August 4, 2016

Most Useful Investment Blogs

As with many people these days, most of my investment information comes from the internet. It has taken me years to compile a group of research-oriented blogs and websites that I have found most useful. Here is my annotated list:

Investment Blogs

Quantocracy:  This is an aggregator of quantitative trading links to blog posts and research articles. It covers a broad range of ideas from coding to theory. So not everything will be of interest to everyone. But you can evaluate links quickly, since Quantocracy displays the title and first sentence of each article. Those with any interest in quantitative finance should check out this blog.

Abnormal Returns: This is another aggregator with short content summaries. It is broader in scope than Quantocracy. In fact, about one-quarter of the links have nothing to do with investing. But many are interesting anyway. The blog's daily emails make it easy to find articles of interest.

CXO Advisory: This website is a good way to learn about new investment research posted on the Social Science Research Network (SSRN). If you pay a modest subscription fee, you can read CXO’s analysis of these research papers, which is a big time saver. CXO sometimes does book reviews andr researches other ideas, including momentum.

Quantpedia: Useful for summaries and excerpts of investment research that may not show up on CXO. They use other sources besides SSRN, such as the Cornell University Library.

Alpha Architect: This blog is like an aggregator in that they put out posts almost every day, and many of these cover other people’s research without critical analysis. Other posts contain Alpha’s own research and insights. Wes and his crew try to democratize investing and make academic concepts understandable to the public.

EconomPic Data:  This was once one of the most popular finance blogs. It became dormant for a time due to work constraints on its author, Jake. Now it is back stronger than ever.  Jake usually has thought provoking things to say, and he does some good research. His site is momentum friendly. Jake is also quite active on Twitter.

A Wealth of Common Sense: The author, Ben Carlson, is a member of the Ritholtz posse that includes The Big Picture and The Reformed Broker. All these are interesting , but Ben’s site is my favorite. It does indeed offer a wealth of common sense.

Sharpe Returns: This is the only blog besides my own that focuses on dual momentum. It’s author, Gogi, comes up with original ideas of his own, such as:
1) performance difference between U.S. and non-U.S. stocks depends on the strength of the U.S. dollar
2) dual momentum can do well even during those decades when stocks are overvalued

3) long term performance can be seriously distorted by short term performance, as in the case of gold.

Twitter is also an excellent source of investment information. Not only do those followed on Twitter offer their own insights, but they retweet and comment on worthwhile information from others. Here are the Twitter handles of the above bloggers plus my own:

Quantocracy @quantocracy
Tadas Viskanta @abnormalreturns
CXO Advisory @CXOAdvisory
Wesley R Gray @alphaarchitect
Jake @EconomPic
Ben Carlson @awealthofcs
Gogi Gerwal @sharpeReturns
Gary Antonacci @Gary Antonacci

Here are others I like who have many followers:

Meb Faber @MebFaber
Vanguard Advisors @Vanguard_FA
Cullen Roche @cullenroche

These have fewer followers but deserve more:

Samuel Lee @etfsamlee
The Leuthold Group @LeutholdGroup
Ned Davis Research @NDR_Research

There are many other excellent investment bloggers and Twitter peeps. I follow around 90. Any more and I would not have time to read them all. As with other things in life, you need to find the right balance.

June 13, 2016

Smart Beta Is Still Just Beta

Some say that bull markets climb a wall of worry. This is good news for those already in the market. Worriers will help the market go higher later when they finally decide to jump on the bandwagon. Herding  and regret aversion (fear of losing out on future profits) should eventually overcome loss aversion.

Investors Skeptical

The iconic investor and money manager, Sir John Templeton, said, “Bull markets are born on pessimism, grow on skepticism, mature on optimism, and die on euphoria.”  The current bull market in U.S. stocks, though longer in duration than many previous bull markets, has not yet garnered a lot of investor confidence. It is still in the skepticism stage. Perhaps investors have remained fearful due to the two bear markets of the past 20 years when stocks lost half their value each time.
Even though the U.S. stock market is around new highs, investors are still skeptical about further gains lying ahead. According to the AAII Sentiment Survey, at the end of May the percentage of individual investors optimistic about stock market gains was at its lowest level in 11 years.

Investment flows have also reflected lackluster investor interest. Only 52% of U.S. adults are invested in the stock market. This is tied with 2013 as the lowest level in 16 years. The cumulative flow into mutual funds and ETFs is 25% lower than it was 18 months ago. Among professional money managers, allocations to U.S. equities are near an 8-year low, and cash levels are at their highest level in 14 years, according to the latest Bank of America Merrill Lynch Global Fund Manager Survey.

Overvalued Stocks

With the U. S stock market at new highs, sentiment has shifted from the market being in a “distributional top” pattern to it being “overpriced.” High valuations may mean lower expected returns over the next 10 years, but it does not mean valuations cannot get even higher.  In April 1996, the Shiller CAPE ratio was at 25, near where it is today. But the CAPE ratio continued to rise over the next 3 years until it reached a high of 43 in November 1999. The S&P 500 gained another 138% during that time.

From that level, the S&P 500 lost 9% over the next 10 years. But look at what happened with our Global Equities Momentum (GEM) model that took advantage of shorter-term fluctuations in stocks and bonds to earn extraordinary returns during that time.

Source: Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Please see our Performance and Disclaimer pages for more information.

Smart Beta and Low Volatility

Since most investors are not familiar with the benefits of dual momentum, they have gravitated toward factor-based “smart beta” funds. According to Morningstar, the amount of assets in smart beta funds grew from $103 billion in 2008 to $616 billion at the end of 2015. As of October 1 of last year, $110 billion of that was in “low-volatility” funds, which investors may think lessen the risks of investing.

BlackRock projects that smart beta ETF assets will reach $1 trillion globally by 2020 and $2.4 trillion by 2025 [1]. This is an annual growth rate of 19%, double that of the overall ETF market. Low volatility and factor (multi and single) funds are expected to be key drivers of this growth. They represent more than 60% of new smart beta inflows through 2025.

Smart beta ETFs saw $31 billion in new fund flows globally in 2015 with minimum low volatility ETFs accounting for $11 billion of it.  The largest of these low volatility ETFs, the iShares Edge MSCI Min Vol USA ETF (USMV) has $13 billion, and 40% of those assets were contributed just this year.

The large inflow of capital into low volatility stocks has bid up the return of USMV for 2016 to 8.6% versus 3.5% for the iShares S&P 500 ETF (IVV). The P/E ratio of USMV on a trailing 12-month basis is now 24.8 versus 18.8 for the S&P 500. The P/B ratio of USMV is 3.2 versus 2.5 for the S&P 500. Arnott et al. (2016) show that high valuations of factor and smart beta strategies are negatively correlated with future returns. Investors jumping on the low volatility bandwagon now may be disappointed when prices return to more normal levels.

Smart Beta Issues

What about the advantages that smart beta in general are supposed to give investors? A Vanguard study showed that smart beta outperformance relative to cap-weighted benchmarks from 2000 through 2014 can be traced to systematic risk-factor exposures. After accounting for market, size, and value risk factors, none of the smart beta strategies showed results that were significantly different from zero. In most cases these strategies produced negative excess returns after accounting for their risk-factor exposure.
Source: "An Evaluation of Smart Beta and Other Rules-Based Active Strategies", Vanguard Research, August, 2015

Glushkov (2015) looked at the performance of 164 smart beta ETFs from 2003 through 2014 with respect to benchmarks based on size, value, momentum, quality, beta, volatility and other risk factors. He also found  no conclusive evidence that smart beta ETFs outperformed their risk-adjusted benchmarks over this period.

Data Overfitting

Backtest overfitting is also a serious problem for smart beta strategies. Suhonen et al. (2016) examined 215 smart beta strategies across five asset classes. They found a median 73% deterioration in the Sharpe ratio between backtest and live performance periods.

Source: Suhonen et al. (2016)

The deterioration of Sharpe ratios was most pronounced among the most complex strategies. Their reduction in Sharpe ratios was 30% higher than those of the simplest strategies. As other research has shown, intensive back testing and complex modeling often pick up more on noise patterns in the data than on the underlying signal processes.

Unrecognized Risks

Very few still believe that the markets are perfectly efficient. Since there is plenty of contrary evidence now, many think it is not difficult to do better than the market. This can be a costly mistake. Most investors would be better off holding low-cost passive index funds than what they are doing. We should remember that smart beta is still just beta. It does not give higher risk-adjusted returns.
Furthermore, we can define risk in different ways. Academics equate risk with volatility, but that is too limiting. Long Term Capital Management, founded by academics, did well by exploiting derivative mispricing. But unforeseen liquidity risk wiped out all their gains and most of their capital. It also nearly led to the collapse of the world’s financial system.[2]

There are also unrecognized risks among the more popular investment factors. Some people were surprised that value and momentum were left out of Fama and French’s latest factor pricing model. But value investing has had eight steady years of severe benchmark underperformance. I call this kind of tracking error “relative performance risk.” It may explain why investors need higher returns from value investing.
There are unrecognized risks with stock momentum investing as well. Momentum works best with focused portfolios of 100 or fewer stocks and when portfolios are rebalanced frequently. There is now substantial capital invested in single and multi-factor funds that use stock momentum. More capital is coming into momentum at an increasing rate. Every month AlphaArchitect freely discloses (to self-described investment professionals) on their website the top 100 momentum stocks. But stock momentum is a high turnover strategy with 25-30% of the portfolio typically replaced with every rebalance. There is bound to be a significant scalability problem when hundreds of billions of dollars tries to enter and exit the same 25 or 30 stocks each quarter.

Momentum also favors volatile stocks with wide bid/ask spreads. Wide spreads combined with high portfolio turnover lead to high transaction costs that can eliminate much of the excess return we see when we backtest momentum strategies.

Sensible Alternatives

Markets are not easy to beat when you consider all the risks. Ironically, many investors in smart beta or other actively managed funds pay higher expense ratios in order to underperform. Compare that to the cap-weighted Schwab U.S. Large-Cap ETF (SCHX) that holds 750 stocks. Its annual portfolio turnover is just 4%, and its expense ratio is only .03%. That makes SCHX hard to beat as a buy-and-hold investment.

Keep in mind that cap-weighted indexes have a built in momentum slant without scalability or transaction cost issues. As small companies grow and prosper, they naturally become an increasing part of a cap-weighted portfolio, while poor performers receive less weighting over time.Cap-weighting lets your profits run on and cuts your losses short.

For example, the largest stock holding in the S&P 500 index is Apple. It is worth more than General Electric, General Motors, and McDonalds combined and more than the 100 smallest holdings combined. How many bought Apple in December 1982 when it became part of the S&P 500 index at a price of 48 cents a share (adjusted for dividends) and have held it continuously since then?  Investors often prefer more complicated approaches that sound good, like smart beta or multi-factor funds, but simpler usually is better.  

[1] BlackRock Global Business Intelligence, May 10, 2016
[2] See When Genius Failed: The Rise and Fall of Long-Term Capital Management by Roger Lowenstein (2000).

April 28, 2016

What You Should Remember About the Markets

Because I have been an investment professional for more than 40 years, I sometimes get asked my opinion about the markets. These questions usually come from those without  a systematic approach toward investing. Here are some typical questions and answers:

Question: How much do you think the stock market can drop?
Response: 89%
Question: What?!!
Response: Well, that is the most it has dropped in the past. But past performance is no assurance of future success, so I guess it could go down more than that.

Question: I just looked at my account, and it is down. What should I do?
Response: Stop looking at your account.

Question: What are you doing now?
Response: What I always do … following my models.

After these responses, I am usually not asked any more questions.

Simple But Not Easy

Some say investing is simple, but not easy. This is due to myopic loss aversion, which combines loss aversion, where we regret losses almost twice as much as we appreciate gains, with the tendency to look at our investments too frequently.

We should remember that we cannot control the returns that the markets give us, but we can control what risks we are willing to accept. If we do not have systematic investment rules, it is easy to succumb to our emotions that cause us to buy and sell at inappropriate times. The annual Dalbar studies show that investors generally make terrible timing decisions.

But investing does not have to be difficult if we have firm rules in place to keep us in tune with market forces. A sailor cannot control the wind, but she can determine how to take advantage of it to get her where she wants to go.

I have found the most important principle to keep in mind is the old adage “the trend is your friend.” As some say, "the easiest way to ride a horse is in the direction it is headed." To remind me of how important it is to stay in tune with the long-term trend of the markets, I have this on my office wall:


Trend Following

Many are familiar with this saying, but few have the ability to always adhere to it. Much of Warren Buffett’s success is because he had the vision to stick with his approach over the long run no matter how the markets treated him. Buffett once said, “You don’t have to be smarter than the rest. You have to be more disciplined than the rest.” This discipline applies not only to staying with existing positions. It also means re-entering the market when your approach calls for it, even though uncertainties may still exist.

What gives me the ability to stay with the long-term trend of the market? First is knowing how well trend following has performed in the past. Let us now look at that, as well as how I determine the trend of the market.

Absolute Momentum

There are different approaches to trend following, such as moving averages, charting patterns, or various technical indicators. The trend following method I prefer is absolute (time-series) momentum. It has some  advantages over other forms of trend following. First, it is easy to understand and to back test. It looks at whether or not the market has gone up or down over your look back period.

In my research going back to 1927, absolute momentum had 30% fewer trades than comparable moving average signals. From 1971 through 2015, our Global Equities Momentum (GEM) dual momentum model had 10 absolute momentum trades that exited the stock market and had to reenter within a 3 month period. A 10-month moving average had 20 such exits and reentries. The popular 200-day moving average had even more signals. Fewer trades mean lower frictional costs and fewer whipsaw losses. 

You do not need to enter and exit right at market tops and bottoms to do well. In fact, if your investment approach is overly sensitive to price change and tries to enter and exit too close to tops and bottoms, you will often get whipsawed.

Because of whipsaw losses and lagging entry signals, trend following often underperforms buy-and-hold during bull markets. This is the price you pay for protection from severe bear market risk exposure.

But since absolute momentum has a low number of whipsaw losses, the relative momentum part of dual momentum can put us ahead in bull markets over the long run. Absolute momentum can then do its job by keeping us largely out of harm’s way during bear markets. The tables below show how absolute momentum, relative momentum, and dual momentum (GEM) have performed during bull and bear markets since 1971. Dual momentum has outperformed in bull markets while converting bear market losses into crises alpha profits.

Bull and Bear Market Performance January 1971 - December 2015 

Bull Markets
S&P 500
Abs Mom
Jan 71-Dec 72
Oct 74-Nov 80
Aug 82-Aug 87
Dec 87-Aug 00
Oct 02-Oct 07
Mar 09-Jul15
Bear Markets
S&P 500
Rel Mom
Jan 73-Sep 74
Dec 80-Jul 82
Sep 87-Nov 87
Sep 00-Sep 02
Nov 07-Feb 09
Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Please see our Disclaimer page for more information.


My research paper, “Absolute Momentum: A Simple Rule-Based Strategy and Trend Following Overlay” showed the effectiveness of absolute momentum across eight different markets from 1974 through 2012. Moskowitz et al (2011) demonstrated the efficacy of absolute momentum from 1965 through 2011 when applied to equity index, currency, commodity, and bond futures. In “215 Years of Global Asset Momentum: 1800-2014,” Geczy & Samonov (2015) showed that both relative and absolute momentum outperformed buy-and-hold from 1801 up to the present time when applied to stocks, stock indices, sectors, bonds, currencies, and commodities.

Greyserman & Kaminski (2014) performed the longest ever study of trend-following. Using trend following momentum from 1695 through 2013, they found that stock indices had higher returns and higher Sharpe ratios than a buy-and-hold approach. The chance of large drawdowns was also small compared to buy-and-hold.  The authors found similar results in 84 bond, currency, and commodity markets all the way back to the year 1223! Talk about confidence building. These kinds of results are what give me the ability to stay with absolute momentum under all market conditions.

Market Overreaction 

I have some clients though who are less familiar with and sanguine about trend following. They still get nervous during times of market stress, such as August of last year. They need to also understand that stocks do not trend all the time. The stock market can overextend itself and mean revert over the short run. During such times it is important for investors to stay the course and not overreact to short term volatility.

To remind me to remind others about short-term mean reversion, I have this coffee mug in my office:


This tells me to ignore market noise and calmly accept occasional market overreactions that are usually followed by mean reversion. There is no way to get rid of short-term volatility and still earn high returns from our investments. We should, in fact, embrace short-term volatility since it is what leads to superior returns over the long run.

What to Remember

Rigorous academic research confirms the existence of trend persistence and short term mean reversion. Whatever your investment approach, if you respect these two forces you should be able to invest with comfort and conviction. Being aware of these principles gives us the two qualities required for long run investment success. First is the discipline we need to follow your proven methods unwaveringly.

The second is patience.

Warren Buffett said the stock market is a mechanism for transferring wealth from the impatient to the patient. Like Buffett, we also need to patiently accept inevitable periods of short-term volatility and underperformance with respect to our benchmarks.

If you have trouble always remembering the concepts of trend persistence and mean reversion, then do what I do. Get yourself a poster and coffee mug.

March 25, 2016

Momentum for Buy-and-Hold Investors

There are many investors who prefer to remain invested in stocks at all times. Perhaps they think tactical allocation is some kind of voodoo. Maybe they have a strong psychological bias against occasional whipsaw losses and do not mind bear market drawdowns. Maybe they have institutional constraints requiring them to always be in stocks. Whatever the reason for their buy-and-hold orientation, let us see how they or anyone can use relative momentum (half of dual momentum) to get improved investment results.

Our core holding will be the S&P 500. To use relative momentum, we need at least two assets. We will use the MSCI All Country World Index ex-US (ACWI ex-US) as our second one. Each month we will invest in whichever of these two has performed better over the preceding 12 months.

Here are the results from January 1971 through February 2016 for this simple momentum approach rebalanced monthly. Relative momentum allocates to the S&P 500 55% of the time and to the ACWI ex-US 45% of the time. Transaction costs are negligible, since there is on average less than one trade per year. There is also little in the way of tracking error and no whipsaw losses where you are left on the sidelines as the stock market advances.

S&P 500
Annual Return
Standard Deviation
Sharpe Ratio
Worst Drawdown
- 54.2
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.
Using relative momentum, there is almost a 300 annual basis point increase in return compared to holding each asset or a blend of both assets!  Please look closely at the following performance chart to see how these increased profits come about.

How We Earn Momentum Profits

From 1975 through 1990, ACWI ex-US outperformed the S&P 500. Relative momentum invested in the ACWI ex-US then similarly outperformed.  The S&P 500 did better than ACWI ex-US from 1990 through 2000. Relative momentum switched over to the S&P then and so also outperformed the ACWI ex-US. Both indices moved together until 2003 when ACWI ex-US outperformed  the S&P 500. Momentum switched back to the ACWI ex-US and also beat the S&P 500. In 2009, the S&P 500 took the lead again ,and momentum once again moved higher with the S&P 500. It is as if each time a faster train comes along, relative momentum hops on board to win the investment race.

Who would not do something like this to earn an extra 300 basis points per year? You could easily do this strategy using just broad-based U.S. and non-U.S. stock funds in 401K retirement accounts and variable annuity contracts.  If you do not want to bother checking SharpCharts monthly to determine the funds’ annual returns, you can set up a free account with Morningstar. They will regularly email you the annual return information.

Why Global Diversification Works

The only concern I have heard about this strategy is that the world is now more globalized. There may no longer be as much to gain from geographic diversification. It is true that many large corporations derive a significant amount of their revenue from international operations. But corporate profits have little to do with the difference in return between U.S. and non-U.S. stocks. As the following chart shows, the relative performance of these markets depends largely on the strength or weakness of the U.S. dollar.


Chart courtesy of

When the U.S. dollar is strong, U.S. stocks tend to outperform non-U.S. stocks. Non-U.S. stocks outperform when the U.S. dollar is weak. Our simple relative momentum strategy takes advantage of global macro-economic trends. Just as it does not make sense to be simultaneously long and short the U.S. dollar, so it not the best idea to be long U.S and non-U.S. stocks at the same time. It would be better to own U.S. stocks when the U.S. dollar is strong, and to own non-U.S. stocks when the U.S. dollar is weak. Relative momentum automatically puts us on the right side of this macro-economic trend. There is no need to pay for global macro management.

Two Types of Diversification

There are two types of diversification in the world of investing. The usual method of vertical diversification stacks one asset up on top of others. It owns them all at the same time, which means some will underperform and create a drag on performance.

Momentum uses horizontal (or temporal) diversification that invests only in the strongest asset(s). As we saw in the chart above, this translates into higher returns as we move forward in time and rotate our exposure to the strongest asset. Momentum thus depends on persistence in performance. Momentum improves the performance of nearly every asset class from the year 1800 to the present [1].

The question then is should we use momentum in a macro manner as shown above, or apply it to individual stocks as done by most momentum and multi-factor funds? Multi-factor approaches are now becoming especially popular. (See our blog post, “Multi-Factor Investing.”)

Macro Momentum versus Stock Momentum + Value

Let us compare our macro momentum strategy to a multi-factor approach with individual stocks. We will use the two most popular factors: value and momentum. Value and momentum represent the two strongest anomalies. Others have also argued that they complement each other and perform well together.

For value, we use the MSCI USA Value Index that selects the top half of large and mid-cap stocks on the basis of price-to-book, price-to-forward earnings, and dividend yield. This index currently holds 319 stocks and has a 17% annual turnover.

For momentum, we use the MSCI USA Momentum Index that selects the top 30% of large and mid-cap stocks based on a combination of 6 and 12-month momentum adjusted for volatility. This index currently holds 122 stocks and has an annual turnover of 137%.

Both MSCI indices rebalance semi-annually and began in January 1975. None of the indices accounts for  transaction costs. Here is our macro momentum strategy compared to the 50/50 split between these two MSCI indices from January 1975 through February 2016.

MSCI 50/50
S&P 500
Annual Return
Standard Deviation
Sharpe Ratio
Worst Drawdown

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.

Our macro momentum approach had the highest Sharpe ratio. It returned an average annual 150 basis points above the combined stock momentum plus value portfolio. It also had a strong 270 basis point annual return advantage over the S&P 500.

Scalability and Trading Costs

But that is not the whole story. We should also consider scalability issues and transaction costs. Holding fewer stocks and rebalancing more frequently leads to higher returns. The following table shows compound annual growth rates (CAGRs) of value-weighted portfolios using a universe of the largest 500 U.S. stocks.

Table courtesy of AlphaArchitect

The ideal stock momentum portfolio is highly concentrated and rebalances monthly. Momentum fund managers know this, and nearly all of them limit the size of their momentum portfolios to 150 or fewer stocks. Ten of the twelve momentum funds also rebalance their portfolios at least quarterly.

The MSCI momentum index that rebalances semi-annually rather than quarterly has an annual turnover of 137%. Passive indices like the S&P 500 or the ACWI ex-U.S. have an annual turnover of only around 3%.

In 2006, there were no publicly available momentum funds. Today there are a dozen funds dedicated to U.S. stock momentum. There are also more than a dozen multi-factor funds using momentum (see “Multi-Factor Investing”).  Every month our friends at AlphaArchitect post the top 100 momentum stocks. So momentum investing with individual stocks is no longer a neglected strategy.

In their paper, “Are Momentum Profits Robust to Trading Costs?” Korajczyk and Sadka (2004) show that momentum profits drop to zero once the amount of momentum assets reaches $2 to $5 billion. We are already well past that level. Imagine what will happen when hundreds of billions of dollars tries to trade the same small number of momentum stocks each quarter.

Related to scalability is the issue of transaction costs. In “The Illusory Nature of Momentum Profits,” Lesmond, Schill, and Zhou (2002), use a conservative procedure to estimate annual stock momentum trading costs at nearly 7%. This reduces stock momentum profits down to near zero. Momentum is not only  a high turnover strategy, but momentum stocks are often more volatile and have higher bid ask spreads.

Frazzini, Israel, and Moskowitz (2012) of AQR argue that momentum trading costs are manageable based on AQR’s own 12 years of proprietary transaction data from 1998 through 2011. But the amount of capital in momentum strategies is now much higher now. In the latest published research, Fisher, Shah, and Titman (2015) use observed bid-ask spreads and report, “Our estimates of trading costs are generally much larger than those reported in Frazzini, Israel and Moskowitz (2012), and somewhat smaller than those described in Lesmond, Schill and Zhou (2004) and Korajczyk and Sadka (2004).” Also, Jason Hsu PhD, co-founder of Research Affiliates, has a forthcoming report showing large-cap stock momentum returns with quarterly rebalancing being less than the large-cap market return due to trading costs.

Since our relative momentum strategy uses stock indices, scalability is not an issue. We can trade almost unlimited amounts of capital in broad-based U.S. and non-U.S. stock index funds with hardly any impact on trade executions. Transaction costs are also a moot point. There is less than one trade per year with this approach.

The simple momentum strategy presented above can help buy-and-hold investors meet their investment goals without the uncertainties associated with high transaction costs, scalability, or other similar factors. Even without adjustments for those factors, our simple momentum strategy showed an annual 150 basis point advantage over stock momentum combined with value, and a 270 basis point advantage over the S&P 500 index.

[1] See Geczy and Samonov (2015), “215 Years of Global Multi-Asset Momentum: 1800-2014 (Equities, Sectors, Currencies, Bonds, Commodities and Stocks)”. They show that momentum is consistent and robust. It works with and across different asset classes. It works best, however, with stock indices.