Monday, January 2, 2017

Testing Momentum’s Robustness

Happy new year!

I have noticed that my quantitative posts get the most readership and discussion. So this year, I’ll be posting a lot more research and will start the year off by exploring momentum’s robustness.

There are two good ways to test the robustness of a rules-based trading strategy:
  1. The test of time - how does the strategy behave in different market regimes?
  2. Parameter sensitivity – how stable is the performance if the strategy’s parameters are varied
Let’s look at each of these separately.

Test of Time

The goal is to see how well a strategy performs over a very long-term, under different market conditions. Gary Antonacci has some good articles on the importance of having a long-backtest period (see Bring Data and Bring More Data).

The table below is how the Global Equities Momentum (GEM) strategy has performed from 1971-2015. 

While these results are nice, looking at cumulative outperformance over a backtest period is not enough – we should also look at individual periods within the data.

I did a post a while back showing what happens when we add Gold to the GEM model (see Should we consider gold?). GEM’s annual returns (since 1970) jumped from 18% to 21% by including gold. At first glance, this sounds exciting. But a closer look showed all this additional gain came from the 1970s when the US went off the gold standard. No longer being suppressed, the price of gold rapidly rose in just a few years. We need to be careful not to be misled by these types of one-time events.

The graph below shows that equities (red and green lines) had a secular bear market during the 1970s and 2000s, and a bull market during the 80s and 90s. In both market types, GEM (blue line) did well.

Let’s dig further with a longer period of data. How does momentum do on a decade-by-decade basis?

Meb Faber looked at this in his paper “Relative Strength Strategies” (read here). The table below shows the outperformance each decade of a US sector momentum strategy (hold the top performing sector and rebalance monthly) compared to the entire US stock market.   

While some decades were better than others, momentum had positive alpha every decade since 1930. This is an indication that the momentum anomaly has persistence.

OK, all this looks nice however…

While momentum (and all trend-following) strategies tend to perform well in trending markets, they typically fail in very erratic, sideways markets. An extreme market-regime test is to see how momentum would fare using Japan’s Nikkei stock index, which has traded sideways for 30 years. This will be the topic of my next post. Let’s continue on.

Parameter Sensitivity

Any quantitative strategy has one or more input variables. GEM has two: the lookback period (length of time over which past performance of assets is measured) and rebalancing period (how often you check for a new trading signal). GEM’s recommended parameter settings are 12 months for the lookback and monthly for the rebalance.

By varying these input parameters, we want to see how the strategy’s performance changes. I want to be clear: this is NOT done to find the optimal parameter settings. That would be data mining. Instead, this test is done to determine the model’s sensitivity. A sign of a robust trading strategy is one whose performance is not affected by small changes in its settings.

Note: The analysis that is presented below was done using daily data and MATLAB software. Source code and data is available upon request. 

We first look at how GEM’s performance (between 1988-2016) changes as we vary the rebalancing period from 1 to 100 trading days while keeping the lookback period constant at 12-months.

We see from above that a rebalancing period between 15-25 trading days results in returns performance that is stable while providing high returns and low portfolio turnover. This confirms the recommended setting of 20 trading days (1 calendar month).

It’s interesting to see that a rebalancing period less than 10 trading days results in very high portfolio turnover and with lower returns (due to whipsaw losses). There is absolutely no reason to be doing weekly rebalancing with GEM.

Next, we look at how GEM’s performance changes as we vary the lookback period from 30 to 500 trading days, while keeping the rebalancing period constant at one calendar month.

We see above that any lookback period less than 200 trading days results in higher whipsaw losses and higher portfolio turnover. A lookback between 250-350 trading days results in stable performance with fairly low portfolio turnover. This confirms the recommended setting of 12 calendar months (250 trading days).  

The 12 month look back period was first discovered by Cowles and Jones in 1937. Various other research since then has shown momentum works best with monthly rebalancing and a 12-month lookback period. The results above confirm this, as well as demonstrate how the prior research has held up since it was first published.


Momentum has passed several checks for robustness. It has proven itself over a long backtest period and in different market regimes. In addition, the performance of a simple momentum strategy like GEM is not sensitive to small changes in the strategy’s parameters.

I often get asked about using much shorter rebalancing and lookback periods to be able to adapt faster to market changes. Up until now, I have just verbally been telling people that this would create higher # of trades and whipsaw losses. Now I can back up my recommendation with quantitative evidence.

I leave you with Dilbert’s take on model sensitivity.

Results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Additional information regarding the construction of these results is available upon request. Past performance is no assurance of future success. Please see our disclaimer page for more information.

Tuesday, December 27, 2016

The Blogosphere’s Greatest Hits of 2016

As 2016 comes to a close, I want to discuss some of the best writing I’ve read on the financial blogosphere this year. The posts below were written by several different authors. Even though these folks follow their own investment strategies, they all echo the same investment philosophy as mine.

Here are this year’s highlights in no particular order…

1. Simple vs. Complex by Josh Brown
"The world itself is complex, as are the investment markets. So the first notion that many investors begin with is that they need something equally complex to protect them or help them win. This is a logical fallacy, but a widely held one. I’ve come to believe that getting better as an investor is a reductive process rather than a contest to see who can add the most bells and whistles. I’ve been led down this path by evidence. The journey has forced me to let go of a lot more than I’ve been able to add." - Josh
In investing, complexity is not value added. It's the opposite. I always meet people that tell me the strategy I follow is too simple. But the reason it performs well is exactly because it’s simple. Very few moving parts means little data mining bias. Very few trades mean not being fooled by noise. Being systematic means little room for opinions or emotions.

2. The Power of Doing Nothing by Brett Steenbarger
In trading, doing nothing is often the most difficult doing.  A bias toward activity gives us an illusory sense of control, when in fact we often exercise the greatest control when we are not doing.” - Brett
This year had the most amount of frantic market chatter as I’ve ever seen. The January rout. Brexit. Trump. And all throughout it, I did nothing. Despite all the noise, the markets (and my portfolio) are in the green this year. Many others didn't fare so well

3. Learning to say “I Don’t Know” by Barry Ritholtz

One of the best feelings is when someone asks me where the market is headed and I reply “I don’t know.”

The beauty of trend following and momentum investing is that we simply align ourselves with market forces. We don’t question those forces. And we certainly don’t know what those forces will look like in the future. This frees up considerable mental energy to enjoy life.

4. What You Should Focus On by Michael Batnick

Instead of making predictions about the future, focus on what matters and what you can control.

5. Are 3-year track records meaningful? by Corey Hoffstein

Any active strategy will inevitably have a period where it underperforms its benchmark. This period can last years and thus it is not very meaningful to evaluate a strategy over a less than 5-year period. Yet investors (both retail & institutional) keep focusing on short-term results and is ultimately what leads them to abandon the strategy or fund manager.

6. Permanently Bearish Commentary by James Osborne

While it's popular to be bearish, the world will keep getting better in the long run

7. Case for momentum in Expensive Markets by Jake

It’s easy to look at current stock market valuations and become bearish. But we all know that an expensive market can become even more expensive. Trend following (and momentum) help us stay in a bull market right until its end.

8. Diversification Will Always Disappoint by Cory Hoffstein 

We know that stocks give us the highest risk premium. But holding them alone results in too much volatility. Adding bonds to the portfolio reduces volatility without sacrificing an equal amount in returns. It’s why diversification is called “the only free lunch” in investing. Or is it?

Consider the traditional 60/40 diversified portfolio. During stock bull markets, the bond component is a drag. During stock bear markets, the stock component is a drag. It’s much like driving a car with both gas & brakes applied: When you want to move forward, the brakes hold you back. When you want stop, the gas keeps you moving.

Trend following & momentum are a better diversifier. By investing fully in stocks only when they are in an uptrend or “strong,” you reap their full benefit without the bear market side effects.

9. Why Technical Analysis Gets a Bad Rap by Michael Batnick

Technical analysis (TA) is the study of market prices to gauge supply & demand. When prices are trending “up,” buyers are in control and you want to be long. There are two main branches of TA: pattern analysis (charting) and quantitative (eg. Momentum, moving averages, etc).

TA gets a bad rep when people use charts to make predictions and perform exotic analysis (eg. “doomed-house-and-3-peaks pattern will cause big crash”). It also gets a bad rep when people use complex and tuned parameters in quantitative systems (eg. “Buy when the 23-day exponential moving average crosses above the 64-day average”).

10. What You Should Remember About the Markets by Gary Antonacci

Investing is simple, but not easy. To be successful in the markets, you need the discipline to follow a proven method unwaveringly.

11. Ten Things I Believe About Investing by Ben Carlson

Ben generates quality content daily. I could easily list a more of his posts but I’ll keep it to the one above and this next one:

12. You Have to Invest by Ben Carlson
Yes, risk exists in the markets. It’s never going to be easy. But the alternative for stepping out into the unknown is the known of never building your wealth. Don’t invest. Don’t save. Allow fear to control your financial decisions. Stay far away from the markets. That’s a great way to ensure that your future self will hate you.” - Ben

Happy holidays and see you in the new year!

Friday, November 4, 2016

We Are Not Always So Rational, Part 4

A quick recap: In part 1 & 2, we discussed several cognitive & emotional biases that we suffer from, as well as where these biases originated from. In part 3, we looked at the impact of our biases: on ourselves, our portfolios and on the markets.

I had a reader (Nick de Peyster) leave a comment recently that “investing is about 25% knowledge and 75% dealing with emotional and cognitive biases.” I agree.

In this fourth and last post of this series, we discuss ways to minimize the damaging effects of our biases. Other than the post on compound interest, this is one of most important topics in investing. There are a lot of items discussed here and I will likely touch on them again in more detail in the future.

Minimizing the Impact of Our Biases:

1.  Be Self-Aware

Source: hubpages

Managing yourself begins with knowing yourself. We all have a different risk tolerance and different set of behavioral biases. Learn the types of common biases and determine which ones you suffer from. This series of blog posts can be used as a starting point.

Remember, if your biases are mainly cognitive – they can be fixed through education. If your biases are mainly emotional, then read on.

2.   Be Evidence-Based

Source: pinterest

You can be a passive, value, quality or momentum investor – that’s not the point. The important thing is that you prove to yourself with sufficient evidence that your approach is sound and robust. And do not simply rely on conclusions of others. When your strategy is undergoing that inevitable period of under-performance, you are more likely to stick with it if you understand the strategy thoroughly.

It is recommended that you: 
  • Research and formulate a simple strategy. The simpler the better
  • Gather quality data over a sufficiently long time-period, covering different market regimes
  • Perform back-testing to determine if the strategy has significant outperformance while being cognizant of data mining bias
  • Perform stress-testing to check for robustness (eg. are the results highly sensitive to changes in the model’s settings?)
  • Seek out contrary opinions to reduce confirmation bias. Perhaps there is something you missed in your analysis

3.  Be Systematic

Source: clipartkid

We are increasingly seeing the world become more systematic, from computers marking English essays to self-driving cars. As an Electrical Engineer who worked on developing automation products, I think this is a great thing. Machines, if programmed and maintained properly, typically perform tasks with higher accuracy, efficiency and consistency than humans.

So whatever your investment strategy is, it must be systematic. The less you have to think or do, the better. This not only ensures consistency, but it allows little room for your emotions to interfere. 

4.  Optimize For Your Biases

I used to believe that the Sharpe Ratio (ie. risk-adjusted returns) was what you wanted to maximize. I even named this blog after that term. But this approach is only true if we're robots. For humans, choosing a strategy or asset allocation that deviates from the "optimal" (highest SR) is a perfectly reasonable decision if it reduces your anxiety and is something you are likelier to stick with for the long haul.

So even though I believe a systematic trend following approach is the best for me personally, many have emotional biases that will not realize this no matter how much you educate them. For these types, a passive approach may fit their personality better. While not optimal, it is better than not investing at all.

Another approach is to use pyramiding. For many, investing in one strategy (even if it is robust and sound) can be nerve wracking: either too conservative or too risky. They may instead want to layer their portfolio. The majority of their portfolio can be in the optimal strategy, while the rest can either be in something conservative (eg. a 30% allocation to bonds) or aggressive (eg. a 5% allocation to individual stocks). 

5.  Live Healthy

Source: Vegansoceity

Studies have repeatedly shown that nutrition, exercise and meditation are the most effective ways to reduce stress & anxiety, improve sleep and boost self-esteem and energy levels throughout the day.

Nutrition – Most of us skip meals or reach for junk food during times of stress, but this is right when the body has a higher need for nutrients such as vitamin C and many B vitamins. To make matters worse, feeding our sugar craving may give us that quick burst of energy, but it is short-lived and usually followed by an even worse slump in energy (link).

There has been overwhelming evidence demonstrating the power of plant-based foods: greens, fruits, spices, beans, nuts and seeds. And it goes beyond just reducing stress. Dr. Michael Greger, author of the best-seller “How Not to Die,” shows the scientific evidence of how plant-based foods can prevent and reverse the 15 top causes of premature death, such as heart disease, diabetes and high blood pressure. The easiest and most delicious way to incorporate these foods in your day is with a smoothie. A good blender is the best investment you can make.

Exercise – All forms of exercise help the brain release endorphins and serotonin, triggering a positive feeling in the body. One study found that those who exercised at a moderate intensity for 40 minutes, 3-5 days per week experienced the greatest mood-boosting benefits. So get out and go walking, cycling, yoga or doing strength training.

Meditation – Studies have shown meditation to reduce stress, improve your ability to concentrate, lower blood pressure and boost your immune system.

The focus of meditation is to bring you into the present moment, to quiet an overactive brain and even to reflect on things you are grateful for. Sit with a straight back, practice breathing deeply, and try some background sounds. Be patient & committed and you will find over time that your focus will improve. I highly recommend a guided meditation app called Calm (Apple, Google).

6.  Go On An Information Diet

Thanks to our smartphones and social media, we are now bombarded with information more than ever. And not the information found in books or long articles but:
  • Endless social streams with just a few snippets of words at a time
  • Financial apps flashing ticker quotes in real-time from the palm of your hand
  • Financial media trying to convince you that the next crash is around the corner

How can any of that be good for us?

Author Rolf Dobelli has an excellent article titled “Avoid News: Towards a Healthy News Diet.” In it, he talks about how: 
  • News is to the mind what sugar is to the body. It gives us short-term excitement
  • News is toxic – panicky stories spur the release of cortisol which deregulates the immune system 
  • News misleads us, is often irrelevant and even manipulative
  • News makes us passive, distracted, inhibits thinking and kills creativity 

I highly recommend reading Dobelli’s article. Then go on an information diet: turn off CNBC, reduce the apps on your phone and check your portfolio infrequently. You’ll notice you will have more time, less anxiety and deeper thinking.

7.  Have the Right Mindset

“Patience you must have my young padawan” - Yoda

Despite our best laid-out plans, its easy to get caught up in the latest headline and be tempted to override our system. Being firmly rooted in the following beliefs will help:

  • On average, making impulsive portfolio decisions have significantly hurt investor returns (see part 3 of this series). Do not be fooled into thinking it will be any different this time. Any trade decision that is not backed by a logical, evidence-based approach is not worth taking
  • Your ability to stick with a plan is more important than the plan itself
  • Real wealth accumulation happens over the long-haul, through the power of compound interest
  • Stocks have historically been the asset class paying the highest risk premium. Your goal as an investor is to be invested in stocks as often as possible and only switch to bonds through a systematic risk-management process.

8.  Consider A Human Advisor

Source: Carl Richards, The Behaviour Gap blog

A financial advisor’s main job is to prevent you from doing irrational things with your portfolio.

I mentioned in item 3 above that many tasks are now being automated and that this is generally a good thing. One area that recently exploded in growth is the robo-advisor space. And its first real test came this summer during the Brexit craze. You may have heard that industry giant Betterment locked down accounts to prevent clients from irrationally liquidating their portfolios. While this was well-intended, it may not have been as comforting as talking with a human advisor.

What sets a human advisor apart from a robo is their ability to communicate, to listen, to empathize and to care.  This personal connection is more comforting during times of panic.

Human advisors can also help you with item 1 above: to be self-aware. They give you regular risk tolerance questionnaires and personal assessments to help you understand yourself better. They can also help with educating you on any cognitive biases you may have. 

Further sources

There are too many excellent books, articles, podcasts and videos going into detail on the various topics we covered in this 4-part series. Some of the ones to consider are listed below. Enjoy!

  • Thinking Fast and Slow by Daniel Kahneman. Dr Kahneman is a psychologist that won the nobel prize in economics for his work on decision-making. He is considered to be the father of Behavioral Economics, which challenges the assumption of human rationality prevailing in modern economic theory.
  •  Predictably Irrational: The hidden forces that shape our decisions, Dan Ariely. When it comes to making decisions in our lives, we think we're making smart, rational choices. But are we?
  •  Sapiens: A Brief History of Mankind, by Yuval Noah Harari. If you want to know more about how biology and history have defined us, read this excellent book
  • 10% Happier: How I tamed the voice in my head by Dan Harris. The author discusses how he stumbled upon an effective way to rein in the voice in his head, something he always assumed to be either impossible or useless: meditation.  a tool that research suggests can do everything from lower your blood pressure to essentially rewire your brain
  • The Behaviour Gap: Simple ways to stop doing dumb things with money by Carl Richards. The behaviour gap is the distance between what we should do and what we actually do. The author gives great advice on how to prevent emotions from getting in the way of smart financial decisions.

  • You are not so smart podcast by David McRaney. David has done over 80 podcasts, with each episode focusing on a unique behavioral bias. Oh and every episode ends with a cookie recipe, so there’s that.
  • Masters in Business podcast – interview with Daniel Kahneman. Highly illuminating discussion with the father of Behavioral Economics

  • Overcoming Behavioral Biases Through Mindfulness Training by Dr. Ulrich Kirk (CFA Institute, 4th video in the playlist)
  •  Mind over Money, PBS Nova. Explores why we so often make irrational financial decisions and how our emotions interfere with our decision-making. Entertaining!
  • Boom Bust Boom, a documentary that “guides us through the history and the nature of the economic boom-bust cycle and why people repeatedly ignore it to their sorrow” - IMDb


The End. Thanks for reading!

Monday, October 24, 2016

We Are Not Always So Rational, Part 3

Montparnasse derailment, 1895. Source: Wikipedia

In the previous 2 posts, we discussed the common behavioral biases that we suffer and where they originate from. In this third post, we discuss the impact of our biases: on ourselves, our portfolios and on the markets.

Impact on ourselves

The financial markets affect all investors’ mental health, at least to some degree.

Even the most conservative, long-term oriented investors felt some shock during the 1987 ‘Black Monday’ crash, 2008 financial crises and 2010 flash crash. On the other end of the spectrum, there are the aggressive types that treat the markets like a casino. It is this group that is particularly damaging their mental well-being.

Aggressive traders are ones that routinely do one or more of the following:
  • Watch every tick of the market and binge on financial media
  • Trade based on emotion without a process, or use a highly complex process
  • Take concentrated and/or leveraged positions in volatile securities (eg. micro-cap stocks)
  • Over-trade / day-trade

Engaging in these activities chronically can lead to addiction, stress, anxiety and even depression. It cannot be overstated how bad stress is for us. How can we prove there is a definitive link between money and mental health issues?

Source: Scott Camazine—Getty Images

There has been extensive scientific research done on how the brain is affected by money. There’s even an entire discipline devoted to it: Neuroeconomics. Studies from the past two decades have revealed that there is a whole lot happening in our brains when money comes up.

In 1997, a study performed brain scans on 12 people that played a game in which they could win or lose money. What they found was that players who were about to make money had increased neural activity in their nucleus accumbens – the region of the brain tied to reward, pleasure, motivation and addiction. These scan images were compared to those of addicts who were high on cocaine. Remarkably, the scans were nearly identical.

In one 2003 study, test subjects were paired with complete strangers. Each pair was given a sum of money and asked to split it. One person would act as the “proposer” while the other as the “responder.” If the pair cannot agree on a split, then neither walks away with cash. The study found that the responders rejected over half the unfair offers (which is irrational since something is better than nothing). But more interestingly, the study found these unfair offers activated a part of the brain in the responders associated with anxiety, pain and hunger.

In 2005, a study was done at Stanford University using Functional Magnetic Resonance Imaging (fMRI). Brain activity of participants was monitored as they chose between stocks and bonds given limited performance info of each. The researchers found they could predict whether a participant would choose to buy a riskier security, like a stock, or a less risky one, like a bond, just by scanning their brains. The subjects who had naturally elevated stimulation of their nucleus accumbens would most likely buy the stock.


Impact on our portfolios

"When it comes to investing, you are your own worst enemy." – Barry Ritholtz

Not only do biases cause the average investor to suffer health consequences, they also cause serious financial consequences. Our individual biases cause us to make all sorts of portfolio mistakes:
  • Poor allocations: holding concentrated positions in a few stocks or holding too much cash 
  • Poor timing: Holding losers too long, selling winners too early
  • Frequent trading: getting too caught up in day-day noise, falsely believing you can outsmart the market in the short term, trying to irrationally climb out of a loss

Over the 20 year period ending Dec 2008, the folks at Dalbar show us exactly how much damage the average equity investor did to their portfolios: 

Impact on markets

We see that our irrationality in the markets hurts us mentally and financially. Interesting things happen when you look at the behaviour of all individuals as a group.

Each individual investor may make different mistakes (due to their unique biases, genetics, experiences, knowledge, etc.). They may be more loss-averse or suffer greater overconfidence bias than their neighbour. Occasionally, their biases will even cause them to get lucky. However, it turns out that as a group we are extremely consistent at being wrong.

The chart below shows the average individual’s asset allocation between 1988-2010. The average person had a record high allocation to stocks in Jan 2000 (the peak of the tech bubble) and record low allocation to stocks in March 2009 (the exact month the markets bottomed after the 2008 financial crises).  

We can take this one step further.

The chart below shows the average household’s % allocation to equities (blue) and the subsequent 10 year return for the S&P500 (black). This chart is often dubbed the “single best stock market predictor” because of how accurately current investor allocation to stocks can predict future 10-year returns of stocks.

Source: MarketWatch and Ned Davis Research

Note that the scale for the S&P 500 is inverted. Basically, when everyone is in love with stocks, future stock returns are low (and vice versa).

Thus, the collective biases of all market participants cause markets to deviate from perfectly efficient. The momentum anomaly which I discuss often on this blog is partly explained by two behavorial biases: regret aversion ("herding effect") and availability bias ("recency effect"). Other factors are explored in the first post on this blog: Philosophy of Momentum.

In theory, investor sentiment can directly be used to outperform the market. Contrarian investors buy when the herd is bearish and sell when the herd is bullish. But how is sentiment measured? The main methods include: surveys (eg. AAII), money flows, portfolio allocations and options activity (eg. put/call ratios). There are a few research outfits such as and Ned Davis that make a living off selling sentiment research.

However, sentiment trading suffers the same problem as value investing: something that is hated can become even more hated.  A great recent example of this is commodity stocks, which have repeatedly trended lower since 2011 despite breaking all sorts of sentiment records as early as 2013. John Maynard Keynes famously said: “The market can remain irrational longer than you can remain solvent.

Another point I want to make clear is that sentiment is but one factor that drives markets and for the short-term. There are other factors (such as the business cycle, institutional buying/selling, central bank actions) that also influence markets in the short-term. Over the long-term (eg. 10 years), markets have been observed to respect valuations and mean-revert (eg. the current Shiller P/E ratio is a rough indicator of future 10-year stock returns).

Trend following (and momentum) is a much better approach* at outperforming the market. It aligns itself with the market’s trend, which is the collective result of several forces (sentiment being one of them). *It is important to note that this approach must be simple, systematic, evidence-based, robust and of course, forecast & bias free. GEM is one such approach.

To summarize:

Actively investing solely on your cognitive & emotional biases will result in drastically underperforming the broad market and at a cost to your health. The collective irrationality of individuals (among other factors) leads to markets being less than efficient. By being cognizant of this, we can take a trend following approach to outperform the broad market while simultaneously reducing our stress & anxiety.

I will need to add one more post to this series. In part 4, we will look at techniques that will help reduce the impact our emotions have on our investing to ensure we stick to our plan. Stay tuned.

Sunday, October 2, 2016

We Are Not Always So Rational, Part 2

Recall from our previous post that we investors suffer from behavioral biases that lead us to make poor decisions. There are two main types:
  • Cognitive biases (resulting from lack of knowledge, faulty logic and memory errors) 
  • Emotional biases (making decisions based on impulse and feelings)
We discussed some cognitive biases already, so let’s take a look at the other type.

Emotional Biases

  • Loss Aversion (also known as Prospect Theory) – this is when we strive to avoid losses rather than seek gains.
An investor is said to be risk-averse if they feel more pain from a $1 loss than pleasure from a $1 gain (and risk-seeking if they feel more pleasure from the gain). If offered a stock and told there’s an equal chance of it either falling to $90 or rising to $100, the risk-averse investor would not pay more than $95 (ie. the expected value of the stock) while the risk-seeking investor would. 
An investor that is loss averse may initially be risk-averse, but when faced with losses, can become risk-seeking in an irrational attempt to climb out of the loss. The implications of loss-aversion are massive. They include:  
- Holding excessively conservative portfolios (eg. heavy in bonds or cash)
- Not selling losers in order to avoid a realized loss
- Trying to climb out of a loss by doubling down on losers or trading excessively  
  • Overconfidence Bias – Overestimating your own intuitive ability or reasoning. 
Example: Ask an audience how many think they are below-average investors and few hands will go up. In fact, studies show that 95% of us view ourselves as above-average drivers! Truly astonishing.
  • Endowment bias - We give greater value to things we already own or are familiar with. In investing, this leads to holding securities too long or in concentrated sizes. This is also related to the tendency for investors to concentrate their portfolio in their home country, as it's familiar. 
Example: You're deciding between a Toyota Camry and a Honda Accord and have no idea which is better. 6 months after purchasing one, that car becomes familiar and you say "I don't know what I was thinking even considering the other car!
  • Regret aversion - Making choices simply to avoid potential regret. People often do what others are doing in fear of being left behind, leading to the "herd behavior effect"
Example: During the NASDAQ bubble of late 90's, many individuals were buying into the market for fear of missing out. 
  • Status Quo Bias – Comfort with an existing situation leads to an unwillingness to make changes or consider other, better options. 
Example: Selecting the default asset allocation on an employer defined-contribution plan and not changing it with the passage of time. This leads to a portfolio with inappropriate risk
  • Self-Control Bias - Lacking self-discipline and favoring immediate gratification at the expense of not meeting long-term goals. Too many people do not save enough to fund retirement needs

We’ve now looked at 12 cognitive and emotional biases. This just scratches the surface as it turns out there are at least dozens more that we suffer from. The more you study our decisional flaws, you realize that we are nowhere near the rational, number-crunching computers that efficient market theory assumes we are.

Where do our biases come from?

Psychology identifies what our biases are while biology explains where they originate from. 

We humans evolved very slowly over 6 million years from more primitive origins. Each generation produced offspring with some genetic variation. Those with traits providing a better survival edge (no matter how slight) had higher probability of passing on those traits to the next generation. We were shaped in this progressive and cumulative process over millions of years (though the above picture makes you question the “progressive” part!)

The majority of our history was lived in a perilous world. Our traits are well adapted to suit this environment, helping us fend off predators, hunt prey, build shelter & tools, etc. It is only in the last 6,000 years (or 0.1% of our human history) that civilization as we know it has been around, and only 200 years (0.003% of our history) that we’ve been living in an industrialized world. In a very short period, we enjoyed a dramatic increase in our standard of living. Suddenly, we no longer needed to spend the majority of our time and energy worrying about our survival. 

Our mind and bodies, however, have not been able to keep up since evolution is a slow process. It can be argued that this has led to some major health issues we face today from: a sedentary lifestyle, radically different diet and constant barrage of information and interruptions to name a few. We especially are poorly equipped to manage our investment portfolio. Handheld phones with stock prices refreshing every second are sabotaging our ability to maintain a long-term mindset. 

Perhaps we may never fully adapt to this new world: our standard of living is so high that our biological imperfections don’t significantly hurt our chances of survival. You will still be able to eat even if your portfolio isn’t holding the right asset allocation or if you don’t understand what standard deviation is!

Evolutionary Psychology is a separate discipline that attempts to explain mental traits—such as memory, perception, or language—as products of natural selection. On the most basic level, we feel positive emotions (euphoria, excitement, confidence) when we receive things that increase our survival and replication chances. We feel negative emotions (fear, anger, panic, frustration) when it’s the opposite. 

Some of the behavioral biases we discussed can at least be partly explained by Evolutionary Psychology as follows: 
  • Loss aversion: "For an organism operating close to the edge, the loss of a day's food could amount to death, while the gain of an extra day's food could lead to increased comfort but (unless it could be costlessly stored) would not lead to a corresponding increase in life expectancy." - Wikipedia
  • Endowment bias and Status-Quo bias: you stick to what is familiar because it is safer and reduces risk. It could cost your life if you wandered into a new, unfamiliar part of the woods alone. 

So far in the series, we discussed several behavioral biases that cause us to make poor investment decisions and where these biases originate from. In the third (and last) part, we’ll look further into the impact of our biases on our investing as well as how we can minimize this impact. But first…

Quiz Time!

See if you can identify the behavioral bias in each Dilbert comic strip below. Answers can be found on my twitter feed (@sharpeReturns).

Sunday, August 28, 2016

We Are Not Always So Rational, Part 1

A personal note

I’m proud to say that I have recently been awarded the CFA charter.

Although I’m fortunate to have passed each of the 3 exam levels on the first try, it took me a long time to complete the program. I wrote level 1 in 2009, followed by level 2 in 2011. At that time, I was working as an engineer and didn’t see the value in finishing.

Also around that time, I first discovered the work of Meb Faber and Gary Antonacci. I continued to research markets on the side since then and Gary has really been instrumental in accelerating my learning curve. A little over a year ago, Gary nudged me to start this blog. And earlier this year when I met Gary in person for the first time, he encouraged me to finish the CFA program. It’s been a very interesting journey so far and I hope to share more announcements with you in the future.

Incidentally, both Meb and Gary are coming to my hometown Vancouver on Sept 6th to give presentations. Small world. If you live in the area, I highly recommend you attend. Register here.

The most interesting topic in finance

Of the 3 CFA levels, the third one taught material I enjoyed the most. It skips the humdrum accounting and statistics of other levels and instead focuses heavily on portfolio management. There were a couple chapters dedicated to Behavioral Finance (BF) – what I consider to be the most interesting topic in investing.

BF is the study of human nature and its impact on our investment decisions. It challenges the main assumption of traditional finance: that individuals are rational and that the markets they shape are efficient. It is where the world of investing intersects the disciplines of psychology, history and biology.

As we will see, investors suffer from numerous behavioral biases that lead them to wreck havoc on their portfolio. It is truly amazing how many distinct biases there are that they need to be categorized into two main categories:
  1. Cognitive – faulty decisions that arise from the lack of knowledge, information processing errors or memory errors
  2. Emotional – faulty decisions that stem from feelings, impulses or intuition

The remainder of this post will discuss some common cognitive biases. There is so much to discuss on the topic of BF, that we will follow up with 2 more posts:
  • Discussion of common emotional biases, plus a quiz!
  • Impact of our biases, how to minimize this impact as well as additional resources

Cognitive Biases

  • Anchoring – New info is not viewed objectively, but rather in relation to an initial view or thought.
Example: Studies show that when a group is asked to estimate the price of a car, the average estimate tends to be reasonable. However, if asked first what the last digit in their phone number is, people who had a higher digit tend to over-estimate the car's price.
  • Framing - When the same information is presented in different ways, it leads to different outcomes.
Example: Sally is loss averse. When her advisor presents a new fund in terms of historical return and volatility, Sally invests. However, when the advisor presents the same fund in terms of probability of a loss, Sally declines to invest.
  • Availability Bias - Giving undue emphasis on info that is readily available and fresh in our minds. This leads to giving higher importance to recent events rather than old events (the "recency effect"). 
Example: Bob chose to invest with XYZ fund because of a billboard ad he sees on his daily commute.
  • Confirmation Bias – looking for new info to support an existing view.
Example: Soon after buying stock XYZ, you selectively search for bullish articles while ignoring any bearish articles.
  • Hindsight Bias – Overestimating what could have been known. People often remember their correct views while forgetting their errors
Example: “I saw the 2008 crises coming all along” 
  • Conjunction Fallacy – before explaining this one, I want you to participate in this question:
Linda holds very strong views about the environment. Which is more likely?

a) Linda is a bank teller, or
b) Linda is a bank teller that donates to an environmental organization

If you said (b), that is incorrect. But don’t feel bad, 80% of people choose that answer.

The probability of Linda being a bank teller is already small. But for her to make a donation in addition to being a bank teller reduces the probability further. This example shows how we can be tricked into believing that two events have a higher chance of occurring together than either one occurring on their own. That’s the conjunction fallacy.

In part 2, we’ll look at some common emotional biases. Stay tuned

Wednesday, July 27, 2016

Momentum on Individual Stocks vs Asset Classes

I had the pleasure of finally meeting Gary Antonacci earlier this year.

Gary is the creator of the momentum strategy that I follow and have been discussing on this blog.  I first came across his work in 2011 on the blog Abnormal Returns (which should be a daily read for investors). Gary and I have been e-mailing each other ever since. After over 4 years, it was nice to finally see him in person.

Gary gave an excellent 2+ hour presentation on momentum in Seattle. There were over 100 people in attendance and it was the local AAII chapter’s largest turnout. The presentation covered everything: what momentum is, why it works, its history and correct use.

Two main ideas on the correct use of momentum were discussed:
  1. Momentum applied on asset classes works much better than on individual stocks
  2. The role of absolute and relative momentum and the synergistic effect of combining the two
In this post, I will focus on point #1. When momentum is applied on individual stocks, there are 3 main drawbacks:
  1. Low scalability
  2. High volatility
  3. High transaction costs
Let’s discuss each of these in detail.


When applying momentum on individual stocks, trade execution can suffer for large trade sizes or thinly traded stocks. The very act of buying and selling changes the market price, hence reducing the alpha that can be achieved.

Contrast this with momentum applied at the asset-class level. You can enter/exit large positions in an ETF such as SPY (SPDR S&P 500 ETF) and the vast liquidity of this ETF would absorb the buying/selling pressure.

The chart below shows that momentum on individual stocks is theoretically best when both the number of stocks and holding period is small. However, a small number of stocks means low scalability and high volatility while a small holding period means high transaction costs.


The second drawback to trading individual stocks is that they are also more volatile. This is due to company-specific risk such as earnings reports or regulatory changes. It can also be due to stocks being thinly traded or belonging to a volatile industry such as mining.  

The table below shows a momentum strategy using individual stocks compared to the S&P 500. While the returns are higher for the momentum strategy, the volatility is also a lot higher. The Sharpe Ratio does not improve much (after trading costs, it may actually be lower for the momentum strategy).


In an individual-stock momentum strategy, you typically will hold a much larger number of stocks than you would ETFs in an asset-class momentum strategy. This results in a higher volume of trades and hence, transaction costs.

The table below shows that after transaction costs, momentum applied on individual stocks (whether large cap or small cap) actually performs worse than a buy-and-hold strategy.

We can alleviate the drawbacks of scalability, volatility and transaction costs by instead applying momentum at the asset-class level. But which asset classes should we use? 

The book “Stocks for the Long Run” by Jeremy Siegel shows that equities (especially US equities) have had the highest risk premium among all asset classes, so they should be the focus of any momentum model. Bonds should also be included since they tend to outperform equities during recessions. 

The GEM strategy I follow uses 3 asset classes: US stocks, non-US stocks and bonds. You can refer to this page to see how the strategy has fared over the past 40+ years compared to each of the 3 assets on their own. 

Despite all the evidence supporting asset-class momentum over individual-stock momentum, it is astonishing to see so many commercial momentum funds doing the opposite: AQR Mutual Funds (AMOMX, ASMOX, etc), PowerShares ETFs (PDP, PIZ, PIE, etc), iShares ETF (MTUM), Alpha Architect ETFs (QMOM, IMOM). 

Results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Additional information regarding the construction of these results is available upon request. Past performance is no assurance of future success. Please see our disclaimer page for more information.