There are some things impossible to quantify. The deliciousness of your grandma's cookies, or how exciting it is to train a neural network, for example. But financial markets are made of numbers - among other things. They should be measurable, quantifiable. Nobody said it would be easy. But we dare.
New, unlimited and high quality Financial Data. That’s the key for successfully applying AI algorithms for investing. Five years ago, Data Scientists at ETS Factory began using GenAI to generate financial time series data which have provided more consistency for investment strategies.
At ETS Asset Management Factory we are constantly improving our strategies by promoting innovation based on our data, algorithms, team and experience. Each of these elements serves a distinct purpose, collectively forming our company’s four main pillars.Following this philosophy, in today’s post we will be using an advanced algorithm to improve a module of the […]
Learn about the new Forward-Forward algorithm to train neural networks without backpropagation.
The conventional wisdom suggests that by spreading your investments across a wide range of assets, you can mitigate risk and achieve greater long returns. In this article, we will explore the diversification benefits of conglomerate stocks and why they can be valuable additions to a stock portfolio.
The Forex Market is the global marketplace where currencies are bought and sold. It is the largest and most liquid financial market in the world, with trillions of dollars traded daily.
In a previous post we saw how avoiding being in the market during Earnings publications could be a zero-sum game in the long run. In this post our purpose is to study if it is possible to take advantage of the effect in the stock prices based on the behavior of the prices during financial […]
In my post Linking Impact in Divergence Attribution I explained the need to use linking algorithms in order to aggregate single-period returns. I ended my exposition by setting out the formula for adjusted returns using Andrew Frongello’s algorithms (arguably the ones with best qualities in the industry).If you found this final expression of Frongello-adjusted attribution […]
There is a myth that investors have to choose either Value or Growth, but considering both strategies as complementary rather than adversaries can be very beneficial for investors.
This blog has previously covered various approaches to identify outliers. In this case, we are going to explore a different use case and apply a different method.
In a previous post, we saw how to use genetic algorithms to make implicit optimizations. We used that technique to construct a portfolio, but in a very simple manner: we were just limited to 5 stocks, and we were looking for a constant weight for each of them, assuming daily rebalancing. Today, we will focus […]
Wikipedia’s definition of risk is rather straightforward: it is the possibility of something bad happening. As such, it seems like an inherently negative thing and yet, in a dialectical fashion that will be recurring throughout this post, it’s also the foundation upon which many people’s dreams of early retirement are built. More generally, in finance, […]
Financial data is one of kind: we think is non-stationary, and the samples are non-iid, which means one cannot simply apply common machine learning techniques. In this post, we briefly cover some pitfalls when using machine learning algorithms in a financial context.
What are Options Greeks and their definition? What is Gamma in investing and how is it used? How to take advantage of Gamma Squeezes? A squeeze in finance is a rapid and sudden change in the prices of an underlying asset that obligates investors to force their positions. When this effect occurs, there will be […]
The EURUSD currency pair has been one of the most closely watched and traded pairs in the forex market for years. Its movements can have a significant impact on the global economy and particular investments.
How does ChatGPT work? What is behind deep fake images of celebrities? How do we deal with the lack of data in finance? All these issues have in common the same underlying concept; they are based on generative models.
We usually compute return attribution to know how much each asset contributes to portfolio return. This calculation is quite easy because return formula is linear and sub-additive. In that context, one can split the whole portfolio return in smaller parts corresponding to each asset. However, although risk measures have to be coherent (monotonous, sub-additive, homogeneous […]
Bayesian statistics is a powerful field of mathematics that has wide-ranging applications in many fields, including finance, medical research, and information technology. It allows us to combine prior beliefs with evidence to obtain new posterior beliefs, thereby enabling us to make more informed decisions.
The financial industry is constantly searching for models that can help accurately predict the behavior of interest rates. In this article we will explore one of the most widely used models for this purpose, the Nelson-Siegel (NS) model.
The equilibrium exchange rate (EER) can be defined as the rate which, in the absence of official intervention, balances the supply and demand of two currencies, (Williamson 1983).
Volatility is one of the best known and most widely used concepts in finance. Given a price series of a financial instrument, its volatility is defined as the dispersion of the returns. This measure is used to compare securities in terms of risk. But in order to compare, sometimes it is necessary to scale. In […]
Surely everyone has suffered/enjoyed a sudden movement of a stock in a portfolio when the underlying company has reported earnings. Now that the earnings report season is starting you may wonder if there exists a way to avoid those shocks in the stocks without missing performance in your investments.
Fed’s interest rate actions, which have been a topic of much discussion recently, can be very valuable information when making investment decisions. In particular, this post shows how to improve our sector allocation following Fed’s announcements.
When we enter the ESG world, we can fall into an abyss of terminology, extreme currents of thought, emerging regulation, and a lot of marketing.
In previous posts, we have seen the basic RL algorithm, Deep Q learning (DQN). We have also seen it applied, using Neural Networks as the Agent, to an investment strategy. We finally even used it for a cryptocurrency investment strategy. This time, we will implement a slightly more advanced technique, Double Deep Q-networks (DDQN), and […]
For every quantity to be estimated (estimand), there’s a plethora of ways to estimate it (estimators). This raises the question of what properties we should be looking for so as to make a sensible choice. Often highlighted as one of such properties is unbiasedness, which we will discuss below with a particular focus on its […]
The Unscented Kalman Filter allows to deal with nonlinear systems in a different way than the Extended Kalman Filter. Find how it works in this post.
Many investors are looking for the holy grail of investing. They all want a magic formula that tells them which stocks to buy, and which ones to sell. But experienced investors know that there is no such a thing. I was convinced of it… until I discovered the MOIC formula.
The blog has previously addressed interest rates in a post that splits the yield rate curve into three relevant components. This time this post tries to identify the influence of interest rates on fixed income assets by using the Granger causality test. Interest rates obviously have a strong impact on fixed income assets because they […]
Sell in May and go away… Just won’t go away. We test the popular strategy that seems to hold up for the last 25 years.
Traditional Share Class Hedging (SCH) consists of cancelling the exchange rate risk inherent in a share class denominated in a foreign currency, i.e. in a currency other than that of the fund. Hedging transactions necessarily entail costs that affect the client’s final result. It is therefore important to find the smartest way to carry out […]
In recent posts we spoke about companies valuation by the Discount Cash Flow method (DCF), where we could obtain the intrinsic value of a company by means of the calculation of the present value of the future expected cash flows. The other way of valuing a company is with the Multiples approach, which in most […]
Everyone is aware of the importance of the U.S. elections and we take it for granted that, like many other things, financial markets will end up being affected in some way. But have you ever wondered if there is any seasonality throughout those elections that we can take advantage of when making investment decisions? Let’s […]
In a previous post, we explained how self-organizing maps work, with a very simple example. In this post, we will explain how to implement self-organizing maps for an investment strategy.
To hedge or not to hedge is a dilemma that needs to be faced whenever currency risk comes into our lives, stemming from having spread our investments or business in foreign assets. There is no global correct answer, as it will depend on the particular situation you face to: What is the risk currency? USD? […]
We all know that the more indebted a company is, the greater the risk of bankruptcy. But what is really the best way to measure this indebtedness? In this post we will compare two of the best known leverage ratios: Debt/Equity (Debt-to-Equity) and Net Debt/EBITDA (Net Debt-to-EBITDA).
Stochastic processes play a key role in modelling the behavior over time of many financial assets. These mathematical descriptions of reality help making investment decisions. They can be used to price stock market options, make Monte Carlo simulations or define probabilities of expected returns, among others.In today’s post we will explore the origins of two […]
In order to develop complex strategies for a successful asset allocation, portfolio managers need profound knowledge on the field. Apparently, this is the key to be able to consistently beat the market. In this post we will learn how to design investment strategy based in Modern Portfolio Theory in Python. Will we be able to […]
In the financial field, managers usually take advantage of the great development in machine learning techniques to improve their models and get the best performance of their portfolios. These techniques may be clustering, neural networks, or even a more traditional one as optimization algorithms.
What are the key variables that can help as forecast short term inflation? How the market, policy makers and experts reflect their views on inflation? In this article we try to answer these question and view how the current market conditions affect our inflation expectations.
One of the most important measures to compare countries economically is Gross Domestic Product (GDP). This measure shows the market value of all goods and services produced by a country in a given period of time. Moreover, it is usually calculated on an annual basis and there are different ways of calculating it: nominal GDP, […]
Clustering algorithms are one of the main techniques in the field of unsupervised learning. In the machine learning context, we understand by unsupervised learning the process of analyzing and identifying patterns in unlabeled datasets.
When dealing with factors information is important to go to the detail and get insight about how the factor is built. Ratios combination improves robustness.
Whenever dealing with new datasets, or when putting together a summary for stakeholders, we often encounter the problem of having to represent our data in a meaningful and efficient way. Meaningful such that conclusions and comparisons can be drawn from our plots, efficiently such that few plots are necessary.
Graph Theory is widely used in almost every area of interest for visualization or analysis purposes but, for some reason, it is not usually applied in finance. Why not trying to take advantage of its potential in portfolio management?
Random Forests are widely used Machine Learning algorithms. In finance, certain financial ratios are used to try and predict whether or not a company will outperform the market. Can we use the random forest on financial ratios to articulate an investment strategy which outperforms a buy and hold strategy?
In financial time series it is very common to make predictions of single points such as expected future prices or returns. But is there any other way of adding more information in our forecasts?In today’s post we will be making probabilistic forecasts for time series data using recurrent neural networks with pytorch.
Prices are said to contain a good deal of information but, as this is drastically compressed into a single figure, it’s often hard to unravel the original elements involved in an asset’s pricing. Here derivatives come to the rescue, by providing us with many more price series related to the same underlying, we can get […]
Using PyTorch to test the attention mechanism applied to time series forecasting.
It is well known that we investors are full of biases when making investment decisions (loss-aversion, trend-chasing, …), but what is the real impact of these biases on our performance? In this post we will try to answer this question quantitatively, and we will also compare the average investor returns with the average mutual funds […]
Currency hedging is a powerful tool, offering foreign investors access to new opportunities, providing returns very similar to those of local ones. However, it also has some disadvantages to consider.
News have a huge impact in the global stock market, but it’s impossible even for professionals to be constantly updated. One can ask itself: is there any way to automate this procedure?
Historically, portfolio managers have carried out asset allocation combining intuition with deep knowledge about specific market or asset classes in order to beat the market. However, is it possible to design a quantitative investment strategy that provides the optimal balance in the asset allocation?Let’s find out!
In the world there are several pieces of news which help us understand how the market’s behaviour will be. As human beings, it is impossible for us to read each piece of news or comment, so what if we use machine learning, especially tf-idf algorithm, to get the most important information from all the texts […]
Incorporating market expectations and forecasts into asset allocation used to be more of an art than an analytical process in the 80s. In this post we will review Fisher Black’s elegant and very practical solution to portfolio construction, going through a sector allocation example.
You may have seen in news, articles or blogs that a certain stock/company is undervalued or overvalued and that it is an outstanding opportunity to buy/sell that stock. If we stumble on an in depth analysis, we may read terms as intrinsic value of a company, value relative to this or that sector or even […]
Nowadays, inflation is an issue of concern to many people. This is due to it reaching its maximum values. However, what does this mean? And, what are the consequences?In this post, we will to try to answer these questions, and explain what inflation is, what consequences it has, why it is caused and how it […]
The performance of a portfolio during a single period can be attributed to a set of factors, but in order to aggregate those daily factors and get a breakdown of the portfolio’s total performance during a multi-period (for example 1Y), we have to make use of an smoothing algorithm.
When you mention the word “finance”, probably one of the concepts that jumps into someone’s mind are returns (percentage figures); something in the line of 17.8% performance. Indeed, returns sit at the very core of most financial calculations.Today, we are going to look at two different numbers attached to the performance of a portfolio: time-weighted […]
In a previous post we analyzed the performance of US Sectors using SPDR Sector ETFs. Now, let’s dive into the analysis of sectors using S&P 500 components and some measures of its performance.
We can use self-organizing maps for clustering data, trained in an unsupervised way. Let’s see how.
Today’s topic deals with an unavoidable source of friction in the FX hedging markets: Execution Timing Lags. The distance between valuation and execution in currency hedging can have an impact in the mitigation of spot movements. Today’s topic deals with an unavoidable source of friction in the FX hedging markets: Execution Timing Lags. The distance […]
In this post we will show how the properties of a triangle can be used to intuitively obtain insights about the volatilities and correlations of currency pairs.
In recent years we’ve seen an increase in the accuracy of NLP models through the use of Transformers. These models rely on the attention mechanism to identify key features but, how do they work? And most importantly, can we somehow use them in finance?
When valuing a company, one of the most commonly used approaches is Valuation Multiples. But within this approach there are different ratios that can be used, so the question is: which of them is the best? In this post we will compare three of the best known ratios: P/E (Price-to-Earnings), P/B (Price-to-Book) and P/S (Price-to-Sales).
The normal distribution is used in a broad number of fields. In finance, it was first used by Louis Bachelier back in 1900 to describe the movements of a stock price [1] and chances are you have heard about it if you are working in this field. But, where does it come from?
It is widely known that each time the Fed gives an announcement, the whole investing world is watching. So, one may wonder if those events can ruin their investments.
Markov chains are well-known in the world of both mathematics and finance. It is common to describe the market as a group of states, for instance bull and bear. From these two there are different ways to create a great deal of other states. If you want to establish the transition relationship between states, Markov […]
The stock market is a complex system influenced by many uncoordinated decision makers. But correctly identifying the main market drivers can help you generate a winning trading strategy. So today we will go through the key variables you should account for when trading the S&P 500 index.
If you have had the chance to live outside of your home country, you might have faced the dilemma of exchanging currencies. Today we are going to get into the vocabulary of these transactions, and if they are worth optimizing in the scale of a household.
In this post we are going to examine two alternative methods of calculating the factor contribution to the performance of an equity portfolio.
In this article, we are going to explain what a Hedged Share Class is and we are going to run some numbers in order to better understand how they work and the divergences that can result when comparing them to their Reference Classes.
Sometimes it is too costly, even impossible, to explicitly optimize an equation. Today we will see how to optimize implicitly using genetic algorithms.
Purchasing Power Parity (PPP) is a well-known measure used to compare the currencies of different countries in terms of price levels. So, in this post, we are going to explain PPP and study, through an example, its relation with the currency pairs.
Given the exceptional liquidity of the FX swap market, with a daily turnover of 3 trillion USD [1], a consistent mispricing has always seemed rather unlikely. Precisely, this makes the possibility of such event particularly interesting, especially when the data during the last decade point in that direction.
Although linear systems are pretty convenient at many levels, many real world applications cannot rely in this assumption. The Extended Kalman Filter can deal with these nonlinearities in a simple way. Learn how in this post.
We will examine the relationship between annual returns and largest annual drop. Let’s use some well known Select Sector SPDRs and the SPDR S&P 500 Trust (SPY). Using prices from 1999-01-01 to 2021-06-30 we calculate the annual returns and the biggest drop for each year.
You have probably heard about the famous GameStop ($GME) case, in which Reddit’s forum members managed to skyrocket its price. But what really happened? The answer is: a Short Squeeze.
In today’s post we will try to build a Recurrent Neural Network with numpy, in order to get a better understanding of how recurrent algorithms are used in NLP.
Cryptocurrencies are a hot topic in the investing world, but is it possible to create an investment methodology combining modern Reinforcement Learning with classical indicators?
Who has never heard about cryptocurrencies: Bitcoin, Ethereum, Cardano, or even the latest ones, such as Shiba or Safemoon? The investors are rapidly increasing their positions in those assets, although investing in them is usually a pain in the neck.
The concept of entropy has many useful applications in finance such as measuring risk, uncertainty, or noise in a signal. In this post we will focus on transfer entropy, a useful tool for causal inference between financial time series.
In the business of performance measurement, a recurrent task is the breakdown of a stream of returns into meaningful contributions from different factors, in order to identify the driving financial forces or sources of risk.
Using Machine Learning and Deep Learning models to solve scientific problems of greater or lesser complexity is a challenge.
One common problem when looking at financial data is the enormous number of dimensions we have to deal with. For instance, if we are looking at data from the S&P 500® index, we will have around 500 dimensions to work with! If we have enough computing power, we will be able to process so much […]
When looking to generate appreciable returns and increase diversification, it is natural to consider investing in foreign instruments. Currency risk then comes up, since the returns coming from these funds, stocks, bonds… need to be translated into your home currency.
In the field of machine learning, when it comes to extracting relationships between variables, we often use Pearson correlation. The problem is that this measure only finds linear relationships, which can lead sometimes to a bad interpretation of the relation between two variables. Nevertheless, other statistics measure non-linear relationships, such as mutual information.Therefore, in this […]
The puzzle of Covered Interest Parity (CIP) began in 2008 and has remained as such for many years. There have been multiple attempts to solve the mystery but none of them has reached a complete consensus and the debate is still ongoing. Nevertheless, the discussion has lead to a fair amount of interesting insights. CIP […]
We have seen in previous posts what is machine learning and even how to create our own framework. Combining machine learning and finance always leads to interesting results. Nevertheless, in supervised learning, it is crucial to find a set of appropriate labels to train your model. In today’s post, we are going to see 3 […]
In our previous post, Fundamental shifts in factors, are they here to stay?, we warned about a possible trend reversal in the relation between Invesco S&P 500® Equal Weight (RSP), iShares MSCI USA Value Factor (VLUE) and SPDR® S&P 500® Trust (SPY) exchange traded funds. We are going to update that post, adding three months […]
As a continuation to our last post on Time Series Signatures and our running list of posts regarding GANs and synthetic data we now want to present the Signature Conditional Wasserstein GAN, shortened as SigCWGAN, a new GAN architecture presented in [1] that is specifically designed to generate time series of arbitrary length and dimensions.
It is well known that a happy employee performs better at work than one who is unhappy. On the other hand, employee’s happiness is difficult to measure, different people find happiness in different things, but it is clear that salary is usually a key factor.So, the question I ask myself is: will there be a […]
A couple of days ago we were seeing in the news the story about GameStop, and how small investors made some hedge funds abandon their short-selling positions after some big losses. After reading the article I couldn’t resist thinking about short-selling strategies and their performance in the stock market. In today’s post, and hoping to […]
Animating time series is a very powerful tool to show evolution over time, but matplotlib default animations are boring and they are not well suited for comparison purposes.Along this blog, animations are widely used: from explaining how neural networks train, to showing synthetic time-series statistics or indicating which funds are selected by the low volatility […]
One of the most appealing areas of Artificial Intelligence is Reinforcement Learning, for its applicability to a variety of areas. It can be applied to different kinds of problems, in the present article we will analyze an interesting one: Reinforcement Learning for trading strategies.
Let’s introduce three Exchange Traded Funds: the SPDR S&P 500 ETF Trust (SPY), the Invesco S&P 500 Equal Weight ETF (RSP), and the iShares MSCI USA Value Factor ETF (VLUE).
Decision Trees are one of the best known supervised classification methods. As explained in previous posts, “A decision tree is a way of representing knowledge obtained in the inductive learning process. The space is split using a set of conditions, and the resulting structure is the tree“
After many years there are many evidences that the low volatility anomaly works in stock markets. We have also mentioned this topic a long time ago to analysis the costs of it. This anomaly says stocks with less price variability deliver higher returns, contrary to everyone’s belief, which expects that return is supposed to be […]
As we test more and more strategies the overall probability of choosing at least one poor strategy grows. So we must be very careful with how many backtests we run. We should always record all of them, to later deflate the Sharpe Ratio accordingly.
When you are in front of a complex classification problem, often the case with financial markets, different approaches may appear while searching for a solution. These systems can estimate the classification and sometimes none of them is better than the rest.
Clustering data into groups that share common characteristics can be very useful, but using experts to perform this grouping is costly and in many cases decisions are influenced by emotions.
Sometimes described as a sort of physical law in international finance [1], Covered Interest Parity (CIP) has failed to hold after the Global Financial Crisis (GFC) of 2008. This has given rise to an interesting debate during the last decade that has resulted in relevant insights regarding international financial markets in general and FX Swaps […]
Despite the thrilling mathematical and scientific components the financial world has developed in the last decades, the core of the craft remains mostly the same: do not lose money.
The Signature of a time series is a universal description for a stream of data derived from the theory of controlled differential equations. Over the last years, this technique has been used successfully applied in a wide array of Machine Learning tasks dealing with sequential data, such as the chinese character recognition problem or extracting […]
When investing, we spend plenty of time thinking about which securities should we buy but we rarely wonder how much money should we allocate in each asset.Although it does not seem like an important aspect, it is crucial when defining a strategy, up to the point that it can determine the whole performance of your […]
Introduction to Sentiment Analysis, one of the simplest NLP problems as it keep close to pure Statistics. Following this, we also introduce an easy way to get words images based on its frequency
Inside most of the Deep Learning frameworks that are available lies a powerful technique called Automatic Differentiation. If you ever encountered these words but don’t know what they mean or how this procedure works, this post is for you.
Currently, strategies based on premium factors are everywhere: from funds or ETFs built on ratios or statistics perfectly specified, trying to exploit specific factor premia, to boutique instruments more or less opaque that following one or more risk premia.
Extra Trees and Random Forest are two very similar ensemble methods and often a doubt arises as to whether to use one or the other. What is really the difference between them?
In this blog we’ve talked about autoencoders several times, both as outliers detection and as dimensionality reduction. Now, we present another variation of them, variational autoencoder, which makes possible data augmentation. If you have ever faced Machine Learning problems, you will have dealt with the lack of data to train models. Well, this method will […]
Can a Sharpe ratio of 1.55 be better than a Sharpe ratio of 1.63 in a 1 year track-record? Not necessarily. Sharpe ratios are not comparable, unless we control the skewness and kurtosis of the returns.
Although mathematically both are considered parameters, in the context of Machine Learning, parameters and hyperparameters are separate concepts. Let’s see the need for this distinction that occasionally makes things confusing.
Markets are said to be driven by randomness, but this does not imply that they are 100% random and thus, completely unpredictable. In the end, there are always people behind investments and many of them are making decisions based on what they read in newspapers. We will be trying to estimate the returns of a […]
Artificial Neural Networks (ANN) have been applied with success to many daily tasks that needed human supervision, but due to its complexity, it is hard to understand how they work and how they are trained.
The Black-Scholes formula can be used to create a hedge for an option. However, this model is derived in continuous time. What happens when we use it to hedge an option in discrete-time?
In a previous post, we showed that unhedged currency exposure adds unrewarded risk to our investment, hurting risk-adjusted-performance. This risk should either be neutralized through passive hedging; or mitigated and turned into profit with an active overlay, the latter being what ETS has been doing for the last 20 years.
In one way or another, most quantitative models somehow seek to find and exploit relationships between two or more series of returns. Therefore, the usual pipeline has a time-series go through mathematical procedures which condensate in a couple of figures meaningful information: the expected mean, volatility, drawdowns, runups, correlations, among others. That is, the space […]
We are living through unprecedented times. Due to the ongoing global health pandemic, the international markets have plummeted with speeds never seen before, reminiscent of the 1930s and the Great Depression.
Many investment strategies use the mean like an official parameter. However, this estimator can be considered non-robust, being easily affected by outliers. But if we take a look at almost any financial series, we will notice that outliers may appear more often than we might think.
I have always been curious about how deep learning frameworks are created. I use Keras, TensorFlow, and PyTorch and they all are really good, but sometimes I feel like I am playing with a black box (in some frameworks I feel it more than in others) that hides its secrets.If you feel the same way, […]
You may have seen in different papers or websites, analysis of how a specific active portfolio is exposed to different financial factors (Value, Growth, Size, Quality, etc). This insight is very interesting in order to know what to expect from a strategy and to explain and understand its behaviour, compared with a benchmark (which defines […]
We will learn how to implement a simple function using TensorFlow 2 and how to obtain the derivatives from it. We will implement a Black-Scholes model for pricing a call option and then we are going to obtain the greeks.
In previous posts (Visualising Fixed Income ETFs with T-SNE) we have talked about dimensionality reduction algorithms to visualize financial assets and find recognizable patterns. The conclusions were that it didn’t perform well compared to PCA, which is a more classical approach.
Open-High-Low-Close (OHLC) bars are a type of financial data typically used to represent daily movements in the price of a financial instrument. They give us more information about certain characteristics of the series than line charts, such as intraday volatility or daily momentum. Could Generative Adversarial Networks learn to generate series with the underlying structure […]
In FOREX, both the EURCHF and USDCHF series have outliers that can be a problem when applying Machine Learning techniques to them. So, in this post, the performance of an autoencoder detecting these anomalies is going to be studied.
We’ve already talked about dimensionality reduction long and hard in this blog, usually focusing on PCA. Besides, in my latest post I introduced another way to reduce dimensions based on autoencoders. However, in that time I focused on how to use autoencoders as predictor, while now I’d like to consider them as a dimensionality reduction […]
According to Wikipedia “in finance, a trading strategy is a fixed plan that is designed to achieve a profitable return by going long or short in markets. The main reasons that a properly researched trading strategy helps are its verifiability, quantifiability, consistency, and objectivity. For every trading strategy, one needs to define assets to trade, […]
What is feature extraction/selection? Straight to the point: Extraction: Getting useful features from existing data. Selection: Choosing a subset of the original pool of features.
Awesome data visualizations are one of my favorite things in data science. I’m constantly searching for new ways to represent data and relationships. I am a true believer that “actions speak louder than words” and “a picture is worth a thousand words”. I maintain this philosophy in data science, research and analytics in general.
As Nassim Taleb states, ideas come and go, stories stay.So today Maximiliano and myself are going to build for you a story which hopefully will carve in your mind the importance of doing things right; or put differently, of using logarithmic returns instead of arithmetic returns when you should. To do so, I will use a common process carried out in Finance: return annualization. We will build on top of it some concepts and finally end up showing the importance of using logarithmic returns.
We try out some Halloween strategies based on irrational decision making. Check out this spooky stuff. You’re in for a treat.
What good is synthetic data for in a financial setting? This is a very valid question, given that data augmentation techniques can be hard to evaluate and the time series they produce are very complex. As we will see in this post however, it turns out that synthetic series can be very useful! Specially mitigating […]
Image processing is one of the hot topics in AI research, alongside with reinforcement learning, ethics in AI and many others. A recent solution to perform ordinal regression on age of people has been published, and in this post we apply that technique to financial data.
The market is driven by two emotions: greed and fear.Have you ever heard that quote? It is quite popular in financial circles and there may just be some truth behind it. After all, when people, with short-term investments, think are going to lose a lot of money, many of them sell as fast as they […]
Deep Learning is a sub-class of Machine Learning algorithms whose peculiarity is a higher level of complexity. So, Deep Learning belongs to Machine Learning and they are absolutely not opposite concepts. We refer to shallow learning to those techniques of machine learning that are not deep.
Generative Adversarial Networks are a quite powerful tool for generating synthetic samples. Visual inspection has been used as a traditional measure of performance. However, it is quite hard to inspect when a time series looks realistic or not! Which methodology can be used then? In order to measure sample quality, topological tools could provide us […]
Although we find currency risk particularly interesting, it is not often the case with many investors for whom it is no more than a necessary inconvenience. As such, they tend to neglect it, accepting undesirable non-remunerated risks and missing potential opportunities. To prevent this, in this post we will try to provide an understanding of the […]
Who deals with big dataset in order to use Machine Learning techniques knows that it is vital to keep data clean and to avoid data which is weird. In this point, outliers are a pain in the neck because they may make the results be misunderstood. Several methods can be used to remove outliers from […]
Have you ever thought about the bias of your portfolio to specific countries or asset types? Do you know that high concentration in one region implies a riskier path for your portfolio? If you want to know how to improve your portfolio using Graph Theory, first you’ll need to understand the basics.
This is a follow-up post to a recent post in which we discussed how to generate 1-dimensional financial time series with Generative Adversarial Networks. If you haven’t read that post yet we suggest you to do so, since it introduces the building blocks used in this one.Here we will go over the process behind generating multidimensional […]
When dealing with mathematical modeling, choosing the right scale to frame the equations can make the difference between a successful and lasting model, or poor description of reality.In today’s post, we explore two important scaling procedures that arise in finance: the annualisation of returns and volatility. These are common terms in the industry and building […]
Neural networks have turned into the top Machine Learning algorithm. Progress in this field is plenty on fire and it is really impressive all the goals nets have achieved, like painting à la Van-Gogh, writing a Beatles song, creating a person who does not exist, making everybody dance and even bringing the Mona Lisa to life. These awesome accomplishments […]
Understanding classification of market regimes is fairly important in finance. It all comes down to correctly predicting the way prices are going to move. But prediction isn’t the only crucial thing; knowing how to describe what has already happened is also of great importance. In this QuantDare post we look at types of classification of […]
Alphabet, the largest Internet-based company, has based its success on sophisticated information retrieval algorithms since its origins. Now, 20 years later, one of its divisions is open-sourcing part of its secret sauce, drawing attention from developers all over the world.
Topology could be used to gain insight on the shape of our data, as we explained in our last post. Today, we will put this theory into practice by analyzing the 2008 financial crisis.
One of the hardest and most frequent tasks for anyone in the quantitative finance world is to summarize or visualize in a simple way a vast amount of data to represent a company.In this blog, we have covered different Machine Learning techniques that allow us to summarize information through dimensionality reduction. These techniques let us […]
The scarcity of historical financial data is a big hindrance in algorithmic trading model development. In the ever-changing economic reality we live in, countless models are tried and evaluated. Most of these models seek to extract information from the market by measuring a set of reasonable variables. Through backtesting, an overwhelming amount of these models […]
The application of Machine Learning for ranking is widely spread. This application of Machine Learning is a little different from the classical ones of classification and regression.In the case of ranking, the interest is not in the accuracy of an estimated value (regression) or the guess about the membership of an element in a cluster […]
Dealing with fixed income is becoming a headache for managers who would like to know when it is a good moment to invest. Some tend to analyse the relationship between fixed-income assets and external factors. There may be numerous factors that have influence in the fixed income series, such as, interest rates, currencies movements, politics, […]
Mutual funds are one of the most used investment vehicles in the world. In this post let’s see how they behaved in recent years.
In a previous post, we took a look at the computation of a portfolio’s exposure to its allocations. Then, to show the effects of active management, we compared the return made by two portfolios. But there is so much more to look inside the financial time series.Since we left a couple of cliffhangers, let’s jump […]
Both portfolio valuation and management have many facets, but one they have in common is attribution, that is, how much each asset or collection of them is contributing to the return. Thus, in these series of posts, we are going to wax technical about the computation of asset exposure. We will show how an initially […]
Factor investing is a broadly used approach in asset management, specially for the equity market, but, can we apply this idea in order to explain currency returns?The idea at the core of factor investing is that there are different sources of risk in the market and that the exposure of the different assets to these […]
If you are working in finance, you have almost surely heard of risk-reward ratios and probably used some of them to evaluate the performance of a stock, ETF, or any other investment strategy. Among the different alternatives, the most popular risk-reward ratio is the so-called Sharpe ratio, first introduced by William F. Sharpe in 1966.
We always look at prices to understand the evolution of markets. But, what about the movement of capital in investment funds? How much cash flows from certain funds to others? In this post, we take a look at asset migrations.
In line with the previous post, Group Funds with the Sun, we continue exploring new ways to visualise and analyse financial data.We will take annual data from the current components of Dow Jones Industrial with data going back to 2000 to play around.
In this post we take a look at some impressive data visualisation techniques applied to tree structures. Our data: the entire mutual fund universe. Our mission: to make data both understandable and attractive.
Deep Reinforcement Learning applications in finance are still largely unknown. Nonetheless, recent developments in other fields have pushed researchers towards exciting new horizons.
Have you ever needed to estimate the probability of a rare event? So rare that you haven’t been able to encounter it in real data? Well, what if I told you that there exists a way to calculate a statistically correct approximation. Oh, and you won’t even need a calculator!
It is often useful to know what shape your data takes. Linear regression is one example, where you want to find out how well your data fits a straight line. Knowing that your data fits a straight line reasonably well gives you an advantage for understanding your data. For instance, you know that your data […]
Gradient Descent is one of the most important algorithms in Machine Learning. It is an iterative method to find the minimum of a given function. That is the reason why today we will go through the intuition behind it and cover a practical application.
If all finance developers around the world were asked to choose the main nightmare they have to face on daily basis, I bet most of them would choose ‘overfitting’. Furthermore, imagine you have to develop an algorithm which has only one ‘ingredient’ to be modelled, only one time-series representing the historical information… Yes, in that […]
Smart Beta ETFs are achieving an increasing popularity, seen as the perfect equilibrium between passive investment and active management. But, what’s the difference between them and the traditional ones? Is it possible to create our own ETF with some previous experience and without assuming higher trading costs? Would it be worthwhile?
One of the most asked questions when dealing with several features is how you can summarise or transform them to similar scales. As you probably know, many Machine Learning algorithms demand the input features be in similar scales. But, what if they aren’t? Can we just work with raw data in the hope that our […]
Take your favourite newspaper and write down all the numbers you can find in it. Then take the first, leftmost digit of each number. This is called the most significative digit (MSD). What is the frequency you expect to observe for these digits? If your answer is that all digits from 1 to 9 have the […]
Let’s start with a simple question: what is the first thing to think about when you create a portfolio? I’m sure several ideas spring to mind, but let’s go to the heart of the matter: what is the relationship between the assets in a portfolio? That is one of the greatest managers’ concerns. They want […]
Value at Risk and Expected Shortfall are related to the risk taken by a portfolio but… Which one is the best? Let’s learn together the differences between these two measures.
Class imbalance can seriously damage the precision of your binary classifier. In this post you will learn some simple ways of evening the size of your classes before training to prevent your classifier from cheating.
In financial markets, some agent’s goal is to beat the market while other’s priority is to preserve capital. However, what we know for sure is that all the agents wonder if they made their optimal choice. Having the right tools can help us to make better investment decisions.
I fell in love with k-Nearest Neighbors algorithm at first sight, but it isn’t blind love. I have plenty of reasons to be mad about it.
Building profitable portfolios has been giving investment managers headaches for decades. Many approaches have been used up until now, some of the most well-known being Markowitz’s Efficient Frontier and Risk Parity.Today, we are presenting a brand new approach to this recurrent problem developed by Dr. Marcos López de Prado applying Modern Graph Theory and Machine Learning techniques.
There are many problems that a data scientist encounters when “fighting” financial data for the first time: nothing is normally distributed, most problems are tough (low signal to noise ratio) and non-stationary high-dimensional time series are ubiquitous.In Quantdare we have spoken many times about one of the main sources of non-stationarity in financial time series: […]
For those of us working with time series, the autocorrelation function (ACF) is a fundamental tool to understand how the values in a series correlate with others certain distance away.
In this post, we’ll take a brief look at biclustering algorithms. They reveal easily interpretable patterns in our data and give us more information about the links between observations and features than simpler clustering algorithms usually do.
When dealing with data we (almost) always would like to have better and bigger sets. But if there’s not enough historical data available to test a given algorithm or methodology, what can we do? Our answer has been: creating it. How? By developing our own Synthetic Financial Time Series Generator.
In recent years sector rotation strategies, using the S&P 500 sectors, have struggled to outperform the index. In this post we are going to see how the index behaviour has changed compared to its sectors using our friends the monkey quants.
My favorite moment of the film The Social Network takes place when Mark Zuckerberg asks his roommate Eduardo Saverin to explain the Elo system to him. This algorithm is used to rank chess players. At that time, Zuckerberg was developing the just-for-fun website Facemash, an early predecessor of Facebook targeted at Harvard students. In this […]
We have talked about outliers several times in this blog. Examples include how to detect them or how to transform the data to remove them. Here we have another technique to detect outliers in our big data set: the isolation forest algorithm.
Today is QuantDare’s 4th birthday. I want to celebrate by doing a quantitative clustering, as an alternative to the traditional sectors clustering. To do so, let’s use some Machine Learning techniques seen in this blog along the years.
Is the bitcoin market (Ethereum, Dash and Litecoin) efficient?After reading the paper, “Persistence in the cryptocurrency market”, which tries to answer that question, I was challenged by a colleague to replicate its results. This led me to write this post to highlight the great variability of the Hurst exponent estimation, not only between implementations but […]
Nowadays the benefits of diversification as a business or financial strategy are acknowledged by most players. In this post, I will argue that the ultimate frontier for diversification is to be intrinsically diversified, as nature does it, by building teams as dynamic populations of diverse individuals. Diversity is not only fair and good for karma, […]
Rabbits, triangles, and triplets. These three things are linked by an important series often characterised by shells and flowers. But what do the Fibonacci numbers (and their subsequent sequence) have to offer the world of finance?
Survivorship bias is one of the most common biases in finance, and it’s easy to fall victim to it. Let’s find out how to remain vigilant and overcome this hurdle.
Forecasting the market or the outcome of a gamble is important. Deciding how much to invest or bet based on how confident you are about the prediction is similarly as important. But don’t let the pressure get to you; the Kelly criterion is here to help us make this decision.
Thought you knew everything about correlation? Think there’s no fooling you with the question of correlation with financial prices or returns? Well maybe, just maybe, this post will enlighten you.
Financial markets are complex systems where millions of people buy and sell and millions of dollars change hands each microsecond. When you think about markets in this way, there’s no question as to why they are so incredibly hard to understand, predict and beat.In order to unravel this huge puzzle of financial markets, we can […]
Rankings are everywhere. They are sometimes useful and, at other times, contradicting. In such a case, we need to come up with a consensus ranking but… how do we evaluate ranking consensus?
The relationship between series can be measured by different methods. The most common is to check if both series move in the same way. We’d like to go further, and see if the difference between them is always the same. We call it cointegration.
In funds management, we can find as many strategies as drops in the ocean. If we told you about one which had practically zero costs and allowed us to limit the maximum spread loss, would you say it’s a clever move, or a lazy workaround?
Is it possible to foresee the future movements of a stock? Let’s use Machine Learning techniques to predict the direction of one of the most important stock indexes, the S&P 500.
Clustering has already been discussed in plenty of detail, but today I would like to focus on a relatively simple but extremely modular clustering technique, hierarchical clustering, and how it could be applied to ETFs. We’ll also be able to review the Python tools available to help us with this.
In this post we’ll talk about dropout: a technique used in Machine Learning to prevent complex and powerful models like neural networks from overfitting.
In the financial markets, how can we predict support and resistance levels, and how can we determine price objectives by using Fibonacci retracement and extensions? Let’s dig into it!
Assigning weights to portfolio assets is challenging when we have to consider multiple constraints. Asset allocation may be seen as a constraint satisfaction problem (CSP), and some algorithms allow us to define our own restrictions and look for an optimal weight distribution.In this post, we will show how to define a CSP for your portfolio […]
There are different ways to measure portfolio risk, and one such way is with copulas. Join us to discover why using copulas is a great alternative, and let’s put it into practice.
Once we are familiar with the theory surrounding Risk Parity, thanks to the posts written by T. Fuertes and mplanaslasa, it’s time to put the strategy into practice and try out the algorithm for ourselves. In this post we discover how it works, analyse the strategy and create our own portfolios.
Often in financial markets, as in our daily life, we imitate the decisions of predecessors, instead of analysing available information and making our own decisions. This decision imitation could lead to collective hysteria, and investment calls may be influenced by these panicked situations.
Markov chains say that any information that can be used to predict tomorrow’s price is contained in today’s price. Let’s do a little talking about that.
Volatility is a synonym of risk in terms of portfolio management; so that everyone wants to take to their heels when they hear from it. However, you shouldn’t be afraid because there are several methods to control it. Let’s see two of them and the differences between them: risk parity versus inverse volatility strategies.
How often have you heard that there are connections between financial series? In particular, it’s common to hear that series representing the economy of a region or country are related.The whole world is influenced by certain major factors, such as wars, economic crises, and political events. There are other connections, too, between geographic locations and […]
The Kalman filter is a method for estimating unobservable state variables from observable variables that may contain measurement errors.This algorithm requires two types of equations: those that relate the state variables to observable variables (main equations) and those that determine the temporal structure of state variables (state equations).
Investors, just like animals, make their best bets based on the information available to them and their previous experience. Working on quantitative neuroscience and animal behaviour for almost 10 years has given me a rich view on decision making.In my personal view, animals collect information from their senses, directly or by interacting with other individuals, […]
Artificial neural networks are mathematical models that try to reproduce the function of the nervous system: they capture information, process it and generate a response adapted to each situation. It’s a computational technique that’s used today in many fields: medical applications, market, and customer analysis, data mining, industrial process optimisation, financial and economic modelling… Its appeal […]
Everybody would like to see the future. If you’re a portfolio manager, you’d definitely love to see the future.Many posts here on QuantDare deal with the challenge of predicting the future (with Prophet, Random Forests, Lasso, etc). This time, we talk about something different: imagine we are able to predict the future exactly. Now what? […]
The Stochastic portfolio theory (SPT), a relatively new portfolio management theory, was first introduced in 1999 by Robert Fernholz. It can be combined with Machine Learning and Bayesian statistics. This allows the investor to generate trading strategies. It’s a very attractive theory for several reasons: it’s theoretical, it’s not very well known and, most importantly, […]
We are rather used to reading this disclaimer (or some variation thereof) in mutual fund prospectuses or investment vehicle webpages. Despite warnings, investors and advisors insist on considering past performance (and some other related metrics) as important factors in asset selection. But, are they really wrong? In this post, I will try to shed some […]
Prophet is a Facebook Research project launched in February 2017. In another post, we have been playing with it by using financial time series. In this time we compare the produced forecast with the actual real price in our chosen interval.
We often face the problem of having to sell an asset within a specified period of time. This problem worsens if we also lack information about our asset’s historical prices. Under this circumstance, when should we sell our asset?
A while ago, I began the course ‘Exploratory Data Analysis’ within the ‘Data Science’ specialisation on the Coursera website (which, by the way, I recommend to anyone who’s curious about the subject).In one of the first classes, which outlined the basic principles of visual data analysis (and in particular the convenience of displaying multivariate data), […]
Regardless of which trading system you use, there will always be varying degrees of success. Such results are normal, of course, as different systems are designed to work optimally under certain conditions. Unfortunately, the market does not always work to the assumptions made by individual systems. This is a problem, but it does have a […]
Does the saying ‘Sell in May and go away’ really work? To disinvest for a large portion of the year doesn’t make any sense… does it? See our findings here.
The S&P 500 index (SPX) is an American market index based on the stocks of 500 large companies. It’s one of the world’s most important market indexes and, therefore, predicting its movements is the goal of many finance analysts. In previous posts we have reproduced the SPX through clustering of stocks or even through powerful […]
We’ve spoken previously about different clustering methods many times: K-Means, Hierarchical Clustering, and so on. However, this field does not end here. In this post, I will try to find how K-Means clustering works in an investment solution.
In our last post, we asked: Are we able to find any advantages from Lévy flights in order to improve activities related with the stock markets?As we always deliver the goods, we’ve looked for an example of a particular kind of Lévy Flights’ usefulness. In particular, we’re interested in ‘Truncated Lévy flights’ (TLF). Before showing the results obtained with […]
Bootstrapping method DefinitionFaced with growing uncertainty in financial markets, investors are worried about the future of their investments. Travelling in time to check the future reality is not yet a possibility. For that reason, we use techniques and create measures to gain confidence in our investments’ future behaviour.Bootstrapping is a financial technique that allows us to get […]
It’s uncommon to open the technology section of a newspaper or specialised blog and not see an article about Artificial Intelligence (AI) or Machine Learning (ML). Most of the time, both terms are used as interchangeable buzzwords, removing much of their technical meaning. This fact may leave many wondering if they are somehow synonyms and, if not, what […]
Have you heard about the new Facebook Research project? In February 2017, the giant social network launched Prophet, an amazing forecasting tool available in Python and R. And it looks that you can play with it by using financial time series.
How to improve portfolios based on momentum factor? We propose you to use two strategies for getting it: dual momentum and dual plus momentum.
Random forest is one of the most well-known ensemble methods for good reason – it’s a substantial improvement on simple decision trees. In this post, I’m going to explain how to build a random forest from simple decision trees, and to test how they actually improve the original algorithm.
How can we predict future returns of a series? Many series contain enough information in their own past data to predict the next value, but how much information is useable, and which data points are the best for the prediction? Is it enough to use only the most recent data points? How much information can […]
Classification trees are used, as the name suggests, in solving classification problems. Here are some definitions and Matlab tips to help you dabble in this subject.
Imagine we had a table with the distances between some European cities, but we don’t know any Geography. It would be a complicated task to correctly place them on a map:However, using “Multidimensional Scaling” the task becomes simple:Similarly, given distances between time series (in this case NAVs of investment funds) we could carry out the same […]
When talking about quantitative trading, there are a large number of indicators and operators we can use as a buy/sell rule. But apart from deciding what indicator to follow, the most important part is in setting the correct parameters. So, one method we can use to find adequate parameters without spending too much time in the simulation of a […]
When you’re working with a huge data set, knowing how to deal with them is as important as representing them in a proper way. In the machine learning world, you can find a great many ways to represent data, and most of them are visually fantastic. In this post, we want to introduce you the graph […]
Lévy flights shows up in nature, marketing, cryptography, astronomy…even in social media. Here you have a couple of examples of it for “dummies”.
“Machine Learning” or “Data Science” are trending concepts. There are different websites (like Kaggle) where Data Scientists can analyse big datasets to resolve some real problems using Machine Learning techniques. These techniques are applied to huge amounts of information, to learn the relationships between its features.Machine Learning algorithms use all the values of the dataset. If we […]
Principal Component Analysis (PCA) is a technique used to reduce the dimensionality of a data set, finding the causes of variability and sorting them by importance. How?If you have a set of observations (features, measurements, etc.) that can be projected on a plane (X, Y) such as:You can display the previous graph from X* and […]
IntroductionWe’re all familiar with the standard forms of graphs and charts used in almost every report or dashboard. Bar charts, line graphs, pie charts are widely used almost everywhere; there are built-in templates within most standard reporting tools such as Excel, Tableau…In this post we will introduce the Chord Diagram. This chart offers visualisation of datasets in […]
Time series pervade financial markets and, although some embrace the so-called efficient market hypothesis, stating that current market prices reflect all available information about a security into its price, I’m more inclined to think they provide us with a lot of information that we rarely know how to exploit for our own benefit.I agree that […]
Ladies and gentlemen, place your bets! Today we’re going to do our best to beat one of the most frightening opponents that you can face in finance: a monkey.As you probably already know, on this blog we are all quite obsessed with predicting trends and returns. You can find other brave attempts in ‘Markov Switching Regimes say… bear […]
It’s hard enough deciding which Machine Learning technique to use, but after selecting an appropriate clustering algorithm the next challenges begin: how good is the separation and into how many groups should you divide the data?Maybe three is not always a crowd… First, let’s set the sceneWe want to create a diversified investment strategy using a set of predictions and […]
In this post we are going to develop an initial approach to an investment strategy which aims to beat Euro Stoxx 50 Index. With this objective in mind, we are going to use Machine Learning and Data Science techniques (for some background, you can read the post titled “Machine Learning: A Brief Breakdown“). How do […]
In recent articles, we talked about PCA and ISOMAP, as techniques for dimensionality reduction. On this occasion, we put the focus on T-SNE, in relation with visualisation and understanding of multidimensional datasets in a low dimension space, where the human eye can find patterns easily.T-SNE was developed in 2008 by Laurens van der Maaten and Geoffrey Hinton. It comprises of two […]
The Machine Learning world is quite big. In this blog you’ll find posts in which the authors explain different machine learning techniques. One such method is clustering and here’s another method: Hierarchical Clustering, in particular the Ward’s method. You can find some examples in ‘Reproducing the S&P500 by clustering’ by fuzzyperson, ‘Returns clustering with K-Means algorithm’ by psanchezcri or ‘”K-means […]
There are a wide variety of Machine Learning techniques that help us to solve Big Data problems. In this post we talk about how to apply Lasso Regression in Portfolio Management. You may have heard of this technique in the past, and for that reason I’ll try to keep the introductory explanation brief. Lasso definitionLeast […]
We continue with our last OBSSESION… trying to capture an index trend while at the same time, not playing with future information.We are going to introduce the Markov Switching Regimes (MSR) model which, as its name indicates, tries to capture when a regimen has changed to another one. This may be a change between opposite trends, […]
Tail (or extreme assets) returns have been extensively studied. In his amazing paper: “Empirical properties of assets returns: stylized facts and statistical issues”, Rama Cont provides a framework on statistical analysis of price variations in various types of financial markets. He presents “Heavy tails” in asset returns as a stylised fact, i.e., statistical properties common […]
Futures are financial instruments created to avoid the uncertainty of future price evolution of all kind of underlying assets, whether it be stocks/indexes, commodities, bonds, currencies, etc. The future contract is an agreement to buy or sell a specified asset on a certain future date at an agreed price. What is the fair price of the […]
It is known that data mining algorithms are not perfect, and can fail under certain conditions. K-Means is an example of that triviality, but there is a good alternative: K-Medoids.In a previous post, “Machine Learning: A Brief Breakdown” we already mentioned that K-Means is the cluster analysis algorithm par excellence and it is one of the […]
Bagging and Boosting are both ensemble methods in Machine Learning, but what’s the key behind them? Bagging and Boosting are similar in that they are both ensemble techniques, where a set of weak learners are combined to create a strong learner that obtains better performance than a single one. So, let’s start from the beginning: […]
The Beta of a stock indicates the movement relationship between the Stock and “the market”. A beta less than 1 indicates that the Stock is less volatile than the market, while a beta more than 1 the contrary. How is it calculated?If we plot the daily/weekly/monthly returns of the Stock versus the daily/weekly/monthly returns of […]
Outliers are annoying. Analysis would be easier if they did not exist. So why not to remove them? As Libesa told us in her last post titled “Machine Learning: A Brief Breakdown”, the world is going crazy with Machine Learning, and now we use it in all domains. In this post, we will see another application […]
In this post we are talking about autoregressive models and their application to a financial world. This model follows the idea that the next value of the serie is related with the p previous values. Definition of p-order autoregressive modelAn autoregressive model, or AR, is a type of modelling that explains predicted variables as a […]
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 […]
Is everyone around you talking about Machine Learning? Have you heard about some algorithms and techniques but are missing the bigger picture? This is a good place to start… A new generation of intellectMachine Learning is a hot topic in the science world right now. By combining the powers and capabilities of both computers and […]
One question often asked in forums and blogs is how to adjust stock prices in order to take into account dividend payments. There are several reasons why we may be interested in adjusting stock prices: Analysing total returns, taking into account dividend reinvestments for reporting (performance, historical volatility, etc.). Applying trading strategies based on the stock […]
The world of finance is no stranger to fashion, and Low volatility equity investing has recently attracted serious interest from the investment community. Its popularity has led to doubts regarding the valuation level for this overcrowded arena.Just look at the current market caps of the most representative ETFs of the low volatility anomaly. If we […]
Is it possible to predict the next return’s sign by looking for historical patterns?One of the main problems when trying to develop investment algorithms is finding an estimator (with the intention to predict future returns) that minimizes error between the estimation and the real return.As we can see in “Vecinos cercanos en una serie temporal“, there are […]
ISOMAP is a non-linear technique for dimension reduction which allows you to find relationships in an unordered dataset. What do we mean by non-linear? As opposed to other linear techniques used for dimension reduction like PCA or SVD, data points that, in appearence, are close to each other (small Euclidean distance) could in fact be farther (Geodesic distance) […]
It is almost impossible to know the future price of assets, so what if you knew what would be the price movement? It could be enough to earn money!
Everybody knows about the Central Limit Theorem, but have you ever seen a visual demonstration?
Is it possible to classify and predict (yes, predict!) if market trends will be bullish, bear or ranged by using a method called “naïve” and based on something as simple as Bayes’ theorem? Let’s see! Our main objectiveHere, we’re looking to explore machine learning techniques that can help us not only to label series in a posteriori […]
Do you know how a fireman and the direction of a financial time series are related? If your answer is no, you’re reading the right post. An introduction to k-Means: Voronoi diagram Suppose that you a work at an emergency center, and your job is to tell the pilots of firefighter helicopters to take off. You receive an […]
In this post, I want to create a strategy that is able to choose assets that make it look like an index Yt. Then, take the ones most correlated to it.Take a look at the chart below:We can see here that the Xt and the Xt+c series have exactly the same correlation with Yt.From this graph, […]
Markowitz Model is a famous method in the Portfolio Investment Theory. This model provides efficient portfolios, (i.e. portfolios with the highest profitability and lowest risk possible) through mathematical programming. The set of portfolios composes the efficient frontier. The strategy is based on quadratic optimisation, therefore minimizing the estimated risk and negative return. We often calculate the efficient frontier by using a fixed […]
In the field of predictive analytics, a confusion matrix is a table that allows the visualization of the performance of an algorithm, whose objective is to predict the classes of a variable. The name “confusion” stems from it making it easy to see if the system is mislabelling one class as another. The confusion matrix shows two rows and […]
It is well known that an efficient portfolio should be comprised of uncorrelated assets. The objective is to cover possible widespread falls of all portfolio assets. But what is the negative effect of investing in correlated assets? Does the correlation benefit at any point? How often does the correlation work against the earnings? Firstly, we focus […]
Let’s begin with a simple question. Can we use the movement of the main stocks in the S&P 500 to predict the index movement? The second question is…Who are the main stocks? The bigger ones? Maybe the more bullish of them? So, how should we decide who are the most representative companies?In this post we propose a relatively new […]
There are some anomalies that shake the assumption of efficient market. One of the most studied is related to the size of the companies. Some authors have demonstrated that smaller companies (that is, the ones with smaller market capitalization) tend to outperform larger firms. What could be the explanation of this anomaly? In reality it’s […]
The price of gold is an interesting financial series but not an easy one to predict. It is very volatile with large sharp unexpected movements.
Many people incorrectly think that buying an inverse ETF is equivalent to having a short position in the components of the ETF.The mistake arises from assuming that the ETF holds its open positions for days or months. But that’s not the case. Rather, this kind of ETFs is built for day trading, since they close their […]
Wouldn’t it be terrific if we knew that on a specific day of the month, a security is going to grow significantly? We could invest only on those days we know we are going to make money, and go to sleep under the palms the rest of the time.Well, some anomalies do exist in the […]
Predicting a time series is often complicated and frustrating. The series may appear completely random; a volatile sequence showing no signs of predictability. But let’s not despair just yet…there are some options available to us.
In a previous post we looked at the basic characteristics of Bayesian Statistics, and its possible applications in finance. In this entry we analyse a specific example involving stop loss levels, and implement a EURUSD exchange rate strategy. Bayesian Inference example in finance. This post aims to disperse any remaining Bayesian doubts and help you to better […]
Wouldn’t it be great if there was a way to combine statistical probabilities with human intuition and expertise? How can we use Bayesian Inference in finance? Isn’t data more trustworthy when it’s backed by prior knowledge and beliefs about its behaviour? In the light of new evidence, can’t we update previously calculated probabilities? Doesn’t it make […]
Empirical research has shown that return premium may be captured in equity markets if we base our investments on certain factors, included in which are: equity size, value or momentum. The nowadays-popular low-volatility (low-beta) factor may also be include. This (to a certain point) is the basis of this post.Following this factor approach, we are […]