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 “212Years of Price Momentum: The World’s Longest Backtest: 1801-2012”. The length of that study is now exceeded by an 800 year back test 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. This is different from absolute momentum in that it uses total rather than excess returns and short as well as long positions.

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.  Worst drawdown for trend following was also lower than for buy-and-hold. Equities alone with trend following showed a higher Sharpe ratio and nearly a 3% greater annual return than with buy-and-hold from 1695 through 2013.

But 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 have U.S. stock market data available from the Kenneth French data library all the way back to July 1926.

We will first 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 any of these with trend following.

For seasonality, we look at the popular Halloween effect, sometimes called “Sell in May and go away…” Practitioners have known about this 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).

                                                                       Seasonality

US Mkt Nov-Apr Abs Mom Nov-Apr+AM
Ann Return   11.8     9.6    11.5       7.4
Ann Std Dev   18.7   12.1    12.9       9.4
Sharpe Ratio   0.42   0.48    0.58     0.39
Worst DD  -83.7 -56.7   -41.4    -43.8

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 gives reduced volatility and a lower worst 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 worst drawdown than seasonality with almost no reduction in return. There is little 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. 

                                                                         Style

US Mkt
Value
Growth
Large
 Small
Ann Return
11.8
16.2
11.3
11.5
 16.6
Ann Std Dev
18.7
25.1
18.7
18.1
 29.3
Sharpe Ratio
0.42
0.46
0.39
0.42
 0.41
Worst DD
-83.7
-88.2
-81.7
-82.9
-90.4

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/worst drawdown, but these can be important to investors. Few  would be comfortable with 90% drawdowns.[3] Also, 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 recent 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

MktAbMom
ValAbMom
GroAbMom
LgAbMom
SmAbMom
Ann Ret
11.5
13.3
10.3
11.5
13.9
Std Dev
12.9
17.2
13.3
12.5
21.1
Sharpe
0.58
0.53
0.48
0.60
0.46
MaxDD
-41.4
-66.8
-42.3
-36.2
-76.9

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 lowers worst drawdown. But the biggest impact of absolute momentum is on large cap stocks. Next best is the broad 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 may lie in a study by Lo and MacKinlay (1990) showing that portfolio returns are 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 reduce 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 strategy incorporating both relative strength momentum to select between U.S. and non-U.S. stocks, and absolute momentum to determine market trend and choose between stocks or bonds. I call this dual momentum model Global Equities Momentum (GEM). And what index is the cornerstone of GEM? It is 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 does just fine when 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 popular 10-month moving average because absolute momentum gives better results and 35% fewer trades, which means fewer false signals and whipsaw trades. See our last blog post, "Absolute Momentum Revisited". 
[3] The next largest worst drawdown was 64.8 for value and 69.1 for small cap on a month-end basis, which were again the largest ones. Intra-month worst drawdowns would have been even higher.
[4] See Israel and Moskowitz (2012).
[5] U.S. stock market returns have also led non-U.S. stock market returns. See Rapach, Strauss, and Zhou (2012).

January 4, 2015

Absolute Momentum Revisited

Trend following based absolute momentum is still little known and hardly used by investors. Yet it can be a powerful tool, leading to both enhanced long-run return and especially to reduced risk during bear markets.

The more common type of momentum, based on relative strength or cross-sectional momentum, 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 together is the best approach in that it lets you enjoy 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 want to limit the potential downside risk and enhance the expected return of single asset or fixed asset portfolio. That is why I wrote the paper, “Absolute Momentum: A Simple Rule-Based Strategy and Universal Trend-Following Overlay.” In it, I show how absolute momentum can be applied to manyf 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 research papers, 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. 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 more 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.

Yet 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 than dual momentum, which may be important for taxable accounts, even though higher profits are usually earned using dual momentum. Absolute momentum applied to just the U.S. stock market can give 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 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 87 years. (For those who are curious, a 10-month moving average filter gives a 0.69% lower annual return and a similar worst drawdown compared to 10-month absolute momentum before transaction costs. The moving average also trades 1.43 times/year, versus 1.06 for absolute momentum over these 87 years. This means absolute momentum has fewer false signals and whipsaw trades. It would look even better than the moving average approach after transaction costs.) 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
         
CAGR                        10.72          10.00
ANN STD DEV      12.88           18.69
SHARPE  RATIO   0.58             0.42
WORST 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.

Even though absolute momentum may lag behind during prolonged bull markets, we see that it gives attractive long-run results compared to buy and hold on a risk-adjusted basis. Absolute momentum shows a higher CAGR and Sharpe ratio, reduced volatility, and a better worst drawdown.

Dual momentum, which uses both relative and absolute momentum, is still the premier momentum strategy for most investors, but absolute momentum may be a useful tool for some.