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 absolute momentum 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 12-month rolling returns.

The annual return of this strategy was 13% with an annual volatility of 11% and a Sharpe ratio of 1.16. Anyone who had doubts about the long-run efficacy of trend following momentum should no longer be doubtful.


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 to seasonality and then to the style and factor-based approaches of value, growth, large cap, and small cap. 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.[1] 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
AbsMom
Nov-Apr+AM
Annual Return
11.8
9.6
11.5
7.4
Annual Std Dev
18.7
12.1
12.9
9.4
Annual Sharpe
0.42
0.48
0.58
0.39
Maximum 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 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. 

                                                                 Style


US Mkt
Value
Growth
Large
 Small
Annual Return
11.8
16.2
11.3
11.5
 16.6
Annual Std Dev
18.7
25.1
18.7
18.1
 29.3
Annual Sharpe
0.42
0.46
0.39
0.42
 0.41
Maximum 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/maximum drawdown, but these can be very important to investors. Not many of us would be comfortable with 90% drawdowns.[2] 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 the latest academic research showing a lack of small size premium and value premium associated mostly with micro cap stocks.[3] Let’s now see what happens now when we apply absolute momentum to these market style segments:

                                                    Style w/Absolute Momentum


AbsMom
ValAbsMom
GroAbsMom
LgAbsMom
SmAbsMom
Annual Return
11.5
13.3
10.3
11.5
13.9
Annual Std Dev
12.9
17.2
13.3
12.5
21.1
Annual Sharpe
0.58
0.53
0.48
0.60
0.46
Maximum DD
-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 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.   

We 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.[4]

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 applied simply to large cap stocks.


[1] We use 10-month absolute momentum instead of the more popular 10-month moving average because absolute momentum gives better results. See our last blog post, "Absolute Momentum Revisited". 
[2] 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.
[3] See Israel and Moskowitz (2012). Delisting bias and high transaction costs also reduce the small cap premium.
[4] 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 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 assets or fixed 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.

In my paper, I use data going back to January 1973, since bond index 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 I learned that 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 from stocks. 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. It also trades1.43 times/year versus 1.06 for absolute momentum.) 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 a substantially reduced volatility and maximum drawdown. Due to reduced volatility and smoother equity growth, terminal wealth is higher with absolute momentum than with the market average, even though the average annual return 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 Hi Yield Bonds, and 90 day U.S. Treasury bills.

The reason for choosing credit bonds instead of Treasury bonds for the core of our 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, which have only duration risk. 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. There is little reason then to hold Treasury bonds, since they provide a lower total return without a significant reduction in portfolio 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:


HI YLD
CREDIT
TBILLS
DMFI

Annual Return
9.78
8.58
4.07
11.08

Annual Std Dev
8.54
5.48
0.80
5.15

Annual Sharpe
0.73
0.94
1.09
1.44

Max Drawdown
-33.31
-7.25
0
-5.89

% of DMFI Profits
59
32
9
*

% of Occurrences
35
28
12
*

Avg Credit Rating
B
BBB
AAA
*

Avg Yrs Duration
4.5
7.1
0.3
*




                                            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. But 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.