June 28, 2018

The Evolution of Investing

I began my investment career in 1974. In 1976 I left a large retail brokerage firm to join a premier investment bank. I had both retail and institutional clients. So I had a well-rounded knowledge of Wall Street.

The 1970s was soon after the dark ages of investing. Modern portfolio theory existed in the academic but not the real world.

Looking at how investing has progressed since then, I thought it would be interesting to trace its evolution both in theory and in practice. Perhaps we can learn something from the past.

1960s and earlier

Modern portfolio theory began with Markowitz’s work in the 1950s. He called this approach mean-variance optimization (MVO). Markowitz used quadratic programming to construct efficient portfolios with past returns and covariances as inputs. Efficient portfolios have the least amount of variance at a specified level of expected return or the highest expected return at a specified level of volatility.

The problem with Markowitz’s approach is it did not work well in practice. This is because model inputs, especially past returns, are not stable going forward. Errors are multiplicative and become large due to the quadratic nature of the MVO model. At first, no one knew this problem existed because implementing MVO was impractical then. Matrix inversions with thousands or even just hundreds of stocks challenged computing capabilities at that time.

In the 1960s researchers simplified Markowitz’s approach by developing the Capital Asset Pricing Model (CAPM). This was an elegant solution to the portfolio allocation problem using a linear model. Researchers found they could regress assets against the S&P 500 to create “beta.”  You could determine your risk exposure by looking at the beta of your portfolio. Beta became king in academic finance and with institutional investors. It was used for portfolio construction and capital budgeting. It’s corollary, “alpha”, was used for institutional performance evaluation. All assets and portfolios was characterized solely by their performance relative to the S&P 500 index.

Institutions owned less than 10% of U.S. equities back then. Retail brokerage offices were ubiquitous. Brokers pitched stories about companies to clients who paid high fixed brokerage commissions. When recommended stocks went up, clients were encouraged to lock in profits. When stocks went down or were unchanged, clients were urged to sell and buy more promising ones.

Most brokerage accounts were under diversified and over traded. Brokers recommended glamour stocks to aggressive investors. They touted bonds or defensive stocks, like utilities, to conservative investors. Blue chips were core holdings for most investors.


Even though fixed commissions ended in 1975, most brokerage firms kept their commission costs high. They figured investors would pay them to get recommendations and to keep their accounts at big-name brokerage firms. Discount brokerage firms were largely unknown.

The first public index fund was started by Vanguard in 1976 with $11.3 million. Many called it “Bogle’s Folly.” Malkiel (1995) and Fama and French (2009) showed that active funds underperform the market by the amount of their fees.

But most investors were unwilling to settle for being average. By competing against each other using the same information, investor returns were not average. After costs and fees, they were below average.

Some academics began to question the supremacy of single-factor beta. Barr Rosenberg, a Cal finance professor, setup BARRA as a consulting firm to institional investors. BARRA looked at 20+ additional items when doing linear modeling. Their "extra-market covariances" were the precurser of today's factor-based investing.

Institutional participation in stocks was still low then. The public continued to rely on brokerage firms and their recommendations.


In the 1980s more academic ideas began to filter into the marketplace. Sophisticated investors recognized the need for a portfolio of at least 30 well-diversified stocks to reduce idiosyncratic risk. Mutual funds that performed well garnered attention. Peter Lynch’s no-load Magellan Fund attracted a large following. Many other funds had front-end loads to compensate selling brokers. Investments were promoted and sold to existing clients back then more than they were bought by informed investors.

Research departments began to pay attention to international diversification after academics showed that it reduced portfolio variability. Beta was used more frequently as a measure of market exposure.


In the 1990s there was more recognition of modern portfolio theory. This meant more interest in the efficient market hypothesis and index funds. CAPM expanded to include size and value as additional factors. This was soon followed by momentum.

Discount brokers became accepted, no-load funds gained market share, and institutional ownership of equities expanded. But with average equity returns of 17% per year in the 1980s and 1990s, most investors were reluctant to change how they actually invested. It was still a stock pickers world, but methodical asset allocation began to get more attention from institutional investors.

We began to see more "closet index" funds. These closely tracked passive indices but charged active management fees that adversly affected performance. These number of closet index funds has continued to grow since then.


Investor attitudes changed dramatically in the 2000s due to the severe 1999-2000 and 2008-2009 bear markets. Many investors abandoned equities. Some never returned. There was more focus now on risk exposure. Alternative investments, such as commodities and hedge funds, attracted both institutional and individual investor interest. Advisors stressed greater diversification, often in the form of Global Asset Allocation (GAA). Meb Faber’s popular IVY 5 portfolio was an example of that. Pricing models expanded to include additional factors to better explain asset returns.


Indexing has continued to attract followers. But it still resides in the shadow of active management. According to Morningstar, only 19% of the U.S. stock market is owned by index funds. Thirty percent of mutual funds, 15% of institution investing, and 5% of global investing use low-cost indexing. It is surprising there has not been more interest in indexing given that 83% of mutual funds underperformed the market over the prior 10 years.

The latest “improvement” on index funds is factor investing. Factors (and related smart beta) are based on quantitative analysis of past data. Investors are receptive to factor investing because they think it may offer them better returns than an index fund at a lower cost than traditional active management.

Investors often also think complicated approaches are better than simpler ones. The opposite is actually true. Simpler approaches are less likely to suffer from data snooping, selection bias, and overfitting issues. Complicated approaches are not as viable as simpler methods, but investors will pay up for them.

As with commodities and hedge funds in the 2000s, the performance of factor-based investing has been disappointing since they became popular. The size factor has failed to provide an advantage ever since it was introduced in 1982. Back in 2006 Loughran and Hough presented evidence that cast doubt on the efficacy of value fund investing.

Yet many advisors and investors ignore or dismiss real-world factor performance. They still reference theoretical results. Those rely on data before factors were widely used and their trading impacted asset returns. See here for more on the issues associated with factor investing.


What can we expect to see in the future?  Indexing should continue to grow modestly. Early this year John Bogle said index funds took in $3.3 trillion in net cash flow over the past 10 years. Active funds took in just $150 billion, or only 5% of total industry cash flow.

Institutional investors and fund sponsors are subject to the same prejudices as everyone else, and maybe even more so. They have been exposed to factor research since 1992 or earlier. At least 16 multi-factor funds were set up duriing the past two years. All of them included the value factor, and one-quarter included the size factor.

Entrenched investment prejudices are hard to overcome. Many still think small stocks outperform larger ones on a risk-adjusted basis.

Most of us are used to looking for bargains. We think value investing represents a bargain. But we may not be factoring in the risks associated with value.

Continued growth in factor-based investing is expected from both retail and institutional investors. See here and here.

Trend has now been getting attention from academics. See here for more on this. Below is Meb Faber’s IVY 5 GAA (Buy and Hold) portfolio with the addition of a trend filter to create a Global Tactical Asset Allocation (GTAA) portfolio.

                               Source: Faber (2007), “A Quantitative Approach to Tactical Asset Allocation

Tactical approaches were looked upon as “voodoo” for many years by academics and academically trained investment professionals. Institutional investor prejudice in the opposite direction may make it difficult though for trend to become widely accepted. This is reinforced by the fact that institutional investors continue to have a dominant influence on investing. Individuals now hold only $4 trillion of the $27 trillion invested in U.S. stocks.

This is good news for those of us who use trend as a component of our investment models. Reluctance to accept trend should lessen the chance of crowding out future returns.


There are things we can learn from the history of investing:

1)    It is not easy to beat the market after accounting for risks, costs, and fees

Markets are highly competitive, so it hard to find an edge. There are worse things you can do than buy a passive index fund. Warren Buffett instructed his heirs to put 90% of their inheritance in an S&P 500 index fund and 10% in short-term U.S. debt instruments.

2)    Costs are important and easily controllable

Vanguard estimates that paying 110 bps (the average active management fee) over 30 years would erode a portfolio’s market value by 25%. All investors should pay close attention to their investmment costs. That is the simplest and easiest way to create alpha.

3)    Diversification is still the closest thing to a free lunch

When you invest in multiple assets, your expected return is the weighted average of those asset returns. But portfolio volatility is reduced if those assets are less than perfectly correlated to one another. Diversification can also help mitigate the uncertainty of assets continuing to perform in the future as they have in the past. The downside of traditional diversification is that assets having a lower expected return create a drag on portfolio performance.

Closely associated with trend is the idea of temporal diversification where you invest in the strongest assets over time. This is also the same as relative strength momentum investing. Weaker assets do not create a drag on portfolio performance because you do not invest in them until their performance improves. Using temporal diversification, portfolios can have a higher return than the weighted average return of its individual assets. Relative strength momentum is a more intelligent way to diversify.

4)   Don't be firmly attached to your investment beliefs

As we have seen, investment ideas evolve over time. CAPM was once regarded as sacrosanct.  Fisher Black (who would have received the Nobel Prize had he lived a few more years) said of CAPM, “The theory is right. It just doesn’t work.”  The same is true of MVO. Portfolio insurance is another concept born in academia that failed miserablty in practice. Investors should not be too surprised if today's popular investment approaches do not live up to their expectations.

What should we do then? First, we can keep up on financial research. We should also remain flexible enough to change our approach based on evidence, not convention. If we are unwilling to do these two things, we could do a lot worse than investing in low-cost passive index funds.

April 9, 2018

Common Misconceptions About Momentum

Momentum is one of the most researched topic in financial market literature. A search of the SSRN database on momentum will turn up 1000 papers written over the past three years and 3000 papers in total.

With so much information available, it is not be surprising that many analysts have missed seeing some of the research. Their views of momentum reflect this fact. Based on the way momentum is generally used, it is clear there are some serious misconceptions about it. Here is my discussion of some of the more serious ones.

1) "Momentum is best used with individual stocks."

Initial academic research on momentum by Jegadeesh and Titman (1993), Asness (1994), and others focused on U.S. stocks. This explains why momentum was initally associated with stock investing.

But to see if momentum was robust, researchers soon applied it to other markets. Momentum was found to be effective not only with U.S. stocks. It also performed well with international stocks, industry groups, stock indices, bonds, real estate, commodities, and currencies.

When I started to do my momentum research in 2010, I wanted to look at it from a practical point of view. My goal was to determine how one might best use it. I applied momentum to U.S. stocks, industry and style groups, and world regional stock indices. In 2011, I wrote my first momentum paper called “Global Momentum: A Global Cross Asset Approach.” It showed that momentum worked best with regional stock indices.

In 2015, Geczy and Samonov did a more comprehensive study called “Two Centuries of Multi-Asset Momentum (Equities, Bonds, Currencies, Commodities, Sectors, and Stocks).” They looked at momentum with country equity indices, government bonds, currencies, commodities, sectors, and U.S. stocks back to 1801. Momentum gave significantly positive results versus buy-and-hold in all areas. They also found momentum worked best with geographically diversified stock indices. Below is an example showing geographic stock index momentum.

About half the capitalization of global equities is in U.S. stocks. The other half is, of course, in non-U.S. stocks. We will compare the performance of the S&P 500, representing U.S. stocks, to the MSCI ACWI ex-US, representing the rest of the world. Each month we invest in whichever of the two has had better performance during the past 12 months. 

We use a 12-month look back because that was found to work by Cowles and Jones in 1937. It has been used in research ever since then.  We need not worry about selection bias since we are using all areas of the world. Data mining is also not an issue, since we are using a long-established model parameter for the look back period. There is on average less than one trade per year. So there are no trading impact issues. Here are the results from 1971 when non-U.S. stock index data became available.

1/1971 to 3/2018
S&P 500
Annual Std Dev
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. Positions are rebalanced monthly. Please see our Disclaimer page for more information.

This simple momentum model is always invested in stocks, so there is little tracking error. The momentum strategy shows an increase in annual return of 160 basis points versus both the S&P 500 and a 50/50 U.S./non-U.S. allocation. Most investment managers would be happy over the long-run to outperform the market by 160 bps annually with comparable risk. Yet no one, as far as I know, is using this simple strategy.

Neither my nor Geczy and Samonov’s research took into account the price impact of trading. This would have made equity index investing even more attractive versus momentum applied to individual stocks.

There is considerable controversy regarding trading impact costs when momentum is applied to individual stocks. See here for details. The most recent paper on the subject is by Patton and Weller (2017).  In What You See Is Not What You Get: The Costs of Trading Market Anomalies,” they review previous studies. They then use two different methods to do determine the trading impact of momentum on stocks. They conclude: “Our estimates… imply that implementation costs erode almost the entirety of the return to value and momentum strategies... momentum profits, in particular, may be out of reach for the typical asset manager.”

Despite the issue of price impact and the documented superiority of momentum used with geographic indices, nearly all momentum funds use momentum with individual stocks. One cannot help but wonder why this is. It is likely for the very same reasons momentum works. These include the slow diffusion of information (research results), anchoring to prior beliefs, and underreaction to new information. My experience leads me to think there is also an irrational preference for stocks over indices.  

2)  "Momentum is best used on a relative strength, cross-sectional basis."

There is plenty of research on cross-sectional, relative momentum that compares assets to one another. All momentum research between 1993 and 2010 was of this type. It was not until 2012 that Moskowitz, Oii and Pedersen published a paper called “Time Series Momentum.”  In early 2013, I released a paper called “Absolute Momentum: A Simple Rule-Based Strategy and Universal Trend Following Overlay.” These two papers established absolute (time-series) momentum as another type of momentum.

Absolute momentum is a form of trend following based on autocorrelation. It assumes assets that have been strong over time will continue to be strong.

Absolute momentum is as universal and consistent as relative momentum. Using at least 25 years of data applied to equity index, currency and commodity futures, Moskowitz et al. showed persistent returns for absolute momentum. They found it performed best in extreme markets and had little exposure to standard asset pricing factors. This gives it considerable value as a portfolio diversifier.

My paper applied absolute momentum to stock index, bond index, real asset, stock/bond balanced, and risk parity portfolios.  It showed that absolute momentum can help identify regime change and add value as both a stand-alone strategy and as a portfolio overlay.

In their 2012 paper, “A Century of Evidence on Trend-Following Investing,” Hurst, Oii, and Pedersen applied absolute momentum to equity indices, bond indices, commodity futures, and currencies. They found it was consistently profitable across decades ever since 1903.

The amount of research done on absolute momentum has been catching up with relative momentum. If you do a search on “time series momentum” (the preferred academic term) on SSRN, you will find over 200 papers. One might wonder whether relative or absolute momentum gives better results.

Bird, Gao, and Yeung (2017) in their “Time Series and Cross-Sectional Momentum Strategies Under Alternative Implementation Strategies” applied relative and absolute long/short momentum to stocks in 24 developed markets from 1990 to 2012. They found positive returns from both forms of momentum under alternative implementations. But they concluded that “time-series momentum is clearly superior,” and “momentum is best implemented using time-series momentum.”

On the other hand, Goyal and Jegadeesh (2017) concluded that relative and  absolute momentum performed similary for individual stocks after adjusting for time-varying net long investment.

D’Souza, Srichanachaichok, Wang, and Yao (2017), in their “The Enduring Effect of Time-Series Momentum on Stock Returns Over Nearly 100-Years”, studied long/short absolute momentum in U.S. stocks from 1927 to 2014 and in international stocks since 1975. They found absolute momentum could entirely account for relative momentum. Absolute momentum performed well in both up and down markets. Unlike relative momentum, absolute momentum did not suffer from January losses and market crashes.

Despite the evidence that absolute momentum performs at least as well as relative momentum, almost every momentum fund uses only relative momentum. The reasons for this may be the same as to why investors prefer momentum with stocks instead of indices – the slow diffusion of research results and anchoring that overweights prior research. But there may also be other reasons. First, there is a long-standing bias against tactical approaches such as trend following. What many don’t realize is all momentum is a form of trend following. Relative momentum looks at trends between assets. Absolute momentum looks at the trend of an asset itself over time.

Another reason absolute momentum has not been as well received may be its tracking error, especially during bull markets. Absolute momentum is known to outperform in bear markets. But in bull markets, whipsaw losses and trading lags can constrain the performance of absolute momentum portfolios. That is why some advisors use trend following only for satellite positions within diversified portfolios.

There is no way to eliminate all tracking error. But I show in my post “Why Does Dual Momentum Outperform” that momentum can lead to superior long-run performance in both bull and bear markets. Relative momentum can boost returns during bull markets. This can compensate for the whipsaw losses and performance lags of absolute momentum. Absolute momentum can reduce the downside exposure of relative momentum during bear markets. In my 2012 paper, I introduced the concept I called dual momentum. 

Based on the evidence above, if I had to choose between relative and absolute momentum, I would choose absolute momentum because of its risk-reducing characteristics. But there is no reason we cannot use both. D’Souza et al. looked at both forms of momentum individually, as well as dual momentum. They found that dual momentum applied to long-short stock portfolios generated striking returns of 1.88% per month.

3)  "Momentum (trend following) is not as reliable as diversification in reducing risk."

The first thing we need to understand is that momentum is all about diversification. Momentum diversifies by time as well as by asset class. This makes it adaptive to changing market conditions. Traditional fixed diversification creates a drag on performance from poorer performing assets. Many investors use bonds to reduce the volatility of an all-stock portfolio. But bonds (and most other assets) have a much lower long-run expected return than stocks. This creates a drag on portfolio performance.

Momentum can reduce performance drag by being only in assets when they are performing well. Here is an example comparing the performance of momentum versus a diversified fixed portfolio. For the fixed portfolio we will use Ivy 5 developed by Meb Faber. Ivy 5 holds equal size positions in indices of U.S. stocks, foreign developed stocks, intermediate bonds, REITs, and commodities.

For momentum, we will use the Global Equities Momentum (GEM) model featured in my book. GEM uses 3 assets and holds one at a time. It decides whether to be in stocks or bonds based on absolute momentum. When stocks are selected, it chooses either the S&P 500 or the MSCI ACWI ex-U.S. based on relative momentum.

Stocks have the highest risk premium of any asset class. That is why we want to be in them as much as possible, providing their trend is positive. As you can see, dual momentum has done a much better job in both reducing tail risk and improving risk-adjusted returns.

1/1973 to 4/2018
Annual Std Dev
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 and Performance pages for more information.

There are some who criticize trend following and systematic trading approaches because of what they call "timing luck". With some strategies, results vary a lot depending on what day of the month you rebalance your positions. This uncertainty causes some to trade portions of their portfolios at different times during the month (tranching). It also leads to doubts regarding the efficacy of systematic trading. This can also lead to more emphasis on traditional diversification.

Swinkels and van Vliet (2010) showed that stocks exhibit a statistically significant turn-of-the-month effect. The last trading day of the month and first few trading days of the next month outperform other days. This may be due to institutional portfolio rebalancing at or just before month-end. This rebalancing replaces poor performing stocks with better performing ones. It is sometimes called "window dressing." 

Momentum means persistence in performance. We want to be in portfolios after better performing stocks have replaced the laggards. This lets momentum work in our favor.

Our dual momentum models, which are most of the time in stock indices, do better by rebalancing on the first or second trading day of the month. This lets us exploit the turn-of-the-month momentum effect to our advantage.

AllocateSmartly is a service that tracks some systematic trading models after modifying some of them. Their reporting of our GEM model understates its performance by 90 basis points annually. This is because they substitute the MSCI EAFE index for the broader MSCI ACWI ex-US index that we use to represent all equity markets oouside the U.S. We avoid selection bias by using a non-US index of developed and emerging markets, not just developed ones.

Even though it is a misleading and inaccurate representation of our strategy, AllocateSmartly's analysis of what they call GEM does have some value. They evaluated performance over the past 363 months based on which normalized trading day of the month one uses to rebalance positions.  

Source: www.allocatesmartly.com

We see that the first and second trading days of the month have the highest Sharpe and Sortino ratios. These days are consistent with the turn-of-the month effect. That is why we use them for portfolio rebalancing.

If investors and advisors studied more of the literature on momentum and trend following, they would surely be impressed. There is nothing else that comes close in terms of results over long periods of time.

Besides the research mentioned above, here are a few other studies reinforcing these points. Clare et al. (2014) in “Size Matters: Tail Risk, Momentum, and Trend Following in International Equity Portfolios” looked at 20 developed and 12 developing countries from 1995 through 2013. They found limited evidence for the outperformance of relative momentum stock portfolios. Trend following though was observed to be a very effective strategy delivering superior risk-adjusted returns.  

Geczy and Samonov (2015) showed the effectiveness of absolute as well as relative momentum on 200 years of data. Lemperiere et al. (2014) in “Two Centuries of Trend Following,” looked at trend following across commodities, currencies, stock indices, and bonds since 1800. They found “the existence of trends one of the most significant anomalies in financial markets.” Their results were very stable across time and asset classes.

For those wanting even more history, Greyserman and Kaminsky (2014) in Trend Following with Managed Futures took trend following back 800 years! When applied to 84 different markets, absolute momentum showed a Sharpe ratio of 1.16 versus 0.47 for buy-and-hold. The worst drawdown of trend following was 25% less than buy-and-hold. The duration of its longest drawdown and the average duration of the longest five drawdowns were 90% and 80% shorter. The authors found trend following to have a low correlation with traditional asset classes, interest rate regimes, and inflation. It has also provided consistently positive performance during crisis periods.


The above are serious misconceptions about momentum that I hope I have cleared up. Those who have the wrong ideas about momentum and trend following and who ignore it true potential are missing out on opportunities that one could only imagine in days past.