Applications of machine learning

for volatility estimation and

quantitative strategies

Artur SeppArtur Sepp

Quantica Capital AG

Swissquote Conference 2018 on Machine Learning in Finance

9 November 2018

Machine Learning for Quant Strategies

• Theoretical foundations of Machine/Statistical Learning:

– Approximation vs Estimation error

– Simplicity vs Complexity– Simplicity vs Complexity

• Why Alternative Risk Premia products failed

• Example of supervised learning for selecting volatility models

• Risk-profile of systematic investment strategies

2

Data Overfitting: many solutions to fit data points

locally with different global behaviour

3

Example of perfect in-sample fit for an asset

price path

8

10

5-degree polynomial trend-line with near

perfect explanatory power R^2=98%

Asset price

0

2

4

6

8Asset price

5-degree Polynomial Fit

4

Example of out-sample forecast for short vol ETN• How to prevent ML algorithms from falling into this trap?

10

12

14Out-of-sample forecast for Feb 2018

Short Volatility Exchange Traded Note (XIV)

5-degree Polynomial Forecast

Forecast Return=+45%

5

0

2

4

6

8

05-Feb-16 05-Feb-18

5-degree Polynomial Forecast

Realized Return=-95%

Credit derivatives crisis in October 2008

• Quant models for credit derivatives relied on multi-parameter models with linear fits:

one parameter for market price of each instrument

• The models failed to calibrate and work in distressed markets during the Financial Crisis

S&P 500 Index Daily Movers

Gainers % ↓ Losers % ↑

6

Gainers % ↓ Losers % ↑

WMT 0.30% AIG -23.10%

MCD 0.23% MER -19.56%

KO 0.11% LEH -19.29%

GNW -18.64%

ACAS -18.17%

GE -17.97%

DDR -17.10%

HIG -16.86%

Alternative risk premia (ARP) crisis in October 2018• ARP is marketed by major banks as market-neutral using overstated back-tests

• ARP products proliferated from 2015 with estimated AuM $500 bln at mid of 2018

• Performance of live ARP products from 2015 has been less spectacular than back-tests

HFR Bank Systematic Risk Premia Indices October 2018 YTD Performance

Gainers YTD % ↓ Losers YTD % ↑

Rates Momentum Index 7% Multi-Asset Value Index -61%

Credit Multi-Style Index 5% Multi-Asset Volatility Index -34%

Rates Value Index 4% Equity Volatility Index -27%

Currency Volatility Index 4% Equity Multi-Style Index -26%

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Credit Carry Index 1% Credit Momentum Index -22%

Multi-Asset Multi-Style Index -21%

Multi-Asset Index -20%

Equity Size Index -19%

Multi-Asset Momentum Index -17%

Equity Index -16%

Equity Quality Index -16%

Commodity Volatility Index -14%

Equity Carry Index -13%

Commodity Multi-Style Index -13%

Equity Value Index -13%

Commodity Smart Beta Index -11%

Equity Momentum Index -11%

Equity Smart Beta Index -10%

Trend-Following Index -10%

Currency Carry Index -8%

Credit Index -8%

Rich class of decision rules may reduce the

approximation error but increases the estimation error

Approximation error: the class Estimation error: we are unable

to identify the good rule for

Bayesian learning: select the rule with the highest posterior probability but prior

probabilities are needed(!)

Probably Approximately Correct (PAC) learning: if class D is PAC learnable there exists a

finite sample size of for given level of approximation and estimation error

Hypothesis h1, h2,…

Class D of Decision

rules

“Random” observed

data

Training Data

LearningRule

Selection

Approximation error: the class

D may not have good rules to identify the good rule for

prediction from training data

8

Vapnik-Chervonenkis (VS) dimension measures

the richness of the class of decision rules• VC dimension predicts the bounds of the sample size for PAC learning

• Example using single-parametric threshold classifier: buy if last return is higher

than threshold, sell otherwise: the VC dimension is one

1122412000

Number of years for PAC learning of the classifier from daily data

2465

1007531 322 214 151 111 85

1511

344 144 77 48 32 23 17 130

2000

4000

6000

8000

10000

5% 10% 15% 20% 25% 30% 35% 40% 45%

Approximation Error

10 parameter classifier

Single parameter classifier

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PAC learning using Hierarchy of Decision rules • Restricting the richness of the class may improve PAC learning

but may increase the approximation error

• Split the class D of all decision rules into a sequence of classes Di

which are PAC learnable

• VC dimension is a measure of the complexity of rules in class Di• VC dimension is a measure of the complexity of rules in class Di

• Select a rule by minimizing:

Approximation Error + Complexity

10

D1=the class with simplest decision rules

D2=D1+the class with

more complex rules

D=D1+D2 +…

PAC learning for the process of systematic trading

includes at least three classes of decision rules

Signal

Look for predictors with highest scores

Portfolio

Manage risk allocation and diversification

Execution

Minimize trading costs and slippage

• Examples of inconsistent trading processes

1. Signal that works only on one asset: cannot diversify the portfolio

2. Signal that changes too frequently: execution costs can be too high

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Example of designing strategy for volatility trading:

learning hierarchy to reduce the dimensionalityVolatility Model

Parameters

Split 2-dimensional

Strategy

design Strategy Parameters

*Optimal 1-d set

Strategy Parameters

*Optimal 1-d set

Split 2-dimensional

problem into two

orthogonal

1-dimensional problemsVolatility

Model

Parameters

*Optimal 2-d set

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Model forecast of realized volatility is applied

to estimate the volatility risk-premium• Relative value volatility trading: Sell/buy options with high/low expected spread

and delta-hedge

20%

30%Volatility Risk-Premium=VIX at MonthStart -

S&P500 Realized Monthly Volatility

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-50%

-40%

-30%

-20%

-10%

0%

10%

Ma

r-8

6

Ma

r-8

8

Ma

r-9

0

Ma

r-9

2

Ma

r-9

4

Ma

r-9

6

Ma

r-9

8

Ma

r-0

0

Ma

r-0

2

Ma

r-0

4

Ma

r-0

6

Ma

r-0

8

Ma

r-1

0

Ma

r-1

2

Ma

r-1

4

Ma

r-1

6

Ma

r-1

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Average=4%

Minus Standard Deviation=-3%

Plus Standard Deviation=10%

Multiple classes of volatility models are

applied for the forecast of realized volatility

Sample space estimators

• Close-to-close, Intraday estimators (Parkinson, etc…)

• Assume random walk for the volatility

GARCH models• Garch (1,1), Asymmetric Garch, etc

• Apply long-term history with mean-reversion

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GARCH models• Apply long-term history with mean-reversion

Bayesian parametric models

• Continuous type models with priors for vol forecast

• Apply intraday high/low price data

Hidden Markov Chain Models (HMC)

• Discrete states of volatility

• Classification problem in unsupervised machine learning

Selection of model with the best forecast power

Class of decision rules: all volatility models

Implementation: use 40 models from 4 model classes

Uniform metric for model selectionUniform metric for model selection

Implementation: distribution tests for the stability of the forecast

Select model with the highest score for the asset or asset class

Implementation: Regularly update the tests as new data is available

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Distribution tests is applied for volatility

normalized returns over forecast period

18%

Naive: Close-To-Close Volatility Estimator for HY Bonds ETF18%

Advanced: Hidden Markov Chain Volatility Estimator for HY

Bonds ETF

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0%

2%

4%

6%

8%

10%

12%

14%

16%

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Volatility normalized return

Empirical

Normal (0,1)

0%

2%

4%

6%

8%

10%

12%

14%

16%

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Volatility normalized return

Empirical

Normal (0,1)

Robust estimator provides tight bounds for

volatility forecast with no “surprises”• Robust application for strategies with volatility targeting and time series normalization

0

3

Volatility Normalized Returns for HY bonds ETF

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-15

-12

-9

-6

-3

0

Markov Chain

CloseClose

MarkovChain LowerQuantile

MarkovChain UpperQuantile

CloseClose LowerQuantile

Top-3 models for High Yield Bonds ETF using

the normality test annually

32 32 32 32 3232

Top 3 Estimators with Normality fit for Volatility Normalized Returns for HY bonds ETF

Top - 1 Top - 2 Top - 3

• Use past rolling window of 3 year for one step forecast evaluation

• Each model is numbered (1,2,…)

• Stable ranks for Markov chain (31-32) and GARCH models (21-30)

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28 28 28

3132 32 32 32 32

22 22 22

32

26 26

24

26 2626 26 26

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31-Dec-2009 31-Dec-2010 30-Dec-2011 31-Dec-2012 31-Dec-2013 31-Dec-2014 31-Dec-2015 30-Dec-2016 29-Dec-2017

Top-3 models for the S&P 500 index using

normality test in walk-forward analysis annually

31 31 31 3130

32 32

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31 31

28

3132 32

30

3231

28 28

3232

29 29

Top 3 Estimators with Normality fit for Volatility Normalized Returns for S&P 500 index

Top - 1 Top - 2 Top - 3

• Markov Chain models (31,32) are frequently on the top

• Intraday estimators (1-10) are also reliable while being least complex

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2322

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Quantitative Strategies have changing profile

in different market regimes• Apply the quantile regression of returns on the strategy vs returns on the benchmark

• Three regimes: bear, normal, and bull

• Example using CBOE Put index selling at-the-money put options on the S&P 500 index

y = 1.06x + 0.05 y = 0.43x + 0.02y = 0.24x + 0.04

20%

Quarterly returns on Short Put Index vs S&P 500 index: 1986-2018

BearBullNormal

20

y = 1.06x + 0.05 y = 0.43x + 0.02

-30%

-20%

-10%

0%

10%

-30% -20% -10% 0% 10% 20% 30%

Y=

Re

turn

on

Pu

t In

de

x

X= Return on the S&P 500 index

Risk profile of HFR Bank Systematic Risk Premia

Multi-Asset Index vs SG Trend-following CTAs• Bank Risk Premia Index is short 3× leveraged put and long 5× leveraged call

• Trend-following CTAs replicate protection for bear regimes with overall positive performance

• The difference between amateur and professional applications of ML methods

80%

Quarterly returns on SG Trend-Following CTAs vs S&P 500 index 2000-2018

Bear BullNormal

80%

Quarterly returns on HFR Bank Systematic Risk Premia Multi-Asset Index

vs S&P 500 index: 2007-2018

Bear

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y = -0.88x - 0.04 y = 0.13x - 0.00 y = -1.13x + 0.16

-80%

-60%

-40%

-20%

0%

20%

40%

60%

-30% -20% -10% 0% 10% 20%

Y=

Re

turn

on

SG

In

de

x

X= Return on the S&P 500 index

Bear BullNormal

y = 2.90x + 0.18 y = 1.46x - 0.01 y = 5.30x - 0.47

-80%

-60%

-40%

-20%

0%

20%

40%

60%

-40% -30% -20% -10% 0% 10% 20% 30%

Y=

Re

turn

on

HF

R I

nd

ex

X= Return on the S&P 500 index

Bear BullNormal

Conclusions: Machine Learning for Quant

Strategies

• Machine/Statistical learning models are as good as people behind them

• Nested approach for strategy design to balance between complexity and

approximation & estimation errorsapproximation & estimation errors

• Understanding of how the strategy behaves in different market regimes

• Models adaptation to different regimes: no free or fixed parameters

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Disclaimer

• All statements in this presentation are the author personal views.

• The information and opinions contained herein have been compiled or arrived at in good faith based upon information obtained from sources believed to be reliable. However, such information has not been independently verified and no guarantee, representation or warranty, express or implied, is made as to its accuracy, completeness or correctness. All such information and opinions are subject to change without notice. Descriptions of entities and securities mentioned herein are not intended to be complete. This document is for information purposes only. This document is not, and should to change without notice. Descriptions of entities and securities mentioned herein are not intended to be complete. This document is for information purposes only. This document is not, and should not be construed as, an offer, or solicitation of an offer, to buy or sell any securities or other financial instruments.

• Past performance is not necessarily an indication for future results. This document may not be reproduced, distributed, published or delivered to any other party for any purposes.

• Investments in Alternative Investment Strategies are suitable only for sophisticated investors who fully understand and are willing to assume the risks involved. Alternative Investments by their nature involve a substantial degree of risk and performance may be volatile.

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