February 24, 2015

Do the Right Thing: Consider Persistence and Reversion

I used to always cut fruits and veggies in the wrong directions. I finally got around this problem by  turning them in the opposite direction to the way I initially wanted to cut them. Similarly, many investors and investment managers are making investment decisions the wrong way and need to reverse how they are going about this.

This problem began with the random walk hypothesis (RWH). That idea, popular in the 1960s and 1970s, said that stocks fluctuate randomly (in statistical terms, are independent and identically distributed). RWH is synonymous with the concept of efficient markets. As such, it eliminated serious interest in tactical asset allocation, trend following, or momentum investing among both academics and most institutional investors.

Some practitioners, however, were creating a substantial body of anecdotal evidence that stock fluctuations were not random, but instead showed short and long-term mean reversion, as well as intermediate- term serial correlation. 

Stock exchange specialists and brokerage firm trading desks made large profits going against short-term customer order flow, which gave them high short-term mean reversion profits. The success of momentum traders like Jack Dreyfus and Richard Driehaus showed that stocks could also exhibit price continuation (momentum). Successful long-term value investors, buying depressed stocks that would eventually recover and outperform the market, indicated that one can also earn long-term mean reversion profits from stocks.

In the mid to late 1980, academics began to catch up with practitioners in discovering the flows of RWH. Ironically, Fama and French (1988), two of the pioneers of efficient market theory, were among the first to show that stocks mean revert based on a 3 to 5-year time horizon. Around the same time, Lo and MacKinlay (1988) and Poterba and Summers (1987) came up with compelling evidence to reject RWH. In the early 1990s, Jegadeesh and Titman (1993) in their seminal papers demonstrated convincingly that price continuation momentum exists on a 3 to 12-month basis. Furthermore, they and others showed that stocks are mean-reverting when looking at one-month returns. They therefore skipped those returns when looking at intermediate-term stock momentum.

Showing just how far academics have come in accepting  12-month momentum (indicating positive serial correlation) , one-month mean reversion, and 3 to 5-year mean reversion, all three of these factors are now in the online Ken French data library for researchers to use in their studies.

So how does all this relate to how investors and investment managers are making poor investment decisions? First, there is still a cultural affinity to RWH despite all the evidence to the contrary. This leads many investors to ignore the profit opportunities inherent in momentum investing.

Next, investors and investment professionals often focus on the wrong time frames in judging investments. Goyal and Wahal (2008) report  that plan sponsors and institutional asset managers choose investment managers based greatly on performance over the past 3 years. Yet we know now that 3-year performance is mean reverting, and strong performance over that time frame is not indicative of similarly strong future results.

As another example, the Morningstar rating methodology weights 3-year performance more heavily than 5 or 10-year performance. If longer term performance is unavailable, ratings are based entirely on 3 year performance. The Vanguard Research report "Mutual Fund Ratings and Future Performance" (2010) found that from February 1992 through August 2009, there was no systematic outperformance by funds rated 4 or 5 stars by Morningstar or underperformance by funds rated 1 or 2 stars.The median 5-star fund's excess return was not consistently higher than the median 1-star fund's excess return.  

Vanguard also reported that investment committees typically use a 3-year window to evaluate the performance of their portfolio managers.  Yet we know that investors and asset managers should focus more on performance outside the 3 to 5-year performance window due to mean reversion using that time frame.

The other problem in performance evaluation is often found among individual investors who overreact to short-term results. When I managed investment partnerships in the 1970s and 1980s, my investors would invariably want to add funds after a single month of strong performance, and, conversely, they would almost never add to their accounts following a significant down month. Short-term mean reversion implies that they should have been doing just the opposite. Dalbar's annual "Quantitative Analysis of Investor Behavior"  supports the idea that investors overreact to short-term performance by buying highs and selling lows instead of keeping the big picture in mind, which seriously harms their long term returns. [1]

Doing what may be the wrong thing has even been adopted as an investment strategy by the Global X JP Morgan Sector Rotation ETF (SCTO). This fund buys the strongest U.S. stock market sectors based on only the prior month’s performance. 

So there you have it. Investment committees, institutional asset managers, Morningstar, and others emphasize 3-year past performance as an indicator of future success, when the just opposite is likely to be true. Adding to this confusion, individual investors and others chase after strong 1-month performance by buying these short-term rallies when they would be better off buying dips.  

Investors and investment managers take heed. Do the right thing. Read the literature. And, if you need to, don’t forget to turn your fruits and veggies in the right direction.

[1] One of the advantages of using a trend following filter like absolute momentum (which is half of dual momentum) to identify regime change and reduce drawdown is that can also reduce investors' loss aversion, ambiguity aversion, and the flight-to-safety heuristic. It may therefore give investors more confidence to stay with the trend and even buy dips.

January 21, 2015

And the Winner Is...

Until recently, the longest back test using stock market data was Geczy and Samonov’s 2012 study of relative strength momentum called “212 Years of Price Momentum: The World’s Longest Backtest: 1801-2012”. The length of that study has now been exceeded by an 800 year backtest of trend following in Greyserman and Kaminski’s new book, Trend Following with Managed Futures: The Search for Crisis Alpha. The authors looked at 84 equities, fixed income, commodities, and currencies markets as they became available from the years 1200 through 2013. They established long or short equal risk sized positions based on whether prices were above or below their rolling 12-month past returns.

The average annual return of this strategy was 13% with an annual volatility of 11% and a Sharpe ratio of 1.16. In contrast to this, buy-and-hold  had a return of 4.8%, volatility of 10.3%, and a Sharpe ratio of 0.47.  Maximum drawdown for trend following was also significantly lower than for buy-and-hold. Equities alone with trend following showed a substantially higher Sharpe ratio and nearly a 3% greater annual return than with buy-and-hold from 1695 through 2013.

However, let’s not just look at trend following on its own.  Let’s also compare it to other possible risk reducing or return enhancing approaches and see what looks best. We will base our comparisons on the performance of U.S. equities because that is where long-run risk premium and total return have been the highest. We also have U.S. stock market data available from the Kenneth French data library all the way back to July 1926.

We will compare trend following in the form of absolute momentum to seasonality and then to the style and factor-based approaches of value, growth, large cap, and small cap.[1] We will also see if it makes sense to combine these with trend following.

For seasonality, we look at the Halloween effect, sometimes called “Sell in May and go away…” This has been known to practitioners for many years. There have also been a handful of academic papers documenting the positive results of holding U.S. stocks only from November through April. The following table shows the results of this strategy compared with absolute momentum applied to the broad U.S. stock market from May 1927 through December 2014. With 10-month absolute momentum, we are long stocks when the excess return (total return less the Treasury bill rate) over the past 10 months has been positive.[2] Otherwise, we hold Treasury bills. We also hold Treasury bills when we are out of U.S. stocks according to the Halloween effect (in stocks Nov-Apr, out of stocks May-Oct). 


US Mkt
Annual Return
Annual Std Dev
Annual Sharpe
Maximum 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.

We see that the 6-month seasonal filter of U.S. stock market returns substantially reduces volatility and maximum drawdown but at the cost of reducing annual returns by over 200 basis points. Trend following absolute momentum, on the other hand, gives a greater reduction in maximum drawdown than seasonality with almost no reduction in return. There is no reason to consider seasonal filtering when absolute momentum gives a greater reduction in risk without diminished returns.   

The table below shows the U.S. market separated into the top and bottom 30% based on book-to-market (value/growth) and market capitalization (small/large). We see that value and small cap stocks have the highest returns but also the highest volatility and largest maximum drawdowns. 


US Mkt
Annual Return
Annual Std Dev
Annual Sharpe
Maximum 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.

Most academic studies ignore tail risk/maximum drawdown, but these can be very important to investors. Not many of us would be comfortable with 90% drawdowns.[3] In addition, on a risk-adjusted basis (Sharpe ratio), neither small cap nor value stocks appear much better than growth or large cap stocks. This is consistent with some academic research showing a lack of small size premium and a value premium associated mostly with hard-to-trade micro cap stocks.[4] Let’s now see what happens now when we apply absolute momentum to these market style segments:

                                                       Style w/Absolute Momentum

Annual Return
Annual Std Dev
Annual Sharpe
Maximum 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.

In every case, adding absolute momentum reduces volatility, increases the Sharpe ratio, and substantially lowers maximum drawdown. The biggest impact of absolute momentum, however, is on large cap stocks, followed by the overall market index. The use of a trend following absolute momentum overlay further reduces the relative appeal of value or small cap stocks.   

One may wonder why large cap stocks respond better to trend following. The answer lies in a study by Lo and MacKinlay (1990) showing that portfolio returns are strongly positively autocorrelated (trend following), and that the returns of large cap stocks usually lead the returns of small cap stocks. Since trend following lags behind turns in the market, investment results should be better if you can minimize that lag by being in the segment of the market that is most responsive to changes in trend. That segment is large cap stocks, notably the S&P 500 index, which leads the rest of the market.[5]

In my book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk, I give readers an easy-to-use, powerful strategy incorporating relative strength momentum to select between U.S. and non-U.S. stocks, and absolute momentum to choose between stocks or bonds. I call this model Global Equities Momentum (GEM). And what index is the cornerstone of GEM? It’s.the S&P 500, the one most responsive to trend following absolute momentum and that gives the best long-run risk-adjusted results. 

Einstein said you should keep things as simple as possible, but no simpler. One can always create more complicated models or include more investable assets. But as we see here, trend following momentum is best when it is simply applied to large cap stocks.

[1] There is a study showing the effectiveness of absolute momentum back to 1903 by Hurst et al. (2012).
[2] We use 10-month absolute momentum instead of the more popular 10-month moving average because absolute momentum gives somewhat better results and 35% fewer trades, as per our last blog post, "Absolute Momentum Revisited". 
[3] The next largest maximum drawdown was 64.8 for value and 69.1 for small cap on a month-end basis, which were again the largest ones. Intramonth maximum drawdowns would have been even higher.
[4] See Israel and Moskowitz (2012).
[5] U.S. stock market returns also lead non-U.S. stock market returns. See Rapach, Strauss, and Zhou (2012).

January 4, 2015

Absolute Momentum Revisited

Trend following based absolute momentum, also known as time-series momentum, is the Rodney Dangerfield of investing. It “don’t get no respect.” Absolute momentum is still little known and hardly used by investors. Yet it can be a very powerful tool, leading to both enhanced return during bull markets and reduced  risk during bear markets.

The more common type of momentum, based on relative strength, has little or no ability to reduce bear market drawdown. It may even increase volatility and downside risk. As I show in my book, Dual Momentum Investing, using both absolute and relative momentum simultaneously is the best approach in that it lets you benefit from the return enhancing characteristics of both types of momentum while incorporating the risk reducing benefits of absolute momentum.

But absolute momentum has possible uses on its own for those who simply want to limit the downside risk and enhance the expected return of single asset or fixed asset portfolios. That is why I wrote the paper, “Absolute Momentum: A Simple Rule-Based Strategy and Universal Trend-Following Overlay,” which is now included as Appendix B in my book. I show how absolute momentum can be applied to a number of different indexes and assets, as well as to some common portfolio configurations, such as balanced stock/bond or simple risk parity portfolios.

Absolute momentum is easy to calculate and apply. It is positive if an asset’s excess return (return less the Treasury bill rate) over a specified look back period is positive. One then holds that asset until absolute momentum turns negative. If absolute momentum is negative, then one stands aside.

In my paper, I use data going back to January 1973, since bond index data began at that time and international stock index data began close to it in January 1970. Elsewhere in my book, I also use January 1973 as the start date for my analysis, since my book’s featured Global Equities Momentum (GEM) model relies on the same fixed income and international stock indexes. Those wanting to see additional momentum result history can consult the references I give in the book showing attractive profits from relative strength and absolute momentum back to 1801 and 1903, respectively.

However, I now think it would be a good idea now to extend my back testing of absolute momentum, since some investors are especially attracted to absolute momentum for several reasons. First, absolute momentum trades less frequently then dual momentum, which may be important for taxable accounts. Absolute momentum applied to just the U.S. stock market gives mostly long-term capital gains. The second reason absolute momentum may be worth looking at in more depth is that some investors have only a single investment approach that they are comfortable using. They may want to hold a portfolio that focuses solely on value plus profitability (see my earlier post, “Value Investing Redux”), quality, hedge fund cloning, stock buy backs, dividend appreciation, or other factors. 

So it might be helpful to see how absolute momentum looks when applied to aggregate U.S. stocks using the long-term Kenneth French data library that is available online. I compare results using a 10-month absolute momentum filter to the market index without the use of absolute momentum from May 1927 through December 2014, a period of nearly 87 years. (For those who are curious, a 10-month moving average filter gives a 0.69% lower annual return and a similar maximum drawdown compared to 10-month absolute momentum. This moving average also trades 1.43 times/year, versus 1.06 for absolute momentum over this 87 years.) When we are out of stocks, assets are invested in one month Treasury bills. Here are the results with monthly readjusting of positions:
                        AbsMom    US Market
ANN RETURN       11.48           11.76
ANN STD DEV      12.88           18.69
ANN SHARPE         0.58             0.42
MAX DD             -41.40          -83.70

These are hypothetical results and are not an indicator of future results and do not represent returns that any investor actually attained. Please see our Disclaimer page for additional disclosures.

We see that absolute momentum gives attractive results compared to buy and hold on a risk-adjusted basis. Absolute momentum shows a higher Sharpe ratio and substantially reduced volatility and maximum drawdown. Due to this reduced volatility and smoother equity growth, terminal wealth is higher with absolute momentum than with the market average, even though the average annual return using absolute momentum is slightly lower.

Dual momentum is still the premier momentum strategy for most investors, but absolute momentum may be a valuable tool for many others.

December 23, 2014

Dual Momentum Fixed Income

Momentum is most commonly applied to stocks. But it works just as well, if not better, when applied to bonds. Our Dual Momentum Fixed Income model switches monthly between the strongest one of the following indexes: Barclays Capital U.S. Credit Bonds, Barclays Capital U.S. Corporate High Yield Bonds, and 90 day U.S. Treasury bills.

The reason for choosing credit bonds instead of Treasury bonds for the core of this model is because of modern portfolio theory principles. There is a risk premium associated with credit bonds that is absent from U.S. Treasury obligations. Since an indexed credit bond portfolio holds hundreds of different bonds, nearly all the idiosyncratic risk associated with credit bonds has been diversified away, leaving a premium that can be captured with little practical credit risk. 

One can also argue that applying absolute momentum (by selecting Treasury bills when their returns are higher than bonds) to a credit bond portfolio reduces portfolio stress, which further eliminates systematic risk. 

Here are the Dual Momentum Fixed Income (DMFI) results from applying our model to the following bond indexes. The high yield bond index began in July 1983, so results are from January 1984 through November 2014:


Annual Return

Annual Std Dev

Annual Sharpe

Max Drawdown

% of DMFI Profits

% of Occurrences

Avg Credit Rating

Avg Yrs Duration

                                            Historical data and analysis should not be taken as an indication or guarantee of any future performance.
                                            Please see our website Performance and Disclaimer pages for additional disclosures.

What is especially interesting is that DMFI returns are more than 100 basis points higher than the returns of high yield bonds, while DFMI volatility and maximum drawdown are lower than those of investment grade credit bonds. With average years to maturity of 4.5 and 7.1 for the high yield and credit bond indexes respectfully, dual momentum achieves these impressive results without having to assume a lot of duration risk and interest rate volatility. Instead, DMFI navigates effectively along a relatively short area of both the yield and quality curves, while simultaneously avoiding the drawdowns that accompany high yield bonds. The monthly and yearly returns from DMFI are on the Performance page of our website, where they will be updated each month.

Given the level of current interest rates and the strong bull market in bonds we have had over the past 30 years, if you think there will be comparable bond market results over the next 30 years, then I have a very nice bridge to sell you. Given more modest expectations from the fixed income markets, dual momentum looks like it can offer superior returns to individual intermediate-term fixed income bonds for those who require some exposure to the fixed income markets. More importantly, given the potential risks of higher future interest rates, a dual momentum approach may offer some welcome insulation from the pernicious effects of rising rates on one’s fixed income portfolio.