Bayesian Networks for Financial Markets Volatility

Alessandro Greppi

Università degli Studi di Pavia

The OutlineBayesian Networks and Volatility: Our ApproachThe Innovativeness :

Original methodology for studying the marketMore insightNew view on volatility Learning from data and forecast turning pointsQuantitative methods able to include in efficient way «sentiment indicators»

Data-Driven Approach to VolatilityConclusive Remarks

We Used Bayesian Networks for…

… conducting an analysis on S&P 500 returns volatility based on: Market variables Momentum variables Sentiment variables Price variables

These variables are orthogonal among them and complementary. They provide a complete view of the market.

To our knowledge this is the first time that this tecnique is used in this field.

The Innovativeness of the Approach

The framework developed is innovative and usefull to market operators because:

Currently the tools available do not provide such information It supports investors by following a rigorous approach Its results could be easily interpreted Bayesian networks look as an ideal tool in uncertain situations

S&P 500 Analysis The stock exchange analysed is the S&P 500, because we are assuming that our market is:

Liquid Developed, in terms of investment vehicles used With a large number of data available, in terms of depth and reliability

Volatility Market volatility is a statistical measure of dispersion that provides information on the sentiment about future returns.

The highest volatility period was between 2010 and 2012

Vix median between 2010-2015: 12,2

We detected on average 1,6 high volatility events per month between 2010-2015

Our Approach The Hugin software ( www.hugin.com ) allow us to learn the Bayesian network directly from the data downloaded from Bloomberg ( www.bloomberg.com ).

The variables involved are: Economic variables (Earnings Growth, 3 periods Mov. Avg.) Technical analysis variables (Relative Strenght Index) Market sentiment variables (Put/Call ratio) Valuation variables (S&P 500 P/E Multiple) Volatility variables (Volatility Rolling 20 Days) A Buy/Sell contrarian variable built on the S&P 500 weekly returns (3 periods Mov. Avg.)

The data have been collected on a weekly basis from 01/01/2010 to 09/04/2015.

Data Preprocessing The variables have been discretized into 3 states, that have been obtained in the following way:

The values ABOVE the median + ½ Std. Dev. have been labelled with 2 The values BELOW the median – ½ Std. Dev. have been labelled with 1 The values in the range BETWEEN (median + ½ Std. Dev.) and (median – ½ Std. Dev) have been labelled with 0, the neutral area.

In our simulation we are only interested to observe what happens at the extremes of the distributions, in correspondance of 1 and 2.

Learning the BN from the Data

We learned the network structure directly from the available data For our application we used the Hugin software and we applied a constaint-base algorithm, the Necessary Path Conditions (NPC) The NPC carries out a series of independence tests and construct a graph which satisfies the discovered independence statements We impose some logical constraints according to our market knowledge The conditional distribution have been estimated from the data by using the EM algorithm, whose version for BNs has been proposed by Lauritzen (1995)

The Data-Driven BN

This screenshot provide us a picture of the starting point before simulating any scenario. On the left, we can see the estimated propabilities for each variable.

Introducing Different Scenarios

Once the model has been estimated, we can address a number of queries

Different scenarios can be observed by inserting and propagating new evidences throughout the network:

Scenario 1: High Rsi – Low Rsi

Scenario 2: High Vola 20D – Low Vola 20D

Scenario 3: High Index P/E – Low Index P/E

Scenario 4: High Put/Call ratio – Low Put/Call ratio

Scenario 5: High Earnings growth – Low Earnings growth

Scenario 6: Buy or Sell?

Simulations can be performed in real-time (mouse-click), by using the evidence propagation algorithm.

Scenario 1: High / Low Rsi

LOW RSI• Low P/E: Score 1 from 22,90% to 53,61%• Low Vola: Score 1 from 39,73% to 74,23%• Sell/Buy: Score 1 from 27,67% to 57,73%

HIGH RSI• High P/E: Score 2 from 39,73% to 50,00%• High Vola: Score 2 from 32,66% to 63,33%• Sell/Buy: Score 2 from 25,71% to 34,70%

Rsi plays a central role because is both directly and undirectly related to the target one.

Scenario 2: High / Low Vola

LOW VOLATILITY• Low P/E: Score 1 from 22,90% to 45,76%• Low Rsi: Score 1 from 32,66% to 61,02%• High Earnings growth: score 1 from 26,52% to 38,14%• Sell/Buy: Score 1 from 27,67% to 39,83%

HIGH VOLATILITY• High P/E: Score 2 from 39,73% to 60,82%• High Rsi: Score 2 from 30,30% to 58,72%• Low Earnings growth: score 2 from 11,85% to 14,65%• Sell/Buy: Score 1 fells from 27,67% to 12,56% and Score 2 from 25,71% to 17,90%Volatility plays a central role because is both directly and undirectly related to the target one.

Scenario 3: High / Low Index P/E

LOW INDEX P/E• Low Rsi: Score 1 from 32,66% to 76,47%• Low Vola: Score 1 from 39,73% to 79,41%• Sell/Buy: Score 1 from 27,67% to 46,46%

HIGH INDEX P/E• High Rsi: Score 2 from 30,30% to 38,14%• High Vola: Score 2 from 32,66% to 50,00%• Sell/Buy: Score 2 from 25,71% to 23,34%

Scenario 4: High / Low Put/Call ratio

LOW PUT CALL RATIO HIGH PUT CALL RATIO

In both cases, the Put/Call ratio appears to be the variable whose changes impact the less on the other and on the target variable

Scenario 5: High / Low Earnings growth

HIGH EARNINGS G.• P/E: Score 1 almost unchanged; Score 2 fells from 39,73% to 6,35%• Low Rsi: Score 1 from 32,66% to 36,64%

LOW EARNINGS G.• High P/E: Score 2 from 39,73% to 56,80%• Volatility: Score 1 + Score 2 from 72,39% to 88,64%• Low Rsi: Score 1 from 32,66% to 40,00%

Earnings g. plays a central role in determining the index P/E as reflected in both our simulations. Sell/Buy signals appear not to be conditioned by earnings g. changes.

Scenario 6: Buy or Sell?

BUY SIGNAL• Low Rsi: Score 1 from 32,66% to 68,14%• Low Vola: Score 1 from 39,73% to 57,19%• Low P/E: Score 1 from 22,90% to 38,44%

SELL SIGNAL• High Rsi: Score 2 from 30,30% to 40,90%• Low Vola: Score 1 from 39,73% to 41,91%• P/E: Score 1 from 22,90% to 19,04%; Score 2 from 39,73% to 36,07%

Conclusive Remarks (1/3)

Our analysis evidence that:

• Score 1 Rsi• Score 1 Index P/E• Score 1 Vola

• Score 2 Rsi• Score 2 Index P/E

Sell Signal

Buy Signal

Conclusive Remarks (2/3)

• Score 1 Rsi• Score 1 Vola• Score 1 Target variable: Buy signal

• Score 2 Rsi• Score 2 Vola• Score 2 Target variable: Sell signal

Expensive Market

Cheap Market

Conclusive Remarks (3/3)

• Strong impact on Index P/E• Low impact on Buy/Sell signals

• Lowest impact on the BN variablesPut / Call ratio

Earnings growth

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