post list
QuantDare
categories
all

Neural Networks

alarije

all

Foreseeing the future: a user’s guide

Jose Leiva

all

Stochastic portfolio theory, revisited!

P. López

all

“Past performance is no guarantee of future results”, but helps a bit

ogonzalez

all

Playing with Prophet on Financial Time Series (Again)

rcobo

all

Interviewing prices: Don’t settle for less

jramos

all

The Simpson Paradox

kalinda

all

Seeing the market through the trees

xristica

all

Shift or Stick? Should we really ‘sell in May’?

jsanchezalmaraz

all

What to expect when you are the SPX

mrivera

all

K-Means in investment solutions: fact or fiction

T. Fuertes

all

Lévy Flights. Foraging in a Finance blog. Part II

mplanaslasa

all

How to… use bootstrapping in Portfolio Management

psanchezcri

all

What is the difference between Artificial Intelligence and Machine Learning?

ogonzalez

all

Playing with Prophet on Financial Time Series

rcobo

all

Prices Transformation Cheat Sheet

fjrodriguez2

all

Dual Momentum Analysis

J. González

all

Random forest: many are better than one

xristica

all

Non-parametric Estimation

T. Fuertes

all

Classification trees in MATLAB

xristica

all

Using Multidimensional Scaling on financial time series

rcobo

all

Applying Genetic Algorithms to define a Trading System

aparra

all

Graph theory: connections in the market

T. Fuertes

all

Lévy flights. Foraging in a finance blog

mplanaslasa

all

Data Cleansing & Data Transformation

psanchezcri

all

Principal Component Analysis

j3

all

Comparing ETF Sector Exposure Using Chord Diagrams

rcobo

all

Learning with kernels: an introductory approach

ogonzalez

all

SVM versus a monkey. Make your bets.

P. López

all

Clustering: “Two’s company, three’s a crowd”

libesa

all

Euro Stoxx Strategy with Machine Learning

fjrodriguez2

all

Visualizing Fixed Income ETFs with T-SNE

j3

all

Hierarchical clustering, using it to invest

T. Fuertes

all

Lasso applied in Portfolio Management

psanchezcri

all

Markov Switching Regimes say… bear or bullish?

mplanaslasa

all

Exploring Extreme Asset Returns

rcobo

all

Playing around with future contracts

J. González

all

“K-Means never fails”, they said…

fjrodriguez2

all

What is the difference between Bagging and Boosting?

xristica

all

BETA: Upside Downside

j3

all

Outliers: Looking For A Needle In A Haystack

T. Fuertes

all

Autoregressive model in S&P 500 and Euro Stoxx 50

psanchezcri

all

Machine Learning: A Brief Breakdown

libesa

all

Approach to Dividend Adjustment Factor Calculation

J. González

all

Are Low-Volatility Stocks Expensive?

jsanchezalmaraz

all

Predict returns using historical patterns

fjrodriguez2

all

Dream team: Combining classifiers

xristica

all

Stock classification with ISOMAP

j3

all

Could the Stochastic Oscillator be a good way to earn money?

T. Fuertes

all

Central Limit Theorem: Visual demonstration

kalinda

all

Sir Bayes: all but not naïve!

mplanaslasa

all

Returns clustering with k-Means algorithm

psanchezcri

all

Correlation and Cointegration

j3

all

Momentum premium factor (II): Dual momentum

J. González

all

Dynamic Markowitz Efficient Frontier

plopezcasado

all

Confusion matrix & MCC statistic

mplanaslasa

all

Prices convolution, a practical approach

fuzzyperson

all

‘Sell in May and go away’…

jsanchezalmaraz

all

S&P 500 y Relative Strength Index II

Tech

all

Performance and correlated assets

T. Fuertes

all

Reproducing the S&P500 by clustering

fuzzyperson

all

Retrocesos y Extensiones de Fibonacci

fjrodriguez2

all

Size Effect Anomaly

T. Fuertes

all

Predicting Gold using Currencies

libesa

all

La Paradoja de Simpson

kalinda

all

Inverse ETFs versus short selling: a misleading equivalence

J. González

all

Random forest vs Simple tree

xristica

all

S&P 500 y Relative Strength Index

Tech

all

Efecto Herding

alarije

all

Cointegración: Seguimiento sobre cruces cointegrados

T. Fuertes

all

Seasonality systems

J. González

all

Una aproximación Risk Parity

mplanaslasa

all

Números de Fibonacci

fjrodriguez2

all

Using Decomposition to Improve Time Series Prediction

libesa

all

Las cadenas de Markov

j3

all

Clasificando el mercado mediante árboles de decisión

xristica

all

Momentum premium factor sobre S&P 500

J. González

all

Árboles de clasificación en Matlab

xristica

all

Fractales y series financieras II

Tech

all

Redes Neuronales II

alarije

all

El gestor vago o inteligente…

jsanchezalmaraz

all

In less of a Bayes haze…

libesa

all

Teoría de Valores Extremos II

kalinda

all

De Matlab a Octave

fuzzyperson

all

Cointegración

T. Fuertes

all

Cópulas: una alternativa en la medición de riesgos

mplanaslasa

all

¿Por qué usar rendimientos logarítmicos?

jsanchezalmaraz

all

Análisis de Componentes Principales

j3

all

Vecinos cercanos en una serie temporal

xristica

all

Redes Neuronales

alarije

all

Fuzzy Logic

fuzzyperson

all

El filtro de Kalman

mplanaslasa

all

Estimación no paramétrica

T. Fuertes

all

Fractales y series financieras

Tech

all

In a Bayes haze…

libesa

all

Volatility of volatility. A new premium factor?

J. González

all

Caso Práctico: Multidimensional Scaling

rcobo

all

Teoría de Valores Extremos

kalinda

all

“Let’s make a deal”: from TV shows to identifying trends

mplanaslasa

17/03/2016

1
“Let’s make a deal”: from TV shows to identifying trends

Can the famous Monty Hall Problem be used in a stock index context? We think so.

For those of you unfamiliar with the Monty Hall Problem, the name originates from ‘Let’s Make A Deal’, a popular 60s American TV show hosted by – that’s right – Monty Hall. The show’s premise was simple: contestants were offered something of value, and could then either keep it, or made a ‘trade’ with the host.

At one point in the show, contestants are given a choice of three doors. One of them has a prize behind it, and the remaining two doors open to show nothing.

They pick Door #1, and the host (who knows what’s behind the doors), opens Door #3, which turns out to be empty. Monty then turns to them, grins, and says, “Do you want to pick the other door instead?”

letsmakeadeal

The question is:

                                      Is it to the contestant’s advantage to switch their choice?

Put yourself in their shoes. Your intuition will probably say of course I shouldn’t switch! But sometimes, intuition can be misleading. Mathematically speaking. While Door #1 has a 1/3 chance of having something behind it, since you now know that Door #3 is empty, switching to Door #2 still gives you a 2/3 chance to win something. That’s double the odds!

Take a look at the video below, which takes you through the whole process.

So, there you have it. The best chance you have is in changing your original choice and selecting Door #2.

The key is to remember that Monty already knows which door hides the prize. This makes the chance to change your door a conditioned action. Once Door #3 is opened, the remaining doors no longer have the same probability they did before.

For a more formal solution, we recommend reviewing Bayes Theorum, and this link to a more step-by-step solution, in particular.

Very curious but… how can we apply this in a financial environment?

I have designed a “metaphor” between this problem and the problem of identify trends in the Euro Stoxx 50 Price Index. In my last post I presented a method to predict trends based on the Naïve Bayesian classifier. (If you want to refresh your memory, go directly to Sir Bayes: all but not naïve!). It was a fair method (in the sense that it didn’t play with future information). It also drove results in stocks, with a bias in favour of success in predictions (>50%). I have tested this in the indexes S&P 500 and Euro Stoxx 50 and the results for S&P 500 show a bias in favour of success, correctly predicting 53% of the days. They were not as good in Euro Stoxx 50, however, where the success is an  insufficient 42%.

To solve this weak result in Euro Stoxx 50, we want a more rewarding prediction of this index. To gain this, we are going to use the following relationship of causality:

causality

We start then from the hypothesis that S&P 500 has an impact on Euro Stoxx 50
table(with a lag of one day due to the physical location of time zones) in a “direct” mode:

So the simile between Monty Hall problem and the task we are going to test are:

  • Which mix will be Monty Hall, the TV showman?

traje

For us, our version of Monty is the Naïve Bayesian Classifier (from now on, referred as NB) applied to S&P 500. I have assumed a big simplification with a difference within the MH Problem. In the famous problem, Monty has absolute certainty about where the prize is; not the case in our NB method.

 

  • Which situation is the simile of Monty Hall opening a door which has no prize?  It has to be a situation that makes the participant think that he could have selected the correct door. In our case this will be:“ B Method applied to S&P 500 indicates the trend is ranged market and NB Method applied to Euro Stoxx 50 indicates that yesterday it was in trend. This means bullish or bearish so… we have to make the choice of not continuing to bet today for bullish or bearish markets for the Euro Stoxx 50, and going out of the market (this means, betting for ranged market).

str

We have also rejected the possibility of:

NB Method applied to S&P 500 indicates bullish/bearish and NB Method applied to Euro Stoxx 50 indicates that the yesterday was bullish/bearish (positive relationship). I therefore decide to change my bet in an extreme way to the opposite trend, and I estimate that today Euro Stoxx is in a bearish/ bullish trend:

                      nostr

We have not contemplated this option because we would be changing the bet in favour of something that goes against our initial hypothesis of a positive relationship between both indexes. This means that we are only applying the Monty Hall solution when the bet is not “clear” for Monty. That is, when Monty shows that S&P 500 is not in trend, and I’m not sure if I’ve chosen the correct trend (= the correct door) for Euro Stoxx 50.

Conclusion

Well, after our tests, the sad result of 42% success in Euro Stoxx prediction, has become 52%. This is not a result we should throw away.

If you want to know more interesting applications of the MH Problem, I suggest you read about “The principle of restricted choice“.

See you next time!

Tweet about this on TwitterShare on LinkedInShare on FacebookShare on Google+Email this to someone

add a comment

[…] Let s make a deal : from TV shows to identifying trends [Quant Dare] How about trying to find any use of the famous Monty Hall problem in a stock index context? Let your imagination run First of all, some of you may be confused because neither Monty Hall problem nor Lets make a deal are familiar to you so I will refresh you what these names are concerned to. Monty Hall was a TV presenter for Lets make a deal, a famous American show in the […]

wpDiscuz