Quantopian is committed to being a company and community of substance. We want to ask hard questions, and invest the effort to find detailed answers. Everything we do demands our best performance: our platform, our algorithm portfolio, our events, our office, our lectures. Everything requires thoughtful design. Including our logo.
We want a logo that is honest, scalable, and special to Quantopian. It should convey simplicity and ease, just as our product does. It should be open and encouraging, like our community.
We often refer to ourselves as “Q,” and I think it's because we have a quiet determination to make an amazing product. We build for quants. We have talented engineers and designers who know that quants are always where we start. Our logo should reflect that aspiration to keep growing and to keep solving important problems.
We believe great design boils down to determination, the willpower to keep working, and iterating until we have the best answer. We’ve been testing our new logo internally for over a year. It gave us the opportunity to experience and improve it before it was worthy of becoming part of Quantopian.
Our logo is not merely “new,” it’s a smarter identity as a whole. It’s concise and specific to certain uses, which makes it easy to fit into a variety of mediums. This flexibility is a technical win for Q on the front end.
Our logo is not purely technical, it is also a reflection of our community and our company culture. We have an amazing community of quants, students, statisticians, professors, research scientists, mathematicians, and professional investors.
People around the world make up Quantopian, and we now have a mark to back them up.
Our community reached a watershed moment in Q4 of 2015: the first community authored algorithms were chosen and deployed with capital. We analyzed tens of thousands of algorithms, and then we made six-figure allocations to 3 of them. We are writing to the whole community to say thank you — this is something we accomplished together. We also want to share some details, and to encourage and inspire you to keep writing great algorithms.
Allocation and Compensation
The allocation process worked out just as we had hoped that it would. We approached each of the chosen authors with a contract. The terms of the contract promise that a portion of the returns be paid to the author as compensation. The contract also covers the other things you'd expect - length of the contract, maintaining the intellectual property as the author's, etc.
We then did some additional diligence with the authors and worked with them to make the algos more robust for live trading. For instance, one of our author's algorithms had some brittle rebalancing logic that failed during stress testing, and we asked him to correct that before we deployed it with real money. Once the contract was signed and diligence was complete, we deployed the algorithm using our capital.
Algorithm authors were paid for their 2015 performance, and we look forward to writing checks again.
These allocations are in addition to, and separate from, the real-money trading we have done for Quantopian Open winners. These new allocations were made on the basis of analysis by our quant research team, using tools like pyfolio tearsheets, and not the contest rules.
More Allocations Coming
We are making additional allocations this quarter and going forward. We expect our allocations to increase in size over time.
All algorithms with at least 6 months of out-of-sample data are being considered. We evaluate the algorithms by looking at their in-sample and out-of-sample performance; we never look at the code itself. As we have outlined, we are looking for well-hedged, low-beta, low-volatility algorithms. Obviously, they also have to be profitable. Finally, they must have low correlation with other algorithms we have allocated to.
Many algorithms we have considered were promising but fell short in one vital area or another. We've been contacting these community members and have been working with them on improving their algorithms. After additional out-of-sample time passes we hope to provide them with allocations.
These allocations are all being made from Quantopian's own balance sheet - we believe in this model enough to risk our own capital. This is proprietary trading, or "prop trading." We are using prop trading to refine our algorithm selection process, our risk management, and our algorithm portfolio construction. We are very pleased with the progress in all of these areas.
Our business growth depends on making much more capital available to your algorithms. More capital also means you can earn larger royalties by licensing to Quantopian. We are working to ramp both the number and the size of capital allocations to your algorithms by transitioning from prop trading to a hedge fund.
Keep Writing Algorithms!
These allocations are the latest step in the progress of our community and in our business, but it is far from the last step. The platform is improving and expanding. There is much more capital still to allocate.
Most importantly, there are more algorithms for you, our community, to write. These allocations are how we can convert your hard work and insight into your profit. The great algorithms you're writing today are the allocations we will be making tomorrow.
Note: Past performance is not an indicator of future returns. This note does not constitute an offer or solicitation to invest in any securities.
Parameter optimization of trading algorithms is quite different from most other optimization problems. Specifically, the optimization problem is non-convex, non-linear, stochastic, and can include a mix of integers, floats and enums as parameters. Moreover, most optimizers assume that the objective function is quick to evaluate which is definitely not the case for a trading algorithm run over multiple years of financial data. Immediately that disqualifies 95% of optimizers including those offered by
cvxopt. At Quantopian we have long been, and continue to be, interested in robust methods for parameter optimization of trading algorithms.
Bayesian optimization is a rather novel approach to the selection of parameters that is very well suited to optimize trading algorithms. This blog post will first provide a short introduction to Bayesian optimization with a focus on why it is well suited for quantitative finance. We will then show how you can use SigOpt to perform Bayesian optimization on your own trading algorithms running with
This blog post originally resulted from a collaboration with Alex Wiltschko where we used Whetlab for Bayesian optimization. Whetlab, however, has since been acquired by Twitter and the Whetlab service was discontinued. Scott Clark from SigOpt helped in porting the code to their service which is comparable in functionality and API. Scott also co-wrote the blog post.
Bayesian Optimization is a powerful tool that is particularly useful when optimizing anything that is both time consuming and expensive to evaluate (like trading algorithms). At the core, Bayesian Optimization attempts to leverage historical observations to make optimal suggestions on the best variation of parameters to sample (maximizing some objective like expected returns). This field has been actively studied in academia for decades, from the seminal paper "Efficient Global Optimization of Expensive Black-Box Functions" by Jones et al. in 1998 to more recent contributions like "Practical Bayesian Optimization of Machine Learning Algorithms" by Snoek et al. in 2012.
Many of these approaches take a similar route to solving the problem: they map the observed evaluations onto a Gaussian Process (GP), fit the best possible GP model, perform optimization on this model, then return a new set of suggestions for the user to evaluate. At the core, these methods balance the tradeoff between exploration (learning more about the model, the length scales over which they vary, and how they combine to influence the overall objective) and exploitation (using the knowledge already gained to return the best possible expected result). By efficiently and automatically making these tradeoffs, Bayesian Optimization techniques can quickly find the global optima of these difficult to optimize problems, often much faster than traditional methods like brute force or localized search.
At every Bayesian Optimization iteration, the point of highest Expected Improvement is returned; this is the set of parameters that, in expectation, will most improve upon the best objective value observed thus far. SigOpt wraps these powerful optimization techniques behind a simple API so that any expert in any field can optimize their models without resorting to expensive trial and error. More information about how SigOpt works, as well as other examples of using Bayesian Optimization to perform parameter optimization, can be found on our research page.
Historically quant traders have used many price based signals to define an investment strategy. Many of these signals have been implemented into the popular TA-lib library, with an available Python library here. Typically, a price based signal takes in historical prices as input to compute the signal's value. For example, RSI (Relative Strength Index), is commonly used for mean-reversion and momentum trading. To compute RSI one must first choose the number of pricing days over which to compute the signal. Then, the trader chooses a range of valid values to trigger trade entry. The valid values for RSI is between 0 to 100. If a stock has undergone a sharp selloff recently, RSI values will trend towards 0, and after a strong rally, trend towards 100. A common trading strategy is going long a stock when RSI is below 20, betting on mean-reversion. Similarly, to go short when RSI is above 80. However, other groups of traders have found success betting on persistent momentum in the stock (rather than mean-reversion) when RSI reaches an extreme reading. In which case, the trader will go long when RSI is above 80, for example, betting that the stock will continue going higher.
This poses several questions:
Each decision made regarding specifying our trading signal (e.g. RSI) or how to interpret the signal's value for making a trading decision is effectively a free parameter in our system, and depending upon the range of reasonable values each free parameter can take, it can quickly explode the total combinations of possible parameter settings. Each signal added to the strategy can quickly increase the total combinations into the many millions and even billions; we'll see this firsthand in the example below that incorporates only 2 signals.
A discussion of strategy model overfitting, and evaluating how overfit a trading backtest may be, will not be addressed here, and will be the topic of a future blog post. An excellent introduction for how to address trading strategy overfitting in your own algorithms can be found here and here.
The large parameter space of millions, or billions, of combinations over which our strategy will need to be tested in order to determine the subspace where the global maximum is likely located is why Bayesian Optimization can be so effective at quickly evaluating potentially profitable trading strategies. Brute force grid-search over a billion combination parameter space is often intractable, even if each combination only takes 30-seconds to complete. Bayesian optimization decreases the evaluation of the model over the global search space by an order of magnitude, as described in the previous section.
The trading algorithm we implement below will create a simple structure for the passing in of free parameters into any simple price based trading signals (simplified to work more easily with ta-lib functions). Then each signal is evaluated each trading day, and when all the conditions are true, a trade is entered, and held until the next signal evaluation period (where evaluation period is yet another free parameter).
For the purposes of this optimization, our objective function will be the Sharpe Ratio of the strategy. A broadly accepted metric from industry for evaluating trading strategy performance. However, the framework implemented below allows for ease of swapping in any objective function desired by the analyst.
To illustrate how you can use Bayesian optimization on your zipline trading algorithms and how it compares to other naive approaches (i.e. grid search) we will use a rather simple algorithm comprised of a trading trigger based on two commonly used signals from the ta-lib library, RSI (Relative Strength Index) and ROC (Rate of Change).
The trading algorithm will implement what might be considered a sector rotation strategy, and search for trades across these Select Sector SPDR ETF's:
By running the trading logic across all of these ETF's we will be implementing a simple sector-rotation strategy.
Buy the ETF only if it meets both the RSI signal and ROC signal criteria. When an ETF is bought long, then an equivalent dollar amount of SPY will be shorted, creating a hedged, dollar-neutral portfolio.
By hedging all of our trades, it serves to "tease-apart" the actual usefulness provided by these signals (RSI, ROC) since it extracts upward movement in the stock simply occurring because the rest of the stock market is going up. As a result, the profit achieved by this hedged strategy can be perceived as more "pure alpha," rather than highly-correlated to the direction of the broad stock market.
The 7 free parameters of our trading strategy are as follows:
It's worth noting that even with just 2 price based signals, we have 7 free parameters in this system!
Reasonable Ranges for each of the 7 free parameters above (assuming each is an integer, with integer steps):
Multiplying the valid ranges of each yields a total combination count of:
Obviously grid-searching through all those combinations is unreasonable, though a skilled practitioner can prune the search space significantly by only grid-searching across each parameter using wider steps based on their intuition of the model they are building. But even if the skilled practitioner can reduce the grid-search to 10,000 combinations even that number of combinations may be unwieldy if the objective function (e.g. trading strategy) takes 1-minute to evaluate, which is quite frequently the case with trading strategies. This is where the benefit of having access to a Bayesian optimizer becomes extremely helpful.
Below is the result of an analysis accomplish in an ipython notebook comparing SigOpt's Bayesian Optimizer's results from 3 independent experiments, of only 300 trials each determined intelligently by their optimizer, to a "smart" grid-search of approximately 3500 combinations chosen intuitively from a reasonable interpretations of sensible RSI and ROC values. Only 3500 trials were chosen for the grid-search approach, because even those few combinations took 48 hours to evaluate. 300 trials were chosen for the SigOpt approach because in practice the SigOpt optimizer is able to find good optima within 10 to 20 times the dimensionality of the parameter space being optimized. This linear number of evaluations with respect to the number of parameters allows for optimization of algorithms that would otherwise be intractable using standard methods like grid search, which grow exponentially with the number of parameters.
(This was seen in 4 out of 5 runs with SigOpt, and the 1 that returned a worse objective value was only a minor shortfall)
In practice SigOpt is able to find a good optima in a linear number of evaluations with respect to the number of parameters being tuned (usually between 10 and 20 times the dimensionality of the parameter space). Grid search, even an expertly tuned grid search, grows exponentially with the number of parameters. As the model being tuned becomes more complex it can quickly become completely intractable to tune a model using these traditional methods.
An example of how quickly SigOpt discovered a parameter combination near our expected global maximum, is shown below, as well as a comparison versus the extremely course (and slow) grid-search:
Next we will inspect aspects of the optimization further. (If you wish to view the entirety of this blog, within the context of the ipython notebook that it was created, you can view it here on Quantopian's public research repo.)
Takeaway: Recognizing how poorly the strategy performs out-of-sample shows how important it is to perform additional analysis (cross-validation, out-of-sample testing, etc.) after using parameter optimization to discover a global maximum.
On a positive note, however, by increasing the speed of running the optimization from using the bayesian approach versus grid-search, we we able to assess our out-of-sample performance much more rapidly --because grid search to over 2-days to finish! The bayesian optimization via SigOpt allowed us to continue our research process 10x faster - in a matter of hours, rather than days.
For completeness, and to put the entire analysis together across backtest and out-of-sample, below is a pyfolio tearsheet allowing visual inspection of the strategy as it transitions from in-sample to out-of-sample.
If you wish to work on this analysis, or view the code used to accomplish the above, feel free to clone our research repo on GitHub.
Algorithmic trading used to be a very difficult and expensive process. The time and cost of system setup, maintenance, and commission fees made programmatic trading almost impossible for the average investor. That’s all changing now.
We’re excited to announce that Quantopian has integrated with Robinhood, a zero commission brokerage. This partnership has made the process of algorithmic trading, from start-to-finish, completely free.
From initial brainstorming with research, to testing and optimizing with backtesting, and finally, commission-free execution with Robinhood, algorithmic trading has never been easier.
Here’s What Users Get
How To Get Started
If you have an existing Robinhood account, you can begin trading today. If you’d like to open an account, you can sign up directly at Robinhood - the process takes less than five minutes to complete. For more information and video tutorials, our community post has you covered.
P.S. Attached is a sample algorithm that's geared and ready for live trading. It's based off Mebane Faber’s Tactical Asset Allocation. The allocation Faber proposes is designed to be "a simple quantitative method that improves the risk-adjusted returns across various asset classes." You can read the original academic paper from Meb Faber, or the previous discussion of the strategy on Quantopian.
When I give talks about probabilistic programming and Bayesian statistics, I usually gloss over the details of how inference is actually performed, treating it as a black box essentially. The beauty of probabilistic programming is that you actually don't have to understand how the inference works in order to build models, but it certainly helps.
When I presented a new Bayesian model to Quantopian's CEO, Fawce, who wasn't trained in Bayesian stats but is eager to understand it, he started to ask about the part I usually gloss over: "Thomas, how does the inference actually work? How do we get these magical samples from the posterior?".
Now I could have said: "Well that's easy, MCMC generates samples from the posterior distribution by constructing a reversible Markov-chain that has as its equilibrium distribution the target posterior distribution. Questions?".
That statement is correct, but is it useful? My pet peeve with how math and stats are taught is that no one ever tells you about the intuition behind the concepts (which is usually quite simple) but only hands you some scary math. This is certainly the way I was taught and I had to spend countless hours banging my head against the wall until that euraka moment came about. Usually things weren't as scary or seemingly complex once I deciphered what it meant.
This blog post is an attempt at trying to explain the intuition behind MCMC sampling (specifically, the Metropolis algorithm). Critically, we'll be using code examples rather than formulas or math-speak. Eventually you'll need that but I personally think it's better to start with the an example and build the intuition before you move on to the math.
Table of Contents
Andreas originally hails from Sweden, then moved to the United Kingdom for his university studies. In the UK, he studied mathematics and then stayed to pursue a career in the finance industry, before embarking on a graduate degree in mathematical physics. He is currently a PhD student in Spain continuing his journey in mathematics. Andreas stumbled across Quantopian while traversing the web, and was immediately hooked. With no previous background in Python, he started learning how to create trading algorithms. He shares, "I started coding up some basic algorithms and was impressed by how easy it was to get going. There was also a great community forum and tutorials that had answers to most questions." His Python skills improved and Andreas began coding a variety of algorithms and trying different strategies.
Andreas was focused on the data. "For me, quant research is all about the data. Analysing and understanding the data always comes first (and backtesting last!). Quantopian has a number of interesting data feeds (that I hope it will continue growing!). My algo uses some of these data feeds to select baskets of stocks to trade". Quantopian provides 13 years of pricing data and fundamental data, along with 22 (and growing) datasets in the store.
Andreas continues to improve his current ideas and test new strategies using the research environment and backtester. "I know how much work it goes into creating a proper backtesting and research environment, and that Quantopian makes one available to you for free is quite amazing!" He is currently in the first phase of his prize, undergoing a quant consultation session. Afterward, he will enter the second phase and begin trading a $100,000 brokerage account for 6 months, and keep all the profits. We'll write him a check monthly for his earnings!
We've already paid out over $2300 in contest earnings. Are you the next contest winner? If so, submit your algorithm by the next deadline on Nov. 2 at 9:30AM ET to start your 6 months of paper trading.
Every student in every school should have the opportunity to learn computer science.
Code.org is a non-profit dedicated to expanding access to computer science, and increasing participation
by women and underrepresented students of color in this field. They believe computer science should be part of the core curriculum, alongside other courses such as biology, chemistry, or algebra.
We at Quantopian believe in Code.org's vision to bring computer science to every student. To help them achieve this goal, we have decided to donate all revenue generated by our live stream ticket sales for QuantCon 2016 to them.
QuantCon 2016 will feature a stellar lineup including: Dr. Emanuel Derman, Dr. Marcos López de Prado, Dr. Ernie Chan, and more. It will be a full day of expert speakers and in-depth tutorials. Talks will focus on innovative trading strategies, unique data sets, and new programming tips and tools. The goal? To give you all the support you need to craft and trade outperforming strategies.
A live stream purchase will also include first-access to all QuantCon recordings and presentation decks. For tickets or more information, please visit www.quantcon.com.
Strata, the conference where cutting-edge science and new business fundamentals intersect, will take place September 29th to October 1st in New York City.
The conference is a deep-immersion event where data scientists, analysts, and executives explore the latest in emerging techniques and technologies.
Quantopian Talks & Tutorials
Our team will be presenting several talks and tutorials at Strata. The topics range from how global-sourcing is flattening finance, to a Blaze tutorial, to a review on pyfolio and how it can improve your portfolio and risk analytics, to an out-performing investment algorithm on women-led companies in the Fortune 1000.
To see our entire lineup, please click here.
If you would like to attend the conference, RSVP here and enter discount code QUANT for a a 20% discount on any pass.
We hope to see you there!
Authors: Sepideh Sadeghi and Thomas Wiecki
This blog post is the result of a very successful research project by Sepideh Sadeghi, a PhD student at Tufts who did an internship at Quantopian over the summer 2015. Follow her on twitter here.
All of the models discussed here-within are available through our newly released library for finance performance and risk analysis called pyfolio. For an overview of how to use it see the Bayesian tutorial. Pyfolio is also available on the Quantopian research platform to run on your own backtests.
When evaluating trading algorithms we generally have access to backtest results over a couple of years and a limited amount of paper or real money traded data. The biggest with evaluating a strategy based on the backtest is that it might be overfit to look good only on past data but will fail on unseen data. In this blog, we will take a stab at addressing this problem using Bayesian estimation and prediction of possible future returns we expect to see based on the backtest results. At Quantopian we are building a crowd-source hedge fund and face this problem on a daily basis.
Here, we will briefly introduce two Bayesian models that can be used for predicting future daily returns. These models take the time series of past daily returns of an algorithm as input and simulate possible future daily returns as output. We will talk about the variations of models that can be used for prediction and how they compare to each other in another blog, but here we will mostly talk about how to use the predictions of such models to extract useful information about the algorithms.
All of these models are available through our newly released library for finance performance and risk analysis called pyfolio. For an overview of how to use it see the Bayesian tutorial. Pyfolio is also available on the Quantopian research platform to run on your own backtests.
At Quantopian we have built a world-class backtester that allows everyone with basic Python skills to write a trading algorithm and test it on historical data. The resulting daily returns generated by the backtest will be used to train the model predicting the future daily returns.
Lets not forget that computational modeling always comes with some risks such as estimation uncertainty, model misspecifications and implementation limitations and errors. According to such risk factors, model predictions are not always perfect and 100% reliable. However, model predictions still can be used to extract useful information about algorithms, even if the predictions are not perfect.
For example, comparing the actual performance of a trading algorithm on unseen market data with the predictions generated by our model can inform us whether the algorithm is behaving as expected based on its backtest or whether it is overfit to only work well on past data. Such algorithms may have the best backtest results but they may not necessarily have the best performance in live trading. An example of such an algorithm can be seen in the picture below. As you can see, the live trading results of the algorithm are completely out of our prediction area, and the algorithm is performing worse than our predictions. These predictions are generated by fitting a linear line through the cumulative backtest returns. We then assume that this linear trend continuous going forward. As we have more uncertainty about events further in the future, the linear cone is widening assuming returns are normally distributed with a variance estimated from the backtest data. This is certainly not the best way to generate predictions as it has a couple of strong assumptions like normality of returns and that we can confidently estimate the variance accurately based on limited backtest data. Below we show that we can improve these cone-shaped predictions using Bayesian models to predict the future returns.
In the Bayesian approach we do not get a single estimate for our model parameters as we would with maximum likelihood estimation. Instead, we get a complete posterior distribution for each model parameter, which quantifies how likely different values are for that model parameter. For example, with few data points our estimation uncertainty will be high reflected by a wide posterior distribution. As we gather more data, our uncertainty about the model parameters will decrease and we will get an increasingly narrower posterior distribution. There are many more benefits to the Bayesian approach, such as the ability to incorporate prior knowledge that are outside the scope of this blog post.
Now that we have answered the problem of why predicting future returns and why using Bayesian models for this purpose, lets briefly look at two Bayesian models that can be used for prediction. These models make different assumptions about how daily returns are distributed.
We call the first model the normal model. This model assumes that daily returns are sampled from a normal distribution whose mean and standard deviation are accordingly sampled from a normal distribution and a halfcauchy distribution. The statistical description of the normal model and its implementation in PyMC3 are illustrated below.
This is the statistical model:
mu ~ Normal(0, 0.01) sigma ~ HalfCauch(1) returns ~ Normal(mu, sigma)
And this is the code used to implement this model in PyMC3:
with pm.Model(): mu = pm.Normal('mean returns', mu=0, sd=.01, testval=data.mean()) sigma = pm.HalfCauchy('volatility', beta=1, testval=data.std()) returns = pm.Normal('returns', mu=mu, sd=sigma, observed=data) # Fit the model start = pm.find_MAP() step = pm.NUTS(scaling=start) trace = pm.sample(samples, step, start=start)
We call the second model the T-model. This model is very much similar to the first model except that it assumes that daily returns are sampled from a Student-T distribution. The T distribution is very much like a normal distribution but it has heavier tails, which makes it a better distribution to capture data points that are far away from the center of data distribution. It is well known that daily returns are in fact not normally distributed as they have heavy tails.
This is the statistical description of the model:
mu ~ Normal(0, 0.01) sigma ~ HalfCauchy(1) nu ~ Exp(0.1) returns ~ T(nu+2, mu, sigma)
And this is the code used to implement this model in PyMC3:
with pm.Model(): mu = pm.Normal('mean returns', mu=0, sd=.01) sigma = pm.HalfCauchy('volatility', beta=1) nu = pm.Exponential('nu_minus_two', 1. / 10.) returns = pm.T('returns', nu=nu + 2, mu=mu, sd=sigma, observed=data) # Fit model to data start = pm.find_MAP(fmin=sp.optimize.fmin_powell) step = pm.NUTS(scaling=start) trace = pm.sample(samples, step, start=start)
Here, we describe the steps of creating predictions from our Bayesian model. These predictions can be visualized with a cone-shaped area of cumulative returns that we expect to see from the model. Assume that we are working with the normal model fit to past daily returns of a trading algorithm. The result of this fitting this model in PyMC3 is are the posterior distributions for the model parameters mu (mean) and sigma (variance) – fig a.
Now we take one sample from the mu posterior distribution and one sample from the sigma posterior distribution with which we can build a normal distribution. This gives us one possible normal distribution that has a reasonable fit to the daily returns data. - fig b.
To generate predicted returns, we take random samples from that normal distribution (the inferred underlying distribution) as can be seen in fig c.
Having the predicted daily returns we can compute the predicted time series of cumulative returns, which is shown in fig d. Note that we have only one predicted path of possible future live trading results because we only had one prediction for each day. We can get more lines of predictions by building more than one inferred distribution on top of actual data and repeating the same steps for each inferred distribution. So we take n samples from the mu posterior and n samples from the sigma posterior. For each posterior sample, we can build n inferred distributions. From each inferred distribution we can again generate future returns and a possible cumulative returns path (fig e). We can summarize the possible cumulative returns we generated by computing the 5%, 25%, 75% and 95% percentile scores for each day and instead plotting those. This leaves us with 4 lines marking the 5, 25, 75 and 95 percentile scores. We highlight the interval between 5 and 95 percentiles in light blue and the interval between 25 and 75 percentiles in dark blue to represent our increased credible interval. This gives us the cone illustrated in fig f. Intuitively, if we observe cumulative returns from an algorithm that are very different from the backtest, we would expect it walk outside of our credible region. In general, this procedure of generating data from the posterior is called a posterior predictive check.
Now that we have talked about the Bayesian cone and how it has been generated, you may ask what these Bayesian cones can be used for. Just to give a demonstration of what can be learned from Bayesian cones, look at the cones illustrated below. The cone on the right shows an algorithm whose live trading results are pretty much within our prediction area and to be more accurate even in high confidence interval of our prediction area. This basically means that the algorithm is performing in line with our predictions. On the other hand, the cone on the left
shows an algorithm whose live trading results are pretty much outside of our prediction area, which would prompt us to take a closer look as to why the algorithm is behaving according to specifications and potentially turn it off if it is used for real-money live trading. This underperformance in the live trading might be due to the algorithm being overfit to the past market data or other reasons that should be investigated by the person who is deploying the algorithm or selects whether to invest using this algorithm.
Lets take a look at the prediction cones generated using the simple linear model we described in the beginning of the blog. It is interesting to see that there is nothing worrisome about the algorithm on the left, while we know that the algorithm illustrated on the right is overfit and the fact that the Bayesian cone gets at that but the linear cone does not, is reinforcing.
One of the ways by which the Baysian cone can be useful is detecting the overfit algorithms with good backtest results. In order to be able to numerically measure by how much a strategy is overfit, we have developed Bayesian consistency score. This score is a numerical measure to report the level of consistency between the model predictions and the actual live trading results.
For this, we compute the average percentile score of the paper-trading returns to the predictions and normalize to yield a value between 100 (perfect fit) and 0 (completely outside of cone). See below for an example where we get a high consistency score for an algorithm (the right cone) which stays in the high confidence interval of the Bayesian prediction area (between the 5 to 95 percentiles) and a low value for an algorithm (the left cone) which is mostly out of predicted area.
Estimation uncertainty is one of the risk factors, which becomes relevant with modeling and it is reflected on the width of the prediction cone. The more uncertain our predictions, the wider the cone would be. There are two ways by which we may get uncertain predictions from our model: 1) little data, 2) high volatility in the daily returns. First, lets look at how the linear cone deals with uncertainty due to limited amounts of data. For this, we create two cones from cumulative returns of the same trading algorithm. The first only has the 10 most recent in-sample days of trading data, while the second one is fit with the full 300 days of in-sample trading data.
Note how the width of the cone is actually wider in the case where we have more data. That's because the linear cone does not take uncertainty into account. Now let's look at how the Bayesian cone looks like:
As you can see, the top plot has a much wider cone reflecting the fact that we can't really predict what will happen based on the very limited amount of data we have.
Not accounting for uncertainty is only one of the downsides of the linear cone, the other ones are the normality and linearity assumptions it makes. There is no good reason to believe that the slope of the regression line corresponding to the live trading results should be the same as the slope of the regression line corresponding to the backtest results and normality around such line can be problematic when we have big jumps or high volatility in our data.
Having reliable predictive models that not only provide us with predictions but also with model uncertainty in those predictions allows us to have a better evaluation of different risk factors associated with deploying trading algorithms. Notice the word “reliable” in my previous sentence, which is to refer to the risk of “estimation uncertainty”, a risk factor that becomes relevant with modeling and ideally we would like to minimize it. There are other systematic and unsystematic risk factors as is illustrated in the figure below. Our Bayesian models can account for volatility risk, tail risk as well as estimation uncertainty.
Furthermore, we can use the predicted cumulative returns to derive a Bayesian Value at Risk (VaR) measure. For example the figure below
shows the distribution of predicted cumulative returns over the next five days (taking uncertainty and tail risk into account). The line
indicates that there is a 5% chance of losing 10% or more of our assets over the next 5 days.
Today, we are happy to announce pyfolio, our open source library for performance and risk analysis. We originally created this as an internal tool to help us vet algorithms for consideration in the Quantopian hedge fund. Pyfolio allows you to easily generate plots and information about a stock, portfolio, or algorithm.
Tear sheets, or groups of plots and charts, are the heart of pyfolio. Some predefined tear sheets are included, such as sheets that allow for analysis of returns, transactional analysis, and Bayesian analysis. Each tear sheet produces a set of plots about their respective subject.
Here is part of a tear sheet analyzing the returns of Facebook's (FB) stock:
pyfolio is available now on the Quantopian Research Platform. See our forum post for further information.