero (1998) From catstrophe to chaos - A general theory of economic discontinuities J. Rosser (1991) Forecasting financial markets - Exchange rates, interest rates, asset management C. Dunis (1996) Statistics and neural networks - Advance at the interface J. Kay, D. Titterington (1999) New directions in mathematical finance P. Willmott, H. Rasmussen (2002) Probability and finance - It's only a game G. Shafer, V. Vovk (2001)

16

17 What are the benefits of using neural networks? Neural network performance is at least as good as classical statistical modeling, and better on most problems. Neural networks build models that are more reflective of the structure of the data in significantly less time. Neural networks develop models through learning rather than programming. Programming is very timeconsuming, and requires you to specify the exact behavior of the model. Neural networks teach themselves the patterns in the data, freeing you for more interesting work. Neural networks can build models when more conventional approaches fail. Because neural networks learn to recognize patterns in the dataset they can easily model data which is too complex for traditional approaches, such as inferential statistics or programming, logic. Neural networks are flexible in a changing environment. Rule-based systems or programmed systems are limited to the situation for which they were designed. When analysis conditions change, they are no longer valid. Although neural networks may take some time to learn a sudden change, they are excellent at adapting, to constantly changing information. Neural networks now operate well with desktop computer hardware. Although neural networks are computationally intensive, the routines have been optimized so they can now run well on personal computers. How do neural networks differ from statistics? Neural networks analyze data differently than traditional statistical methods. When applied to your data, neural networks learn from experience to recognize patterns that exist within the dataset. If you have an idea of the underlying relationships in the data, it is in some ways easier to build a model with statistical methods than with neural networks. The problem is that you often don t know the structure of the model. So you assume a model form, test its accuracy and repeat until the best model is found. Neural networks give better models faster than statistical methods when the form of the data is unknown, when the problem is complex or when the data are nonlinear. Neural networks are more flexible than statistical methods. Which are the typical areas of applications? Stock market forecasting Forex forecasting Bond yield forecasting Fund ranking Credit risk classification Real estate estimation How much data do I need to train my model? It depends on your specific application, but a guideline for the minimum amount of data required for training is 10*(M+N) where M equals the number of predictors and N equals the number of predictions What are the practical steps in model construction? Data collection Data filtering Model training Testing Validation Sensitivity analysis Interpretation How do neural networks work?

18 There are many types of neural networks. The most basic approach is built of many nodes. Each node takes many inputs simultaneously and sums them, then produces a response dependent on the level of inputs received. If the sum of the inputs is high, the node has a strong response; if the sum of the inputs is low, the response is The response triggers an activation function which adds weight to high-value pattems and ignores the low-values. How may I use neural networks in daily work? The most user friendly implementation applies the model in an Excel spreadsheet as a new function operating on the columns of input variables.