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:

Source: Quotatium.com

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:

Source: Quotatium.com

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 Earned 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 SharpeReturns.ca

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 show that momentum trading costs are manageable based on AQR’s own 12 years of proprietary transaction data. But in the latest published research, Fisher, Shah, and Titman (2015) use observed bid-ask spreads and say, “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.

February 25, 2016

Dual Momentum and Dollar Cost Averaging

Last month a millennial emailed me saying he liked my book. But he wondered if the outperformance of dual momentum would disappear if he used dollar cost averaging (DCA) because he would not be able to buy  cheaply during bear markets. This is because dual momentum reduces bear market drawdowns. I showed him logically that he would actually end up with more shares at a lower average cost by using dual momentum along with DCA. I promised to post a more complete analysis using actual monthly returns.

DCA Benefits

Meanwhile, there was an internet article last week called “How Great Is Dollar Cost Averaging? You Don't Know the Half  of  It” by Eric D Nelson. The point of the article was that lackluster returns provide an opportunity to buy more shares at depressed prices.  Nelson gave an example of how the S&P 500 returned only 4.1% per year since 2000, but a DCA approach during these same years returned 8.5%. This is because you could buy more shares in the weak market years of 2001, 2002, 2008, and 2011. This turned volatility into a benefit.  Nelson concluded by saying DCA works well with stocks and not as well with portfolios containing both stocks and bonds.

Josh Brown (The Reformed Broker) in his post, "How to Make Volatility Your Bitch," used Nelson’s logic to make the point that a portfolio dropping in half twice during a 15 year period would outperform a portfolio having the same return but with zero drawdowns. This is due to the rebalancing profits of DCA. Our friend Jake (EconompicData) in his "Combining Momentum and Dollar Cost Averaging for Smoother Results," showed that regardless of volatility, a trend following moving average overlay applied to DCA could outperform DCA alone over the long run.

Relative Momentum

I will move this discussion forward and show how momentum and DCA reinforce and complement each other. Let us first look at a simple two asset relative strength momentum portfolio. We will use the S&P 500 and the MSCI All Country World ex-U.S. (MSCI World ex-U.S. before 1988) indices from January 1971 through January 2016. Every month we buy or hold whichever index had the higher total return over the past year.

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.

An initial $1000 investment would have grown to $265,176 for our relative momentum portfolio versus $86,443 for just the S&P 500 and $98,055 for a benchmark made up of the S&P 500 and MSCI indices in the same 55% to 45% ratio as the amount of their use in the relative momentum model over those 45 years [1]. The compound annual growth rate of the relative momentum portfolio was 13.2% versus 10.7% for benchmark portfolio and 10.4% for the S&P 500. The average number of transactions per year with relative momentum was less than one, so relative momentum did not suffer from high trading costs or scalability issues, as can happen with momentum using individual stocks. There is an annual 250 basis point advantage here over the benchmark portfolio by using relative momentum.

There is a mountain of academic research supporting the use of relative momentum. Geczy and Samonov (2015) showed that relative momentum has outperformed buy-and-hold all the way back to the year 1800, and momentum using stock indices has outperformed individual stock momentum. This was before  transaction costs. After transaction costs, the contest wasn’t even close.

We should take note that the world is now more globally connected than it once was. Many large U.S. corporations derive a large part of their revenue from international operations. Portfolio diversification using h U.S. and non-U.S. stocks now has more to do with the strength or weakness of the U.S. dollar than it does with stock market returns.

Source: Sharpereturns.ca

Since it is counterproductive to be both long and short the U.S. dollar, it makes more sense to invest in only U.S. stocks or non-U.S. stocks depending on which is stronger, rather than in both together. Adaptive diversification based on market condition is the key to momentum investing.

DCA with Relative Momentum

Let us see now how relative momentum does when combined with DCA. We start with $1000 and this time add $100 every month. The ending value of a DCA relative strength portfolio after 45 years is $2,844,126 compared to $1,073,465 for a DCA benchmark portfolio without the use of momentum. The internal rate of return (IRR) for the DCA relative momentum portfolio is 13.4% versus 10.4% for the DCA benchmark portfolio that does not use momentum. We get a 300 basis point annual increase in return by adding relative momentum to our DCA benchmark portfolio.  

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.

DCA with Dual Momentum

We will now extend our earlier logic where we said you cannot be both long and short the U.S. dollar, and we used relative momentum to select the better scenario. We can also say that the stock market cannot be going both up and down at the same time. Following the same logic as before, we will be in stocks when they are in an uptrend and move to the safety of bonds when stocks are in a downtrend. This is absolute momentum. When in stocks, we will use relative momentum to see whether we should be in U.S. or non-U.S. stocks. We will use DCA with this dual momentum and see what it does to our DCA profits. The dual momentum DCA benchmark will be 45% S&P 500, 25% MSCI All World ex-U.S., and 30% Barclays Capital U.S. Aggregate Bond (Ibbotson Intermediate Government Bond before 1976) index. This  is the allocation to each of these assets over the 45 year period using dual momentum.

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 Performance and Disclaimer pages for more information.
As with relative momentum DCA, the dual momentum DCA strategy has an initial $1000 investment with $100 per month additions. The dual momentum DCA strategy gives an ending value of $9,467,595. During this same period, the non-momentum DCA benchmark portfolio grew to $882,763. The IRR of the DCA portfolio with dual momentum was 17.0%, versus 9.8% for the DCA non-momentum benchmark portfolio. We get an increase in return of  over 700 basis points per year by adding dual momentum to DCA.We also get downside protection from being largely in bonds during bear markets in stocks.

When Bonds Are Good

The non-momentum DCA benchmark portfolio that is without bonds has a higher IRR than the non-momentum DCA  benchmark portfolio that uses bonds (10.4% versus 9.8%). The IRR of the dual momentum DCA portfolio that uses bonds adaptively to reduce bear market risk is substantially higher then the IRR of the relative momentum DCA portfolio that does not include bonds (17.09% versus 13.4%). But better returns is only half the story. The worst drawdown of the DCA dual momentum portfolio is less than half the worst drawdown of its non-momentum benchmark DCA portfolio.


Rules-based approaches are a good thing. They can provide a disciplined framework to help us overcome self-defeating behavioral biases. DCA is a worthwhile approach since it can counteract our natural tendency to buy as we become greedy and sell when we become fearful. This is the opposite of what we should do, according to Warren Buffett.

Adding relative momentum to DCA more than doubles DCA’s ending capital after 45 years. Adding dual momentum instead of relative momentum to DCA gives more than a ten-fold increase in ending wealth, and it does so with considerably less downside risk exposure.

DCA and dual momentum complement each other well. DCA converts volatility into higher returns, while dual momentum converts differential returns into higher  returns and provides important downside portfolio protection. Both DCA and dual momentum make it easier for investors to accept the volatility of their investments. For those who have to accumulate investment capital over time rather than go all in at once, DCA with dual momentum can be a great combination.

[1] This is about the same allocation as the capitalization weighted MSCI All Country World Index (57% S&P500 and 43% MSCI) that includes both U.S. stocks and non-U.S. stocks.