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D.E Allen, R. Powell and A. K. Singh Edith Cowan University

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Reading questions 1. What is short selling and why is it controversial? 2. What are Support Vector Machines (SVM) and why are they a useful technique? 3. Explain what kernel estimation is. 4. Why are different kernel estimators available? 5. Explain what logistic regression is. 6. What does Beta Measure? 7. Why are Sharpe ratios a useful investment metric? 8. How does Beta differ from Sharpe ratios. 9. How do we measure mean absolute error? 10. Why is out of sample forecasting important? 2

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Introduction Forecasting future stock price movement using financial indicators. Evidence from past for predictability power of financial factors e.g. Beta, E/P, B/M, past returns etc. Support Vector Machines (SVM), capable of handling large amount of unstructured, noisy or nonlinear data. SVM classification useful in prediction of future price direction (+1,-1). 3

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SVM in Classification SVM are characterized by Mapping input vectors into higher dimensional feature space. Structural risk minimization Non linear modelling with Kernel Functions Kernel density estimators are non-parametric density estimators with no fixed structure. They depend on all the data points to obtain an estimate. Classification of classes using optimal separating hyperplane. 4

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SVM Optimal Separating Hyperplane. 5

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SVM SVM use following kernel functions Linear: Polynomial: Radial Basis Function (RBF): Sigmoid: Here and d are kernel parameters. Study Uses RBF kernel for its robustness on non linear data. 6

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Data Dow Jones Industrial Average sample Stocks daily data for a period of 5 years (1/03/2005-9/03/2010). Factors Used for forecasting FactorsUnderlying rationale Previous 2 days daily log returns. Indicator of the historical performance, which is widely used in time series analysis. Beta (six months rolling window) Return dependence on the market return in the long run. Price to Earnings Ratio Indicator of the current company value which effects the price movement. Book to Market RatioFama- French (1992, 1993) Traded Volume Indicator of the performance of the stock in the market. Dividend YieldIndicator of company performance. Blume (1980) 7

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Methodology Standardization of Data Direction of price change classified into binary -1 and 1 using Testing sample is created using last 130 days data. Kernel parameters, cost and gamma are optimized using grid search. A systematic way of seeking optima. The model is built on training data and is used for forecasting which is tested on out sample data (130 days) SVM results are compared with Logistic Regression results (with same training and testing data). Simple investment strategy used to check the predicted directions 8

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Forecasting Results StocksResultsSVMLogistic Regression Stock 1 Correctly Classified Instances77 (59.2308 %)67 (51.5385%) CGamma Incorrectly Classified Instance53 (40.7692%)63 (48.4615 %) 7240.1Mean Absolute Error0.40770.5015 Stock 2 Correctly Classified Instances112 (86.1538%)109 (83.8462 %) CGamma Incorrectly Classified Instance18 (13.8462%)21 (16.1538 %) 10240.12Mean Absolute Error0.13850.316 Stock 3 Correctly Classified Instances76 (58.4615%)67 (51.5385 %) CGamma Incorrectly Classified Instance54 (41.5385 %)63 (48.4615 %) 14480.003162Mean Absolute Error0.41540.4962 Stock 4 Correctly Classified Instances76 (58.4615%)69 (53.0769 %) CGamma Incorrectly Classified Instance54 (41.5385 %)61 (46.9231 %) 7243Mean Absolute Error0.41540.4963 Stock 5 Correctly Classified Instances80 (61.5385%)59 (45.3846 %) CGamma Incorrectly Classified Instance50 (38.4615 %)71 (54.6154 %) 14480.56Mean Absolute Error0.38460.5091 9

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Investment Strategy Results Final ReturnSharpe Ratio SVMLOGISTICSVMLOGISTIC Stock120.10167056-12.036217.42748-13.0499 Stock27.2461990936.0096454.3560553.369538 Stock316.3355632915.3047714.7850913.72405 Stock414.335684245.61143714.839014.495077 Stock518.27861273-5.4912514.62362-6.39905 DJIA10.123795248.10426878 The final net returns of the stocks are compared using the Sharpe Ratio. 10

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Conclusion SVM classification outperforms logistic regression in classifying price direction. Simple stock trading strategy also reveals the efficiency of SVM in stock trading. Further applications can include prediction of other financial time series. SVM regression can be further tested for similar work 11

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