missing link between technical analysis and algorithmic trading · · 2017-03-15statistics:...

Statistics: Missing Link between Technical Analysis and Algorithmic Trading

Manish Jalan MD & CEO Samssara Capital Technologies LLP, Mumbai, India

MARCH, 2017

The statistical modeling building blocks

Define End Goal Define Set of Rules

Collect Data Back-test Optimize Simulate

Connect to OMS

Connect to Exchange Manage Risk

Improve and Maintain

Modeling Building

2 Statistics: Missing Link between Technical Analysis and Algorithmic Trading

Why Mathematics & Statistics?

Pure Technical Models

Moderate ROI when model is working

Large draw-downs when model stops

Long stretch of continuous bleeding in returns

User might lose confidence

Technical & Statistical Models

Superior ROI when model is working

Flattish ROI when model stops

Shorter stretch of continuous flattish period

User can diversify and make multi-models


The Mathematics

Data Distributions

Time Series Modeling

Market Microstructure


The Volatility

5

2

1

1 ( )n

ii

xn

σ µ=

= −∑

Volatility Is deviation from mean

in daily, 5 min, 10 min etc.


The normal distribution

Normal Distribution

Most popular data distribution

Standard normal distribution curve

Source: Wikipedia


Mean ixn

µ = ∑

Standard deviation

2

1

1 ( )n

ii

xn

σ µ=

= −∑

Variance 2 2

1

1 ( )n

ii

xn

σ µ=

= −∑

Correlation ( , )

x y

Cov x yrσ σ

=

Beta ( , )( )s p

sp

Cov r rVar r

β =

The normal distribution


Normal vs. other distributions

CAUCHY DISTRIBUTION

BETA DISTRIBUTION

BINOMIAL DISTRIBUTION

CHI-SQUARE DISTRIBUTION

LAPLACE DISTRIBUTION

POISSON DISTRIBUTION

EXPONENTIAL DISTRIBUTION


Behavior of the time-series of data – Mean reverting, Trending or Random Walk – 50-60% time series is random walk – Focus should be on the other 40%

Key elements: Mean and Variance

Different behaviors – Mean reverting (E.g.: Pairs Trading) – Non-mean reverting (E.g.: Trend) – Constant variance (E.g.: Pairs Trading) – Increasing variance (E.g.: Trend)

Time series modeling


Mean and Variance

0

2

4

6

8

10

12

Constant Mean

0

2

4

6

8

10

Constant Variance

0

10

20

30

40

Increasing Mean

0

5

10

15

20

25

30

Increasing Variance


Mean reversion modeling Co-integration: Stationary mean and variance

Time series is stationary when – The mean is constant – The variance is constant

Test for co-integration – If |r| < 1, the series is stationary – If |r| = 1, it is non-stationary (Random walk)

Most popular test: ADF (Augmented Dickey Fuller)

If ADF < -3.2 (95% probability of co-integrated series)

1t t ty ry e−= +


Variance Ratio Test: Test for variance alone

Useful when mean is varying w.r.t to the time

Ornstein-Uhlenbeck Process: Test for mean reversion alone

Useful when only mean reversion rate matters

Generic time series modeling

( )( )( )

k t

t

Variance rVR kk Variance r

∆

∆

=×

( )t t tdx x dt dWθ µ σ= − +


0.00%2.00%4.00%6.00%8.00%

10.00%12.00%14.00%16.00%18.00%20.00%

0 10 20 30 40 50

Gro

wth

P/E Ratio

Cluster analysis and PCA Grouping of similar data and pattern

Useful in factor modeling

PCA: To identify principal component


Regression

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

2

0.6590.720

y xR=

=

Useful in identifying alpha-generating factors

y mx c= +


1001.50 13 1001.00 19 1000.50 2 1000.00 17 999.50 9

999.00 10 998.50 4 998.00 16 998.00 7 998.00

Last Traded Price

Bid-Ask Spread

Price Ask Qty Bid Qty

Used in UHFT, HFT, Agency Trading

Market microstructure


Market microstructure

09:15 09:30 09:45 10:00 10:45 10:30 10:15

1005.00 1007.50 1004.50 1003.00 1008.00 1010.50 1009.50

5n = 1006.70µ =

2

1( ) 35.3

n

ix µ

=

− =∑ 2.657σ =

Market Price of Reliance in 5 min buckets


The spread

( )Spread Ticks BestAsk BestBid= −

( )( ) 10000( )2

BestAsk BestBidSpread BP BestAsk BestBid−

= ×+

Spread in BP

Spread in Ticks


0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

09:00 09:50 10:40 11:30 12:20 13:10 14:00 14:50

The market curve Volume / Market curve

BucketVolumeVolumeRatioDaysTotalVolume

=


1055.00 2 1054.00 7 1053.00 15 1052.00 25 1051.00 31 1050.00

42 1049.00 20 1048.00 15 1047.00 11 1046.00 6 1045.00

1 2 1 3 1 4 1 50 1 2 3 5( ) ( ) ( ) ( )eqVB B B B B B= + + + +

1 2 1 3 1 4 1 50 1 2 3 5( ) ( ) ( ) ( )eqVA A A A A A= + + + +

( , ) eq

eq

VAf Bid Ask VB=

High frequency example – for execution

Bid-Ask Density function using equivalent volumes


High frequency example

Short Term Upward Momentum

10:00:00 10:00:30 10:01:00

Trades hitting the Bid

Trades lifted on the Offer

10:01:30


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Conclusion

Statistical modeling can help you reduce draw-downs in technical analysis

Statistics can help filter for high probability trades

Statistics can enhance the returns on capital deployed

Technical analysis can be used for entry / exits and statistics can be used for filtering those entries and exits

Statistics can help you re-fine your stop losses and portfolio optimization

Statistics can help in making trade execution better and reduce slippages per trade


22

Recommended referrals

Prop trading

• Statistical Arbitrage: Algorithmic Trading Insights and Techniques by Andrew Pole

• High-Frequency Trading: A Guide to Algorithmic Strategies and Trading Systems by Irene Aldridge

• The Encyclopedia of Trading Strategies by Jeffrey Owen and Donna McCormick

Agency trading

• Algorithmic Trading and DMA: An introduction to direct access trading strategies by Barry Johnson

• Quantitative Trading: How to Build Your Own Algorithmic Trading Business by Ernset P. Chan

Web forums

Wilmott forum: www.wilmott.com Nuclear Phynance: www.nuclearphynance.com


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Manish Jalan MD & CEO Samssara Capital Technologies LLP, Mumbai, India

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missing link between technical analysis and algorithmic trading · · 2017-03-15statistics:...

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