MoneyGeek - Latest entries

Announcement: Moving to enjine.com

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 25 Nov 2019 13:20:48 -0600

Image Credit: bearsky23 / Shutterstock.com

I started this blog in the year of 2013. I was a bright eyed newbie entrepreneur at the time, with the ambition to create a robo-advisor before the term "robo-advisor" was even a thing. But instead of raising a whole bunch of money to create a robo advisor, I wanted to test out the concept first. So, I created MoneyGeek, a platform to help DIY investors.

It was only after launching MoneyGeek that I started to understand how hard running a business is. I struggled in particular with how to get MoneyGeek's name out. I realized that it didn't matter if I offered the best product or service in the world. If people didn't know about it, I wouldn't be able to build a business.

It was at this point that I decided to create the blog section of MoneyGeek. I resolved to try to give free education in order to attract people to my site. Writing the first few articles was painful and time consuming - I had a lot to grow as a writer, but I steadily improved and so did my web traffic. At its peak, MoneyGeek drew 300 unique visitors a day, placing it as one of the more highly trafficked finance blogs in Canada.

But alas, it wasn't enough. I concluded that MoneyGeek's business wouldn't scale, so I stopped pursuing it as a business a few years ago. But I didn't want to abandon the loyal readership I had built, and I enjoyed writing anyway, so I kept at the writing.

Fast forward some months, I started a new business creating custom software for quantitative investment managers, which I in my moment of vanity named ENJINE. This business is doing much better, and we're now up to 6 full timers.

Unfortunately, running ENJINE, as with running most other types of business, is all consuming. I've therefore found myself wishing I didn't have to write articles on MoneyGeek, not for any lack of enjoyment, but purely for lack of time. I've also come to realize that ENJINE, just like MoneyGeek, would not grow if I don't tell other people about it.

So after much consideration, I've decided to move this blog to https://www.enjine.com/blog/. Starting today, I will stop posting new articles on this site. If you want to checkout my new articles, please go straight to enjine.com instead. This way, I get to keep my commitment to continue blogging, and I get to spread the word about ENJINE.

I'd like to thank my regular readers for your continued support. I'm amazed by the quality of readership that this blog continues to draw. This blog is read by statisticians, programmers, engineers and other highly sophisticated members of our society. I hope that I can continue to give value to you through the new blog.

My University Admissions Story And The Pitfalls Of Using Simple Algorithms

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 11 Nov 2019 14:50:41 -0600

We recently shot a short video describing our company, and it begins with the story of how I originally came to Canada from Ireland. You can watch the video below:

In the video, I explained that I had applied to some Canadian universities, and that the first letter I got was a rejection from McMaster. However, I didn’t get to explain why they rejected me in the video.

I had applied to three universities in Canada: the University of Waterloo, the University of Toronto, and McMaster. Of the three, I viewed McMaster as my fallback choice in case I couldn’t get into either of the first two (no offense, McMaster grads!). So it was a worrying moment for me when the first letter from Canada was a rejection letter from McMaster.

As it turned out, applying from Ireland caused a couple of complications. The first is that Irish highschools are called Colleges, so they initially thought I was applying to grad school. So I had to clear that up. But even after I had done so, they still rejected me because they said my marks were not high enough.

My grades in Ireland averaged in the low 80s. By Irish standards, this was very high. To give you an idea, out of the more than 100 students in my year, only around 5 people would get an A (marks of 85 or higher) in any given subject. Straight As were virtually unheard of. Some classes such as English almost never handed out As, and I was a perennial C student in English.

By contrast, Canadian highschools appear to hand out As like candy. After I came to the University of Waterloo, I was surprised to learn that almost everybody I met had straight As. Now, granted this was Waterloo, which is picky about who it admits. But still, I got the sense that my marks would have been much higher if I’d completed my highschool in Canada. Perhaps then McMaster would have accepted me.

Now, why do I bring up this story? I’m not doing this to figuratively yell, “In your face!” to McMaster. Rather, it’s because this story illustrates an important challenge we face when we make decisions using data.

McMaster’s admissions officers probably took a data driven approach when they rejected my application. They probably had a minimum threshold that my grades had to meet, and since I fell short, the decision to reject was probably automatic, or nearly so. One would argue that they should have considered the context surrounding my application (i.e. prevailing grades in Ireland), but they didn’t.

Quantitative investment algorithms can fall into the same trap.

An obvious example arises when we perform analysis on US companies and companies from other countries. US companies report their financials on an accounting standard known as Generally Accepted Accounting Principles (GAAP). Other countries tend to report using another standard known as the International Financial Reporting Standards (IFRS).

Due to the differences in these standards, the same company can report significantly different numbers depending on the standards used. For example, one of the big differences between GAAP and IFRS is that GAAP allows the use of Last-In, First-Out (LIFO) inventory accounting rules whereas IFRS does not. As this article shows, the use of LIFO can result in reporting significantly lower profits, thereby making the company look more expensive (companies’ valuations are often judged relative to their profits). A quantitative algorithm that doesn’t take the difference in accounting standards into account could end up biasing against companies that use LIFO.

Now, one could argue that this particular problem is not significant. Accounting authorities have slowly been bridging the gap between GAAP and IFRS. Many quantitative algorithms are also only designed to work in specific regions (US only, Europe only, etc.), precisely to avoid accounting and other region-specific biases. However, many quantitative algorithms in use today pervasively suffer from the lack of contextual data in other ways.

Current quantitative investment algorithms tend to utilize linear regressions involving just a few factors. For example, the famous Fama French three factor model is a linear regression involving 3 factors. AQR’s factor model extends that model to make it 6 factors.

Unfortunately, such linear regression models have very limited capacity to consider a myriad of contextual information. Take the Fama and French’s ‘value’ factor, for example. The factor is calculated such that a company is considered “cheap” if the stock’s price is low compared to its book value. It doesn’t take into account any other contextual information. If the company is considered cheap according to this rigid metric, the model assigns a higher probability that the stock will outperform.

But intuitively, it would make more sense to consider more contextual data before judging whether a stock is cheap. For one, the model doesn’t consider what components make up book value. It would probably matter if book value mostly consisted of goodwill as opposed to real estate. One would also guess that book value matters less for software companies vs. an auto manufacturer. In other words, such quantitative models are making the same mistakes that McMaster’s admission officers made with me, by treating all valuation or grades the same.

The prescription for such problems, of course, is to consider additional context. But then the challenge becomes how to incorporate additional information into the model. Take the admissions process, for example. Should McMaster bell curve grades from other countries? If so, by how much? The answer is not obvious.

Fortunately, in the realm of quantitative finance, there is an obvious answer, and that’s to use machine learning. Machine learning systems can digest many more pieces of information than linear regression models generally can. For example, you can feed them the breakdown of assets belonging to a company, and you can also feed in sector information. By using the additional information, machine learning systems can remove many of the biases that persist in simpler systems.

Our company has been working hard in recent months at creating a machine learning investment model. Machine learning’s ability to remove bias is one reason why I’m very excited about this project.

Why Machine Learning Hasn't Caught On In Finance - A Theory

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 28 Oct 2019 10:09:28 -0500

Image Credit: eamesBot / Shutterstock.com

You’d think that machine learning would thrive in finance. After all, the whole industry operates on data. Banks look at your credit history (data!) before they approve your mortgages. Credit card companies look at payment patterns (data!) to sniff out fraud. Investors use financial statements (data!) to select stocks to invest in.

Anytime there’s an abundance of data, you can often use machine learning to make better decisions, more quickly and with lower costs. You may therefore be surprised to learn not only that machine learning adoption has been slow in finance, but also that many finance professionals are skeptical of its potential.

Over the past number of years, I’ve heard the same basic refrain over and over again from the skeptics: “I knew so-and-so who started a hedge fund based on machine learning, and it collapsed,” or “We hired a machine learning PhD, but his algorithm didn’t perform any better than our existing methodology.” In other words, the slowness of adoption is not for lack of trying. Rather, machine learning just hasn’t produced good results for those who tried it.

The data lends credence to this disappointment. From Sep 2014 to Sep 2019, the Eurekahedge AI Hedge Fund Index, which tracks machine learning powered funds, returned 45.5%. Investing in an S&P 500 index fund, on the other hand, would have generated over 66% in returns.

But why has machine learning failed to produce positive results? Whenever I’ve seen that question asked, I’ve heard two types of answers.

The first type of answer involves blaming the machine learning practitioners for their lack of financial knowledge. A physicist, for example, may not be aware of the difference between a financial statement’s fiscal and filing dates. Such deficiencies in knowledge probably have led to flawed machine learning models.

The second type of answer for why machine learning has failed to generate results comes from mathematicians such as Lopez de Prado, who have criticized the statistical methodology employed by investment firms. For example, de Prado points out that many firms have abused backtesting by running them over and over again until firms got results that they liked. Many firms have undoubtedly fallen into the traps that de Prado describes, which accounts for their failure.

In summary, those with finance backgrounds blame the architects’ lack of financial knowledge for machine learning algorithms’ failures, while mathematicians blame the finance folks for their lack of mathematical knowledge. But is this the whole story?

For the past number of months, my firm has been working on a sophisticated machine learning model that we hope to turn into a fund. In the process of creating the model, it occurred to me that there’s one particular challenge that nobody ever talks about, a challenge that could have resulted in many machine learning models not working as expected. The lack of discussion surrounding this challenge is a shame, because I think it is the most difficult component of machine learning to manage.

So what is this challenge I’m talking about? I’m referring to the mundane topic of producing code without bugs.

While we humans are good at a lot of things, avoiding mistakes is not one of them. Some people estimate that there are typically between 1 and 25 bugs per 1,000 lines of code. That’s a wide range. There are several factors that determine whether the defect rate is high or low, and I believe that the business nature of software is one of them.

Unfortunately, coding financial software lends itself to high defect rates. Think about it. Let’s say a programmer is developing a content management system for a website, which lets users change the background colour of their websites. It would be very easy to see if such a system was working or not as either the background colour would change as specified or it wouldn’t. In such a case, the programmer would fix any bugs in this area very quickly.

But things are not so obvious with software that deals primarily with numbers. For example, let’s say a programmer created a function that calculates the standard deviation of a list of numbers. He then observed that when the array [1, -2, 5] was fed in, the function returned the value ‘0.8’. Now, if you’re a good statistician, that answer might make you pause and re-evaluate the function. But a typical programmer without that background may not see that there’s a problem.

Some people think the answer to this problem is to get finance and statistics people to double check the programmers’ work. But in my experience, this method isn’t very effective. I have yet to meet anyone who enjoys manually double checking programmers’ work, and lacking interest, they tend to do the job poorly. Also, I’ve seen finance and statistics people point out errors to programmers, only for programmers to fix the problem for that specific scenario and leave the root problem intact.

This is a much more severe problem than many people realize. As an anecdote, we once took over a software project where the client had previously contracted offshore developers to create financial algorithms. We found that none, and I mean none, of the major calculations were being done correctly, despite the fact that the client double checked the developers’ work. I don’t think it’s any different at major banks or financial institutions. I should know, since I used to work for a bank.

Yet the consequences of even a single bug can be severe for a machine learning algorithm. As an example, imagine mistakenly including some out-of-sample data with the training data. The algorithm would probably appear to perform really well, but fall flat when used in the real world. Just one bug would be responsible for the illusion of a strong performance.

Unfortunately, it’s difficult to avoid such mistakes even if you’re extremely meticulous. Machine learning projects tend to be a lot bigger than your traditional investment algorithm projects, giving them much more room for error. Our project, for example, consists of over 10,000 lines of code, not counting all the third party libraries we use. Even if we assume a very low defect rate of 1 bug out of 1,000 lines, that still means we probably have over 10 bugs in our software. For similar sizes projects written by programmers without finance/math knowledge, there may even be over 200 bugs.

Of course, there are ways to mitigate this problem. We blanket our code base with tests. We also ensure that multiple people review code before it gets merged into production. We only hire people who are detail-oriented. (We’ve had to let go of people in the past for making too many mistakes.) But I’ve found that none of these methods is a panacea. We have to fight the never-ending battle of discovering and fixing bugs.

Thankfully, I feel confident that we’ll develop an algorithm free of major bugs. We’re able to do this because at least some of our programmers have the finance, math and programming knowledge to be able to recognize bugs and write good tests. But whenever we find an unintuitive bug that could have derailed our results, I wonder, how many other firms currently have similar defects in their machine learning algorithms?

FRDM - The Better Way To Invest In Emerging Markets

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 14 Oct 2019 16:49:59 -0500

Image Credit: Rawpixel.com / Shutterstock.com

Owning emerging market stocks could benefit your investment portfolio in two ways. First and more obvious, owning emerging market stocks would make your portfolio more diversified, thereby lowering risk. Second, emerging market economies tend to grow much more quickly than developed economies, so many people assume that emerging market stocks will outperform developed market stocks.

Unfortunately, that second assumption has not held up in recent years. The following chart shows the comparative performances of the Vanguard FTSE Emerging Markets ETF (VWO), and the SPDR S&P 500 ETF (SPY), in the 10 year period ending Oct 12, 2019.

Source: Yahoo Finance

As you can see, US stocks, as represented by SPY, have done incredibly well over the past 10 years. Emerging market stocks, on the other hand, appear to have gone almost nowhere. What gives? A look under the hood of VWO gives us a clue.

VWO tracks the FTSE Emerging Index. According to the index’s fact sheet, Chinese stocks constitute 35% of the index, far more than any other country’s allocation. So how have Chinese stocks done over these past 10 years? Not great.

Source: MarketWatch

The graph above shows the Shanghai Composite Index, which tracks the performance of mainland Chinese stocks. As you can see, the index has gone nowhere these past ten years, mirroring the performance of VWO.

But how can this be? The Chinese economy has grown rapidly during this time, so shouldn’t its stocks have gone up as well? Unfortunately, things are not that simple. Even if a country as a whole gets wealthier (which China undoubtedly has), there’s no guarantee that the wealth accrues to shareholders of its companies.

One factor that determines whether shareholders benefit is the strength of investor protection. If investor protection is weak, then controlling shareholders could make decisions that benefit themselves at the expense of minority holders (e.g. pay themselves an unreasonably big salary).

Another factor is the rule of law. Without it, shareholders can become victims of fraud and other crimes that siphon value from companies. Corruption also harms companies’ prospects by going against meritocracy. In other words, it prevents the best individuals from rising to the top within companies, and it prevents the best companies from rising to the top within a given country.

Even without corruption, centralized economic planning can also harm shareholder value, as companies in industries that go out of political favour can end up losing a lot of money. The Chinese electric car industry, for example, has fallen on hard times recently as China has cut back its subsidies.

Unfortunately for Chinese shareholders, the three factors stated above play a negative role in the Chinese markets. The Strength Of Investor Protection Index scores China at 4.5, well below the world median of about 5.5 (Canada is at about 7.5). China ranks highly on the Corruption Perceptions Index which by itself is not unusual for an emerging market economy, but China also has the dubious honor of having many of its rich end up dead or sent to prison. Lastly, no one can deny that China, while it has some hallmarks of a market economy, is still dominated by the Chinese Communist Party.

Now, it would be unfair to give the impression that China is alone in this situation. Other countries suffer from substantially the same types of problems too. One such example is Russia, which has also seen its stock market stagnate this past decade.

At this point, we might be tempted to disregard emerging market stocks altogether, but that might be like throwing the baby out with the bathwater. Some emerging markets suffer less from the problems just discussed. It would be great if we could invest only in those countries. This is where the Alpha Architect Freedom 100 Emerging Markets ETF (FRDM) comes in.

FRDM tracks the Life + Liberty Freedom 100 Emerging Markets Index, which scores each country by their human and economic freedom metrics and chooses to allocate higher percentages into countries with higher scores. If a country’s score is too low, the index doesn’t include the country’s stocks at all. This is very different from a traditional emerging market index, which weights each country simply by the size of their stock markets. This is why China tends to get the highest allocation in traditional emerging market indices.

FRDM’s unique index methodology would have allowed it to perform better than traditional emerging market ETFs such as VWO. If you look into FRDM’s index, you’ll notice that Taiwanese and South Korean stocks have the biggest weights in FRDM. As the chart below shows, investing in either of those stock markets would have generated decent returns - perhaps not as great as investing in US stocks, but decent nonetheless.

Source: Yahoo Finance

But apart from the monetary incentive to invest in FRDM, there’s something that just feels “right” about investing in those countries that gives protection for the less wealthy and upholds the rule of law. It is for this reason that, had I still continued to publish MoneyGeek’s portfolios, I would have included FRDM in them.

So if you’re looking for ways to diversify your investment portfolio further, it would probably be a good idea to give FRDM a look.

Disclosure: MoneyGeek doesn’t receive any compensation from Alpha Architect nor Life + Liberty Indexes for publishing this piece. MoneyGeek also doesn’t have any business relationship with Life + Liberty Indexes, past or current. It does have a past business relationship with Alpha Architect in which MoneyGeek created software for AA.

The Bias/Variance Trade-off And The Limits of Machine Learning Models

peter.white@enjine.ca (Peter White) — Mon, 30 Sep 2019 19:08:29 -0500

Image Credit: pathdoc / Shutterstock.com

A Machine Learning model is a bit like a marriage - no matter how hard you try, it's never going to be perfect. The same way every marriage has its issues, so does every machine learning model. Real world data is like real world people: unpredictable. Real world events don’t conform precisely to a perfectly predictable pattern, so no matter how clever your algorithm, there will always be some irreducible error. The trick is to focus on the things you can change - the reducible error. If you’re in a marriage where there are some communication issues, that’s a reducible error. You can work on that and improve. But if you’re in a marriage where one of you is deathly allergic to nuts, and the other person is Mr. Peanut, there isn’t much you can do. That’s an irreducible error.

The trick to creating an accurate machine learning model is to identify the error that you can reduce and concentrate on that. Luckily, there are only two main sources of reducible error that we need to investigate: bias and variance.

Bias

Bias is a measure of your model’s ability to precisely fit the training data. The closer you fit your model to your training set, the lower the bias for that particular data set, and the better the accuracy of your predictions for that training data. Reducing your bias is usually achieved by adding complexity to your model, allowing it to better represent the data on which it's being trained.

Variance

Variance refers to your model’s sensitivity to the specific data on which it was trained.The outputs of a model are strongly linked to the data on which it has been trained. Therefore, when the input data is different, a high variance model’s outputs will be quite different. Hence, the results will be unpredictable and unreliable. To reduce your variance, you often need to simplify your model. This frees the model somewhat from the specific data points, allowing more robustness in its signal generation.

The Trade-off

From the outside looking in, some people might think you could just lower the bias and the variance in your machine learning model and then live out the rest of your days in wealth and happiness. If these people had ever been married, they’d know that nothing is that simple. The relationship between bias and variance is far more complicated. There is a real give and take between them that must be understood in order to achieve the best results possible. It takes some complex math to fully describe the interplay of bias and variance, but the concept is surprisingly intuitive. In fact, the tradeoff is analogous to something most of us are quite familiar with: throwing a ball.

Think of yourself as a baseball pitcher trying to throw a fastball past a hitter at the plate. You want your pitch to be as fast as possible: the faster the pitch, the harder it is to hit. But, you also want your pitch to be accurate. If you throw it outside the strike zone, it's a ball. And, if you throw a pitch down the middle of the plate, the batter is likely to hit a homerun - your entire middle school team will laugh at you, and you won't get to kiss anyone for quite some time (I know from experience). Clearly, the stakes are high, so you need your pitch to be as accurate as possible, as well as fast.

However, as most people are aware, the harder you try to throw something, the harder it is to be accurate with it. The inner workings of your body are such that in order to improve your accuracy you need to decrease the speed. The inverse also applies: to increase the speed, you need to accept lower accuracy.

This is similar to the bias-variance trade off. We want a model with low bias and low variance, but the reality is that the only way to lower one is to increase the other. Because of the logic inside machine learning algorithms, the two are intrinsically connected.

In general, the way to reduce bias is to increase the complexity of your model. This fits your model more precisely to your training data. But, the closer you fit your model to the data, the more your model works to find patterns in the data that may be caused by something other than the signal. It could be anything from random noise, to measurement error, to a physical anomaly. Anything that isn’t part of the signal will weaken your results. So, while your model may fit the training data perfectly, it will give you different results with different data. This is an increase in variance. So, if you want to throw the ball harder (reduce your bias error), you end up being less accurate (increasing the variance error).

But, if you go too far the other way and reduce the complexity to reduce the variance, you capture less of the signal and reduce accuracy in your predictions. This is in increase in bias error. You, as the pitcher/data scientist, need to find a compromise between speed and accuracy that minimizes the overall error and gives you the best result. The figure below shows this concept graphically.

Fig 1: https://i.stack.imgur.com/GEJIM.png

Application

Trying to model the stock market is an insanely difficult task. If it weren’t so difficult, someone would have perfected it by now, and the rest of us would have given up. In fact, controlling the bias-variance tradeoff is especially important in finance, where data is scarce. Combine that with the low signal-to-noise ratio that is present in stock prices and it’s easy to find yourself with an unacceptably high variance.

So, when creating your machine learning models, you need to be as vigilant as possible about reducing error. You want to find the point at which the bias and variance errors are at their combined minimum, thus creating the happiest marriage possible. Unfortunately, you can't just buy your model chocolates tell it you love it and make things better, you have to actually put in some work.

The first and most obvious step is to ensure that the algorithm you are using is right for your data. There's no paint-by-numbers guide for this, it takes time and experience to learn how to choose correctly. Then, once you have your algorithm, you want to make sure you have the cleanest, most complete data possible. As you can imagine, a model is only as good as the data it was trained on. Most algorithms, then, contain a set of parameters that control the level of fitting to the data. Through a series of calculations, as well as trial and error, you can tune these precisely to minimize the bias-variance combined error, and maximize your predictive power.

Creating a good model requires understanding of the bias and variance tradeoff, much as understanding the compromises of living together creates a good marriage. And while it might not be as snappy as “Happy spouse, happy house”, “Accurate model, Accurate predictions” is just as good a motto to live by.

Is Passive Investing A Bubble?

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 16 Sep 2019 12:10:16 -0500

Image Credit: EtiAmmos / Shutterstock.com

Within each industry, there are certain topics that divide participants and make them battle each other with religious fervour. Among programmers, the topic might be Windows vs. *nix. Among physicists, I’ve heard of dissent against string theory.

There are several topics that similarly divide financial professionals. One such topic revolves around the issue of whether passive investing is harmful or beneficial to financial markets. Passive investing, in contrast to active investing, involves an attempt not to pick individual stocks. Instead, it diversifies as much as possible, owning every stock in an index.

Until today, it seemed as though the vast majority of knowledgeable investors believed that passive investing was good, or at least neutral. However, there’s been growing dissent to this widely accepted opinion, and debate erupted recently when a highly respected investor went so far as to call passive investing a “bubble”.

The investor in question is a man named Dr. Michael Burry, who became famous as a result of being profiled in Michael Lewis’ book, “The Big Short”. Burry was one of the very few investors who predicted and profited from the subprime mortgage bust. It was therefore disconcerting when during a recent interview, he compared passive investing to Collateralized Debt Obligations (CDOs), the instrument he bet against during the subprime bubble years.

The reaction to Burry’s interview was swift. Cliff Asness, who runs a $200 billion investment giant, hit back by claiming the worries are “silly”. Ben Carlson, who runs a popular investment blog called “A Wealth of Common Sense”, quickly put out a blog post arguing against the notion that passive investing is a bubble.

I’ve already addressed the “price discovery” worries (they are exaggerated to the point of silly but sound really smart):https://t.co/fkIKwKXzq7

And why stop at CDOs? Why not CDO^2s? https://t.co/wXK4hSjZvi
— Clifford Asness (@CliffordAsness) September 4, 2019

But after reading the responses to Burry’s interview, it struck me that none that I’ve read so far has seemed to directly address his central concern. I think this is because although Burry heavily hinted at the concern, he was never explicit, perhaps because he assumed others would naturally arrive at the same conclusions he did. But seeing how that’s not the case, I thought I would help explain the concern.

To understand Burry’s point, it may first help to understand Burry himself. Burry is an extremely detail oriented investor, who likes to dig in to the exact mechanics of how investment vehicles work. When he bet against subprime CDOs, he did so after spending countless hours poring over legal documents that govern the mechanics of these CDOs. He may have been the only person to dive into such granular detail. So when he makes a big statement about passive investing, you can be fairly certain he’s thinking about the mechanics of index funds.

The chief concern Burry raised in his interview concerned liquidity. On that topic, this is what he had to say:

“In the Russell 2000 Index, for instance, the vast majority of stocks are lower volume, lower value-traded stocks. Today I counted 1,049 stocks that traded less than $5 million in value during the day. That is over half, and almost half of those -- 456 stocks -- traded less than $1 million during the day. Yet through indexation and passive investing, hundreds of billions are linked to stocks like this.”

Let’s unpack this statement. The Russell 2000 holds roughly the 1000th to 3000th largest US stocks. The bottom half of these stocks (the 2000th to 3000th stocks) have market caps that range from roughly $50 million to $150 million. The Russell 2000 is a market cap weighted index, and the allocation to each stock in this bottom half range from 0.01% to 0.03%. This sounds like a small fraction, but it’s really not.

As Burry states, hundreds of billions of dollars are linked to the Russell 2000. I don’t know the exact number, so let’s assume that $200 billion are linked to the Russell 2000. That means the bottom half of Russell 2000 stocks have between $20 million and $60 million invested by index funds linked to the Russell 2000, which amounts to roughly 40% of these companies’ market caps.

But, as Burry says, these stocks don’t trade that much. Almost a quarter of them don’t even trade $1 million a day, which means that Russell 2000 index funds own at least 20 times the daily trading volume of their smallest constituents.

This poses a big problem if there’s a rush to sell Russell 2000 funds. Let’s say that for whatever reason, investors decided to sell 10% of Russell 2000 index fund holdings in a single day. That means the funds themselves would need to sell between $2 and $6 million of the bottom half stocks in a single day. But the problem is, there’s not enough trading volume to handle such huge sell orders. Many of these stocks trade less than $1 million a day to begin with, but once investors see a deluge of sell orders arriving, chances are these investors will refuse to buy those stocks until the selling appears to ebb.

If a traditional active fund faced the prospect of wanting to sell stocks for which there were no buyers, the fund would probably decide to pause selling. Once the selling stopped, the prices of the small stocks would have time to recover, and a market crisis in general would be averted. But such is not the case with index funds, and there lies the rub.

Index funds, unlike actively managed funds, must follow a strict rule. If an investor buys a Russell 2000 index fund, exactly 0.02% of that money must go towards buying a stock with the index weight of 0.02%. The opposite is true as well:when an investor sells the fund, the fund must sell 0.02% worth of the aforementioned stock.

This can therefore lead to a situation where there are literally sell orders for stocks with no corresponding buy orders. We’ve had a taste of this scenario during the flash crash of 2015. For a brief period during the crash, buy orders for Accenture stock completely dried up, and the price went from over $40/share to literally $0.

Now, I’m not suggesting that such an extreme scenario is likely. There may be some stock market mechanisms that would prevent hundreds of stocks from going to 0. It’s also possible that there’s virtually no scenario under which investors would stampede out of index funds. I’m therefore agnostic about whether passive investing is a bubble or not.

That said, I do think it’s important not to dismiss out of hand Dr. Michael Burry and other investors’ concerns around passive investing. As I’ve said, I have yet to see someone convincingly argue against the problems regarding liquidity. Until then, I think it’s right to be cautious about passive investing.

Outlier Detection: Border Security For Your Model

peter.white@enjine.ca (Peter White) — Mon, 02 Sep 2019 19:38:53 -0500

Image Credit: zhu difeng / Shutterstock.com

You might not know it, but outlier detection is a big part of your life. The ability to notice diseased or rotten food, or spot a person in a crowd who might be unstable or dangerous is a very important human skill. Many of us had extra detection-training as children.

So can we reliably spot outliers? For extreme examples, we're pretty good. Say you ask 100 people, “what is the ideal indoor temperature?” and 99 of them answer, “somewhere between 16 and 22 degrees Celsius”, while the other one answers, “banana”. You don't have to be a Family Feud judge to know that there's something up with that banana answer. It's obviously an outlier. But, as the data gets more complex and convoluted, outliers start to get orders of magnitude more difficult to spot.

In machine learning, especially with financial models, outlier detection is incredibly important. Outliers can severely warp your training set, leaving you with a less accurate model and more errors in predictions. It's like using faulty materials to build the foundation of your house. Your training set can be contaminated by a number of different sources depending on how the data is collected. Anything from a clerical error to a computational anomaly to plain old human stupidity. (Never underestimate human stupidity--it's not an outlier as a cause of outliers.)

In some cases of machine learning you might be interested in investigating these outliers; those that are actual anomalies can hold lots of interesting information. However, for the case of predicting future returns, you are best served removing these outliers from your data before creating your model.

Removing them is the easy part, finding them is the real challenge. Outliers are sneaky things; they are completely dependent on the rest of the dataset. If you're a 400-pound man wearing nothing but a cloth diaper and a ponytail, you're a huge outlier in most situations. But, in a dohyō, you're just another data point.

The textbook definition will tell you that an outlier is an observation that lies outside the overall pattern of a distribution, but that's a bit of a vague explanation. It leaves us with some questions, the main one being: how far outside the pattern does a point have to be to be an outlier? It's like following one of your grandmother recipes. You just end up screaming at the page: “I DON’T KNOW HOW MUCH A 'HEALTHY DOSE' OF SALT IS GRANDMA, WHY CANT YOU BE SPECIFIC?”

So, if these outliers are so elusive, how do we find them? Luckily, some very smart people have discovered some very smart methods to help us in our task, such as

Z-Score

The z-score is like a hammer: basic, simple, easy to use. Not every situation calls for a hammer, but when something needs to be hammered, there's no better tool. The z-score is simply a measure of how many standard deviations a data point is from the sample's mean. Anything beyond a specified threshold (often 2.5-3.5 standard deviations) is deemed an outlier. It's surprisingly powerful given its simplicity, but there's a major catch: it requires your data to be approximately normally distributed, and your independent variables to be few. Also, because this tool relies on standard deviation, and standard deviation is sensitive to outliers, the very outliers you’re trying to detect could interfere with your calculations. That is why some people prefer the slightly modified Z-score method that uses Median Absolute Deviation instead of standard deviation. This reduces the effect of the outliers on your detection.

Z-Score isn't a method for every situation, but, when the stars align, it's an easy-to-implement, efficient solution.

DBSCAN

DBSCAN is as clever an algorithm as it is clunky an acronym. It stands for Density Based Spatial Clustering of Applications with Noise (obviously), and it works by determining the number of neighbouring points that exist for each data point in the set. By setting a distance, ɛ, you tell the algorithm how far to search for neighbours. You also set the minimum density of the neighbours that you're searching for, and set it to work. The algorithm classifies each point into one of three categories: 1) Core points, 2) Border points 3) Outliers.

If a point has at least the minimum number of neighbours within ɛ distance in any direction, it's considered a core point. If a point doesn't have the minimum number of neighbours, but is within ɛ distance of a core point, it is considered a border point. If it doesn't fit into either of those classifications, it's an outlier. By modifying ɛ and the minimum number of neighbours, you are able to fine-tune the outlier classification.

It's an easy to visualize method, and it works very well for searching for multidimensional outliers, but it's not without its drawbacks. It’s difficult to fine-tune the parameters ( ɛ and minimum number of neighbours). A small change in values can cause a dramatic change in outliers detected. You also need to scale your values in the feature space appropriately, lest you wreck your results.

Isolation forest

Despite sounding like a place that you'd get banished to in some Alice in Wonderland-esque tale, an isolation forest is actually a non-parametric method of outlier detection. It's a thorough machine-learning algorithm that seeks to determine how isolated each data point is, and give it an according score. This is done using decision trees in the following order. For each data point, you randomly select a feature. For that feature, you take a random value between the minimum and maximum to function as your split value. If the current data point has a value above the split value, you now use only the data above that point. If it's below, use only the data below. You then choose another feature at random, and another value in between the minimum and maximum, and repeat the process. Continue to do so until the data point is completely isolated from the rest of the set.

(picture reference: https://cs.nju.edu.cn/zhouzh/zhouzh.files/publication/icdm08b.pdf )

Because outliers (X0) will be further from the rest of the data than an average point (Xi), it should take substantially fewer steps to isolate an outlier (Figure 1). By comparing the number of steps it takes with the benchmark value that you decided on, you can determine if the data point is an outlier. It's a very clever algorithm, but, if it's not implemented properly, it can be very slow and computationally expensive.

Much like with Z-Score, there is also an extended isolation forest method that improves the consistency and reliability of the algorithm by re-imagining how the splits are calculated.

Conclusion

Outlier detection is incredibly important in machine learning. You want to protect the borders of your model from bad data with the fury of a wall-loving Donald Trump, but with the cleverness of anyone but. Be as vigilant as possible. In practice, you may need a combination of these methods to get a complete sense of your data. We employ both z-score and isolation forest techniques in our projects to ensure that we are using the cleanest possible information to create predictions. It may seem labor intensive, but every little edge can turn into a greater alpha on the other end.

Can Yield Curves Predict Stock Market Direction? - A Machine Learning Perspective

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 19 Aug 2019 08:54:55 -0500

Image Credit: dani3315 / Shutterstock.com

Many investors are concerned about the yield curve today. Generally speaking, a positive sloping yield curve (i.e. where long term interest rates are higher than short term rates) portends future economic health. By contrast, negative sloping yield curves (a.k.a. “inverted” curves) have tended to precede recessions.

Today, the yield curve is the most inverted it’s been since before the financial crisis. This has led some investors to wonder: should they sell stocks today to protect their portfolios? Or should they hold onto them because, despite widespread belief, yield curves may not be the predictor they are often made out to be?

Academic Paper And Its Problems

At least one set of academics has come out with a purported answer. Just last month, Fama and French published a draft paper that examined a market timing strategy based on yield curves. The strategies they examined gradually unloaded stocks when yield curves were inverted, and gradually added them back when yield curves sloped upwards. They found that such strategies ended up underperforming the simple buy and hold strategy where the investor never sold stocks.

Personally, I found the paper to be wanting. I know that’s a bold thing to say considering one of the authors - Eugene Fama - is a Nobel laureate. But, hear me out. All that the paper proved was that the specific strategies devised by Fama and French didn’t work. This might be okay if the strategies made good use of the yield curves, but I’m not convinced.

The chart below shows the ten to two year treasury yield spreads. As you can see, the spread tended to go negative (i.e. yield curve inverted) before a recession. However, there tended to be significant lags between the timing of the inversion and the beginning of the recession. For example, the yield curve inverted the last time in 2006, a full two years before the recession started.

Stock prices reacted more or less in sync with economic health during the last recession, rising until 2007, and falling big in 2008. But if you had followed Fama and French’s strategy, you would have sold stocks until 2007, and started buying them back in 2008, which is the wrong strategy to follow. Does this mean that we shouldn’t use yield curves to inform our investing decisions? No, it just means we shouldn’t use it the specific way Fama and French outlined.

If you want to know if yield curves can be used in any fashion to make investment decisions, it’s better to see if yield curves have any predictive power over the stock market. To answer whether that’s the case or not, I turned to machine learning.

My Machine Learning Model

Now, before we go any further, let me warn you - what I’m about to show you doesn’t qualify as rigorous academic research. If I wanted to make this a proper academic study, I would conduct a lot more tests, use more data, etc. This is more like tinkering in a lab.

In order to see if there’s any connection between yield curves and stock prices, I first downloaded two data sets from Quandl - historical treasury yields of different maturities, and the monthly performance of the S&P 500.

Since I was interested in whether the shape of the yield curve predicted stock prices, I constructed a time series consisting of the following interest rate differentials.

1yr - 3mo
2yr - 1yr
5yr - 2yr
10yr - 3mo
10yr - 2yr
30yr - 3mo
30yr - 2yr
30yr - 10yr

I didn’t choose these differentials based on any rigorous scientific reasons. Rather, I guessed that these would contain the essence of the shape of the yield curve. These data points constituted the inputs to the machine learning model.

The target output of the model consisted of the ensuing 12 month S&P 500 returns in excess of the 3 month treasury bill interest rates. This is consistent with what Fama and French used in their paper.

I then divided the data set into two - one for training, and the other for testing. The training set consisted of all data until the end of 2009. The test set consisted of all data thereafter. There were 229 data points in the training set, and 104 data points in the test set. Experienced data scientists will note that this is a rather simplistic way to evaluate the model. If I were to do more rigorous research, I’d use a method like the combinatorial purged cross validation. But as I said, I’m just tinkering here.

With the inputs and targets defined, I pondered which machine learning model to use, and I decided that some type of RNN (Recurrent Neural Network) made the most sense. I had a theory that in addition to the current shape of the yield curve, the evolution of the yield curve mattered as well, and RNNs had the ability to make use of the evolutionary information. In order to make use of RNNs, I modified the inputs such that each input consisted of 12 months’ worth of yield curve history.

Unfortunately, I discovered that many of the popular types of RNN didn’t work for this problem. With only 229 data points available for training, the more sophisticated RNNs like GRU and LSTM persistently overfit, even when using only 1 output unit. The only RNN that didn’t overfit to uselessness was the simple RNN, with 1 output unit.

Fortunately, the simple RNN seems to work decently well. The graph below shows a set of predicted S&P 500 returns vs. actual for the test data set.

As you can see, though the predictions are not super accurate, it suggests that the model does appear to have some predictive power. The slope of the line is 0.48, which suggests an R squared of 23% - a fairly high number. However, I suspect that this overstates the model’s predictive capability. Indeed, if you tweak the model just a little bit, then you end up with a somewhat lower R squared. For example, if I lower the batch size of training from 8 to 4, I get an R squared of roughly 10% instead.

But even an R squared of 10% is significant, and it suggests that yield curves can be used in some fashion to get an idea of where the stock market is headed next. I also suspect that yield curve data would be even more useful if used in conjunction with other data, such as inflation data. If this is true, I believe investors would be able to craft some investment strategy that uses yield curves to beat the buy and hold strategy outlined in Fama and French’s paper.

But before we get too excited, let me reiterate that there’s no guarantee my model does work. It appears to work at first glance, but really confirming that would take more effort, and I’m unwilling to put in that effort. If someone would like to continue where I left off, feel free to do so. I’ve made my code available for download here in the Jupyter notebook format. If you do use my code, I would appreciate it if you could credit me.

Finally, you’re probably curious about what the model says about where stock prices are going. I do have an answer for you. It says stocks will go down slightly (roughly -3%) in the next 12 months. I think this is in line with many investors’ gut feelings on where stock prices are headed.

Discontinuing MoneyGeek's Portfolios

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 05 Aug 2019 10:23:56 -0500

Image Credit: William Potter / Shutterstock.com

On the first Monday of every month (like today), I normally give an update on MoneyGeek’s portfolios. But as you can tell from the title, today is different. Today, I’ve decided to remove the model portfolios feature from this website.

I know that many of you have been using my model portfolios to invest real money, so I feel that I owe you a full explanation.

Early last year, I started work on a successor website to the model portfolios’ page. I called it ‘Portfolio Expo’, and it was going to contain some big enhancements. PE would have let users create and publish their own portfolios. It would have also included some sophisticated analytics of each portfolio, and enabled people to discuss the portfolios.

A couple of months ago, I felt that the site was almost ready to launch, so I started demoing it to other people. One of the people I demoed the site to recommended that I contact the regulators, to make sure the site wasn’t contravening any regulations. When I met with the regulators, they had some bad news. They felt that we would need to be regulated, given the features we had planned for the site.

Becoming regulated is a big deal. There are many requirements that must be met, ranging from keeping extensive records to having a certain amount of cash in the bank at all times. But perhaps the biggest challenge for us was in finding someone who could become the chief compliance officer.

To qualify as the officer, one needs to have either a CFA or a CIM designation, as well as a few years of relevant work experience. I come close to qualifying, since I’ve passed two out of three levels of the CFA, and have the requisite work experience. I therefore considered taking the third CFA exam, but decided not to. Taking that last CFA exam would mean reserving one to two hours a day to study, and I simply don’t have the time right now.

Even if I decided to spend the time, I would have to wait until June of next year to take the exam. Assuming I passed, my company would have started being regulated at the end of 2020, which I judge is too long a time to wait.

As an alternative, I could hire someone else to become the compliance officer. I’ve considered this option, but decided against it. Such people are expensive, and I don’t feel confident enough about our cash flow situation yet.

After ruling out the options above, I tried to think of ways that I could launch PE without being regulated. I was willing to gut some key features if need be, so I contacted some securities lawyers for advice. Unfortunately, they had some bad news as well.

As they saw it, any website that provided even the most basic analytics and tools needed to be regulated. This included automatic performance tracking, and calculators that showed exact trades in order to implement a portfolio. I was willing to gut some features from PE, but gutting every feature that met the regulatory threshold would have left the site hollow - which brings us back to MoneyGeek.

As you may know, MoneyGeek’s portfolios section already provides many of the same features that meet the regulatory threshold. This means that the regulators could in theory choose to shut down my site any time they wanted. In fact, I had that exact experience some years ago.

In late 2013, just a few months after I launched MoneyGeek, the regulators found out about the model portfolios section and asked me to take it down, which I complied with promptly. I later sat down with the regulators to explain the situation, and they allowed me to put the site back up. I believe a big reason I was allowed to continue publishing the site was because the rules were unclear about websites like MoneyGeek. Fintech was very nascent at the time, so they hadn’t yet issued guidelines.

But fast forward a few years to the present, and things have changed. Robo advisors have become a thing, and many websites have started to straddle the line between providing tools and giving advice. The regulators have now provided guidelines, which means taking more clear cut stances towards websites like MoneyGeek.

My own circumstances have changed too during these past few years. I have a lot more to lose today. I run a business employing six people besides myself, so drawing the ire of regulators could affect not just my own life, but the lives of six other people as well.

This is why, after some careful consideration, I have decided to shut the model portfolios section down. From now on, this site will essentially be just a blog, which is acceptable from the regulators’ point of view.

If this decision affects you financially, please accept my apologies. For those who are wondering about alternatives, I would suggest two things.

If you have a decent amount of savings (over $200,000), I would recommend retaining a financial advisor with a fiduciary obligation. A fiduciary is obligated to have your interest at heart, and while not foolproof, I do believe it lessens the chance that the advisor will end up taking advantage of you. Any advisor with a CFA is bound by fiduciary duty. If you don’t know of any advisor like that, please email me at info@moneygeek.ca and I’ll introduce you to one.

If you don’t have that much money saved up, I would recommend that you follow the Canadian Couch Potato’s model portfolios. Some of you may see the irony in this, as I’ve written articles critical of CCP’s model portfolios in my early years. As time has passed, however, I’ve come to regret my decision to write those critical articles. Although I still feel that I made some good points, my negative tone was unwarranted. The truth is that CCP’s model portfolios are good portfolios. Are they perfect? Probably not. But they’re a lot better than some of the stuff other advisors recommend.

I wish that I didn’t have to write this article. I wish instead that I’d be announcing the exciting launch of Portfolio Expo, a platform that will revolutionize DIY investing. I wish that regulation hadn’t stood in the way of that dream. But I accept reality as it is. Regulators have a job to do, and from my conversations with them, they really do care about protecting the little investor. I hope to someday get the resources to be regulated, and finally launch Portfolio Expo.

The Zeta Coefficient – A New Way to Forecast Returns Using Risk

peter.white@enjine.ca (Peter White) — Mon, 29 Jul 2019 14:13:29 -0500

Image Credit: Debby Wong / Shutterstock.com

Risk comes from not knowing what you’re doing

Warren Buffett

As far as superhuman powers go, the ability to accurately forecast returns probably wouldn't be many people's first choice. It's not as sexy as super speed or laser eyes. But, imagine the edge you'd have as an investor if you could look at an opportunity and predict the returns with precision. You would essentially remove all of the risk from investing: you'd be playing the game on easy mode!

Risk and returns are inter-twined. If you can assess risk accurately, you can generally predict returns accurately as well. Risk is the secret ingredient to investing in the same way that love is the secret ingredient to cooking. So, risk assessment is one of the most complex parts of investing and underpins many of our decisions. But, how well do we really understand it?

Each of us develops an intuitive understanding of risk during the course of our life, but it's a very difficult thing to quantify. It’s like trying to put a number on fun. The concept is too abstract, too vague to measure. We all know that dinner with friends is more fun than getting punched in the face, but how can you show that mathematically? The same issues arise when trying to compare investment risks. There's no obvious way to objectively measure risk, so, we often have to make a judgement call. And, you don't need me to tell you that when it comes to judgement calls that people don't always make the right decisions.

So, while you understand risk as a concept, it's not inherently clear how to factor it into your investment decisions. It's arguably the most important thing, but you can't really put it in the recipe because it's not tangible. You want a meal made with love, but if you saw a recipe that called for one cup of love, you'd be a bit sceptical. So, how do you properly factor risk into your return predictions?

CAPM – An Old Friend

It seems as though everything under the sun has been used to predict returns at one time or another, but one of the most well-known methods is the capital asset pricing model. Most financial professionals are familiar with CAPM and its ingenious method of exploring the relationship between risk and reward. It's a beautiful model that won over people's hearts and even won a Nobel Prize in 1990.

CAPM is a beautiful theory, but, much like origami master Robert J. Lang, only works on paper. Beyond the laundry list of assumptions it makes, CAPM has been around for so long and is in use by so many people that it's virtually impossible to gain an edge with it. And, despite the shortcomings, CAPM is still widely used as a tool because it simply and elegantly predicts expected returns in the face of risk. However, there are few--if any--who would say that CAPM is a complete and perfect model.

ZCAPM – The New Kid in Town

If Jay-Z has taught us anything, it's that if you want something to seem cool, you add a Z to the name, and ZCAPM is no different. Developed earlier this year by Wei Liu, James W. Kolari, and Jianhua Z. Huang, the ZCAPM is like CAPM on steroids. CAPM compares a security's return to the return of the market. ZCAPM adds another important factor, which it calls Zeta. Much like Beta in CAPM is a measure of a security's volatility compared to market returns, Zeta analyzes a security’s volatility compared to the cross sectional return dispersion of the market. That is, it measures how much a stock moves compared to the standard deviation of all of the individual stock returns during a particular period.

The idea that return dispersion is a predictive factor is nothing new (the idea has been well documented), but using it in this application is a real leap forward. ZCAPM is ready to be applied to portfolio construction, and, although the tests are minimal so far, early results are quite promising. Long only portfolios showed similar volatility to the CRSP index, but with somewhat higher returns (between 1.06% and 1.10% to the CRSP’s 0.89%). Other numbers are similarly impressive, although the results have yet to be verified by others.

So, what's the catch? Firstly, it's really hard to say “ZCAPM” aloud, which I think will really hold it back. But, more importantly, the premise is new and untested. Lots of models with long only portfolios look promising under initial test conditions, but they fall apart under rigorous examination. Also, further research is needed into how ZCAPM applies to other asset classes, including bonds and real estate, as well as international stocks. However, while both the scope and the breadth of the zeta coefficient are limited, the results are such that it is worth taking the time to investigate it further.

Zeta and Machine Learning

ZCAPM is an interesting concept, but for you to really tap into the full power of the coefficient, it's better to incorporate it into a machine-learning model. There is so much unavoidable risk when it comes to investing that you want to do your best to remove any potential source of human error that might compound it. And, the best way to remove human error in decision-making is to remove the human. Machine-learning algorithms can allow us to spot patterns and trends that are either too subtle for humans to notice or buried under too much data. And, more importantly, algorithms are free of the cognitive biases that haunt our choices, leaving them free to potentially make better decisions.

That said, machine-learning models are only as good as the inputs you feed them. The more significant the inputs, the more accurate the model. Think of your model like a dog sled where the inputs are your noble huskies. The more good dogs you have, the better the result. The ZCAPM results seem to indicate that the zeta coefficient contains an important signal about future performance, and you can harness that in your predictions. That's the sign of a good husky.

Investing is as much about beating everyone else as it is about beating the market, so, you need to stay a step ahead. Doing what everyone else is doing is not enough; you have to actively seek out the next thing. Machine learning helps immensely in this task as it allows you to develop and test new factors and models with a level of efficiency and complexity that human beings can never replicate. If the right algorithm can develop Star Trek like translating abilities, imagine what it can do for your portfolio.

Why Decision Trees Work Well For Investment Analysis

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 22 Jul 2019 15:29:36 -0500

Image Credit: Boo-Tique / Shutterstock.com

What is the best machine learning algorithm? The answer is, unsurprisingly, “it depends.” There are many different types of machine learning algorithms, each with their own unique way of modelling the real world in some fashion.

Tradeoffs on Model Complexity

The best algorithm is generally one that most closely mirrors the real world. Think of each machine learning algorithm as a set of lego boxes, each containing different shapes of bricks. If you’re going to build an airplane, you’re going to do better with lego boxes containing wing shaped bricks.

However, the complexity of the algorithm comes into play as well. Some people may think that more complexity is always better because it can more accurately model real world phenomena, but this would be a mistake. Indeed, complex algorithms have greater capacity to learn the “wrong” lessons. Let me show you an example.

Let’s say we want to create a model that predicts the probability of a coin coming up heads. We therefore toss a few coins, record their outcomes, and train an algorithm on that data. The outcome is as follows (‘H’ denotes head and ‘T’ denotes tail).

T T H T H H

A very simple algorithm may only look at the number of Hs relative to Ts, and conclude that the probability of an H coming up is 50%. But a more complex model that remembers past outcomes may think that the probability of H is more likely after T T or H T. The complex algorithm, though more powerful, has yielded an inferior model.

Another problem with using complex algorithms is that they are generally more difficult to interpret. One reason linear regression is still so popular in the investment community today is because linear regressions, being simple mathematically, are also simple to interpret. For instance, the Fama French 3 factor model says that the smaller the stock, the higher the expected return for that stock. By contrast, it’s rarely possible to explain the process behind machine learning models using just one or two lines.

There therefore exists a tension around choosing the complexity of the machine learning algorithm. Too simple, and the algorithm doesn’t have the ability to accurately model real world phenomena. Too complex, and the algorithm learns the wrong lessons, and/or it becomes too hard to explain the model’s inner workings. The best machine learning algorithm is one that can bring the benefits of complexity while paying as little as possible for them.

In the domain of investment selection, I find that algorithms that employ the ‘decision tree’ model often do a good job of achieving this balance. Let me show you why.

Strengths and Weaknesses of Decision Trees

First, let me give you an overview of how decision trees work. Let’s say that we start with some input data and their corresponding output data. For instance, the input data may include the return on equity, and the output may be the percentage change in the price of the stock.

To form a decision tree, first we identify the input variable which is the most important factor in determining what the output will be. For example, the tree algorithm may decide that P/E is the most important variable to consider.

We then analyze how the values of the variable are associated with the output, and divide the data into separate sets using a critical value. For instance, we may see big differences in outputs between stocks with P/E less than 15 versus those with P/E equal to or greater than 15. If this is the case, we would divide all stocks into two sets based on this criteria.

After the data has been split, we have the option of splitting the data set further using either the same or another input variable. For example, in the data set containing stocks with P/E less than 15, we may find that 6 month momentum matters most, and split the data set further based on whether 6 month momentum is positive or negative. On the other hand, for stocks with P/E more than 15, we may find that P/E still matters most, but we may choose to split on a P/E value of 40 this time.

After some point, it will no longer make sense to split data sets further. Instead, we would assign some score for all data that belongs to a set. Such scores may indicate that we should buy a stock, or vice versa. The chart below depicts the example we’ve followed thus far.

In this example, we may conclude that we should buy stocks with P/E less than 15, that have positive 6 month momentum. Perhaps this represents the GARP (growth at reasonable price) stocks, and the data indicates that the strategy works. On the other hand, the model may tell us to avoid stocks with P/E less than 15 that have negative 6 month momentum. Perhaps these are value traps, which the data says often leads to bad outcomes.

One of the major strengths of decision trees is the fact that they can model many different contexts. We’ve already seen an example of this, where stocks with P/E less than 15 were treated very differently depending on whether momentum was positive or negative. Not all machine learning algorithms are as flexible.

Another strength of decision tree algorithms is that they can handle missing data gracefully. In finance, missing data occurs often. This is sometimes due to an error with the data vendor, but at other times, the data simply doesn’t exist. For example, profitability margins don’t exist for companies that have yet to make a sale.

In decision trees, missing data can be treated as its own class of data, and the algorithm only needs to decide whether to go left or right down the tree path when it encounters missing data. Other machine learning models typically can’t handle missing data out of the box, and while there are good workarounds, I feel that they don’t handle missing data as gracefully as decision trees can.

Decision trees are particularly great when there are relatively few data points to work with. Because the outcome is modeled to be the same for all stocks that belong to the same context, decision trees tend to be more resistant to ‘overfitting’ than other more complex algorithms. In other words, a decision tree algorithm tends not to learn the “wrong lessons” we talked about earlier. However, this is a double edged sword since by the same token, decision trees can’t model differences between stocks that belong to the same context.

Finally, decision trees are easier to interpret compared to other more complex algorithms. Modern software packages allow us to view graphs of decisions that have been constructed, and through them, humans can at least trace the decision paths that have led to a particular outcome.

Now, does this mean that decision trees are always the best algorithm for handling investment data? Certainly not. Time series, for instance, may be better handled by some types of neural networks. However, in situations where there are relatively few data points and a high proportion of missing data, decision trees can shine, and in finance, those situations occur frequently.

It's Not Just Hype - Why Machine Learning Holds So Much Promise

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 08 Jul 2019 14:38:50 -0500

Image Credit: Grigorita Ko / Shutterstock.com

In the book “MoneyBall”, author Michael Lewis documented the story of the Oakland A’s baseball team. Despite their shoestring budget, the A’s consistently contended with teams with far bigger budgets, such as the New York Yankees. The secret of the team’s success boiled down to one thing - the use of statistics. Instead of relying on the subjective judgements of scouts, the A’s made rational decisions on player acquisitions using data.

Unfortunately, the story doesn’t have a good epilogue. Not long after the book’s publication in 2004, the team’s standing began to slide. Whereas the team had finished either first or second in its division from 1999 to 2006, the A’s often slumped to third or fourth during the 2007 to 2011 period. Then after a couple of good years, the A’s finished fifth three seasons in a row from 2015-2017. The reason for their failure to achieve top results is simple - other teams caught on to the A’s methodology and started adopting it themselves. Inefficiencies in player trading had been arbitraged out.

I sometimes wonder if a similar story is unfolding in the quantitative investing world. As I wrote a couple of months ago, many mainstream quantitative strategies have failed to perform recently. The strategies may have yielded good results when they were first discovered, but would the strategies still work going forward once most financial advisors learned about them? No one can say, but it’s possible they won’t.

Now, I understand what people advocating such strategies would say. They’d say the strategies will continue to work because they exploit people’s behavioural biases. For example, value strategies work because investors generally become too pessimistic about many companies’ prospects, tanking their stock prices below their intrinsic values. Momentum works because people’s minds are anchored to the last traded stock price, and so they underreact to good news. These are all good points, and they might be right, but they might also be wrong in a world where investment decisions are increasingly driven by algorithms.

So if you’re worried that mainstream quantitative strategies won’t be as effective going forward, how then should you look for superior returns? To answer this question, I think it’s helpful to keep the different sources of investing edge in mind.

Sources of Investing Edge

Investing edge refers to the competitive advantage an investment manager may have over his or her competitors. Some theorize that there are three sources of investing edge: informational, behavioural and analytical advantages.

Informational advantage refers to having exclusive access to important information. Such information may include a pending takeover bid of a company, or legal documents that no one else bothers to read. The problem with exploiting informational advantages is that they’re often costly, illegal or tedious to gather.

Behavioural advantage refers to the willingness to sit through emotional discomfort. In late 2008, for example, many investors knew that stocks were trading at very cheap levels. But they were afraid to act because they had the real risk of losing a lot of money in the short term. If investors could bring themselves to not care about the short term pain, they would have made a lot of money. Of course, making such decisions is often easier said than done, especially for financial professionals who have to answer to their clients.

Lastly, analytical advantage refers to the ability of the investment manager to synthesize and analyze information better than others. Mainstream quantitative strategies attempt to exploit this advantage. Computers are used to conduct quick analysis of stocks that would take human analysts a long time to do.

Of the three potential advantages, pressing for the analytical advantage seems the most attractive since it involves the investor working smarter, not harder. Unfortunately, analytical advantage can be fleeting, and as I’ve mentioned previously, we may have already reached that stage where the advantage offered by mainstream quantitative strategies has evaporated.

The good news is that it’s still possible to gain an analytical advantage without using mainstream quantitative strategies. But gaining the advantage requires the investor to use more sophisticated analytical tools. I believe that machine learning provides those tools.

Limitations of Linear Regression Models

Many of the mainstream quantitative strategies today makes use of linear regression models. For example, the famous Fama French Three Factor Model is a linear regression involving three input features:Total Market Returns, Size Premium and the Value Premium.

Linear regressions consider each feature in isolation. For example, in the Fama French model, a higher Value Premium of a stock always leads to a higher expected rate of return for the stock. Moreover, increases in feature values will always have the same effect, regardless of their starting base values. For example, the Size Premium going from 0.0 to 0.3 would have the same effect on the output as an increase from 2.0 to 2.3.

Unfortunately, this rigid structure prevents linear regressions from being able to model many types of real life situations. A famous example of this is called the ‘Exclusive Or’ problem. Let me explain using an example.

Suppose that we want to create a model that predicts whether a pair of dogs can breed or not. We know that in order to breed, one of the dogs has to be male, and the other has to be female. A linear regression model would look like this:

Y = 𝜔₀ + 𝜔₁X₁ + 𝜔₂X₂

‘X₁’ and ‘X₂’ would denote the genders of the first and second dog, respectively. X₁ would be 0 if it were male, and 1 if it were female. ‘Y’ would denote whether they could breed or not, with 1 being Yes, and 0 being No. The values of 𝜔 should be set during model training such that Y would be correct given the values for X.

If you try to train the model using a statistical package, however, you’d get the following values: 𝜔₀ would come out to be 0.5 while 𝜔₁ and 𝜔₂ would come out to be 0. Since anything multiplied by 0 is 0, the equation would reduce to the following:

Y = 0.5

In other words, the linear regression model wouldn’t consider the genders of the dogs at all. It would always say the chance of whether the dogs can breed or not is 50/50. For all intents and purposes, the linear regression model would be useless.

The linear regression model failed to yield a useful model because it considered each input in isolation. It tried to see whether the gender of the first dog influenced the probability of breeding, without taking the gender of the second dog into account. It’s like sending one analyst to check the gender of the first dog, and another analyst to check the gender of the second dog, and asking them to vote on the outcome without allowing them to talk to each other.

There are many situations in finance where some input features likewise have to be evaluated in the context of other features. Take insider transactions, for example. It is said that insider purchases are stronger signals of insiders’ confidence in the stock if the stock has been rising leading up to the purchase. But linear regression models wouldn’t be able to model the different contexts.

Another limitation of linear regression arises from the fact that the relationship between input features and outputs are too rigid. Let me give an example from finance.

Every investor would agree that it’s never good to see companies with very high leverage ratios. For such companies, increasing the leverage ratio further would result in lower expected returns, since the chance of bankruptcy goes that much higher.

However, it’s also true that companies can have too low a leverage ratio. Equity’s cost of capital is generally higher than that of debt, so it’s good for a profitable company to have some debt. For underleveraged companies, higher leverage ratios should result in higher expected returns for the stock.

Unfortunately, linear regression models don’t have the ability to distinguish between the two scenarios. Adding leverage ratios would either reward companies all the time, or it would penalize companies all the time. As a result of these limitations, research that uses linear regression models can miss a lot of important insight. For example, it may wrongly conclude that leverage ratios don’t affect expected returns.

Modern machine learning models, on the other hand, overcome these problems by allowing for more flexibility. Their structure allows input features to interact with other features, and for input features to influence output in complex ways. When you train machine learning models on financial problems, the model teases out insight that’s not immediately obvious to human analysts. This allows the model user to wield analytical advantage over other investors, which can lead to superior investment returns.

Now, you may be wondering,if this is all true, why aren’t machine learning models more popular? I think that’s a great question, and a topic for another time. But for now, let me just say this: Many of the objections to machine learning I’ve come across are rooted in misconceptions or lack of knowledge about the subject. I hope that in the coming weeks, we can answer those objections. Machine learning models are powerful, and it’d be a shame for someone to discard it because of misconceptions.

Gold Moves Up - But Will It Continue To?

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 01 Jul 2019 15:55:47 -0500

Image Credit: photo BC / Shutterstock.com

At the beginning of every month, I brief members on how MoneyGeek's Regular portfolios have performed and comment on the state of the financial markets. In this update, I’ll also share my thoughts on gold.

June Performance of Regular Portfolios

The performance of MoneyGeek's Regular portfolios for the month of June 2019 were as follows:

	Last Month	Last 12 Months	Since Apr 2013
Aggressive	+3.4%	-5.5%	+90.2%
Growth	+3.0%	-4.2%	+76.0%
Balanced	+2.6%	-3.2%	+62.2%
Conservative	+2.2%	-2.2%	+49.1%
Very Conservative	+1.8%	-1.0%	+36.9%

I've chosen to list below the performance of some of our competitors. For the sake of brevity, I've decided to show only those portfolios that have a similar risk profile to MoneyGeek's Regular Aggressive portfolio.

	Last Month	Last 12 Months	Since Apr 2013
RBC Select Aggressive Growth	+2.5%	-0.7%	+40.6%
TD Comfort Aggressive Growth	+2.3%	-7.0%	+36.9%
CIBC Managed Aggressive Growth	+2.4%	+1.0%	+52.7%
Canadian Couch Potato Aggressive	+2.5%	+6.7%	N/A

In contrast with our competitors, MoneyGeek’s Regular portfolios employ stocks/ETFs that follow the value investing strategy (QVAL, IVAL and BRK-B), and also allocate a larger percentage of the portfolios toward Canadian oil and gas stocks (XEG.TO) and gold (CGL-C.TO). If you would like to take a look at our portfolios, I invite you to sign up for our free membership.

The Regular portfolios outperformed its competitors in June. QVAL went up by 6.1% during the month, beating the US stock market average which went up by 4.0%. Gold prices lent a helping hand as well, going up by 4.3%.

Gold made headlines among financial publications for the first time in many years. After the 2009 to 2013 period in which some investors made overly optimistic predictions, the price of gold had stayed stuck in a range between $1,100 and $1,300 an ounce. Last month, however, gold broke out of that range, causing some investors to ask why.

Source: https://goldprice.org/gold-price-history.html

Different sets of factors drive gold’s long term and short term price movements. Of these, the long term movement is easier to understand, since it’s mainly driven by inflation.

A piece of gold, once purchased, neither changes in size or quality. This is different from owning stock in a company, which has the potential to grow significantly. The price of gold could still increase significantly if demand for it continues to increase exponentially and/or supply decreases continuously. However, neither has been the case historically, and I fail to see how it would be different in the future. So barring any fundamental changes, gold prices will track inflation in the long term.

The short term movement of gold, however, is trickier to understand. As I see it, there are two factors that drive gold prices, and they are flight to safety and low interest rates, which often go hand in hand.

Historically speaking, gold enjoyed bumps up in prices when the world seemed close to a major war or a recession. People view gold as the ultimate store of value, and as a universal currency. This property of gold hit home for me when I read an anecdote of two commodity traders discussing what they’d prefer to own should world war 3 erupt.

The first trader asserted that he’d want to own oil. Waging a war is very energy intensive as tanks and airplanes guzzle oil, while the supply of oil may see disruptions. The second trader, however, said he’d rather own gold. The only reason the second trader was alive was because his grandparents escaped Nazi Germany by bribing soldiers with gold.

Now, it’s hard for me to imagine the world descending into such chaos that I’d want to own physical gold to escape calamity. But some people do view the world through rather cynical lenses, and increasing talks of wars and recessions can stoke their cynicism. It would also be wrong of us to dismiss all pessimists’ concerns out of hand. After all, no one knows the future, and most people were equally bewildered when the first world war erupted the way it did.

The other short term factor that can push gold prices up is the prevalence of low interest rates. Sometimes, interest rates could be so low that investors become disinterested in putting money into bonds. Instead, they look for something - anything - that would generate better returns. Money tends to flow towards high risk, potentially high reward investments in such circumstances. In the past few years, the destination of this money were growth stocks (e.g. Uber) and cryptocurrencies. But gold also has the potential to be a similar destination, as was the case in 2012.

Since interest rates tend to come down during recessions, you could argue that the two short term factors driving gold prices are linked. It therefore stands to reason that gold would do well if the world does slip into a recession soon, and vice versa.

While no one knows for sure whether we’ll have a recession or not, most thoughtful investors would agree that the chance of having one seems high. That’s why I still choose to keep gold in MoneyGeek’s Regular portfolios, to act as a hedge in case stocks in the portfolios go down.

My TFSA Update May 2019 - The Final Article

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 17 Jun 2019 20:35:17 -0500

Image Credit: Fotokostic / Shutterstock.com

In this series, I (Jin Choi) talk about my journey of investing in my TFSA account. If you want to know what a TFSA is, I recommend you read my free book. In this update, I’ll explain why I’m discontinuing this series, and how the content of this website will change in the future.

May Results: Down 13.8%

At the end of May, I had $40,416 in my TFSA account, which is down by 13.8% since the end of last month. By comparison, the Canadian stock market went down by 3.3% while the U.S. stock market went down by 5.4% in Canadian dollar terms. Therefore, my portfolio underperformed.

The majority of my portfolio consists of Canadian oil and gas stocks. Oil prices crashed in May, going from $63.83/bbl to $53.49/bbl (in US dollars). There is just one big reason for this crash. As I explained in my previous article, global economic growth has slowed dramatically, to the point that we’re now teetering on the brink of a recession. Global oil demand has fallen as a result, bringing prices down with it.

This latest stumble of my portfolio has forced me to think long and hard about my own investing acumen, and by extension the value I’m providing through this site in general.

For a long time, I considered myself a good value investor. I’d always excelled in academics, particularly on subjects involving numbers. I also believed I had good business instincts, a belief which I’d say is supported by the fact that I’m currently running a growing business. However, as I read through Michael Lewis’ excellent book called ‘The Big Short’, I’ve been convinced of the fact that in addition to intelligence, you need a specific temperament to succeed as a value investor, a temperament that I don’t possess.

The Big Short tells the story of several money managers who foresaw the collapse of the subprime bubble and profited from it. Although these managers had very different backgrounds, they all had one thing in common: they dug deeper into research than any of their peers. Michael Burry read legal documents that nobody else bothered to read. The principals at Cornwall Capital didn’t make huge bets until they spoke to everyone who could possibly tell them they were wrong.

If I’m honest with myself, I simply don’t have the patience or the interest to conduct such deep dive research. Rather, I’m motivated by ideas, and predisposed to building stuff. I think up new ideas for a web tool or a research project, and start coding before the ideas are fully formed.

Now, this doesn’t mean I’m doomed to fail at investing. Rather, it means that I need to concentrate on a style that works for me.

The investing style exhibited by the heroes in the The Big Short is called fundamental analysis. This style of investing requires an investor to focus on only a few ideas at a time, and since such investors don’t have the capacity to analyze every idea deeply, they generally end up with concentrated portfolios.

A good analogy would be that of picking apples in an orchard. A fundamental analyst would inspect each apple carefully before putting it into his basket. While there’s a higher chance that the apples in his or her basket are good, the basket would generally contain only a few apples.

On the other hand, there is an equally effective style of investing called quantitative analysis. This style of investing makes heavy use of statistics to analyze all companies at once, assigning ratings to each company. Investors who employ this style would then take some number of highly rated stocks and put them in portfolios. While investors wouldn’t place great conviction in any one company, they’d be confident that the companies they’ve chosen would be good overall.

In the orchard analogy, quantitative analysts would be like those who pick apples based on a set of well defined criteria, such as size and colour. Because the apple picker only cares about such limited set of criteria, he’d fill the basket a lot quicker, but he risks having some bad apples thrown in the basket. Both fundamental and quantitative styles have merit - you generally get better quality with the former, and more quantity with the latter.

Given my skill set and temperament, it’s clear to me that I’m more suited toward the quantitative style of investing rather than the fundamental. It’s a shame because I still hold some romance towards the fundamental style, which is probably why it’s taken me so long to come to this realization. But now that I’ve come to the realization, I’ve decided to change not just my investing style with my own money, but the orientation of this site as well.

Starting next month, I will discontinue ‘My TFSA’ series. Instead, I will start writing about the machine learning model that my company has been hard at work on. I will begin by giving a high level overview of the machine learning paradigm, and go on to discuss specific features and techniques we employ in our models.

I’m excited about this new direction, because I feel that we’ll be offering something truly unique. There are a good number of quantitative investing blogs out there, but none that I know of that focus purely on machine learning. Most quantitative analysts still rely on more basic statistical tools such as linear regression. But having worked on machine learning models, I know that machine learning can add a lot of value that these basic statistical tools can’t.

If you’re wondering about MoneyGeek’s portfolios, I don’t anticipate any major changes for now. I will continue to write about them, but I will perhaps put more emphasis on including ETFs with quantitative strategies in the portfolios.

Writing about my failures managing my TFSA account has not been fun. I’m also not convinced that it was the best material to write about from the reader’s perspective. I therefore look forward to putting this behind me, and start providing better value for your time.

Is A Recession Coming Soon?

jin.choi@moneygeek.ca (Jin Won Choi) — Mon, 03 Jun 2019 09:23:04 -0500

Image Credit: Jenson / Shutterstock.com

At the beginning of every month, I brief members on how MoneyGeek's Regular portfolios have performed and comment on the state of the financial markets. In this update, I’ll also talk about some economic indicators that point to a weakening global economy.

May Performance of Regular Portfolios

The performance of MoneyGeek's Regular portfolios for the month of May 2019 were as follows:

	Last Month	Last 12 Months	Since Apr 2013
Aggressive	-8.9%	-7.9%	+84.0%
Growth	-7.8%	-6.4%	+70.9%
Balanced	-6.7%	-5.1%	+58.1%
Conservative	-5.5%	-3.8%	+45.9%
Very Conservative	-4.4%	-2.4%	+34.5%

	Last Month	Last 12 Months	Since Apr 2013
RBC Select Aggressive Growth	-4.5%	-2.3%	+37.1%
TD Comfort Aggressive Growth	-3.5%	-8.5%	+33.8%
CIBC Managed Aggressive Growth	-3.3%	-0.5%	+49.1%
Canadian Couch Potato Aggressive	-4.0%	+5.5%	N/A

Regular portfolios heavily underperformed our competitors in May. Funds containing value stocks were largely to blame, as QVAL, IVAL and XEG went down by 13.1%, 11.1% and 11.7% respectively. Although gold prices went up, the increase was not nearly enough to offset the damage wrought by the value funds.

The broader stock market also declined in May, although not by as much. In Canadian dollar terms, the S&P 500 (the US stock market benchmark) declined by 5.6%, while the TSX Composite (the Canadian stock market benchmark) fell by 3.3%. I believe value stocks underperformed because investors are choosing to dump the losers in the portfolios while keeping the winners. Indeed, momentum funds like QMOM held up well last month.

It’s hard to say when value stocks will stop underperforming relative to the rest of the stock market. However, I still strongly believe that value investing’s day will come. By investing in value stocks, we are implicitly saying that we prefer companies that are generating cash today. The investing public, on the other hand, seems to be saying it prefers companies that are predicted to gain big in the future, even if that prediction is highly uncertain. For example, Beyond Meat, a company that generated just $88 million in revenue last year, went up by 58% last month to be valued at $6 billion. Companies rarely live up to such lofty expectations.

It will be interesting to see how such companies fare in the coming economic environment. A lot of warning signs are currently flashing that suggest we may be entering a recession. Let me show a few data points that suggest this is so.

Let’s start with China. One measure that’s highly correlated with economic growth is diesel consumption, since it’s used heavily to move goods and people via trucks and trains. Unfortunately, Chinese diesel consumption has dropped dramatically in March and April.

The official Chinese Purchasing Manager Index (PMI) tells a similar story. The PMI is a gauge that tells whether companies are seeing improvements in their businesses, and is an important leading indicator of economic growth. As this article shows, the Chinese PMI has been trending down since late last year.

European PMI is not looking good either. As this link shows, European countries registered very high PMIs in the beginning of last year. But the PMI numbers have deteriorated steadily since, and as of the latest data points, many countries are reporting PMIs low enough to indicate economic contractions.

Finally, it appears that even the US economy is slowing down. During the past couple of years, the US proved to be a particularly bright spot in the global economy. Unfortunately, multiple leading economic indicators suggest the growth might be coming to an end.

US growth has completely rolled over.... pic.twitter.com/JikUBOdhBD
— THE LONG VIEW ⚫️ (@HayekAndKeynes) June 2, 2019

The latest economic data points are making investors more wary. In a previous article, I explained how the “yield curve” tends to invert when investors think a recession is coming. That is, long term interest rates tend to fall below short term interest rates. Not only is the yield curve inverted today, but the curve has been getting steeper as well.

It has been about ten years since the world last experienced a recession. I’m fairly convinced that we’re about to see another recession soon, in part because I believe we're due for one. Historically, value stocks have tended to outperform growth stocks during recessions. I hope that will be the case again, so that MoneyGeek’s portfolios will start to outperform its competitors once again.