D.E Allen, R. Powell and A. K. Singh

Edith Cowan University

Reading questions1. 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?

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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).

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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.

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SVM Optimal Separating Hyperplane.

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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.

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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

Factors Underlying 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 Ratio Fama- French (1992, 1993)

Traded Volume Indicator of the performance of the stock in the market.

Dividend Yield Indicator of company performance. Blume (1980)

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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

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Forecasting Results Stocks Results SVM Logistic Regression

Stock 1Correctly Classified

Instances 77 (59.2308 %) 67 (51.5385%)

C GammaIncorrectly Classified

Instance 53 (40.7692%) 63 (48.4615 %)

724 0.1 Mean Absolute Error 0.4077 0.5015

Stock 2Correctly Classified

Instances 112 (86.1538%) 109 (83.8462 %)

C GammaIncorrectly Classified

Instance 18 (13.8462%) 21 (16.1538 %)

1024 0.12 Mean Absolute Error 0.1385 0.316

Stock 3Correctly Classified

Instances 76 (58.4615%) 67 (51.5385 %)

C GammaIncorrectly Classified

Instance 54 (41.5385 %) 63 (48.4615 %)

1448 0.003162 Mean Absolute Error 0.4154 0.4962

Stock 4Correctly Classified

Instances 76 (58.4615%) 69 (53.0769 %)

C GammaIncorrectly Classified

Instance 54 (41.5385 %) 61 (46.9231 %)

724 3 Mean Absolute Error 0.4154 0.4963

Stock 5Correctly Classified

Instances 80 (61.5385%) 59 (45.3846 %)

C GammaIncorrectly Classified

Instance 50 (38.4615 %) 71 (54.6154 %)

1448 0.56 Mean Absolute Error 0.3846 0.5091 9

Investment Strategy Results

Final Return Sharpe Ratio

SVM LOGISTIC SVM LOGISTIC

Stock1 20.10167056 -12.0362 17.42748 -13.0499

Stock2 7.246199093 6.009645 4.356055 3.369538

Stock3 16.33556329 15.30477 14.78509 13.72405

Stock4 14.33568424 5.611437 14.83901 4.495077

Stock5 18.27861273 -5.49125 14.62362 -6.39905

DJIA 10.12379524 8.10426878

The final net returns of the stocks are compared using the Sharpe Ratio.

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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

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