Thursday, August 3, 2017

Revised RSS Link


I renamed the blog URL. Please please kindly update your RSS feed with the address below:


Wednesday, July 5, 2017



Dear readers,

It’s been 2 years since I started this little blog.

This site has been a great way to journal my investment philosophy and present some quantitative research. Along the way, I’ve received lots of great feedback from many of you in the comment sections and by e-mail.

I want to announce that I am moving this blog to a new site: The purpose of the new website is to allow for a bit more functionality.

If you are using an RSS feed, please kindly update it with the address below:

Thanks again for your readership and support!


Tuesday, June 20, 2017

Asset Allocation Part 1: The Basics

Source: Randy Glasbergen,

As investors, we want to reap the power of compound interest over the long-run. That is how we build real wealth. But what should we invest in and how can we most efficiently allocate our savings?

This is a 3-part series of posts on asset allocation that forms the foundation of my investment philosophy. This series will tie together a lot of items I’ve been writing about over the past 2 years. Here is an outline for this series:
·         Part 1: The basics – what are asset classes, why stocks form the core of portfolios and how traditional diversification in other asset classes helps improve our Sharpe Ratio
·         Part 2: Strategic Asset Allocation (SAA) – determining the allocation for a specific investor, comparing passive vs. active funds for implementing SAA, and looking at the pros & cons of SAA
·         Part 3: Tactical Asset Allocation (TAA) – how we can more efficiently allocate to asset classes and achieve higher risk-adjusted returns

Let’s begin with the basics…

A Brief Look at Major Asset Classes

The investable universe can be categorized into what’s known as asset classes, or groups of investments that are liquid, distinct and not highly correlated with each other. 

The most common asset classes are equities (stocks) and fixed income (bonds). Domestic and foreign equities are treated as separate asset classes, since they have different risk & return profiles. Then there are the alternative asset classes such as commodities, real estate and private equity.

Historically, stocks have provided the highest returns with bonds coming in at second place. Wharton professor Jeremy Siegel shows this over a 210-year period from 1802-2012:

Source: Stocks for the Long Run, Jeremy Siegel

Let’s look at the characteristics of each major asset class to help us understand the above chart better.


Equities are part-ownership in businesses. When we invest in a broad stock index, we’re investing in many of the largest companies across all industries and sectors. And as owners of these companies, we believe society will continue to innovate and prospser as it has for all of human history. In the 2013 Berkshire Hathaway Shareholder Letter, Warren Buffet wrote:
"Charlie and I have always considered a 'bet' on ever-rising U.S. prosperity to be very close to a sure thing. Indeed, who has ever benefited during the past 237 years by betting against America? If you compare our country's present condition to that existing in 1776, you have to rub your eyes in wonder. And the dynamism embedded in our market economy will continue to work its magic. America's best days lie ahead." – Warren Buffet

Equities give investors returns through dividend income and capital growth. One key feature of equities (unlike owning commodities or physical real estate) is that they benefit from the power of internal compounding: many companies typically re-invest part of their earnings back into expanding the business.

Another key reason that equities provide significantly higher returns than other asset classes is due to the risk they carry. Equity earnings face uncertainty of future demand, input costs and competitive forces, to name a few. Shareholders share in the fortunes and misfortunes of companies, with no guarantee of principal repayment. And as well all know, bear markets in stocks can be severe both in terms of magnitude and duration: 



A bond is a loan that gives investors returns primarily through interest income. This income stream is relatively stable and the investor’s principal is returned at maturity.

The major risks surrounding bonds are interest rate and credit risk. Bonds are offered in various lengths (time to maturity). The greater the length of the loan, the higher our exposure to various risks. Let’s first look at interest rate risk.

If we buy a single bond issue, then as rates rise, the value of our bond falls. This is because we are stuck receiving the older (lower) interest rate. However, we have less interest rate risk if we instead invest in a bond fund. A bond fund holds a collection of several bond issues and tries to maintain a target length. As some bond issues in the fund mature, they are replaced with new funds. Thus, if interest rates were to rise, we would take a hit on the bonds currently in the fund but we would get a discount on new bonds added to the fund. Therefore, bond funds are less sensitive to interest rates.    

Even during the 60s and 70s, when 5-year Treasury rates went from 4% to 16%, investors in a 5-year Treasury bond fund didn’t lose much sleep:

Source: US Federal Reserve Board,

Investors in government bonds have fairly low credit risk, as governments (particularly in developed countries) have stable revenues through taxes. This lower credit risk generally results in lower bond yields for investors.

Investors of corporate bonds carry company specific-risk, but not as much as shareholders do. This is because corporate bond investors not only receive coupon income and principal repayment, but also have priority claim on company assets over shareholders in the event of bankruptcy. Due to their lower risk profile, bonds don’t provide as high returns as stocks.


Commodities include base metals (eg. copper, aluminum), precious metals (eg. gold, platinum), agriculture (wheat, soybeans) and energy (eg. oil, natural gas).

The return potential for commodities is not as high as stocks for several reasons:
  • By definition, commodities and inflation are tied together:
  • Commodities have storage costs, don’t generate any income, and their returns can’t be compounded internally the way that stocks do.
  • Companies take raw commodities as inputs and continually manufacture new, innovative products at a markup (thanks to barriers to entry, intellectual property, brand power, etc.).

Real Estate:

An investment in Real Estate can either be direct (eg. owning property) or indirect (eg. REITs).

Direct real estate provides rental income and capital appreciation. The downsides are that direct real estate is illiquid, has high transaction costs and on-going costs (eg. property taxes and maintenance). Furthermore, the return potential for direct real estate is not as high as stocks for several reasons: 
  • Increasing supply is used to meet increased demand, which helps curb price appreciation
  • Local housing prices are anchored to inflation through rents and incomes. If housing prices are rising rapidly faster than rents and incomes, it is not sustainable since it means residents are either stretching themselves to own a home, or that the alternative to buying (renting) is more economical.
  • Real estate prices are impacted by interest rates the way bonds are. When rates rise, mortgages are tougher to afford, and housing prices fall. Conversely, when rates fall, housing prices rise. In a low interest rate environment like today, housing prices are high. If you were to buy a home and rent it out, the rental yield would be low, similar to the interest yield on a bond.
  • The local salaries that drive real estate prices are generated by the business sector. It would be unsustainable for companies to increase wages for their employees faster than the growth in business revenue. This is an indirect way to show that real estate is inferior to stocks.

The following chart shows US home prices in real terms since 1880. We see that housing has barely outperformed inflation over the long-term despite a growing population. 

Source: Robert Shiller, 2012

It should be noted that REITs (real estate investment trusts) on the other hand act more like stocks, since companies are re-investing capital to buy new properties or finance the development of new projects.

Before we conclude the brief tour of asset classes, I would like to point out that each asset class doesn’t operate in a vacuum. See our previous post: Markets are Interconnected.

How Diversification Helps

Because of their high long-term return potential, equities form the core of traditional investment portfolios. However, we cannot passively have our entire portfolio in equities since they are volatile. 

Source: prabook

In 1952, Harry Markowitz discovered an interesting property: by adding bonds to an equity portfolio, you can significantly reduce portfolio volatility without sacrificing much in the way of returns. The graphical representation of this is called the Efficient Frontier and forms the basis of Modern Portfolio Theory. It is shown below.

The purpose of the Frontier is to show that proper asset allocation can give investors more reward per unit of risk that they take. For example, portfolio B on the Frontier contains 33% bonds while portfolio D contains 100% bonds yet B has significantly higher return for the same level of risk as D.

How can this be? The key is that stocks and bonds tend to be uncorrelated. While both stocks and bonds have positive expected returns in the long run, they tend to respond differently to market forces (though not always). So, by diversifying into multiple, uncorrelated assets, a downturn in a single holding won’t necessarily spell disaster for your entire portfolio.

Stay tuned for part 2, in which we’ll look at strategic asset allocation.

Sunday, April 30, 2017

Scenarios for Momentum Investing

source: babaimage

In the previous post, we reviewed momentum’s robustness and saw how it stood the test of time. We also stress-tested the Global Equities Momentum (GEM) strategy and saw that its performance is not overly sensitive to changes in the strategy’s settings (i.e. the 12-month lookback period and the monthly rebalance period).

In this post, let's run various scenarios to see how us momentum investors would fare in each of them.

Base-case scenario:

The most likely scenario is that society continues to innovate and prosper as it has for all of human history. In the 2013 Berkshire Hathaway Shareholder Letter, Warren Buffet wrote:

"Charlie and I have always considered a 'bet' on ever-rising U.S. prosperity to be very close to a sure thing. Indeed, who has ever benefited during the past 237 years by betting against America? If you compare our country's present condition to that existing in 1776, you have to rub your eyes in wonder. And the dynamism embedded in our market economy will continue to work its magic. America's best days lie ahead." – Warren Buffet 

I will expand on this in a future post and include items from the excellent book “Stocks for the Long Run” by Jeremy Siegel.

Nonetheless, we want to test all types of negative scenarios to see what impacts they would have on portfolios that follow a systematic momentum model such as GEM.  Let’s begin with the most unlikely scenario.

Armageddon scenario:

A nuclear holocaust. Killer contagion. Supervolcano eruption. An asteroid hitting the earth.

While these and other doomsday scenarios have a low likelihood of occurring, they could cause equity markets to suffer heavy and sustained losses. But if such a scenario were to happen, you would have far bigger things to worry about than your portfolio.

Gradual equity market decline scenario:

This can be due to changing demographics, falling population levels, etc. This is a bit more realistic than an Armageddon scenario.

The chart below shows our long-term population growth

source: Wikipedia

Since 5000 BC, population growth has roughly doubled every millennium. But starting around the 1800s, population growth entered an accelerated growth period. It can be argued this population explosion has been the main driver for long-term GDP growth and hence equity returns. It may be argued that this growth is not sustainable forever, leading to a stagnant population growth at some unknown future time. Population rates have also been shown to fall as developing countries gain an increased standard of living. 

Whatever the underlying reason is, let's suppose hypothetically that equity markets decline gradually. How would a trend following or momentum strategy like GEM adapt? The trend of equities would be down and we would simply be in the safety of bonds. But what's less easy to answer quickly is if equity markets go sideways. Let's take a look.

Erratic, sideways equity market scenario:

As discussed in a previous post, current equity market valuations and bond yields mean that we should set low returns expectations for passive balanced portfolios over the next 10 years. It is likely that equities can churn sideways for the next decade or more.

Trend following and momentum strategies tend to suffer in these types of erratic, sideways markets. But what, quantitively, would be GEM’s performance in such a market?

In the post linked above, we looked at the 10-year sideways equity market that began in 2000. We showed how over this period, GEM produced an 11.4% annual return compared to just 2.8% annual for a 60/40 stock/bond balanced portfolio.

In this post, let’s test an even more extreme scenario: How would momentum perform during the 30-year sideways market in Japanese equities that began in the late 80s? 

We test an absolute momentum strategy that each month-end, invests in the MSCI Japan index if the past 12-month performance of that index is greater than that of T-bills. Otherwise we invest in the US Aggregate Bond Index. Simple.

The chart and table below shows what happens since Jan 1971. 

We see that Absolute Momentum outperformed Japanese equities significantly. The strategy produced an extra 560 bps of return while also considerably reducing volatility and maximum drawdown. The strategy made an average of just 1.5 trades per year and was invested in Japan for 56% of the time since 1971.

OK. You might be thinking “Yes, but you had the benefit of switching into US bonds, which were in a major bull market in the past 30 years.” Fair enough.

Let’s see how our momentum strategy fared if we could only switch into cash for safety. The chart below shows we still would have outperformed.

We see that Absolute Momentum now produced only slightly better returns than Japanese equities. However, we still benefited from having significantly reduced our maximum drawdown. And this was done with an average of just 1 trade per year and being invested in Japan for 64% of the time since 1971.

I should note these are results for absolute momentum (comparing a risky asset to cash). You would reduce the concern of a sideways-market scenario by adding another equity market and running dual momentum.

Rising interest rate scenario:

We touched on the idea that future bond returns will be nowhere as great as they have been over the past 30 years. This will reduce the performance of momentum/trend following strategies that use bonds for safety, but it won’t hurt performance too much for 2 reasons:
  1. The GEM strategy has only been in bonds 30% of the time since 1970. If we replace bonds with cash, GEM’s annual returns fall from 17% to about 14.5%. This would still be a respectable return.
  2. Even in the worst-case interest rate environment (1962-1982 when 5-year yields went from 4% to 16%), an aggregate bond fund still doubled (growing at 3.5% annually). This is due to the nature of bond funds continually replacing maturing bonds with new issues to maintain a constant maturity. See chart below

 Thus, dismal future bond returns won’t be the end of the world for momentum strategies.

OK, but what if the stock-bond relationship changes? The chart below shows stock-bond correlations over the past 100 years.

Despite the relation changing significantly over this time, momentum strategies have been shown to work (on a decade-by-decade basis) over this period as we saw in the last blog post.

Structural market change scenarios:

Thanks to technology, the speed at which industries are changing has never been faster. We are seeing some companies rapidly gaining market share while some are becoming obsolete. As Google’s Sergey Brin discussed in a recent interview, it is next to impossible to know what the future will look like. Because the GEM strategy invests in large, diversified ETFs, this uncertainty is not a major issue.

What about a scenario where emerging markets gain dominant market share - would this threaten the rest of the world? We showed in a previous post that this is not a major concern, since the GEM strategy invests globally. Furthermore, companies in all parts of the world are growing their global presence.

How about baby boomers retiring in large numbers - will they destroy the stock market? Ben Carlson has a blog post up today that looks at this question and shows why this is not a concern. 

What about currency risk? Non-US GEM investors may see their domestic currency rise rapidly while they are holding foreign assets required by GEM. For example, from 1985-1995, the Japanese Yen rose over 300% relative to the US dollar. We showed that despite this, Japanese investors still would have come out ahead by following GEM.

There are far too many of these scenarios to list here. The perma-bear approach is to worry excessively about every negative scenario, to never invest and never grow your wealth. This is a sure way to ensure that your future self will hate you.    

Concluding thoughts:

We can summarize the main scenarios and our findings as follows:
  • Trending (up or down) equity market - During bull markets, a momentum strategy such as GEM is concentrated in equities and during bear markets, it is concentrated in bonds. This more efficient asset allocation allows GEM to significantly outperform a traditional approach (passive 60% equity, 40% bond portfolio) in terms of both excess returns and reduction in volatility & drawdown.
  • Sideways equity market - GEM still wins. During the 2000-2010 sideways market in global equities, GEM did an 11% annual return compared to just 3% annual for the traditional portfolio. In an extreme scenario where we switch only between a single, sideways equity market and cash for 30 years, momentum still shows slightly higher excess returns. In both these examples, momentum provided a significant reduction in volatility and drawdown.
  • Sudden catastrophic event scenario - GEM would underperform buy-and-hold, assuming it is fully in equities at the time of the event. 

The likely very-long-term scenario is growing economic prosperity and equity markets. However, the next decade may be a period of dismal returns and sideways markets due to current equity valuations and bond yields. A catastrophic event scenario, while possible, is not very probable. 

That being said, we don’t know what the future will bring. The beauty of trend following and momentum is we don’t need to make any forecasts. Trend following adapts to market environments and actually requires less faith than other approaches. For example:   
  • Someone that has all their savings stowed under the mattress requires faith that cash will do better than inflation
  • Those that invest in the traditional portfolio require faith that future expected returns (despite being very low) are still worth the risk compared to being in a high interest savings account
  • Value investors constantly require faith that markets will mean revert

(we will do a more in-depth comparison of trend following and momentum to other investing strategies in a separate post).

Finally, I always get asked a lot about a scenario we didn't discuss here: What would happen if everyone began following a momentum strategy? Despite everything presented in this post, trend-following and momentum strategies are not a slam dunk way to riches. It takes a lot of discipline to stick to an active strategy when it suffers the inevitable period of volatility, uncertainty or under-performance. More on this in a future post. 

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.

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).

In 1937, Cowles & Jones did the first paper showing that 12-month momentum works. In 1967, Robert Levy did the first computer backtest on momentum. In 1993, Jegadeesh & Titman wrote their seminal paper showing 3-12 month momentum works. Also in that year, Eugene Fama (father of the efficient market theory) called momentum the "premier anomaly."

In 2013, Geczy and Samonov published a paper showing a momentum backtest that went back over 200 years. The following year, Greyserman and Kaminski did an 800 year backtest. Both papers show that the momentum anomaly is persistent over the long-run.

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.