August 10, 2015

Bring Data

When doing financial modeling, one of the first things to look at is if your empirical work makes sense. In other words, are there valid economic reasons why a model should work?  This can help you avoid drawing erroneous conclusions based on creative data mining.[1]

Next, you should look for robustness. This can take several forms. One of the most common robustness tests is to see how well a model does when it is applied to somewhat different markets. Even though equities have historically offered the highest risk premium, it is desirable to see a model do well when it is also applied to other financial markets.

Another robustness test is to see if a model is consistent over time. You do not want to see success based on spurious short periods of good fortune. Similarly, you would like to see a model hold up well over a range of parameter values. Getting lucky can be good in some things, but not in financial research. 

Relative and absolute momentum have held up well according to all of the above criteria. But now that momentum is attracting more attention, it is important to remain vigilant and to keep robustness in mind. What makes this especially true is the natural tendency to come up with modifications and "enhancements" that can add complexity to a once simple model.

An interesting new paper by Dietvorst, Simmons, and Massey (2015) called “Overcoming Algorithm Aversion: People Will Use Algorithms if They Can (Even Slightly) Modify Them,” shows that people are considerably more likely to adopt a model if they can modify it. Giving people the freedom to modify a model makes them feel more satisfied with the forecasting process, more tolerant of errors, and more likely to believe that the model is superior. Everyone likes to feel that they have some involvement with and control over a model. and that they may have made it better. Data mined “enhancements” may fit the existing data well but not hold up on new data or over longer periods of time.

I have seen dozens of variations and "enhancements" to momentum, and I will undoubtedly see many more in the days ahead. One variation that attracted considerable attention a few years ago was by Novy-Marx (2012) who found that the first six months of the look back period for individual stocks gave higher profits than more recent six months. This became known as the “echo effect.” However, it never made much sense to me. So I tested the echo effect on stock indices, stock sectors, and assets other than stocks. I was not surprised when incorporating the echo effect gave worse results than the normal way of calculating momentum.

A subsequent study by Goyal and Wahal (2013) showed that the echo effect was invalid in 37 markets outside the U.S. Goyal and Wahal also demonstrated that the echo effect was largely driven by short-term  reversals stemming from the second to the last month. Over reaction to news leading to short term mean reversion of individual stocks does make sense. Prior to that time, only the last month was routinely skipped when calculating momentum for stocks.[2] Based on this finding, the latest research papers skip the prior two months instead of just the last month when calculating individual stock momentum. [3]

While robustness tests are very important, the best validation of a trading model is to see how it performs on additional out-of-sample data. The statistician W. Edwards Deming once said, “In God we trust; everyone else bring data.”

When I first developed the dual momentum based Global Equities Momentum (GEM) model, my back test went to January 1974. This is because the Barclays Capital bond index data I was using began in January 1973. I am now able to access Ibbotson bond index data, which has a much longer history. My GEM constraint has now changed to the MSCI stock index data going back to January 1970.

Having this additional bond data, I have another three years of out-of-sample performance for GEM. My  new back test includes the 1973-74 bear market and shows dual momentum sidestepping the carnage of another severe bear market.

GEM is more attractive than it was previously on both an absolute basis and relative to common benchmarks. Here is summary performance information from January 1971 through July 2015. 60/40 is 60% S&P 500 and 40% Barclays Capital U.S. Aggregate Bonds (prior to January 1976, Ibbotson U.S. Government Intermediate Bonds). Monthly returns (updated each month) can be found on the Performance page of our website.

  GEM S&P500  60/40
Ann Rtn   18.2    11.9   10.2
Std Dev   12.5    15.2     9.8
Sharpe    0.91    0.38   0.44
Max DD  -17.8   -50.9  -32.5

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our GEM Performance and Disclaimer pages for more information.

In our next article, we will look at longer out-of-sample performance using the world’s longest back tests. Fortunately for us, these were done to further validate simple relative and absolute momentum.

[1] For example, between 1978 and 2008, U.S. stocks had an annual return of 13.9% when a U.S. model was on the cover of the annual Sports Illustrated swimsuit issue versus 7.2% when a non-U.S. model was on the cover
[2] Short term mean reversion is not an issue with stock indices or other asset classes, so the last two months do not need to be excluded from their momentum look back period.
[3] See Geczy and Samonov (2015). Discovery of  two month mean reversion is an example of the Fleming effect in which different but related research can lead to serendipitous results.

July 20, 2015

Back to Fundamentals

After winning two consecutive national championships, the Green Bay Packers lost a game due to sloppy play. Coach Lombardi called a meeting the very next day to get his team back to fundamentals. When all the players were assembled, Lombardi held a football high up in the air and declared, “Gentlemen, this is a football!” From the back of the room, running back Paul Hornung shouted back, “Coach, can you slow down?”

Sometimes we all need to be reminded of fundamentals. The fundamental goal of investing should be to receive the most gain with the least pain. The question then becomes, how do we achieve this?

Asset Returns

The first step is to select the best investment assets. The following chart shows the annualized real returns of U.S. stocks, bonds, and Treasury bills since the years 2000, 1965, and 1900.

Source: Credit Suisse Global Investment Returns Yearbook 2015 

Over the past 100+ years, stocks have provided more than three times the real return of bonds despite the unusually strong bond market of the past 35 years. A much higher long-run return from stocks makes sense, since stocks are considerably riskier than bonds. They should therefore compensate investors with a higher risk premium.

The following chart by Wharton professor Jeremy Siegel shows the same dynamic over 200 years from the years 1802 to 2012.

Source: Stocks for the Long Run, 5th edition, Jeremy Siegel

Again we see that over the long-run, stocks have earned the highest return by a large margin. The annualized real return of U.S. stocks has been nearly twice as high as the annualized return of bonds since 1802.


Even though returns are maximized, the problem with holding only stocks in one's portfolio is their high volatility and negative skewness. These create considerable left tail/drawdown risk. There have been two bear market drawdowns in U.S. stocks greater than 50% during just the past 15 years.

Not only can large equity erosions create discomfort and uncertainty in the minds of investors, but they can  cause investors to react in ways that are counter to their own best interests. The yearly Dalbar studies show that investors underperformed the funds they were invested in by an average of 4% annually over the past 20 years. Poor timing by investors is often attributable to emotionally induced buying and selling.


In order to reduce the emotional stress and poor timing decisions triggered by high stock market volatility, investors have traditionally diversified their portfolio into assets other than stocks. The main alternative has historically been bonds. However, as we saw from the above charts, our long-run expected return decreases substantially as we add bonds or assets other to an all stock portfolio.

Yet this diminished return has not stopped investors from adopting so-called balanced portfolios, such as the common one that allocates 60% to stocks and 40% to bonds.  Even Harry Markowitz, the father of modern portfolio theory, split his personal investments equally between stocks and bonds.

Based on financial planning principles, some investors start off with a higher allocation to stocks in their early years and then switch to a greater allocation to bonds as they grow older. This may no longer be as prudent a strategy as it once was. The average life expectancy today of someone reaching the age of 65 is 19 years. The lengthening of retirement years and emphasis then on bond investing can aggravate the problem of portfolio under performance. Investors may need a way to keep growing their investment assets well beyond their retirement age.

Wealth Accumulation

What exactly does the old paradigm of a balanced stock and bond portfolio mean in terms of wealth accumulation over the long-run? To determine this, I looked at a rolling 40-year window comparing the performance of the S&P 500 to a portfolio invested 60% in the S&P 500 and 40% in10-year U.S. Treasuries from 1900 through 2014.

During that time, the average annual total return of the S&P 500 was 10.0%, compared with 8.3% for the 60/40 stock/bond portfolio.[1] Applying these average rates of return to a 40-year investment horizon, a $10,000 initial investment in the S&P 500 would have grown to $537,000 before expenses and taxes, while a $10,000 investment in the 60/40 stock/bond portfolio would have become only $273,500. Due to the power of compounding, an all-stock portfolio would have resulted in almost twice the accumulated wealth of a 60/40 balanced portfolio.

Many do not realize the impact over time of an extra 1-2 % per year in return and what a large difference it can have on one's accumulated wealth. (There might be far less money under active management now if investors were fully aware of this fact.)

High Costs of Diversification

In addition to lower expected risk premiums, there are substantially higher costs associated with diversification that many investors are not fully aware of. In their study “Fees Eat Diversification’s Lunch,” Jennings and Payne (2014) state that fees on diversifying assets are astonishingly high relative to their benefits. (On a real time basis, other assets have to compete with U.S. stock index funds having annual expense ratios of only 4 or 5 basis points.)

 In the 1970s, U.S. investors started to look seriously at the diversifying their stock holdings internationally, despite the fact that non-U.S. stocks since 1900 have returned on average 2% less per year than U.S. stocks. Jennings and Payne found that fees reduced the benefit of international diversification by one-third for small institutional investors. Fees almost completely eliminated any diversification benefit from investing in emerging market bonds, hedge funds, and private equity. In looking at 45 different asset classes, Jennings and Payne found that fees consumed over half the expected benefit in more than 60% of those markets.

A Practical Solution

Is there anything investors can do to reduce their downside exposure during equity bear markets without giving up half their accumulated wealth in the process? Our dual momentum based Global Equities Momentum (GEM) methodology diversifies one’s portfolio in a more intelligent way.[2] GEM’s core holding is the S&P 500 in order to capture the highest long-run risk premium. GEM switches between U.S. and international stocks according to relative strength price momentum, which can improve the expected return from holding stocks. The GEM model also switches between stocks and bonds in accordance with trend-following absolute (time-series) momentum. When equities have been going up according to the rules of absolute momentum, GEM stays fully invested in stocks. When the trend of the stock market turns negative, GEM switches into low-duration aggregate bonds. Bear markets in stocks often foreshadow economic recessions with falling or flat interest rates. These are often the best times to hold bonds. Dual momentum is an adaptive approach that diversifies in a temporal way, which makes the most sense.

Here is the performance of GEM compared with the S&P 500 index and a portfolio allocated 60% to the S&P 500 and 40% to10-year Treasuries from January 1974 through June 2015. Positions are rebalanced monthly.

Performance of GEM

  GEMS&P 500 60/40
Ann Rtn 17.73 12.33 10.76
Std Dev 12.36 15.43   9.74
Sharpe   0.89   0.41   0.50
Max DD-17.84-50.95-30.54

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our GEM Performance and Disclaimer pages for more information.

GEM has a considerably lower maximum drawdown than the 60/40 stock and bond portfolio. In addition to providing greater downside protection than afforded by the 60/40 portfolio, GEM returns have been significantly higher than the returns of the S&P 500 portfolio. Large losses in the S&P 500 need to be recouped before stocks can again show a net profit. For example, it takes a 100% gain to get back to even after a 50% loss. By sidestepping severe bear market losses, GEM can earn higher overall profits. 

GEM remains in stocks when the trend of the stock market is positive in order to capture all it can of the high risk premium associated with stocks. GEM retreats to the safety of bonds during the 30% of the time when stocks are weak and bonds are often their strongest.

Possible Concerns

Why would anyone want to adopt a permanent stock/bond portfolio with its fixed income drag on performance when a simple dual momentum approach like GEM has shown considerably less downside exposure and substantially higher expected return than either an all-stock or a balanced stock/bond portfolio? 
The first reason for some is that the future may not be like the past. However, dual momentum is a simple model with several hundred years of out-of-sample performance to support it. The GEM look back parameter used by Cowles and Jones in 1937, has held up well back to the early 19th century and up to the present time. There are also good reasons, as described in my book, why the momentum effect should continue to persist.

The next concern may be occasional re-entry lags when a new bull market begins after dual momentum has protected your portfolio from the preceding bear market. There may also be occasional whipsaw trades at other times that can cause dual momentum to temporarily lag behind the stock market. Over the past 40 years, GEM underperformed the stock market in 1979-80 and 2009-10. No strategy can outperform all the time.

Career risk associated with tracking error, long-standing aversion to market timing, and confirmation bias may keep institutional investors from ever using dual momentum.[3] As an encouraging note for the rest of us, this attitude should help keep momentum from being over exploited.

Since bonds make up 20% of GEM's profits, there may be some concern that bonds may not perform as well in the future as they have over the past. GEM uses aggregate bonds with around only a 5.3 year average duration, which gives them relatively low sensitivity to interest rate changes. GEM uses bonds when there are bear markets in stocks. These often precede recessions which often lead to falling rather than rising interest rates.

Finally, the trend-following component of GEM is slow moving so as to minimize whipsaws. This means that GEM is still subject to the volatility associated with short-term stock market fluctuations. Very conservative investors can always allocate a modest portion of their portfolio permanently to bonds in order to attenuate this volatility.

Volatility Attenuated Dual Momentum

Here is what would have happened if we had allocated 75% of our investment portfolio to GEM and 25% permanently to aggregate bonds from January 1974 through June 2015.

Annual Rtn
Std Dev
Max DD

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

The GEM/25 allocation now has the same volatility as the 60/40 portfolio, but GEM/25 has a substantially higher annual return and Sharpe ratio. The maximum drawdown of GEM/25 is only 39% as large as the maximum drawdown of the 60/40 portfolio.

We see that dual momentum in various forms meets our fundamental goal of investing – the most gain with the least pain.

[1] Both portfolios had the same 40-year minimum average return of 5.4%. On the basis of avoiding the lowest average portfolio return, the 60/40 portfolio was not any better than the S&P 500 portfolio over a 40-year time frame.
[2] The GEM model is fully disclosed in my book, Dual Momentum Investing. It takes less than 5 minutes per month to apply it.

[3] Even those who understand and appreciate momentum can be subject to long-standing biases that keep them from using momentum in a significant way.