Two Schools of Quants

I recently read this question off the Quant Finance subforum of StackExchange, a Q&A website for programmers: "Which approach dominates? Mathematical modeling or data mining?"

Basically, it seems that there are two schools of quants. This is my possibly over-simplified and generalized interpretation of the distinction.

1. Background: mathematicians / theoretical physicists / computer scientists / academic economists

Inference: deductive

Epistemology: rationalist

Type of knowledge: a priori

Beliefs: "There exist absolute immutable truths of the markets."

"I can discover these truths by superior thinking."

"With the right theories, I can make money."

2.  Background: scientists / statisticians / engineers / programmers / business economists

Inference: inductive

Epistemology: empiricist

Type of knowledge: a posteriori

Beliefs: "I cannot know if there exist any immutable truths of the markets."

"However, I can asymptotically approximate these truths through superior observation."

"With the right models, I can make money."

I think that's the essence of it, although the commenters in that post seem to be using many more words than I am. To boil it down to even simpler terms (at the risk of evaporating some meaning), the theoretical dominates for the former whereas the data dominates for the latter.

How would you begin to identify your "school" of quant strategy? I guess the first thing to do is to ask yourself, why did I make that trade? If you say, in historically similar situations, the price of this security responded this way, and I'm going to assume that this will continue to happen in the future, then you're probably in the latter camp. On the other hand, if you respond with, there's this theory which proves that security prices moves this way, given certain assumptions and axioms, then you're probably in the former.

However, there's problems with this answer. On the StackExchange post, "Quant Guy" makes a good observation about the Fama-French models: 

As more complex/realistic theories are devised, there is also the concern whether the theory itself was formed after peeking at the data - i.e. devising theories to explain persistent patterns or anomalies which an earlier theory could not 'explain' away. In this context, Fama-French's model is not a theory - it spotted an empirical regularity which was not explained by CAPM, but it is not a theory in the deductive sense.

Some background: CAPM (Capital Asset Pricing Model) explains the return of an asset as a function of a single factor: "beta", or more specifically, "market beta". As time went by, however, market participants noticed that this single factor couldn't explain all asset returns, as some low beta stocks outperformed and high beta stocks underperformed. In stepped Eugene Fama and Kenneth French of the University of Chicago, who noticed that even after correcting for market beta, small cap stocks and cheap stocks tend to outperform large cap stocks and expensive stocks: hence the Fama–French three-factor model, which adds a small cap factor and a value factor.

There is even a four-factor extension called the "Carhart four-factor model", which adds a momentum factor. We can quickly see the problem with the progression of such theories: they are not theories at all! The reason is simple: they were not conceived independently in the mind of the theoretician from logical principles and axioms, but rather, were given birth by the data. With each new market anomaly that cannot be proven by existing models, we can explain it away with a new factor, creating an n+1 factor model.

I often give the hypothetical example of a Keynesian who believes in the Phillips curve, which is the inverse relationship between unemployment and inflation, being confronted by a disbeliever. The disbeliever shows to the Keynesian a counterexample: the US in the 1970s, in which stagflation - the co-occurrence of high unemployment and inflation - is rampant, and exclaims triumphantly, "HA! There is no way that the Phillips curve can explain this! Now you must throw away your theories!" To which the Keynesian calmly replies, "On the contrary, this gives me a new theory, which is the Phillips2 curve. It's exactly the same as the old Phillips1 curve, and indeed the inverse relationship between unemployment and inflation still holds everywhere and always. Except with one important modification: when Nixon is president."

Of course, this is a ridiculous example, but it shows exactly how Fama-French is not a theory. In statistics, we call this overfitting. One might asks which is the better approach, theory or data, but I'm not sure if there is an answer. I'm not even sure if you can be strictly in one camp and not the other, as there seems to be more of a continuum than a strict dichotomy. In the real world, it is hard to really make the distinction between theory and models, as theories are often suggested by the data. Indeed, it's impossible NOT to be influenced by real world, unless you live in a cave with no Bloomberg terminals or something.

I guess ideally, you should be a quant who finds the middle way and melds the two approaches, but I'm not sure what that would look like... pragmatism?

Word of the Day

I do a word of the day with my friend Christina. No real criteria except that it has to amuse me. Anyway, here's what we've done so far:

Apocryphal [uh-pok-ruh-fuhl]

1) of doubtful authorship or authenticity

2) false, spurious 

3) in a biblical context, it means non-canonical.

Milquetoast [milk-tohst]

1) weak, ineffectual, timid, unassertive, bland person, place or thing.

If it sounds like "milk toast" that's no coincidence.

Shibboleth [shib-uh-lith, ‐leth]

1) pronunciation, custom, principle, belief, behavior, mode of dress, etc. distinguishing a particular class or group of people. 

2) common saying with little current meaning or truth. 

3) slogan, catchword.

Some examples: the pronunciation of Nevada ("a" as in "dad", rather than as in "father") and Boise ("boysee" instead of "boyzee") is used as shibboleth to identify locals. In computer security, shibboleth refers to digital credentials (such as passwords) or physical credentials (such as RFID cards or fingerprint scans) used to protect computer access. Interestingly, the word "shibboleth" itself was once used as shibboleth: in the Old Testament, Gileadites pronounced it as shibboleth, which distinguished them from Ephraimites who pronounced it as sibboleth.

Sangfroid [sahn-frwa]

1) composure or coolness as shown in danger or under trying circumstances.

If you know French, then you know that sang is blood, froid is cold, so sangfroid literally means cold-blooded. Sometimes spelled with a hyphen, as in sang-froid.

New words for this week:

Palaver [puh-lav-er, ‐lah-ver]

1) noun: prolonged and idle discussion 

2) verb: to talk unnecessarily at length.

Protean [proh-tee-uhn, proh-tee-]

1) variable, readily assuming different shapes or forms.

Protean comes from Proteus, the Greek shape-shifting sea-god.

edit: added pronunciations, another definition to shibboleth, and a new word, milquetoast.

Automation and Labor

FT Alphaville recently had a thought experiment on how things would have gone if "the US, rather than taking advantage of cheap labour in China, had kept things at home and heavily invested in automation".

This is one of my favorite themes: the rise of automation in manufacturing and its effects on the global economic balances. Recently, over the past year or so, multiple research publications and journals (such as the FT, The Economist, GS, BofA, BCG, Gavekal, ISI) have featured this supposed inevitable renaissance as robotics and 3D printing revitalize manufacturing in the US.

It's an exciting and sexy theme I will probably cover in greater detail in the future. Today, however, I am interested in very specific component: labor.

Luddites

Low-cost production techniques could soon become so advanced and so low cost — thanks to developments like 3D printing — that even the tiniest salaries in Africa will not make it worthwhile to employ human beings at all.

In the 1800's, the Luddites were a group of disgruntled skilled weavers who displayed their discontent by destroying the automated looms that made it possible to hire unskilled (and cheaper) labor in their place. Of course, in hindsight, these productivity-enhancing machines were a good thing: it freed up future generations of educated men and women towards more interesting work, e.g. as innovators of new industries. In other words, would-be weavers became engineers, inventors, thinkers, etc. instead.

Are we falling prey to this Luddite fallacy today? It's clear that on its own, automation cannot be said to be a job-killer. Generally, as the prices of goods fall with the productivity gain made possible by automation, demand for goods increases, which results in increasing demand for labor. This gives us more employment, rather than less.

However, the current round of automation (the third industrial revolution, as The Economist likes to put it) is potentially different.

source:

This is unlike the job destruction and creation that has taken place continuously since the beginning of the Industrial Revolution, as machines gradually replaced the muscle-power of human labourers and horses. Today, automation is having an impact not just on routine work, but on cognitive and even creative tasks as well. A tipping point seems to have been reached, at which AI-based automation threatens to supplant the brain-power of large swathes of middle-income employees.

In previous industrial revolutions, machines replaced our "hardware", that is, our bodies and our physical labor (bad analogy, but let's roll with it). This was fine, because as long as our ideas added value and machines couldn't automate our thought processes, we could remain employed in an intellectual capacity. However, machines are now able to simulate many of our thought processes - and not just the purely computational ones - with the industrial implementation of artificial intelligence and machine learning techniques. Machines are now replacing our "software", that is, our minds and our intellectual labor.

Modern Luddites like to point at today's unprecedented levels of long term unemployment as evidence for this. However, if this were true, why is there continuing high demand for skilled workers?

source:

Nearly 60 percent of survey participants expect to increase their workforce (compared to 50 percent in the fall), but finding qualified workers to fill open positions continues to be a concern for the industry – an unusual dichotomy, given that national unemployment rate remains high," said Kurek. "The need for a skilled workforce could be one of the greatest impediments to growth for U.S. manufacturers and distributors, and makes it difficult to compete in the global market."

source: 

For many manufacturers, finding the best people to fill these new positions is far from assured. Respondents to ThomasNet.com's IMB lament the skilled labor shortage, and are vocal about what needs to be done to fill the gap. One noted that we need to "improve the attitude within the U.S. regarding the desirability of manufacturing for the next generation." And many respondents want to see education reform with the aim of giving America's youth the skills needed to join the manufacturing workforce.

Usually, automation draws labor demand away from the high-skilled towards the low-skilled. So what is going on here?

Perhaps it's simply a matter of perspective.

Skills and Training

In the long term, it may be true that we are on the cusp of a post-scarcity world of maximal leisure and obsolete labor thanks to the ever increasing intelligence of machines. In the short term, however, human intellectual capital is very much in demand.

[In the 1990s] the US went for massive outsourcing. However, Germany and Northern Europe in general went for automation. The reason why the latter region went for automation is that they were already fighting high labour costs as early as 1980, so they already were well on the path to automation.

At least in Northern Europe, the big automation revolution that we saw starting around 1980 seems to be coming to an end. The reason is the full exhaustion of engineers/skilled technical workers.

This is why some have proposed working hour limits, e.g. instead of a few investment bankers working 100 hour weeks, twice as many bankers working 50 hour weeks are hired. Of course, the policy's track record isn't that great (consider France's 35 hour/week limit and look at their economy) and furthermore, it falls victim to the lump of labor fallacy. However, this perhaps helps us in understanding the liberal's curious characterization of an ambitious overachiever taking excessive overtime for himself as somehow "greedy" due to his theft of his fellow man's labor hours. Compare with a conservative's view that all hard work is deserved and efficiently allocated to those who are most deserving.

However, considering the theory that we are on the cusp of a post-scarcity world, perhaps the liberal is right.

We live in a world were there is too much work for highly educated workers and not enough work for low educated ones. This at a time of general decline in education standards as demonstrated by many PISA studies. The forces of the market would have it that wages of the educated will rise and wages of the non-educated will fall.

This is why we need cheap, effective and widely available STEM (science, tech, engineering, mathematics) training (and retraining) opportunities in the US. This is both for new entrants to the labor force as well as for existing workers who have been displaced. A "liberal arts" education may be more intellectually pure, but for the majority of the population, it's simply irresponsible. The German education system, which emphasizes vocational schools alongside industry apprenticeships, is a good model (already these are starting to pop up in the US). This would also serve to help students avoid taking on excessive student debt as costs are lower than traditional research universities, and full time offers are often made by the employer to their apprentices upon graduation. Businesses would also be more willing to hire new graduates (as opposed to experienced hires) as job-specific training has already been completed (avoiding expensive on-the-job training programs as in the US).

However, the fundamental problem remains that the exponential pace of technological progress may simply be too fast for the skills mismatch gap to close. This is why I am optimistic about online education opportunities such as Udacity, Coursera, Codecademy, iTunes U, which meet many of the above requirements for good STEM training: cheap (it's free), effective (taught by professors, some of whom are at Ivy League universities) and widely available (anyone with internet). Recently, Udacity announced that they will offering certification exams in Pearson testing centers in conjunction with their job placement program. Unlike inflexible bureaucratic universities, online education is subject to the free markets: courses are offered in the subjects where the demand is, course demand goes where the opportunities are. This should go a long way towards minimizing the skills mismatch gap.

Future

Demand for unskilled labor will disappear or at least be significantly diminished. Although AI, robotics and 3D printing may have the potential to completely eliminate labor as a factor of production, as some modern Luddites claim, in the short term, the modern day equivalents of machine-operators (programmers, engineers, technicians) will be in high (and probably increasing) demand.

As the ultra-low labor costs in emerging markets no longer matter, jobs may initially come back to the the developed world. However, this job reshoring may be limited in impact as the emerging markets will seek to rapidly catch up (look at the growth of India's IT talent), especially as knowledge becomes freer and more easily available (such as through online courses). Thus, the most sustainable way for developed markets to compete will probably be through superior education and training.

Betting/trading strategies- Martingale

Introduction to betting strategies
Something I have been thinking about recently has to do with different trading/betting systems. I'll probably be doing a series of blog posts on this. Let me first define what I mean by a trading/betting strategy- this is a set of rules that dictate what you should do next based on your prior streak of wins/losses and your present P&L in the game (eg: gambling game, stock market...). The goal of this strategy may be to make money, but may also be to minimize variance (risk), avoid losing too much on money that has already been laid on the table (ie. successfully exiting losing positions), or to exploit a certain effect (eg: mean reversion, autocorrelation)...

For background, look at these 3 strategies:

• Martingale strategy
• Daily re-balancing strategy
• Kelly's criterion

Martingale is generally considered fatally flawed; daily re-balancing is a hot topic right now in finance (I'll explain more later); and Kelly's is actually a mathematically proven betting strategy.

In this post I will examine Martingale and a close cousin of it (trading version) and return to other strategies in later posts.

Mathematics behind the Martingale strategy
The Martingale basically says this: bet $1. if you lose, double down. if you lose again, double down again. So  you are "guaranteed" to win $1 at the end (unless you just keep losing ad infinitum). The major problem with this is that you only have a limited bankroll. eg: say after you've lost 10x in a row, you may be out of money and the casino/brokerage firm won't let you double down anymore (because you won't be able to pay if you lose again) At this point, you are close to bankrupt and you can't double down to recoup your losses anymore.

So the hidden downside is actually that you might go bankrupt before you win once. So the question is actually what is the probability that you would go bankrupt? Let's say in a 50/50 game you budget 1023x the initial bet (ie. you could lose 10 times and then be bankrupt). Then the chance of you going bankrupt per attempt to win $1 is around 0.1% (precisely 1/1024). Now let's look at the probability that you will go bankrupt as a function of how many times you attempt:

Note that while the curve (first graph) is bounded by 1, initially (say first 100 attempts- second graph), your chance of bankruptcy is almost linear to your # of attempts n. This is because Pr(bankruptcy) = 1-(1023/1024)^n  = 1 - (1 - 1/1024)^n ≃ 1 - (1 + n/1024)  = n/1024. This result is from first order Taylor series approximation (given small enough x = 1/1024 around the point a =1)

So for example, if you plan to attempt to win $500 (try 500 times), there is a 1-(1023/1024)^500 = 38.6% chance that you will "go bankrupt' before you reach 500 (ie. lose $1023- notice that you would still have the $499 or however much you collected before you go bankrupt). If you did go bankrupt before you reach 500, on average you would have gone bankrupt on attempt #230 (you get this by doing sum[Pr(n) * n] / sum[Pr(n)]. where Pr(n) = Pr(bankrupt on n-th turn) = (1023/1024)^(n-1) * (1/1024). I just summed this over excel- is there another way to do this?)

Soooo. let's see if this all makes sense.
EV = 38.65% * (-1023+230.2) + 61.35% * (+500) = 0

Betting strategies = transform your return distribution
So as you can see, by following the Martingale betting strategy and stopping at 500 wins, we can actually consider this whole strategy as one single bet of [win $500 with 61% probability or lose $793 with 39% probability], which is still 0 EV. ie. We have not gone anywhere from the original single bet of [win $1 with 1023/1024 probability or lose $1023 with 1/1024 probability] which is also 0 EV. Essentially the betting strategy has allowed us to change the distribution of returns while keeping your expected profit (EV) the same. This is an interesting topic that we will revisit later (probably when we talk about Kelly's criterion).

The interesting thing about this is that you can "see" your P&L progress over time. ie. instead of one single bet where you have 0 info about if you are going to win or not and that becomes 100% certain right after the dice roll, here, as you make successful attempts, you are slowly but surely moving towards the +$500 outcome (instead of the -$800 outcome. ie. the odds are slowly tilting in favor of you. One significant difference between gambling and trading is that trading is more continuous. ie. even though your trades are discrete, the market price changes rather continuously during trading hours. This is similar to what is happening here where you can see your P&L slowly accumulate before you finally exit the trade.

In trading, I would would look at this strategy as having positive theta (ie. as time passes, you start to make money). In this case, the reason why there exists positive theta is because you are taking extra risks on every iteration/bet/time period. Here, the risk you are taking is the 1/1024 chance that you lose 1023. When these risks are not realized, you make money. This is the case for say short gamma positions in trading. Short gamma positions basically mean that large price movements are bad for you. (vs long gamma positions ie. the people betting against you are betting on large price movements) So every second/minute/hour/day (remember trading is more continuous) that there is no large price movements materializing, these mini bets for large price movements are expiring worthless for the long gamma guy and you are making money because you have lived to fight another day/minute/second.

Further topics (to be discussed next)
So strats like these are highly dependent on budgeting. On a totally unrelated note, in poker, there's this concept called chunking- basically say you expect 3 more rounds of betting till showdown. Then you size up your opponent's (assuming he has less chips than you) stacks and figure out how to size the bets to get him all-in at the third bet. So for example, in a $15 pot right  now and your opponent having $100 stack left, you would say bet $15, $30, $60. The bets scale up every time because the pot has gotten larger. You for a small pot, it might turn out that you need 4 bets to be all-in- in which case you need some action (ie. a raise) to be able to go all-in. But the point of this discussion is that you need to do the same thing when you are budgeting for Martingale betting. ie. if I am going to bet 1,2,4,8,16 then give up, then I need to budget $31. And this $31 hopefully lasts me for the craziest price swings ever. ie. Let's say AAPL trades in $10 range 60% of time, $30 range 90% of time, and $50 range 99% of time. You should be betting say $1 for a $5 deviation from the median (whatever that means), $2 for a $10 deviation, $4 for a $15 deviation, $8 for a $25 deviation, and really really hold tight before you make your $16 bet at the end. ie. at what pt you double down is highly dependent on how rare of an outcome this pt is.

ok- back to martingale and its cousin trading strategy. The cousin trading strategy that I wanted to talk about was the following:

Buy the stock. Set take profit level at say +10%. If stock trades down, sit and wait. If it keeps trading down, sit and wait more. Since variance increases with time and is not bounded, this means that eventually stock will trade to +10% and you can exit at a profit. So this is similar to the Martingale in some respects. What I mean is this:

If you look at the chart above, the range of estimates for the stock increases the further you go into the futures. This is in part because the stock is expected to trade in a bigger and bigger range given longer and longer time periods. This means that it is easier for you to reach any pre-set level as time goes on, potentially even if the drift (general trend) of the stock is downwards (ie. the opposite direction to your bet).

This post is getting pretty long, so I'm actually going to talk about this strat more in the next post before going on to other strats. In the mean time, key thoughts about this strat:

It is also highly dependent on the return distribution. Need to compare how much increased variance over time contributes to probability of hitting target take profit level  (eg: 50% chance of touching x in y days, -> 50% chance of touching sqrt(2)x in 2y days) to "breakeven drag". ie. how much stock will have to trend down for you to have deteriorating chances of hitting target level (have negative theta).

Thoughts of the Week - Big Bank Inefficiencies

Here is a recent article by Zerohedge on big bank inefficiencies.

I usually try not to cite ZH, but this has a lot of good links. It reminds me of an HBS article I read recently about bees and risk management. The tendencies of bees towards decentralization is a risk management tool to prevent TBTF.

Take, for example, their approach toward the "too-big-to-fail" risk our financial sector famously took on. Honeybees have a failsafe preventive for that. It's: "Don't get too big." Hives grow through successive divestures or spin-offs: They swarm. When a colony gets too large, it becomes operationally unwieldy and grossly inefficient and the hive splits. Eventually, risk is spread across many hives and revenue sources in contrast to relying on one big, vulnerable "super-hive" for sustenance.

In fact, when hives divide, it is the old queen who departs, leaving the old hive to a young virgin queen. Contrast this with normal corporate M&A and spin-off behavior in which risk remains concentrated.

One classic argument in favor of TBTF is that big banks are in a better position to capitalize on economies of scale, and the fact that breaking up large banks simply doesn't prevent bank runs. The ZH article attacks the first point through a discussion of diseconomies of scale (which I quoted almost verbatim from here):

1. atmospheric consequences due to specialization - as firms expand there will be increased specialisation, but also less commitment on the part of employees. In such firms, the employees often have a hard time understanding the purpose of corporate activities, as well as the small contribution each of them makes to the whole. Thus, alienation is more likely to occur in large firms.
2. bureaucratic insularity - as firms increase in size, senior managers are less accountable to the lower ranks of the organisation and to shareholders. They thus become insulated from reality and will, given opportunism, strive to maximise their personal benefits rather than overall corporate performance. This problem is most acute in organisations with well-established procedures and rules and in which management is well-entrenched.
3. incentive limits of the employment relation - the structure of incentives large firms offer employees is limited by a number of factors. First, large bonus payments may threaten senior managers. Second, performance-related bonuses may encourage less-than-optimal employee behavior in large firms. Therefore, large firms tend to base incentives on tenure and position rather than on merit. Such limitations may specially affect executive positions and product development functions, putting large firms at a disadvantage when compared with smaller enterprises in which employees are often given a direct stake in the success of the firm through bonuses, share participation, and stock options.
4. communication distortion due to bounded rationality - Because a single manager has cognitive limits and cannot understand every aspect of a complex organisation, it is impossible to expand a firm without adding hierarchical layers. Information passed between layers inevitably becomes distorted. This reduces the ability of high-level executives to make decisions based on facts and negatively impacts their ability to strategize and respond directly to the market. Even under static conditions (no uncertainty) there is a loss of control.

The Alternative Banking working group of OWS (Occupy Wall Street) prefers TIBACO to TBTF. It stands for Too Interconnected, Big and Complex to Oversee, which I think is a more apt description of what exactly is wrong with these banks.

Things I am up to:

- I recently downloaded Anki, a flashcard program, to help me study for the CFA (Chartered Financial Analyst) exam. I've always wanted to try Anki, but I never got around to it. It displays flashcards on increasing time intervals based on the principle of spaced repetition. One example of this is the following image, where successive "boxes" show their cards less frequently, e.g. the flashcard program will draw from box 1 half of the time, box 2 one quarter of the time, etc.

- Learning R. There is a lot of vibrant community support (especially in finance) for R. Some of my favorite quant finance bloggers - Timely Portfolio, Systematic Investor, Milktrader, CSS Analytics - use R. Non-finance R bloggers can be found on the excellent R-bloggers. So far, I have already been able to link my R environment to Bloomberg terminal data as well as free data sources such as Yahoo Finance and FRED (Federal Reserve Economic Data) using community packages.

Books I would buy my friend if he had my exact interests and his birthday were coming up very soon (say, in 3 days):

Haidt, Jonathan - The Happiness Hypothesis
Koo, Richard - The Holy Grail of Macroeconomics
Postman, Neil - Amusing Ourselves to Death
Schelling, Thomas - Micromotives and Macrobehavior
Singer, Peter - Animal Liberation
Strausse, William & Howe, Neil - Generations
Wolfram, Stephen - A New Kind of Science