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

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15 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

104 εμφανίσεις

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

Edith Cowan University


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

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

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

SVM


Optimal Separating Hyperplane.














5

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

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
)

7

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

Forecasting Results

Stocks

Results

SVM

Logistic Regression

Stock 1

Correctly Classified
Instances

77 (59.2308 %)

67 (51.5385%)

C

Gamma

Incorrectly Classified
Instance

53 (40.7692%)

63 (48.4615 %)

724

0.1

Mean Absolute Error

0.4077

0.5015

Stock 2

Correctly Classified
Instances

112 (86.1538%)

109 (83.8462 %)

C

Gamma

Incorrectly Classified
Instance

18 (13.8462%)

21 (16.1538 %)

1024

0.12

Mean Absolute Error

0.1385

0.316

Stock 3

Correctly Classified
Instances

76 (58.4615%)

67 (51.5385 %)

C

Gamma

Incorrectly Classified
Instance

54 (41.5385 %)

63 (48.4615 %)

1448

0.003162

Mean Absolute Error

0.4154

0.4962

Stock 4

Correctly Classified
Instances

76 (58.4615%)

69 (53.0769 %)

C

Gamma

Incorrectly Classified
Instance

54 (41.5385 %)

61 (46.9231 %)

724

3

Mean Absolute Error

0.4154

0.4963

Stock 5

Correctly Classified
Instances

80 (61.5385%)

59 (45.3846 %)

C

Gamma

Incorrectly 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.


10

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