ROBUSTICITY! What it is and why it's important

In the systematic trading and investing world, you see it all the time. Someone will design a system or rule set that shows tremendous historical returns - returns that seem too good to be true. They will start trading the system in real time with their own money. Or worse, they will go out and market that strategy, luring in naive investors who lack the training or experience to recognize an improperly built system when they see it.

The actual results come in much weaker than implied by the test data. After a few days, weeks or months of lackluster returns, the system is tossed into the waste pile.

Trading systems can fail for a number of reasons. Among the most common are inaccurate estimates of slippage and commissions, issues with trade execution, or that the system was simply based on a weak market anomaly that is easily arbitraged away. In many cases, however, the deeper reason is that the designer failed to keep robusticity in mind.

What, exactly, is robusticity? Robusticity is simply the ability to withstand changes in environment, and in this context, “environment” refers to market conditions. A robust system is one that can survive widely varying market conditions across a long span of time. It flexes with market conditions, and it is unlikely to fall apart due to a market regime change. The longer a system has been working, and the more asset classes and countries it has been working on, the more likely it is to continue working. This is called the Lindy Effect - what has been around a long time is likely to be around a long time.

The opposite of a robust system is one that is “curve-fit” or “over-parameterized,” Such a system is designed (knowingly or not) to perform optimally in the narrow market conditions upon which it was tested. Extremely high returns over a short test period are a red flag, as a robust system is unlikely to be the very best performing system on any narrow time frame.

Markets are ever evolving, so designing systems with robusticity in mind is of utmost importance if one hopes to have success with live systematic trading and investing. So how do we design and implement a robust trading strategy? Some points for consideration:

Does the backtest work on multiple assets, or just a single security?

A system based on a backtest using just Apple stock or even just the S&P 500 index would be suspect. We would want to test the rules on a wide range of stocks (for instance, all stocks in the S&P 500) or a wide range of equity indices (the German Dax, the Hong Kong HSI, the Japanese Topix, the Australian All Ordinaries, etc.). A rule set that was designed to generate trading profits on a narrow universe is likely “over-fit,” meaning that if market conditions change in that instrument, the system could break. Now if we go out and confirm that it works on a wider range of assets, we might be onto something.

Does the backtest work when we vary the underlying parameter values?

If we design a system that creates buy and sell logic based on the 200 day moving average, we would want to stress test the system using parameter variation of that moving average. We would want to try a whole range, perhaps 50 days to 400 days, sampling results at 10 day increments. If the system performs well using a 200 day lookback, but the results fall apart when testing with a 150 day or 250 day lookback, the system is likely not robust. Chances are that market conditions will be different in the future than they were in the past, so the success with the 200 day was likely due to luck rather than a true edge. If the 200 day moving average signal is truly an edge, then so too should be other time frames within the same order of magnitude.

Has the system been tested on different market regimes?

If we test a system that shows solid results on US stocks from 2010 to 2018, that is a good start, but we would never put money to work based on this alone. From 2010 to 2018, interest rates have been low, the economy has been in expansion, and stock valuations have been rising as smoothly as they ever have. For greater confidence, we would want to see how the system performs during bull markets, bear markets, rising rates, falling rates, inflation, deflation, and stagflation, not to mention the time before and since the introduction of computerized trading. While we can never test all possible scenarios (indeed, new and unfathomable scenarios are bound to occur in the future), generally, the more data and the more variability in market regimes, the more confidence we can glean from our testing.

Putting the concept of robusticity into practice in testing:

How does a systematic trader guard against over-parameterization and do the best he can to ensure robusticity? Stress test! Using something called Monte Carlo simulation, a system designer is able to vary the parameters in their simulations and see if and how things break.

For example, in our Alpha Momentum Strategy, we vary parameters such as the moving average filters we apply at the index level and individual stock level, using both long-term and medium-term moving averages. Thus, we have multiple signals that influence if and how much of the portfolio will be invested, and which individual stocks will be held.

Here is a chart of the output from a Monte Carlo test on our long-term individual stock-level moving average. It shows the result of thirty backtests where all parameters of the system are held constant except for the moving average lookback, which we test in the range of 100 days to 400 days in 10 day increments. So we are testing the system using a 100 day moving average, a 110 day moving average, a 120 day moving average, etc. all the way up to a 400 day moving average and plotting the results along a curve. For each of these simulations, all other parameters of the system are held constant.

We can see the annualized return that corresponds to each moving average lookback on the Monte Carlo curve here. Be aware that when we are doing this type of analysis, (1) we do not want to look at compound annual returns and (2) we want to look at measures of system success other than just returns, but we are using this chart for illustrative purposes.

What we are hoping to see in this analysis is a large “flat spot” on the Monte Carlo curve, indicating that the exact choice of this parameter (lookback days) isn’t all that important. If we had seen instead a jumpy pattern or just a single peak, we would suspect that any good results were due to luck and not a true market phenomenon. What we see above though is parameter stability, indicating that this element of the system is likely robust to a change in market conditions. If conditions change such that markets “move faster”, we should be ok, as we should be if they start “moving slower”. Again, this is just one test among many that we would require before committing live capital. We ask, “what if,” and don’t assume the future will be like the past.

Putting robusticity into practice in live trading:

While the concept of robusticity is vitally important in the testing phase, we can extend this concept into implementation phase as well to reduce volatility. By breaking up the portfolio into tranches and running the live system using different parameters across the parameter value curve, we can increase our consistency in live trading and thus make the system more comfortable to trade and easier to stick with in real time.

We want to do this because there is a tremendous amount of noise and randomness in markets. Before we started trading using systems, we always knew there was a fair amount of randomness to asset prices, but we never truly grasped how random markets were until we were able to test rules and vary parameters systematically.

So while running a system with the 250 day moving average may provide results that are indistinguishable from a system that uses a 200 day moving average or a 300 day moving average over a 10 or 20 year period, in the short run, the results will likely be radically different.

The same goes when you substitute say the Dow for the S&P in a multi-asset system that uses US stocks as one component. Over the long-term, the difference will be minimal, but results in any given year may look surprisingly different. A bad run in a good system may fool a trader, perhaps causing him to change the parameters, only to have the original parameters then start outperforming the new ones! There are many such cases.

Imagine the following scenario:

You design a system that generates signals based on a stock’s relation to its moving average. You test the parameterization of the moving average for robusticity and find that over a 20 year period, the moving average “works” for lookbacks of 100 days to 200 days. In the spirit of simplicity, you decide to split the difference and use a 150 day lookback for your moving average in live trading.

3 months go by and you check the performance of your system. Unfortunately, performance is not that great. The system is flat. You take a look at how the system would have done had you used the 200 day moving average and you find that it would have been up 10%.

Disappointed, you decide that going forward, you are going to use the 200 day moving average instead of the 150 day moving average.

You check back in three months and performance is still flat. You play with your parameters and find that the 150 day moving average system was up 10% since you switched to the 200 day moving average. Had you stuck with your moving average at 150 days or had you started trading using the 200 day moving average from the start you would be up 5%. Instead you are flat. The system was robust, but your execution was not, and you did not have the emotional fortitude to stick with your system throughout the execution (perhaps a topic for a future blog post!).

To be clear, this was a behavioral error. You designed a robust system, but you didn't consider how a short-term period of underperformance based on randomness associated with your parameterization might affect your mindset and emotions, you overrode your strategy, and created slippage relative to how the model should have performed.

Using the concept of robusticity, you could have avoided this situation. How?

Back to our starting point, remember, you tested lookback values from 100 to 200 days and you found that over a 20 year period, the results were pretty much indistinguishable from each other over the long term no matter the lookback for your moving average. Now you realize, however, that market randomness can cause a system that uses the 150 day moving average to greatly underperform a system that uses the 200 day moving average over the short-term (or vice-versa).

A solution? Chop up your portfolio into tranches and use different lookbacks for each tranche. Perhaps you could split your portfolio into three tranches, trade one tranche using the 100 day moving average, the second tranche using the 150 day moving average, and the third tranche using the 200 day moving average. You have effectively diversified some of the randomness associated with the particular lookback that you choose out of the system and you are now more effectively leveraging the signal provided by the indicator. Institutional quant funds are known for running lots of essentially identical strategies using various lookbacks side-by-side for exactly this reason.

The downside to this solution is now you have added extra complexity to your process. Here it is important for the systematic trader to balance both the positive and negative effects of this added complexity, and these decisions will be personal – they should be based on an individual’s tolerance for short term volatility of performance relative to signal and emotional makeup.

A Real Application:

Our Alpha Momentum Strategy, which we track on a bi-monthly basis, is essentially the synthesis of two systems - one using medium-term lookbacks, and one using long-term lookbacks.

We find generally, that for our type of trading, long-term lookbacks tend to do better than short and medium-term lookbacks over a long investment horizon. That said, we recognize the risk of short-term underperformance from the use of a single system. Therefore, we integrate the medium-term lookbacks into our system to help smooth returns and make the system easier to stick with as a whole. To be sure, our performance over the long run will likely be inferior to a system using solely the long-term lookbacks, but we sacrifice some performance for peace of mind, reduced volatility, and thus a better chance of being able to stick with our system. There is also the chance that when we look back at the next 60 years we’ll find that medium-term lookbacks have outperformed long-term lookbacks over this period.

This approach is precisely the opposite of curve-fitting. We consciously choose parameters that make our headline simulation numbers look worse than they could, which is a small price to pay for increased robusticity.

We’re already seeing the benefit of this choice in real time. Since we started tracking our performance live on our website back in March of this year, our medium-term sub-strategy has substantially outperformed our long-term sub-strategy despite our long-term sub-strategy showing clearly better returns in our test period going back all the way to the 1950’s. The table below shows the breakdown of live performance of our two underlying sub-strategies.

Robusticity and diversification at work!

Thanks for following along!

A special announcement from The Intelligent Allocator:

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A special announcement from The Intelligent Allocator:

For those of you who have been following along with us at The Intelligent Allocator, you may have noticed that while we have continued to update the Alpha Momentum model twice a month, we have not published a long form article in some time.

The reason is that we have been doing R&D to build a comprehensive asset management solution. While the Alpha Momentum model is a very strong strategy, astute investors know that US equities should only comprise a portion of a well-rounded portfolio.

A well-rounded portfolio should include exposure to foreign equities, commodities, and various fixed-income instruments, in addition to US equities. To that end, we have been working with our friends at Fortuna Investors to build comprehensive portfolio solutions.

Fortuna Investors is an investment firm based out of Miami Beach, FL specializing in an asset management strategy called “Global Tactical Asset Allocation,” or GTAA for short. GTAA is a well-established investment style that systematically allocates among diversified asset classes, with the goal of generating strong, consistent returns with low risk regardless of the economic environment. Like the Alpha Momentum model, it is fully quantitative and highly attuned to the downside, which is actually far easier when you are working with the whole world of uncorrelated asset classes, rather than just US equities and cash.

Our relationship with Fortuna was born out of a mutual passion for systematic, data-driven investing, with the goal of significantly outperforming more mainstream investment methods. As we collaborated on system research and development, we found that we had independently developed complementary investment methods, and that in combination, we could create something truly special.

Fortuna’s approach to GTAA harnesses global trends across a diverse set of asset classes. This is a far superior way of achieving diversification, risk mitigation, and strong performance than the conventional portfolios with static allocations used by most advisors. As a fully-quantitative strategy, GTAA can be stress-tested and examined over the long sweep of market history, giving investors confidence in its robusticity, without any need for economic or market forecasting.

Here on The Intelligent Allocator side, our concentrated, risk-governed equity momentum portfolios harness trend and momentum in US stocks. This is a far superior way of achieving diversification, risk mitigation, and strong performance than passive buy & hold or mainstream active fundamental strategies. Concentrated systematic equity momentum strategies have the potential to generate substantial absolute and risk adjusted returns, as showcased via our Alpha Momentum Strategy.

While GTAA and equity momentum strategies can each stand on their own, when combined, they create the potential for truly stunning returns. This is because GTAA and equity momentum strategies generally have a low correlation to each other.

One of the core tenets of modern finance is diversification. By combining asset classes that move in different ways at different times (low correlation to each other), an investor is generally able to achieve higher returns with lower risk than by investing in any single asset class. Even simple, static diversification produces higher risk-adjusted returns than any single asset class.

While most investors understand the benefits of stock or asset class diversification, the majority of investors fail to leverage system diversification. System diversification, much like asset class diversification, can enhance returns while reducing risk simply by using a portfolio of uncorrelated strategies (in this case, GTAA and equity momentum).

Over the last several months, The Intelligent Allocator and Fortuna have taken the best of our respective frameworks and brought them together to create a comprehensive, turnkey asset management program that is suitable for an entire portfolio allocation. We call this solution the Global Enhanced Alpha strategy, as it is a total solution designed to capture alpha (outsized returns relative to risk) across the whole world of asset classes. There are four versions of the strategy, each designed to cater to an individual investor’s unique risk profile (Ultra, Aggressive, Moderate, and Conservative).

We invite you to take a look at what we’ve built, a summary of which can be found here:

We welcome your comments, questions, and feedback on this new suite of strategies.

As for The Intelligent Allocator and the Alpha Momentum Strategy, for the time being we remain officially independent of Fortuna. The Intelligent Allocator is not an investment advisor, and we will continue to blog and maintain the Alpha Momentum Strategy for the foreseeable future. But we encourage you to investigate how our approach fits into a comprehensive global portfolio, and to make sure that all of your investments are managed with the same rigor as your stock selections.

Thanks for following along!

-The Intelligent Allocator

About those damn taxes...

About those damn taxes…

Ahhh, tax time! The time when working Americans get to tally up everything they made in the previous year, hunt for every deduction possible, squeeze in contributions to tax advantaged investment accounts, and then figure out if Uncle Sam owes them money, or if it is them who will be cutting a check to the government. The joys of it all!

While the average American probably only considers taxes a few times a year (assuming they are not one of those people who stare at their pay stub every other week and fume about those taxes, like me), those who manage investments should ALWAYS be thinking about taxes.

Why is that? Because here in the US, the government treats investments that are held for different periods of time in different ways, and thus the after-tax returns – which are really the only type of returns that matter – can vary greatly depending on the average hold time of an investment..

To provide some context, investment gains and losses are considered “short term” if held for a year or less. Short term gains are taxed at an investor’s marginal tax rate (ordinary income tax rate) at the federal level and at the state level.

Investment gains and losses are considered “long term” if held for over a year. Long term gains are taxed at a favored tax rate at the federal level (usually 15%-20%) but still usually at the ordinary income tax rate at the state level.

Note: Everything in this article will apply to ordinary brokerage accounts. Some accounts such as 401ks and IRAs are tax advantaged, meaning that capital grows within those account types untaxed. Taxes are either paid before the contribution is made to the account or as distributions are taken from the account, but as the account grows, taxes are not levied on capital gains, meaning that capital gains are able to compound at a higher rate in tax sheltered accounts than they are in non-tax sheltered accounts. Bottom line – for tax advantaged accounts, absolute and risk-adjusted returns are really the only considerations that matter. For non-tax advantaged accounts, net-of-tax returns are just as important a consideration!

So perhaps just as much as the investments in an account matter, hold time matters. Let’s take a quick example. Say I buy a stock and sell it 365 days later, netting a before tax return of $10k. Let’s assume I am in the top tax bracket, I live in California, and this is for tax year 2017. My tax burden on this gain will be 39.6% (max federal tax bracket) + 13.3% (max California bracket) = 52.9% (ignoring the deduction for state income taxes). Congrats to me! The government made more off my trade than I did! I fork over $5,290 of my $10k gain to the government and I am left with $4,710. That’s depressing.

Now let’s say that I hold the stock for one more day and then sell it. I have now held the investment for over a year, so I qualify for the long term capital gains rate at the federal level. While I still owe 13.3% to California, instead of owing 39.6% to the feds, I owe *only* 20% to Uncle Sam. As such, my total tax burden is 20% (federal long term capital gains, max rate) + 13.3% (max California rate) = 33.3%. I fork over $3,330 to the government and I am left with $6,670 to keep. By holding for one extra day, my after-tax return is up over 40% relative to the short term trade.

Taxes matter, thus investment hold times matter!

Perhaps the most important aspect of this issue is that short term capital gains require taxes to be paid in the year they are earned, thus short term capital gains can be extremely destructive to the growth of an account because they reduce the effect of compounding within the account. This effect is especially pronounced over long hold times.

Let’s take a look at another example to illustrate the negative effect on compounding of an account with regards to short term capital gains. Say we have two investors – investor A and investor B. Both investors are high income earners living in California. This means that short term capital gains will be taxed at 39.6% and 13.3% at the federal and state levels, respectively (total tax burden of 52.9% for short term cap gains), while long term capital gains will be taxed at 20% and 13.3% (total tax burden of 33.3% for long term cap gains).

Investor A buys a fund that annualizes 9% a year over a 10 year period. He never rebalances the fund and the fund never trades (impossible assumptions, I know, but we are using an extreme example here). As such, his account will compound at 9% per year and he will need to pay long term capital gains on the final gain when he takes a distribution at the end of the 10 year period.

Investor B invests in a fund that also happens to achieve a 9% annualized return. Investor B’s fund manager, however, is very active. He turns over the portfolio aggressively (trades a lot), and the fund’s 9% gain is treated as a 100% short term capital gain every year. As such, investor B needs to take money out of his account every year to pay taxes on that capital gain.

At the end of the 10 year period, how do investor B’s AFTER TAX returns compare to investor A’s? They are lower by about 0.5% annualized!

To go further down the rabbit hole, the effect of incurring short term versus long term gains will change drastically depending on your hold time! Let’s look at the exact same example as above, but instead of a 10 year period, let’s analyze over a 30 year period. So Investor A holds his low-turnover strategy for 30 years and doesn’t pay any taxes until the end of the hold period, while investor B pays short term capital gains every year for the 30 year time period…

Holy taxes! Over the longer time frame, the effect of taking taxes out of the account every year really has an effect! Investor A’s after tax rate of return is almost 2x that of Investor B’s. This is the effect of compounding. Since investor A doesn’t need to pay taxes until the end of his investment period, his capital base compounds to a much higher degree than investor B’s.

As an investor, it is important to not only manage the investments, but the tax burden as well. As an investment manager, if you aren’t managing to after-tax returns – you aren’t managing investments at all!

So how does a systematic trader think about taxes in relation to a trading strategy? Well, given that a systematic trader attempts to model future possibilities and probabilities as best as possible, a systematic trader will include taxes in their models!

So next time you are evaluating a mutual fund or next time you speak with an investment manager that is touting a strategy, make sure that you understand the tax consequences of the strategy and how it will affect the returns. You may just find that the after-tax returns are inferior to a benchmark or buy & hold strategy, even though the headline return numbers are impressive.

The moral of the story? You cannot only pay attention to headline returns. When evaluating a money manager or fund, you need to consider the tax consequences too. Consider strategies in light of where they fit within your portfolio as a whole, how the strategies blend with the other strategies in your portfolio (e.g. do they provide diversification of return streams amongst each other), and be sure to consider after commission, after fee, and after-tax returns.

And for God’s sake, max out your tax deferred accounts! The more money you can get into tax deferred accounts, the more ability you have to take advantage of high turnover strategies that have the potential to significantly outperform the market, but whose outperformance is significantly hindered outside of a tax-advantaged account. this an indictment of active strategies?

The short answer is no.

If you are considering an active strategy, make sure that the strategy has a solid, evidence-based foundation upon which it is built. Make certain that the strategy gives you a good chance of realizing superior after-tax returns relative to buy & hold.

Remember that time horizon matters. Depending on the investment horizon, an active strategy that has high turnover can potentially need to outperform buy & hold significantly on a pre-tax basis to still outperform on an after-tax basis. Remember that over longer term time horizons, high turnover strategies will need to have a higher degree of outperformance in pre-tax returns to offset the compounding benefit that low turnover strategies exhibit. For shorter term investment horizons (10 years or less, generally) the hurdle caused by realizing short term capital gains will be much, much lower to overcome, and a solid active strategy may be the right choice.

Consider allocating dollars in your tax advantaged accounts to your higher turnover strategies, while allocating dollars in your taxable accounts to more passive strategies.

And lastly, never forget that returns, even net-of-tax returns, should NEVER be considered in a vacuum. The return profile of a strategy always needs to be considered in light of the risk characteristics of that strategy, your individual risk tolerance, and how the strategy fits within your broader portfolio. The S&P 500 lost over 50% in 2008, and if you couldn’t hold through the drawdown, then your passive strategy became active very quickly!

Finance, investing, and trading are complex, and considering tax implications doesn’t do anything to reduce that complexity, but it is of paramount importance. Do your homework, do your diligence, or find a trustworthy fiduciary to help you with it.

More to come...

When the Drawdown Cometh…

There is an unfortunate truth about trading and investing that you must know:

EVERY strategy will go through bad times at some point.

Good strategies will have bad days.

Good strategies will have bad months.

Good strategies will have bad years.

Ask any trader or investor who has been in the business for a long time. Markets wax and wane. Strategies go through good times and bad. The balance of an account ebbs and flows.

If someone wants to help you invest your money but will not have an open and honest discussion about risk and drawdown – run for the hills from that person.

For US stocks, since the beginning of the second quarter of 2016 until the recent highs put in around the end of January, stocks have enjoyed a smooth and pleasant ride higher. Corrections were shallow and traders who “bought dips” or sold volatility were consistently rewarded.

My how things have changed!

There is an old adage in the trading world – Volatility happens fast – and nothing could be truer with regard to the recent spike in volatility.

On a closing basis, as of Friday, 3/23, the S&P 500 was down about 10% from its 1/26 closing high. And while 10% corrections are fairly common in the world of investing, after seven quarters of easy money, many investors are feeling jittery about their exposure to equities.

And to be honest – so are we!

As the S&P is off its highs, so is the Alpha Momentum Strategy.

To borrow lyrics from one of our favorite bands, Daft Punk, “we are human, after all.” And even though we have extensive experience in markets, we have studied market history, we have a well thought out, well researched, well tested strategy, and we know that our systems will experience trying times, that doesn’t necessarily make it any less difficult to stick with our system in those trying times, like now.

So what can we do to make trying times less difficult?

Simple – gain a little perspective.

In our opinion, this is what makes systematic, or rules based trading like our core strategy, so helpful.

Before we invest a single dollar, we outline our rules. We test those rules across various market cycles. IF, and this is a key point, IF our rules are robust and not curve fit to the data, we see what has happened in the past, and therefore, we can get a sense for how those rules are most likely to respond to future markets.

That is not to say that surprises cannot happen. They absolutely can. But with a robust and well tested system, we can get perspective which can not only help us in our asset allocation decisions (e.g. how much money to invest in any particular strategy or asset class), but which can help us put market conditions in context in real time.

And context in real time helps us stay calm in times of stress. It helps us keep a long term perspective. It helps us not to panic. It helps us stay the course.

So with all that said, lets gain some context.

Currently, the Alpha Momentum Strategy is in drawdown (for more discussion on the topic of drawdown, see our previous article here). The strategy is -8.5% of its last high seen on 1/22, meaning that we have now been in drawdown for about 2 months or about 40 trading days. Note that we are not currently at the low of this drawdown which (at least thus far) was on 2/7 when we closed at a drawdown of -12.5%; so we are off our lows a bit. Let’s see how this compares to previous drawdowns.

*NOTE – Drawdowns can be viewed over different time frames, depending on the data being analyzed. Typically for long term investors, drawdowns are measured based on month end returns. Most people usually look at their monthly account statements rather than their daily statements. People who do look at their statement every day don’t necessarily look at it every hour. We can analyze drawdowns on any time frame really - quarterly, monthly, daily, hourly, even down to the tick if we want to get neurotic about it. Note that the more granular the data, the larger the drawdowns will be.

Since we are trying to put the recent action in context, we will look at daily drawdowns.

Also note that, when analyzing drawdowns in this way, we must define a threshold for drawdowns. We can’t know what constitutes a drawdown unless we have specified a threshold to define the drawdowns! For the purpose of this analysis, we will define a drawdown threshold of -10%.

So let’s look at the data. From 1985 through the end of 2017, the Alpha Momentum Strategy had 66 daily drawdowns of -10% or worse. That’s 33 years of data, meaning that, on average, the system sees a drawdown of -10% or worse about twice per year!

How is that for some context!? This is pretty darn normal for the system!

Let’s look at drawdown length now. Since the drawdown isn’t over, we don’t know how long it will actually last. That said, we are currently about 40 days into this drawdown. The average length of a drawdown that is -10% or worse has been 43 days. So this drawdown, at least thus far - is about average. Given that we are not too close to coming out of drawdown, this will probably end up being a longer than average drawdown. The longest drawdown for the system, occurring in 1993, was 642 trading days. If there are 260 trading days in a year, that is a drawdown lasting almost 2.5 years! How is that for a possibility?! It can happen!

Let’s look at the worst drawdown now. The worst drawdown for the system was 1987 (no surprise there) at -40% on a daily basis. That means that at one point the system would have been 40% off of its highs!


All of a sudden a -10% drawdown doesn’t seem that bad, eh?

This, again, is the beauty of systematic investing. While we do believe the old adage that “your worst drawdown is always the one in front of you,” doing this type of analysis helps us prepare for what could happen and helps us stay the course when things get difficult.

Before we started trading, we understood this risk and SIZED OUR ACCOUNT ACCORDINGLY.

We recognized that we could lose up to 50% (or more) of our money allocated to the system and only invested an amount that we were comfortable with given that risk. This is also why we do not employ leverage (in this context).

We invested in not only this system, but others which have historically been uncorrelated to this system to reduce risk across the portfolio. We prepared ourselves mentally. And we have context – and context will help us stay the course.

Comparison of drawdowns – system vs S&P 500

Some readers may be reading this commentary and thinking something along the lines of “Woah! 40% drawdowns? 2.5 years+ without making money? Why would I ever invest in something that can produce that type of pain?”

Well, if you are invested in an index or mutual fund exposed to US stocks, you probably have more risk in your equity portfolio than we do in the Alpha Momentum Strategy. As we have demonstrated here the Alpha Momentum Strategy has historically been less risky than simple buy and hold strategies. Lets extend that analysis here and talk about drawdowns going back to 1985, but also include return numbers for more even more context.

The numbers speak for themselves – no further context necessary.

More to come.

RISK! How to measure it like a pro


Quick! What are the best measures of risk and risk-adjusted returns[i] in a portfolio or asset class?

If you asked most financial advisors, financial journalists and those in some form of financial profession, I am guessing you would hear “standard deviation” and “Sharpe Ratio” as an answer to each question, respectively. And those answers would be WRONG!

These measures, by far, are the industry standard metrics when people talk about risk and risk adjusted returns -- despite the fact that they are actually fairly poor evaluations of risk in a portfolio on their own.

While many think that standard deviation and the Sharpe Ratio measure risk and risk adjusted returns, what they actually measure is volatility and volatility adjusted returns. While related, these are decidedly NOT the same.

A quick primer on standard deviation and the Sharpe Ratio:

Standard deviation, as you may remember from your statistics classes, is simply a measure of dispersion around an average – kind of like the measure of how different from the average the “average” data point is.

If I have two sets of returns that both average roughly the same return over time, but one has higher “dispersion” of returns (higher absolute variances from the mean), the one with the higher dispersion will have a higher standard deviation. This is best exemplified with a numerical example, as shown below:


In this example, return stream A and B both have the same average return: 0.3% (we are not accounting for compounding here). Return stream B, however, is more volatile since it has a couple data points that are farther from the mean than return stream A. Specifically, data points 6 and 10 are where the differences lie:

            Data point 6:

                        Return stream A: 6%

                        Return stream B: 9%

            Data point 10:

                        Return stream A: -3%

                        Return stream B: -6%

Since all the other data points are the same, these two data points are what account for the higher standard deviation in data set B. Note that the average does not change from return stream A to B, but the standard deviation is higher for return stream B than it is for return stream A.

While both return streams have the same average return (again, not factoring in compounding), return stream B is more volatile.

In evaluating investment systems and allocations, most investors (in theory) seek to maximize the amount of return they receive for a given level of risk or volatility that they are willing to withstand – that is, they seek to maximize the risk adjusted return of their portfolio. As such, investors often look at what is called the Sharpe Ratio to measure risk adjusted returns.

The Sharpe Ratio is simply the compound annual return for a given asset (CAGR), minus the risk free rate (RFR) (usually the rate of Tbills in the home country of the investor), divided by the standard deviation (SD) of the return stream.

Sharpe = (CAGR – RFR) / SD

The Sharpe Ratio does a good job of explaining “volatility adjusted returns” or how much VOLATILITY an investor has historically experienced in a strategy in order to achieve the return offered by the strategy. That said, and this is a key point…


Volatility and risk are not the same thing, because upside volatility and downside volatility are not the same thing.

What is upside volatility and what is downside volatility? Put simply –

Upside volatility occurs when a trading system or asset class is moving aggressively higher. This is the volatility that we want. The more upside volatility, the better, because we are making money.

Downside volatility, on the other hand, occurs when a trading system or asset class is moving aggressively lower. This is the volatility that we seek to avoid. The more downside volatility, the worse off we are because we are losing money when downside volatility occurs.

Unfortunately, the standard risk and risk-adjusted return metrics of the financial services industry (standard deviation and the Sharpe Ratio) do not take into account this nuance – they treat both upside and downside volatility in exactly the same way.

So if you are ever working with a money manager or financial advisor who is seeking to “avoid volatility” on your behalf – make certain that he or she is focused on avoiding downside volatility and focused on maximizing upside volatility. You want the most upside volatility you can capture as possible (within the constraints of the downside volatility that you can afford to endure)!

So if the industry standard risk and risk-adjusted return calculations of standard deviation and the Sharpe Ratio treat both good and bad volatility as “bad,” what options do we have to look at risk in a more intelligent and thoughtful way? How can we evaluate systems and asset classes in light of the fact that we want upside (good) volatility, but we want to avoid downside (bad) volatility?

Fortunately, more sophisticated investors have several options at their fingertips to help with their evaluations. Our favorite risk metrics are (a) the CALMAR ratio (b) the downside deviation and (c) the Sortino Ratio.

First, lets talk about the downside deviation and the Sortino Ratio since they are the cousins of the more prevalently used metrics that we discussed above.

Downside deviation: This is the cousin of standard deviation and is a much better metric of risk. Recall that we said standard deviation penalizes a system or asset class for both upside (good) and downside (bad) volatility. Downside deviation, on the other hand, eliminates upside (good) volatility from the equation, and only measures the volatility that we care about when discussing risk – downside, or bad volatility.

The way this works is to first choose what is called a “minimum acceptable return” or MAR. Some people use the risk free rate or inflation rate, but we simply like to use 0 as the MAR. This is because we manage portfolios for absolute return - we want to make as much money as possible in good times while losing as little money as possible during bad times (and every investment method will go through bad times at some point).

It really doesn’t matter what MAR we use, as long as we are consistent in its application. These metrics are really meant for comparison purposes after all. Given alternative investment options, the question we are evaluating is: “Which option is compensating me BEST for the risk I am taking.” As such, as long as the MAR chosen is uniform across options being evaluated, it really doesn’t matter what value we choose as the MAR.

So now that we have our MAR (0 in this case), we look at our return series and we eliminate all data points that fall ABOVE our MAR from our following calculations[ii]. Since we only want to evaluate risk, or downside volatility, we are only going to evaluate return points that are below our MAR, since this is the true risk that we are trying to measure. We then take the standard deviation of values that fall below our MAR to get the downside deviation.

The downside deviation is a true measure of risk! While the standard deviation tells us what a “normal” data point looks like with regards to an average, the downside deviation tells us what a “normal” downside data point looks like with regard to an average.

Basically, we are calculating how bad a “normal” data point has been historically. How bad is a “normal” bad month for a system or asset class? How bad is a “normal” bad year for a system or asset class? This is what downside deviation tells us. Note that downside deviation is typically expressed as an annualized number.

Sortino Ratio: Since the standard deviation has a cousin that is more effective at evaluating risk (downside deviation), and since the Sharpe Ratio is a function of the standard deviation, it makes sense then that the Sharpe Ratio would have a cousin that is more effective at evaluating risk adjusted returns. It does, and that is the Sortino Ratio.

We earlier defined the Sharpe Ratio as the compound annual growth rate of a return stream minus the risk free rate, divided by the standard deviation, or:

Sharpe = (CAGR-RFR) / SD

The Sortino Ratio simply substitutes downside deviation for standard deviation:

Sortino = (Compound Annual Growth Rate – Risk Free Rate) / Downside Deviation

So while the Sharpe Ratio provides us with insight as to how much return we have gotten from an asset measured as a unit of volatility, the Sortino Ratio provides us with insight as to how much return we have gotten from an asset measured as a unit of downside volatility or risk. Thus we have a true measure of risk-adjusted returns with the Sortino Ratio that we do not have with the Sharpe Ratio!

CALMAR Ratio: Unrelated to standard deviation, downside deviation, and the Sharpe and Sortino Ratios is the CALMAR ratio. This is sometimes also referred to as MAR (not to be confused with the minimum acceptable return mentioned above), since it was brought to prominence by the Managed Accounts Report newsletter back in the 1970s.

The CALMAR ratio is the compound annual return of a program or asset class divided by the maximum historical drawdown. Given sufficient data, this is a good indication of the historical return stream of an asset in the context of the most pain an investor would have had to endure at any one point in order to achieve that return stream.

For those not familiar with the term drawdown, it is actually quite simple. Investors will, unfortunately, spend the great majority of their investment careers in drawdown. “Being in drawdown” simply means that you are not at an all-time high for performance. If the S&P makes an all-time high today and then closes down 2% tomorrow, the S&P is in a 2% drawdown. Since any legitimate trading system or asset class will not make new highs every day, every month, or every year, most asset classes are in drawdown most of the time.

One of the main things we care about when evaluating risk is the maximum drawdown a program or asset class has experienced (given that the asset or system being analyzed has data over many different types of market environments).

This is because if we are invested in the asset, it is at the points of large drawdown where we are prone to feel the most pain and thus be most susceptible to deviating from our stated investment plan.

Below is a chart of the S&P 500 (including dividends) going back to 1995 which shows the growth of $100k (left axis) along with the drawdown percent (right axis). Notice that when we are at a new all-time high, the drawdown is 0 – drawdown is always bound by 0 on the upside. You can see the two major drawdowns since 1995 on this chart (the dot-com crash after the year 2000 and the Great Financial Crisis around the year 2008).


Back to the CALMAR ratio now. The CALMAR ratio is an expression of the returns generated by the system or asset class, divided by absolute value of the worst drawdown. In the case of the S&P 500, including dividends and since 1995, the CALMAR ratio is about 0.2. The compound annual return over this time period has been ~10% and the maximum month end drawdown was about -50%.

Put another way, an investor in the S&P would have at one point lost 5x the average annual gain of the S&P! It’s scary to think about risk this way, but it is also necessary in order to set expectations!

Here at The Intelligent Allocator, these are some of the things we look at when evaluating risk and return. Our favorites include downside deviation, the Sortino Ratio and the CALMAR ratio.

We seek to minimize downside deviation, maximize returns, and thus maximize the Sortino and CALMAR ratios. At The Intelligent Allocator, we believe we have built something that does just that: The Alpha Momentum Strategy. Below are the summary returns and risk metrics for the strategy and the S&P 500 benchmark over the time period from 1995 through the end of 2017.

According to all of the risk and risk-adjusted return metrics that we have discussed, it is clear that, at least historically, The Alpha Momentum Strategy has been a superior strategy to buying and holding the S&P 500.

One particular nuance that we love to see when we look at this analysis is the interaction of the standard deviation and downside deviations of the two strategies. Notice how the standard deviation for the Alpha Momentum Strategy is higher than that of the S&P, but the downside deviation of the Alpha Momentum Strategy is lower than that of the S&P.

This just goes to show that the system has been effective at capturing upside (good) volatility, while avoiding (at least some) downside (bad) volatility associated with the S&P 500.

So next time your advisor or broker wants to put you in a strategy and touts its “low volatility,” ask him what type of volatility he is talking about. Is it the good volatility or bad volatility that he is trying to minimize? They are not, as you know now, one and the same and there indeed are methods to reduce downside (bad) volatility while not necessarily cutting upside (good) volatility by the same amount!

More to come.

[i] Risk adjusted return is a term used to describe the amount of return an asset has historically produced in terms of the risk to which that asset has historically exposed an investor. The higher the risk adjusted return of a strategy or asset class the better – we always want to be compensated more for taking risk than less

[ii] It is important to note that there are two schools of thought about how values at or above the MAR should be treated when doing these calculations. Some choose to set values above the MAR at 0 and include them in the downside deviation calculation (there will be more data points used in the MAR calculation when including the “dummy” 0 values, and the downside deviation will be a better explainer of both frequency and magnitude of downside deviation). We choose to eliminate values that fall above the MAR. The method that we use provides a better feel for true downside deviation, but at the expense of not being as sensitive to frequency. Which method is chosen is a function of what exactly the researcher is trying to evaluate – is he trying to mainly the magnitude of downside deviation (throw out the values that fall above MAR in this case) or is he trying to evaluate a combination of magnitude as well as frequency of down periods (keep values above the MAR in this case, but set them to 0). As long as the data set is sufficiently big, it doesn’t matter much which method is used so long as the calculation method is consistent across return streams being compared. These calculations are meant for comparison purposes above all, so consistency is important. For more on this subject, Tom Rollinger and Scott Hoffman have a paper ( as do RCM Alternatives (

Who is the Intelligent Allocator?

First off, I have a background “in the industry.” I have worked for several years in finance – on trading desks (both buy & sell side) executing trades for hedge funds, pension funds, ultra-high net worth investors, and mutual funds. I have also worked in the retail distribution side of the business as a salesman of mutual funds, non-traded REITs, and Reg-Ds/private placements to financial advisors. This gives me a unique perspective of the industry and insight into its players, their motivations, and their actions. This experience has shaped my viewpoints on the industry immensely. Firstly, I have a deep distrust of the industry and for the conventional methods of investment. I do not believe in the efficient market hypothesis and I think it is possible to do better than buy & hold. Second, I recognize that the conflicts of interest in this business are ridiculous - while there are certainly many very noble and good actors in the financial services industry, I am still amazed daily by the blatant conflicts of interest and incompetence on display.

Beyond industry experience, I have a passion for finance, investing, and trading that runs deep. As such, I have spent thousands of hours outside of work devoted to studying the world’s best traders and investors in search of finding a better way to invest than the standard asset allocation models, through methods superior to the homogenous (and risky!) advice peddled by the brokerage and low value financial advisor community and now the robo-advisor community. The more I learn, the more the desire to share and contribute grows within me. My blog & articles and the trading systems outlined here are the manifestation of this desire to share and contribute to the investing success and financial well being of others.

A lot of what I write and demonstrate here may seem controversial and will be at odds with conventional wisdom and mainstream advice. A lot of what I write about the industry will be harsh, but it will also be honest. As such, I don’t expect that my opinions on the industry or the methods I discuss to resonate and appeal to most people. That is OK. That said, everything I present here will be rooted in evidence and rigorous research, and I believe firmly that using the methods I discuss will give an investor the best possible chance at outperforming traditional asset allocations or passive stock investing models. I believe firmly in “eating one’s own cooking” and as such, I am fully personally invested in my methodologies myself.

When I say best possible chance, I use the word chance quite literally. The future is uncertain and anyone who tells you with certainty that they know what will happen in future markets is lying to you (or has inside information!). This is one of my core beliefs. Especially in financial markets, uncertainty is the rule and all that we have to rely on are probabilities. Past is prologue, and history has a tendency to rhyme, and the best we can do to increase the probability of future success is to find robust investment frameworks in past data and apply them to current markets.

So if you are tired of the confusion and misinformation peddled by the financial press, tired of salesmen masquerading as advisors who don't add value, if you are skeptical of traditional asset allocation models and you are wary of the high risks associated with passive equity investing, then I welcome you to join me here at the Intelligent Allocator. Here I will look at alternative investments and alternative strategies. Here I will work to piece together portfolios that enable you to take back control of your investments and act in your own best interests. Portfolios that encompass an accurate reflection of your risk tolerance, and attempt to significantly outperform portfolios hinged on modern portfolio theory and that are at the center of most advice offered by the financial services industry.

So, where to start? You can SUBSCRIBE for regular updates to the blog.

If you are interested in learning about a stock trading strategy designed to provide far superior results to traditional buy and hold strategies with much lower risk, head over to the ALPHA MOMENTUM STRATEGY page to learn more.

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