Dual Momentum Investing Is Released Today

October 31, 2014, 6:16 am

≫ Next: Individual Stock Momentum - That Dog Won't Hunt

Today is the official release day of Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk. I wrote the book to help as many people as possible earn attractive returns and minimize bear market drawdowns.

Here is an excerpt from a thoughtful review by Reading the Markets:

Antonacci's extensive research and his clear-headed thinking have led to a book that every investor should read. The academically oriented reader will be grateful for his occasional excursions into the weeds, his carefully laid-out data, and his lengthy bibliography. The practically oriented investor will find a road map for moving ahead and staying out of really big trouble ...This one's a keeper!

Scott's Investments wrote:

Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk is a must-read for individual investors and financial professionals…Antonacci has done the heavy lifting for his readers by thoroughly researching the history and data behind momentum investing. The result is a well-researched and overwhelming argument for momentum investing. Readers are rewarded with a simple, robust strategy that anyone can implement.

And from Alpha Architect...:

Antonacci demonstrates returns to Dual Momentum and the empirical evidence through extensive backtesting across multiple decades; the analysis includes various risk metrics (returns, standard deviations, Sharpe, drawdowns, etc.), and robustness studies, the interpretation of which he explains in detail, so that the reader can have an informed view of the data.

The evidence culminates in a simple but powerful applied momentum model: Antonacci’s Global Equities Momentum (GEM) strategy, which uses these dual momentum ideas to tactically allocate across and among domestic and international equity and bonds. And the results are nothing short of spectacular: superior returns, with low volatility.

The Kindle version of the book was released on October 9, so there are also a dozen reader reviews on Amazon, as well as endorsements from prominent industry professionals. Click here to read these, find out more about the book, or order it now.

There will be a book release party this evening, October 31st. Everyone is cordially invited; just dress up in a costume and wander around your neighborhood to join the celebration.

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Individual Stock Momentum - That Dog Won't Hunt

November 10, 2014, 11:52 pm

≫ Next: Diversification or Deworsification?

≪ Previous: Dual Momentum Investing Is Released Today

Dead or dying academic ideas latched on to by unwary institutional investors litter the investment graveyard landscape. My new book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk, describes some of these, such as the small cap premium, portfolio insurance, and portfolio diversification with passive commodities. Most of these occurred because of incomplete information or omitted variables.
Shortly after Rolf Banz published a paper based on his University of Chicago PhD dissertation that identified a small cap premium from 1936 through 1975, Dimensional Fund Advisors (DFA) and others quickly tried to exploit this "small cap anomaly." They learned later that this apparent anomaly was driven by a mistake in how researchers treated missing data for delisted stocks, many of which were small caps. As noted in my book, studies since then have shown that the small cap premium no longer exists and may never have existed.

Portfolio insurance was based on the elegant idea that you could synthesize protective options through a combination of stock buying and selling combined with short-term borrowing and lending. You could "insure" your portfolio using these synthetic options. However, what portfolio insurers failed to take into account was the short- term mean reverting nature of stocks. At that time, most academics thought stocks followed a random walk and had little or no auto-correlation, even though for many years stock exchange specialists made handsome mean reversion profits by trading against public order flow. Portfolio insurers quietly packed up their bags and disappeared not long after they first appeared.

In the mid-2000s, academics published studies showing that passive commodities could be a decent portfolio diversifier. Investors jumping on to that bandwagon failed to realize that very large inflows of speculative capital from institutional investors could eradicate the premium that had previously been flowing from hedgers to speculators. Front-running costs of over 3% annually from simultaneous rolling over index future contracts would also take its toll on speculative investor profits. After half a dozen years, there were new research papers showing that adding commodities to a stock/bond portfolio was no longer beneficial.

It may very well be that relative strength momentum applied to individual stocks is the latest academic concept doomed to failure because of investors blindly following academics without seeing the bigger picture. Many academic studies of momentum ignore transaction costs, which can be significant. Not only is there high turnover in rebalancing momentum portfolios made up of individual stocks, but Lesmond et al. (2004) show that the stocks generating the largest momentum returns are the smallest, less liquid ones having higher trading costs.

A trading costs study by Frazzini et al. (2012) of AQR, covering 13 years of data in 19 developed markets,states that "...the main anomalies to standard asset pricing models are robust, implementable, and sizeable."However, Lesmond et al. conclude that "… the magnitude of the abnormal returns associated with these trading strategies [stock momentum] creates an illusion of profit opportunity when, in fact, none exists." As pointed out in our recent post, "Value and Momentum Revisited,"Fischer et al (2014), using lower transaction cost estimates than Lesmond et al., also found that transaction costs negate much of the momentum profits from portfolios of individual stocks.

Transaction costs, however, are only half the story. Academic researchers validate cross-sectional relative strength momentum by looking at winners versus losers and segmenting the stock market into deciles, quintiles, quartiles, or terciles. According to Siganos (2007), beyond the first few extreme winners and losers, there is a continuous decline of momentum gains from larger momentum portfolios. Siganos found maximum momentum returns using a portfolio limited to the 40 top and bottom performing stocks.

Yet all publicly available stock momentum funds use more than 40 stocks, and some use ten times more than that! The iShares MSCI USA Momentum Factor ETF holds 125 stocks, and the PowerShares DWA Momentum Portfolio has 100 holdings.The AQR Momentum Fund, AQR Small Cap Momentum Fund, and AQR International Momentum Fund hold 479, 953, and 440 stocks, respectively. These represent nearly 50% of the underlying indexes from which these momentum funds draw their holdings. The annual expense ratios of AQR's momentum funds range from 0.50 to 0.90%. In contrast to this, you can invest in the underlying indexes from which AQR draws their dilute momentum holdings for a cost of only 0.05% per year. When you add in another 0.7% per year that AQR estimates as transaction costs for their quarterly rebalanced large/midcap momentum index, in my mind it raises serious questions about how investors can capture momentum profits from individual stocks.

Yet as they say, the proof is in the pudding. In Chapter 6 of my new book, I show readers a simple way to find style-based alternatives to so-called smart beta funds. In many cases, style-based ETFs with lower expense ratios and lower transaction costs offer similar or better performance than their "smart beta" counterparts. I thought it would be interesting to use the same technique to look at lower cost style-based alternatives to the largest and longest running publicly available funds that use momentum applied to individual stocks. The following comparative charts using momentum funds that can be accurately matched up with stylistic index funds begin at each momentum fund's inception date using the lowest cost class of momentum shares.

The stylistic equivalent fund to the AQR Momentum Fund (AMOMX), with an annual expense ratio of 0.50%, is the Vanguard U.S. Large Cap Growth ETF (VUG), with an expense ratio of .09%.

The stylistic equivalent fund to the AQR PowerShares DWA Momentum Portfolio (PDP), with an annual expense ratio of 0.65%, is the Vanguard U.S. Mid Cap Growth ETF (VOT), with an expense ratio of .09%
.

The stylistic equivalent fund to the AQR Small Cap Momentum Fund (ASMOX), with an annual expense ratio of 0.65%, is the Vanguard U.S. Small Cap Growth ETF (VBK), with an expense ratio of .09%.

The stylistic equivalent fund to the AQR International Momentum Fund (AIMOX), with an annual expense ratio of 0.65%, is the iShares MSCI EAFE Growth ETF (EFG), with an expense ratio of .40%.

The above charts give some evidence of why I am not a fan of using momentum with individual stocks. It should also be mentioned that relative strength stock momentum does little or nothing to reduce portfolio drawdown. To accomplish that, you need absolute momentum and/or cross asset diversification. In terms of both risk and return, momentum is more effective when used with asset classes or broad indexes, and when it incorporates trend-following absolute momentum, as described in my book.

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Diversification or Deworsification?

December 3, 2014, 5:44 pm

≫ Next: Dual Momentum Fixed Income

≪ Previous: Individual Stock Momentum - That Dog Won't Hunt

Most of us learned long ago that diversification is a good thing. In fact, it is often called the closest thing to a “free lunch” in the world of investing. This is because when used wisely, diversification can reduce portfolio volatility with little or no diminution in return. But the key is the phrase “when used wisely.”

Working with individual stocks, diversification is important in reducing company-specific (idiosyncratic) risk that comes from earnings surprises or other bad news that can adversely affect individual companies. A carefully selected (no strong biases) portfolio of 40 or 50 stocks will diversify away most idiosyncratic risk. The main benefits from additional diversification are reduced benchmark tracking error and an increased ability by active managers to handle larger amounts of capital.

Investment managers may want to reduce tracking error for reasons of job security and trade larger amounts of capital to receive more compensation. But from an investor’s point of view, larger portfolios are no better than smaller ones once you eliminate most idiosyncratic risk. Larger portfolios may, in fact, be worse than smaller ones in terms of offering up profit opportunities. Active managers would better serve their clients’ interests by having more focused portfolios of their best holdings rather than diluting their portfolios with less attractive issues. Investors wanting broader based portfolios can purchase less costly index funds.

Over diversification is also a problem for momentum investors because studies show that momentum profits are highest in the most concentrated momentum ranked cross-sections of the market. Top momentum deciles outperform top momentum quintiles, which outperform top momentum terciles. Yet, as I point out in my blog post “Individual Stock Momentum – that Dog Won’t Hunt”, there are some momentum funds that own nearly half their broad universe of individual stocks. Investors in those funds are paying for what amounts to an index fund plus a modest exposure to momentum.

Over diversification can also be a problem with respect to asset class momentum. To better understand this, you need to consider how investors earn their profits. Investors are compensated for giving up use of their capital, which earns them the risk-free rate, and for bearing risk, which earns them a risk premium above the risk-free rate.

Companies receive and employ invested capital for productive purposes when equity investors become beneficial owners of these companies. Stockholders share in the fortunes or misfortunes of such companies and are compensated with a relatively high risk premium. In fact, among all investment opportunities, stocks (especially U.S. stocks) have historically offered the highest risk premium. Those who don’t accept evidence of this that I present in my book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk, should read Stocks for the Long Runby Jeremy Siegel, who devotes his entire book to that subject.

Bonds also provide a risk premium, but one that is substantially lower than stocks because bond investors have a senior claim on company assets and are guaranteed a return of capital when their bonds mature. It is uncertain what kind of risk premium, if any, investors in assets other than stocks and bonds receive. For example, investors in aggregate commodity futures (a zero-sum game, less transaction costs) once received risk premium from commercial interests looking to hedge their business risks by using those markets. But with the proliferation of speculative commodity trading, as well as a substantial number of institutions adding passive commodities to their portfolios, that risk premium has largely vanished. One might sometimes still earn speculative profits from assets other than stocks and bonds, but the odds are much better having a proven risk premium behind you as a tailwind.

The main reasons investors continue to hold assets other than stocks and bonds is the mistaken belief that more is always better with respect to diversification and the idea that holding less correlated assets will lessen portfolio volatility and reduce bear market exposure.

However, many markets that are normally non-correlated now move together under economic stress when everyone wants liquidity. Diversification can fall short when it is needed the most. With increased globalization, the world is now much more inter connected, and widespread diversification is no longer as useful as it once was in reducing downside risk exposure. What is useful for that purpose is trend-following absolute momentum, which has shown the ability to both enhance returns and reduce downside exposure among different assets going back to the turn of the last century.[1] The effective downside protection offered by absolute momentum is all the more reason why over diversification is unnecessary for momentum investors.

A better approach, as presented in my book, is to invest in stocks when they are strong, according to absolute momentum, in order to capture the highest amount of risk premium.[2] When stocks are weak, you can switch to bonds, which offer a more modest risk premium than stocks. However, since the stock market is a leading economic indicator, a weak stock market often indicates a future economic slowdown, declining interest rates, and a healthy bond market. So stocks and bonds can complement each other at the most appropriate times. This is a more effective approach than having a permanent allocation to both.

Diversification into asset classes with lower risk premiums dilutes long-run returns and leads to investment mediocrity. Stocks and bonds are all one really needs for effective investing, especially if it is momentum-based investing.

[1] See "A Century of Evidence on Trend Following Investing" by Hurst, Ooi, and Pedersen.
[2] Our Global Equities Momentum (GEM) model stays mostly in U.S. stocks, where risk premium has been the highest. It switches to non-U.S. stocks when the odds shift in their favor according to relative strength momentum. For validation of this switching approach, see http://awealthofcommonsense.com/avoiding-recency-bias-foreign-stock-markets

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Dual Momentum Fixed Income

December 23, 2014, 7:38 am

≫ Next: Absolute Momentum Revisited

≪ Previous: Diversification or Deworsification?

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. 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.

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Absolute Momentum Revisited

January 4, 2015, 4:47 pm

≫ Next: And the Winner Is...

≪ Previous: Dual Momentum Fixed Income

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, micro caps, 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). 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.

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And the Winner Is...

January 21, 2015, 8:36 pm

≫ Next: Do the Right Thing

≪ Previous: Absolute Momentum Revisited

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 no small size premium and a value premium associated only 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

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 almost always 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.

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 any small cap premium.

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Do the Right Thing

February 24, 2015, 7:33 am

≫ Next: Sustainable Momentum Investing: Doing Well By Doing Good

≪ Previous: And the Winner Is...

I used to always cut fruits and vegies 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 vegies 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.

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Sustainable Momentum Investing: Doing Well By Doing Good

March 27, 2015, 12:04 pm

≫ Next: Understanding Dual, Relative, and Absolute Momentum

≪ Previous: Do the Right Thing

Socially Responsible Investing (SRI), also known as sustainable or responsible investing, is the application of ethical as well as financial considerations in making investment decisions. SRI therefore recognizes and incorporates societal needs and benefits.

SRI may first date back to the Quakers who, in their 1758 yearly meeting, prohibited members from participating in the slave trade. The Quaker Friends Fiduciary has existed since 1892 and continues to manage its assets following SRI guidelines.

Another early adopter of SRI was John Wesley (1703-1791), one of the founders of the Methodist Church. Wesley’s sermon on “The Use of Money” outlined the basic tenets of social investing – do not harm others through your business practices and avoid industries which can harm the health of others. In the 1920s, the Methodist Church of Great Britain invested in the UK stock market while avoiding companies involved with alcohol and gambling.

The first public offering of a socially-screened investment fund was in 1928 when an ecclesiastical group in Boston established the Pioneer Fund. In 1971, a Methodist group organized the PAX World Fund, which appealed to investors who wanted to be sure their profits were not from weapons production. Two years later, SRI went mainstream when Dreyfus, a major mutual fund marketer, launched the Third Century Fund, which grouped together companies noted for their sensitivity to the environment and to their local communities.

In the 1980s, SRI became more widespread with its negative screening of investments in South Africa. SRI practitioners were able to put pervasive pressure on the South African business community. This eventually forced a group of businesses representing 75% of South African employers to draft a charter calling for the end of apartheid.

SRI evolved from ethical exclusionary screening out to include a more proactive approach toward Corporate Social Responsibility (CSR). This SRI/CSR approach became a blend of negative and positive screening methods in order to maximize financial return within a socially aligned investment strategy. Negative screening excludes companies that are incompatible with investors’ ethical values, while positive screening seeks to invest in companies that act in a manner that is consistent with investors’ values. Examples of negative screening factors are involvements with gambling, adult entertainment, alcohol, tobacco, weapons, under age workers, animal testing, and damage to the environment. Examples of positive screening criteria are pollution control, community involvement, energy conservation, consumer protection, human rights, diversity, product safety, employee working conditions, and renewable energy sources. CSR oriented programs can also vote their proxies to advance ethical business practices, such as diversity, fair pay, and environmental protection.

The inclusion of CSR factors further evolved and expanded to include a broader set of Environmental, Social, and Governance (ESG) issues. Interestingly, these were soon found to be correlated with superior risk-adjusted investment returns. ESG was shown to have practical benefits for the companies that employ these criteria, as well as for those who invest in such companies.

There are number of reasons for improvements in performance because of ESG. Corporate responsibility can create good relationships with governments and communities, as well as reduce the risks of onerous regulations and potential conflicts with advocacy groups. It can also influence how consumers perceive a brand and therefore serve a similar role to advertising, which can lead to higher sales and more loyal customers. In addition, corporate responsibility can have a positive influence on companies’ ability to attract and retain talented employees and maintain productive workforces.

According to DB Climate Change Advisors in their 2012 meta-analysis of more than 100 academic studies called “Sustainable Investing: Establishing Long-Term Values and Performance,” 100% of studies showed that companies with high ESG ratings exhibited financial outperformance and had a lower cost of capital than more conventional companies, while 89% of highly-rated ESG companies exhibited market-based outperformance and superior risk-adjusted stock returns.

One typical study is by Eccles et al. (2011), where they compared the performance of 180 large U.S. firms by matching 90 high sustainability firms with 90 low sustainability firms. Beginning in 1993, $1 invested in the high sustainability portfolio would have grown to $22.60 by 2010, while the low sustainability portfolio grew to only $15.40.

From an investment point of view, socially responsible mutual funds have done better in Europe than in the U.S. Europe has always relied more on positive screening criteria, rather than the negative screening criteria that have dominated U.S. funds until recently.

There have been many other studies of socially responsible versus conventional investment performance. One objective survey and assessment of the subject is by the Royal Bank of Canada in their report "Does Socially Responsible Investing Hurt Investment Returns?"

Companies doing well by doing good have not gone unnoticed by investors. The outperformance of high sustainability firms has been attracting considerable investor interest. According to a 2015 survey by the Morgan Stanley Institute for Sustainable Investing, over 70% of active individual investors describe themselves as interested in sustainable investing, and nearly 2 in 3 believe sustainable investing will become more prevalent over the next 5 years.

Looking at actual recent growth, the global sustainable market has risen from $13.1 trillion at the start of 2012 to $21.4 trillion at the start of 2014, and from 21.5% to 30.2% of all professionally managed assets. Europe has the highest percentage of sustainable assets at 63.7%. But the U.S. has been the fastest growing region over this period and now has 30.8% of all global sustainable assets.

The most recent biennial "Report on U.S. Sustainable, Responsible, and Impact Investing Trends" by the Forum for Sustainable and Responsible Investing (US SIF Foundation) shows that U.S. sustainable funds had $6.57 trillion in assets at the start of 2014, up from $3.74 trillion at the start of 2012. This is a growth of 76% in just two years. Assets held in some form of sustainable investment now account for more than $1 out of every $6 under professional management, up from $1 out of every $9 in 2012.

In my book and on my website I show how dual momentum can enhance the performance of many different kinds of investment portfolios, such as global equities, balanced stocks and bonds, equity sectors, and fixed income. So I thought I would now turn my attention toward using dual momentum to achieve the greatest benefits from sustainable investing.

I usually prefer to use low cost, index ETFs as investment vehicles. However, that may not be the best approach with sustainable funds. There are two reasons for this. First, the difference between index ETF and actively managed funds’ annual expense ratios is not nearly as large for sustainable funds. For example, the annual expense ratios for the Vanguard and iShares S&P 500 ETFs are .05 and .07, respectively. The annual expense ratios of the two KLD 400 Social Index ETFs, on the other hand, are much higher at .50. When you compare the sustainability ETFs with expense ratios of .50 to the S&P 500 ETFs with expense ratios of .05 or .07, the sustainability ETFs are at a decided disadvantage to their conventional counterparts.

The second reason that sustainability index funds can be problematic is their short performance records. The earliest U.S. based SRI index is the Domini 400 Social Index, which is now known as the MSCI KLD 400 Social Index. It did not begin until May 1990, and data for it is not readily available. The oldest SRI index fund (Vanguard FTSE Social Index) was established only 15 years ago in May 2000.[1]

For these reasons, as well as the reason that active management might add some value in an area like sustainability, where more informed choices might be better than the mechanical rules of an index, we will look to apply dual momentum to the oldest, actively managed, sustainable equities-based mutual funds.

The three sustainability equity funds that have track records longer than 25 years are Dreyfus Third Century (DRTHX) that began in April 1972, Parnassus (PARNX) that started in May 1985, and Amana Income (AMANX), that began in July 1986.[2]

Looking at these funds now, the only explicit exclusionary screen of Dreyfus Third Century is for tobacco products. However, Third Century has a strong ESG orientation by reason of their mandate to invest in companies that contribute to the enhancement of the quality of life in America, with special emphasis on the environment, product safety, employee safety, and equal opportunity employment. Third Century’s annual expense ratio is 1.01, and the fund is closed now to new investors. However, the institutional class of shares (DRTCX), with an expense ratio of .91, can still be purchased ($1000 minimum) through some financial professionals and brokerage firms.

Parnassus Fund has an annual expense ratio of .86.This fund screens out companies involved with alcohol, tobacco, gambling, nuclear power, and weapons. Parnassus also engages in shareholder activism and community investment. The fund has a strong ESG orientation with its mandate to invest in companies having sustainable competitive advantages and ethical business practices. Parnassus also prefers to buy out-of-favor stocks.

Besides incorporating ESG factors and exclusions for alcohol, tobacco, gambling, and adult entertainment, Amana Income (AMANX) avoids companies with high debt-to-equity ratios and large receivables compared to total assets. Their emphasis on companies with stable earnings, high quality operations, and strong balance sheets free of excessive debt gives Amana a tilt toward quality, which is now recognized in academic circles as a worthwhile risk premium factor.[3]

In addition, Amana prefers to hold shares in companies where management has a sizable stake, and the fund will sell shares in companies where insiders are selling. There is a body of academic literature confirming that insiders are better informed and earn abnormal profits from their trades.[4] Amana Income has an expense ratio of 1.14, plus .25 in 12b-1 fees. However, institutional shares (AMINX) are available with an expense ratio of .90 and no 12b-1 fees. These require a minimum investment of $100,000.

Here are performance figures through February 2015 for our three sustainability funds starting from July 1986, when performance data begins for Amana Income. We also include the Vanguard 500 Index (VFINX) fund as a benchmark. Vanguard 500 has an expense ratio of .17 [5]

	DRTHX	PARNX	AMANX	VFINX
Ann Rtn	9.80	12.63	9.71	11.35
Std Dev	15.79	21.71	12.02	15.32
Sharpe	0.37	0.39	0.48	0.47
Max DD	-59.98	-47.98	-34.70	-50.97

We see that Parnassus has a higher return than the S&P 500 with around the same maximum drawdown, while Amana Income has about the same Sharpe ratio as the market and a lower maximum drawdown. The lack of performance homogeneity among these funds is a good thing for relative strength momentum. So let us see now what happens when we apply dual momentum to these funds.

But first I should mention a potential problem of using higher cost actively managed funds with dual momentum. The performance of actively managed funds may revert toward the mean of all funds and be overtaken by the performance of lower-cost index funds. This may not be such a problem for us though for two reasons.

First, we are not selecting actively managed funds based on their superior past performance that might subsequently mean revert. We are simply using the three sustainability funds that have the longest track records. Second, we can include a low-cost index fund in our dual momentum portfolio. Dual momentum is adaptable. So if there is a falloff in performance of our actively managed funds, dual momentum should automatically move us to our lower-cost index fund. This is how we can confidently use actively managed funds within a dual momentum portfolio.

Here is the same performance we saw above but with the addition of a dual momentum portfolio made up of all three sustainability funds, the Vanguard 500 index fund, and the Vanguard Total Bond (VBMFX) fund as a refuge for when absolute momentum takes us out of equities. The operating logic behind this model that we call ESG Momentum (ESGM) is the same as for our Global Equities Momentum (GEM) model. It is fully disclosed in my book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk.

	DRTHX	PARNX	AMANX	VFINX	VBMFX	ESGM
Ann Rtn	9.80	12.63	9.71	11.35	6.48	16.91
Std Dev	15.79	21.71	12.02	15.32	3.90	13.96
Sharpe	0.37	0.39	0.48	0.47	0.69	0.87
Max DD	-59.98	-47.98	-34.7	-50.97	-5.86	-22.73
% Used	12	35	13	17	23	100

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.

We see that the Sharpe ratio of our ESGM portfolio was more than twice as high as the average Sharpe ratio of the four equity funds, and the ESGM maximum drawdown was less than half as large. By being in bonds 23% of the time, ESGM was able to bypass the full severity of the bear market drawdowns.

ESGM was in the three sustainability funds 78% of the time that it was in equities, so our mission was accomplished of being mostly in investments that contribute to advancements in social, environmental, and governance practices, while simultaneously giving us exceptional risk-adjusted returns through the use of dual momentum. A link to the ESGM model's monthly and annual results is now on the Performance page of our website. It will be updated every month along with the rest of our dual momentum models.

[1] The two social responsibility ETFs, KLD and DSI, began in 2005 and 2006 respectively.
[2] PAX World Balanced began in August 1971 and CSIF Balanced Portfolio began in October 1982, but both funds have large allocations to bonds.
[3] See Asness et al. (2013), "Quality Minus Junk.".
[4] See Seyhun (1998), Investment Intelligence from Insider Trading.
[5] We could have used Vanguard's Admiral shares with an expense ratio of .05 or a low-cost S&P 500 ETF, but we wanted to be consistent with the retail shares we used for our socially responsible funds.

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Understanding Dual, Relative, and Absolute Momentum

April 13, 2015, 6:59 am

≫ Next: Dual Momentum for non-US Investors

≪ Previous: Sustainable Momentum Investing: Doing Well By Doing Good

Years ago when I first started studying momentum, two things stood out in my mind. The first was most momentum research focused on cross-sectional stock studies looking at the future performance of stocks that had been strong versus stocks that had been weak. This was what interested academics most, since abnormal profit from strong versus weak stocks was relevant to whether or not the stock market was efficient. Researchers have done extensive out-of-sample validation testing of momentum.[1] As a further check on the robustness of cross-sectional stock momentum, researchers looked at relative strength momentum applied to other assets and asset classes. The found that momentum worked well on almost everything. Past winners consistently outperformed going forward. This prompted Fama and French, two of the founders of efficient market theory, to call momentum the premier anomaly and to say that it is pervasive.

My first momentum research paper in 2011 applied relative momentum to stock market style, industry, and geographic sectors. I wanted to focus on equities because that is where risk premium and investment returns have been the highest over the long-run. I also reasoned it would be easier to apply momentum to market indexes or sectors rather than individual stocks, and that this would have lower transaction costs than momentum applied to individual stocks.

I also noticed that while relative momentum could lead to higher returns than buy-and-hold, it did little or nothing to reduce left tail risk during bear markets. In fact, bear market drawdown could be higher with relative momentum rather than without it. My first momentum paper dealt with this problem by including short and intermediate term bonds as additional asset classes. When the relative strength of stocks became less than the relative strength of short or intermediate term bonds, my model would switch into bonds. This reduced left tail risk considerably.

My next research paper in 2012, “Risk Premium Harvesting through Dual Momentum,” (winner of the 2012 NAAIM Wagner Award for Advances in Active Investment Management) expanded on what I had done earlier by clearly identifying two types of momentum: relative and absolute.[2]

Researchers had found that both types of momentum were robust across sub-sample periods, look-back periods, and holding periods. Both types of momentum gave higher risk-adjusted returns than buy-and-hold, and both held up well in extensive out-of-sample back testing. Besides comparing and utilizing relative and absolute momentum, my 2012 paper also introduced the concept of dual momentum, a synergistic approach that benefited from the enhanced returns achieved from both forms of momentum, as well as the reduced left tail risk and lower drawdown that come from including absolute momentum.

There has been a massive amount of research on relative momentum over the past 20 years. In fact, relative strength/cross-sectional momentum has been one of the most heavily researched areas in modern finance. However, until recently there has been relatively little research done on absolute momentum. My 2013 paper “Absolute Momentum: A Simple Rule-Based Strategy and Universal Trend-Following Overlay” was an attempt to help balance that mismatch. Two of my more recent blog posts have also focused on absolute momentum.

The post “And the Winner is…” described an 800 year back test of a variation of 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 during 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 trend following 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 only 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.

The “Absolute Momentum Revisited” post was my own out-of-sample research of absolute momentum on U.S. stocks back to the year 1927. Absolute momentum continued to show a higher Sharpe ratio, as well as substantially reduced volatility and maximum drawdown compared to a buy-and-hold approach. I concluded the post by saying, “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 others.”

Before returning to dual momentum, I would like to mention a new study by Zakamulin (2015) called “Market Timing with Moving Averages: Anatomy and Performance of Trading Rules.” The author looked at absolute momentum (which he called the "momentum rule") and 5 different moving average rules, including the 10-month (200 day) simple moving average often written about and used as a trend following filter. The author applied these rules to the S&P Composite stock market index from 1870 to 2010. Estimated transaction costs were accounted for, and all models were invested in U.S. Treasury bills when not in stocks. This 140 year study is now one of the longest back tests of trend following methods, including absolute momentum.

The study found that the majority of the trend following rules had better risk-adjusted out-of-sample performance than buy-and-hold. Absolute momentum was one of two trading rules that showed statistically significant outperformance. The other was a reverse exponential average. Among these rules, absolute momentum.produced the best results. Before getting too enamored with absolute momentum, we need to return to the overall theme of this blog and my book, which is dual momentum.

Here are the updated performance figures from 1974 through March 2015 for the absolute momentum part of dual momentum applied to the S&P 500 and MSCI All Country World Index ex-US (ACWX) indexes used in my Global Equities Momentum (GEM) model featured in my book and tracked on my website. The Barclays Capital U.S. Aggregate Bond Index is the safe harbor asset when absolute momentum exits equities. The GEM model is easy to implement, and its parameters have been validated in many academic papers.

	S&P500 AbsMom	S&P500	ACWX AbsMom	ACWX
Annual Return	14.3	12.3	14.0	11.6
Annual Std Dev	12.2	15.4	12.2	17.2
Sharpe Ratio	0.66	0.41	0.64	0.32
Max Drawdown	-29.6	-51.0	-23.1	-57.4

We see that absolute momentum gave an impressive improvement in risk-adjusted performance compared to performance without the addition of absolute momentum.

Next, we compare the performance of absolute momentum to the performance of relative momentum that switched between the S&P 500 and ACWX indexes based only on their relative strength to each other. More importantly, we also see what happens when we combined both relative and absolute momentum, creating what I call dual momentum.

	Dual Momentum	Relative Momentum	S&P500 AbsMom	ACWX AbsMom
Annual Return	17.7	14.7	14.3	14.0
Annual Std Dev	12.4	15.8	12.2	12.2
Sharpe Ratio	0.89	0.53	0.66	0.64
Max Drawdown	-17.8	-54.6	-29.6	-23.1

Relative momentum, like absolute momentum, gave higher returns than the indexes themselves. Relative momentum, however, unlike absolute momentum, did nothing to reduce volatility or tail risk/maximum drawdown. If I were forced to choose between using relative or absolute momentum, I would choose absolute momentum. However, as I clearly point out in my book, you do not have to pick one over the other. You can use both simultaneously, and that is where the magic happens - combining absolute and relative momentum to create dual momentum.

We see that dual momentum gave us a substantial increase in average and risk-adjusted returns compared not only to the underlying indexes, but also to relative and absolute momentum individually. In addition, dual momentum's maximum drawdown is the lowest of all.

With dual momentum, the whole is greater than the sum of its parts. Dual momentum is clearly the preferred momentum strategy here with respect to large cap U.S. and non-U.S. equity indexes.[3] That is why I call this blog “Dual Momentum,” and my book Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk.

[1] Geczy and Samonov (2012), for example, showed that momentum was highly effective on U.S. equities back to 1801.
[2] Some academics refer to absolute momentum as time series or trend following momentum. However, both relative and absolute momentum are based on economic time series (asset prices), and both are trend following. Relative strength momentum looks at the trend of one asset versus other assets, while absolute momentum looks at the trend of a single asset with respect to its own past.
[3] On the Performance page of my website, I show historical returns and track the real time performance of four other dual momentum models.

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Dual Momentum for non-US Investors

June 2, 2015, 6:31 am

≫ Next: Momentum and Stop Losses

≪ Previous: Understanding Dual, Relative, and Absolute Momentum

Gogi Grewal is an engineer and astute analyst who has been following my work for a number of years. He has an excellent grasp of dual momentum. Since Gogi lives in Canada, he decided to research the best way for non-US investors to utilize dual momentum. Gogi has generously offered to share his findings with us here. Take it away, Gogi....

INTRODUCTION

Momentum is a well-studied anomaly where markets with strong relative strength continue outperforming, while weak markets continue to underperform. Gary Antonacci has furthered this area of research considerably by introducing us to Dual Momentum. By combining trend-following absolutemomentum and traditional relative momentum, investors can increase their expected return while reducing volatility and severe bear market drawdown.

In his book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk, Gary has given us a simple yet robust strategy called Global Equities Momentum (GEM). I have been very interested in implementing GEM but as a Canadian, there are some additional questions that arise. The most obvious question is: How should GEM be implemented by foreign investors?

More specifically, I want to explore how the following decisions affect GEM performance:

1) GEM analysis done in US dollars versus the investor’s local currency
2) Hedged versus unhedged ETFs for execution
3) Alternate stock indices to the S&P 500 and the MSCI ACWI ex-US

4) Trades performed on local stock exchanges versus the US exchange

This study is meant to further the research that Gary has presented and help non-US investors to implement GEM correctly.

METHODOLOGY

Before we explore GEM in foreign currencies, I will first start off by independently replicating Gary’s results in US dollars. I use the same GEM indices, rules, and back test period (1974-2013) that Gary uses in his book .

After alignment with Gary’s results is established, GEM will be tested in the following four currencies: CADUSD, AUDUSD, GBPUSD and JPYUSD. Figure 1below is a graph of normalized performance for these currency pairs.

Figure 1: Normalized Exchange Rate Data, 1971-2015 (Source: US Federal Reserve)

The first 3 rates have fallen between 20-40% since 1971, while JPYUSD has risen more than 3-fold over the same period. When an investor’s home currency falls significantly, the investor benefits by being in foreign currencies. The opposite is true when the home currency rises. Thus, by looking at the chosen currency pairs, we will cover both rising and falling currency environments that a foreign investor can encounter.

Cases Analyzed

For each of the four non-US currencies (CAD, AUD, GBP and JPY), we look at four test cases which are described in the following table:

Table 1: Description of the Four Test Cases

Data Sources

Data sources were from Standard and Poor’s, MSCI, Bloomberg, and the US Federal Reserve. All data represents total returns with dividends and coupons included.

Our back test period is 1971-2014. The start date was restricted by forex data. The Barclay’s US Aggregate Bond Index only has data going back to 1976. I approximated this index between the years 1971-1975 using 5-year US Treasury Bonds.

RESULTS: Part I

Before doing any sort of currency analysis, my first step was to replicate the results Gary presented in his book and on this blog. Below are my results.

	GEM	S&P 500	ACWI ex US	US AGG
Compound Annual Return	16.8%	11.0%	10.2%	7.8%
Average Annual Return	17.7%	12.6%	12.5%	8.0%
% Positive Years	95%	80%	75%	92%
Worst Year	-16.8%	-37.0%	-45.2%	-2.9%
Std Dev of Annual Return	13.1%	15.6%	17.4%	5.5%
Sharpe Ratio	0.97	0.48	0.43	0.55

Table 2:GEM in US$ compared to S&P500, ACWI ex-US, and Aggregate Bonds (1974-2013)

These results are the same as those reported by Gary in his recent blog post in which his average annual return is 17.7% and monthly standard deviation is 12.4%. From these results and Gary’s findings, we see that Dual Momentum provides a significant increase in annual returns while reducing volatility.

RESULTS: Part II

In this section, we look at GEM from the perspective of a foreign investor (Canadian, Australian, British and Japanese). Results are presented for the 4 cases we described in section 2.

CASE 1: Base Case

Foreign investors trade on the US stock exchange when GEM is in equities and on their local stock exchange when GEM is in bonds. When in bonds, investors hold a currency-hedged version of the US Aggregate Bond Index.

Foreign investors do the GEM analysis in USDs, while the transactions are done in their local currency. We use the S&P 500, MSCI ACWI ex-US, and Barclay’s US Aggregate Bond Index.

Below are the results:

	GEM (USD)	GEM (CAD)	GEM (AUD)	GEM (GBP)	GEM (JPY)	GEM (Local)
Compound Annual Return	17.4%	18.1%	21.9%	18.3%	15.2%	15.7%
Average Annual Return	18.3%	19.0%	24.3%	19.5%	16.4%	16.5%
% Positive Years	93%	91%	88%	86%	81%	88%
Worst Year	-8.2%	-5.7%	-15.7%	-6.8%	-12.9%	-16.0%
Std Dev of Annual Return	13.3%	12.2%	17.0%	14.3%	15.2%	12.4%
Sharpe Ratio	1.00	1.14	1.14	1.01	0.75	0.93

Table 3: Performance of GEM in Various Currencies, Base Case

NOTE:“GEM (Local)” is when foreign investors trade permanently on their local stock exchange using currency-hedged ETFs for both equity and bond trades. The results for this fully currency-hedged version of GEM will be the same for all foreign investors, regardless of their country.

The model made a total of 49 trades over the 43-year back test (1.1 trades/year). The model was in US stocks, non-US stocks, and bonds for 40.5%, 39.5% and 20.0% of the time, respectively.

Here are the 3 main observations:

1. All GEM versions (USD, CAD, AUD, GBP, JPY, Local) considerably outperformed the stock & bond indices in terms of annual return and Sharpe ratio. Even GEM in yen outperformed with a 16% average annual return despite the JPY:USD rate tripling over the back test period. This shows that every world investor is much better off using GEM rather than a traditional fixed-allocation portfolio.

2. GEM in CAD, AUD and GBP all outperformed GEM (USD) in terms of annual return and Sharpe ratio. This was expected since these 3 currencies fell against the USD over the back test period. GEM (JPY) underperformed GEM (USD). This was expected since the JPY:USD rate more than tripled over the back test period. Would currency-hedging stocks help?

3. GEM (Local) barely outperformed GEM (JPY) but significantly underperformed GEM in all other currencies. This shows that hedging currency on equities should not be done. Doing so would mean you will significantly underperform when your home currency falls and barely outperform when your home currency rises.

Let’s elaborate further on observation #3. Why does currency hedging underperform so much? Below is a 20-year chart comparing the performance of the US Dollar Index to the performance of the ratio between US and non-US stocks. Notice the strong correlation.

Figure 2:Performance of US Dollar Index vs S&P500:MSCI World ex-US Ratio, 1995-2015

NOTE: Both blue and red lines are displayed in percent gain (since 1995) and smoothed with a simple 10-week moving average. Both the S&P500 and the MSCI World Index ex-US indices are priced in USD.

This chart shows that the US Dollar Index plays a big part in the relative performance between US and non-US stocks. By using currency hedged ETFs, investors (both US and non-US) are losing out on this relative performance. In the case of a US investor that hedges non-US stocks, she does not gain much benefit from having non-US stocks in the model. In fact, when the model is run with only the S&P 500 and bonds, both the average and compounded annual returns drop to 14% - which is in line with the results of the GEM currency-hedged model. For further reading, GMO’s Catherine LeGraw recently wrote an excellent article: The Case for Not Currency Hedging Foreign Equity Investments

CASE 2: Both Analysis AND Transactions in Local Currency

The next step is to see what happens when investors do the GEM analysis in their local currency in addition to transactions, with all else being equal to the base case. Below are the results.

	GEM (USD)	GEM (CAD)	GEM (AUD)	GEM (GBP)	GEM (JPY)	GEM (Local)
Compound Annual Return	17.4%	17.6%	18.1%	15.6%	13.1%	15.1%
Average Annual Return	18.3%	18.6%	19.5%	16.8%	14.5%	15.9%
% Positive Years	93%	93%	91%	81%	77%	91%
Worst Year	-8.2%	-11.5%	-8.5%	-11.4%	-15.4%	-7.7%
Std Dev of Annual Return	13.3%	12.3%	13.5%	13.9%	14.6%	12.1%
Sharpe Ratio	1.00	1.10	1.08	0.85	0.65	0.90

Table 4:Performance of GEM in Various Currencies, Case 2

We see that by doing the GEM analysis with prices in the investor’s local-currency, performance drops compared to the base case. The annual return drops by average of 240 basis points for the CAD, AUD, GBP and JPY versions. However, the standard deviation drops as well by an average of 110 basis points. Overall, the Sharpe Ratio drops by an average of 10.6%.

Thus, foreign investors are better off doing the GEM analysis with prices in USD.

Again, currency hedging the stock indices provides little benefit. We will not be studying it any further.

CASE 3: Using Alternative Stock Indices

In this case, we look at the results for when foreign investors have their portfolio permanently on their own local stock exchange. When GEM is in stocks, investors would use unhedged ETFs. When GEM is in bonds, investors would use either their local country’s aggregate bond index or a currency-hedged version of the US Aggregate Bond Index.

Because foreign investors will likely not have access to an ETF tracking the ACWI ex-US index on their local stock exchange, we will instead use the MSCI US and MSCI EAFE equity indices. This change in indices is really the only consequential difference between this case and the base case.

	GEM (USD)	GEM (CAD)	GEM (AUD)	GEM (GBP)	GEM (JPY)
Compound Annual Return	15.3%	16.1%	19.8%	16.5%	13.3%
Average Annual Return	16.3%	17.2%	22.3%	17.8%	14.4%
% Positive Years	91%	88%	81%	81%	77%
Worst Year	-17.9%	-12.7%	-16.0%	-10.6%	-16.6%
Std Dev of Annual Return	13.3%	12.4%	17.8%	14.4%	14.9%
Sharpe Ratio	0.85	0.98	0.98	0.89	0.63

Table 5: Performance of GEM in Various Currencies, Case 3

The model made a total of 63 trades over the 43-year back test (1.5 trades/year). The model was in US stocks, non-US stocks, and bonds for 40.3%, 39.5% and 20.2% of the time, respectively.

We see that by replacing the S&P500 and ACWI ex-US indices with MSCI US and EAFE, performance drops compared to the base case. The annual return drops by average of 190 basis points for the CAD, AUD, GBP and JPY versions. The standard deviation rises, although only by 20 basis points. Overall, the Sharpe ratio drops by an average of 16%.

Perhaps this drop in performance is because the ACWI ex-US index contains Canada and emerging markets in addition to all the countries in the EAFE index. It is recommended that foreign investors have their portfolio on the US exchange when GEM is in stocks (as in the base case). If foreign investors are restricted to invest on their local exchange, then they should try and find as close of an equivalent to the MSCI ACWI ex-US index as possible. While a direct equivalent is unlikely, there may be an ETF for the World ex-North America index. If not, only then should investors use MSCI EAFE.

CASE 4: Non-Currency Hedging the Aggregate Bond Index

In this case, we look at the results when foreign investors have their portfolio permanently on the US stock exchange. We assume foreign investors will not have an ETF on the US exchange that tracks their home country/continent’s aggregate bond index[1]. Therefore, when GEM is in bonds, foreign investors will be in the Barclay’s US Aggregate Bond Index and therefore exposed to the US dollar. Everything else is the same as the base case.

	GEM (USD)	GEM (CAD)	GEM (AUD)	GEM (GBP)	GEM (JPY)
Compound Annual Return	17.4%	17.8%	22.2%	18.8%	14.8%
Average Annual Return	18.3%	18.8%	24.8%	20.2%	16.3%
% Positive Years	93%	91%	86%	81%	79%
Worst Year	-8.2%	-6.2%	-14.6%	-10.1%	-23.7%
Std Dev of Annual Return	13.3%	12.6%	17.9%	14.8%	15.8%
Sharpe Ratio	1.00	1.09	1.10	1.03	0.71

Table 6: Performance of GEM in Various Currencies, Case 4

NOTE: The trades made in this case are identical to the base case.

We see that by not currency-hedging bonds, performance has a negligible change. Compared to the base case, the annual return increases by an average 20 basis points for the CAD, AUD, GBP and JPY versions. The standard deviation rises, although only by 60 basis points. Overall, the Sharpe ratio drops by an average of a mere 2.6%.

It is expected that results would drop, since when you are in bonds, GEM has no mechanism to control your currency risk like it does when you are in stocks. It is also expected that the performance drop would be minor, since GEM was only in bonds 20% of the time over the past 43 years. The interesting conclusion is that GEM (JPY) was hardly affected despite the JPY:USD rate tripling over the back test period.

Because whether you currency-hedge bonds or not makes little difference to performance, foreign investors are advised to permanently leave their portfolio on the US exchange, the same as US investors. This saves the hassle and cost of switching between US and local exchanges every time GEM switches between stocks and bonds.

CONCLUSION

We performed a 43-year back-test of GEM from the perspective of various foreign investors (Canadian, Australian, British, and Japanese). During the back test period, Japanese investors saw their local currency appreciate considerably (over 300%) against the USD, while the other 3 investors saw their local currency fall (between 20-40%) against the USD.

In both rising and falling currency environments, we have shown that all world investors can still use Dual Momentum to considerably outperform traditional fixed-allocation portfolios.

We see that the ideal way for foreign investors to implement GEM is to permanently have their portfolio on the US exchange. Foreign investors would be exposed to currency risk when the model is in bonds, but this hardly affected GEM performance over the past 43 years. This would give the results in case 4.

The second best way to implement GEM would be for foreign investors to trade on the US stock exchange when GEM is in equities and on their local exchange when GEM is in bonds. In the latter case, investors should either use their local country’s aggregate bond index or a currency-hedged version of the US Aggregate Bond Index, if available. This reduces currency risk when the foreign investors are in bonds, but there would be the on-going cost and hassle of switching between local and US exchanges. This would give the results in case 1 (base case).

We realize it is not possible for all foreign investors to trade on the US exchange. The third best way to implement GEM is for investors to have their portfolio permanently on their own local exchange. However, since an ETF tracking the ACWI ex-US index will likely be unavailable, investors would have to use an ETF tracking the MSCI EAFE index. EAFE is not as good as ACWI ex-US, but at least the investor does not have to worry about currency conversions and currency risk. This would give the investor the results in case 3.

It should be noted that investors wanting to have their portfolio permanently on their own local stock exchange should not use currency-hedged equity ETFs. Doing so would greatly diminish the relative performance between US and non-US equities. Foreign investors significantly outperform a fully-hedged GEM model when their local currency falls relative to USD. And when their local currency appreciates significantly, the fully-hedged GEM model does not perform that much better.

No matter which of the above 3 execution methods are used, foreign investors are best advised to do the GEM analysis in USD. This was shown in case 2. Best wishes to all of you with GEM.

- Gogi Grewal

[1]Looking at this comprehensive ETF Industry Guide published annually by State Street Global Advisors, we see that there are ETFs tracking some foreign countries’ bond indices, but not all. For example, Canada’s Aggregate Bond Index is not available on the US exchange.

↧

Momentum and Stop Losses

June 13, 2015, 12:44 pm

≫ Next: Momentum Due Diligence

≪ Previous: Dual Momentum for non-US Investors

Stop losses are a form of trend following in which you switch from risky assets, such as stocks, to a risk-free or fixed income asset after there are pre-determined cumulative losses. The random walk hypothesis (RWH) was widely accepted in the 1960s and 1970s. It was synonymous with market efficiency. It effectively eliminated any academic interest in stop loss rules. Under RWH, with stock returns being independent, stop losses would decrease a strategy’s expected return.

There remains a cultural affinity to RWH despite strong contrary evidence now. This may explain why there is still considerable indifference to stop loss policies and trend following in general among institutional investors who were schooled in old academic ideas.

In their paper, “When Do Stop-Loss Rules Stop Losses?”, Kaminski and Lo (2013) show both mathematically and empirically that if stock returns have positive serial correlation (there is overwhelming evidence they do), then stops can add value. Over monthly intervals using daily stock futures data from 1993 through 2011, the authors found that volatility-based stop loss rules could increase monthly returns 1.5%, while substantially decreasing volatility. They found that slower moving stops worked best.

In “Taming Momentum Crashes: A Simple Stop-Loss Strategy”, Han, Zhou, and Zhu (2014) showed the effectiveness of a stop loss overlay applied to a momentum-based strategy. The authors examined the top decile of U.S. stocks from 1926 through 2011 based on relative strength momentum over the preceding 6 months (the authors showed similar results using 12-month momentum). They sold any stock if it's daily opening or closing price dropped 10% below the beginning price of the month. They followed the same procedure for short positions. Portfolios were rebalanced monthly.

This stop loss strategy raised the average monthly return from 1.01% to 1.73% (buy and hold was 0.62%) and reduced the monthly standard deviation from 6.07% to 4.67%.[1] Momentum crash risk (from short positions) was completely eliminated. Results from using a 5% stop were even better.

The worst monthly return for buy and hold was -28.98%, while the worst monthly return for an equally weighted momentum strategy was -49.79%, showing the increased risk from applying relative momentum to individual stocks. A 10% stop loss overlay improved the worst monthly return to only -11.34%. For value weighted rather than equal weighted portfolios, the maximum monthly loss for momentum and 10% stop loss portfolios were -65.34% and -23.69%, respectively. Average returns and Sharpe ratios doubled by using stops.

This stop loss strategy also had a positive skewness of 1.86, versus a negative skewness of -1.18 for the original momentum strategy, indicating a dramatic reduction in left tail risk when using stops.

Both these papers show theoretically and empirically that risk control overlays, such as stop loss rules, can have dramatically positive effects on momentum-based strategies. This applies also to other trend following methods of risk control, such as moving average filters and absolute momentum, that can work as well or better than stops (the subject of a future post).

Stop losses and other trend following methods are a way to head off some of the usual pitfalls of human judgement, such as the disposition effect, loss aversion, ambiguity aversion, and flight-to-safety. There is no reason why they should not be used by all momentum investors.

[1] Stop losses increased trading activity by 40%, but increases in return of about 70% helped overcome these high transaction costs.

↧

Momentum Due Diligence

June 18, 2015, 10:09 am

≫ Next: Value and Momentum are Correlated

≪ Previous: Momentum and Stop Losses

Sometimes I get asked how well momentum has done the past year or the past several years. If I am in a snarky mood that day, I’ll respond, “What will that tell you?” The truth of the matter is that, in most cases, short-term performance is indistinguishable from noise and cannot tell you anything meaningful.

Here are the questions that one should ask instead:

1) Why does momentum investing make sense? What is the economic rationale behind it?
2) Why should momentum investing continue to outperform in the future?
3) What are the possible drawbacks to momentum investing?
4) How is momentum investing robust? How much out-of-sample validation is there?

Let us examine the answers to these questions one at a time.

Does It Make Sense?

Until the 1990s, most academics did not accept momentum due to the efficient market hypothesis (EMH). EMH said that nothing could consistently beat buy-and-hold. In the 1990s, Lo and MacKinlay and others showed that stocks have positive autocorrelation (serial correlation). This meant that stock returns are trending, which contradicts the EMH and opened the door for momentum researchers.

In 1993, Jegadeesh and Titman issued their seminal study demonstrating the effectiveness of relative strength price momentum with U.S. stocks. Almost immediately, researchers began searching for reasons that could explain why momentum worked so well. The most cogent explanations have been based on behavioral factors, such as anchoring, herding, and the disposition effect. These can cause stocks to underreact on a short-term basis and overreact longer term. Chapter 4 of my book explores this in more detail. No one knows precisely which factors cause momentum to work so well, but there are plenty of viable explanations for it, and there is no longer any doubt that momentum does offer superior risk-adjusted returns.

Will It Continue?

I also point out in my book that behavioral factors, such as herding, are ingrained in our DNA. They are not easily changed, and they therefore create formidable limits to the arbitraging away of extraordinary momentum profits.

Furthermore, there are plenty of non-momentum investors out there, such as value seekers, fundamentalists, buy and holders, etc. Both relative and absolute momentum are based on autocorrelation, which is trend following. Relative momentum looks at an asset's trend compared to other assets, while absolute momentum looks at an asset's trend compared to its own past. There has been so much prejudice against all forms of trend following that momentum may never attract the attention that it really deserves.

Possible Drawbacks

There are two commonly perceived drawbacks to momentum investing, and they both pertain to relative rather than absolute momentum. First are the so-called "momentum crashes" that occur on the short side of long/short momentum portfolios when stocks rebound sharply at bear market bottoms. In practice, however, very few investors actually use long/short momentum portfolios. Shorting can be problematic, and stocks have a natural upside bias over time.

The second potential problem is the increased left-tail risk (drawdown) associated with relative strength momentum. This can be easily overcome by using both absolute (time-series) and relative momentum together as dual momentum. Absolute momentum not only improves risk-adjusted return, but it can dramatically reduce left-tail risk.[1]

Robustness

Robustness is a key factor in ascertaining the continued efficacy of momentum or any other investment approach. There are several ways to assess robustness. Here are some common ones:

1) How simple and straightforward is the model? Simpler means there is less chance of over fitting and mining the data, which may give spurious results.

Momentum is very simple. It has only one main parameter, the look back period.

2) How well does the model hold up when its parameter values change?

Momentum works well over a broad range of look back periods ranging from 3 to 12 months.

3) How well does the model hold up when it is applied to other markets?

Momentum is effective with and across many different asset classes, including U.S. stocks, non-U.S. stocks, industries, global sectors, country indices, bonds, commodities, currencies, and real estate.

4) How stable are the model parameters over time? How consistent are the results?

Cowles and Jones were the first to discover the effectiveness of momentum back in 1937. They used a 12-month look back period applied to U.S. stocks. This 12-month look back has held up remarkably well ever since. The following table from RBC Capital Markets shows that 12-month based momentum has consistently earned higher returns than buy-and-hold for every decade since 1930:

5) How has the model performed on out-of-sample data? How far back does the new data go?

These are the most important factors, and we will devote the rest of this report to that topic.

Out-of-Sample Validation

The Cowles and Jones study showed momentum earning extraordinary profits with U.S. stocks from 1920 through 1935. The Jegadeesh and Titman study corroborated the research by Cowles and Jones and included a longer test period from 1962 through 1989.

Since Jegadeesh and Titman's paper in 1993, there have been dozens of additional studies validating momentum on new data and additional asset classes throughout the 1990s and 2000s. Several years ago, Ken French added momentum to his online data library allowing researchers to further validate U.S. stock momentum continuously back to the year 1927.

One study using the additional data was by Israel and Moskowitz (2012). The authors found that long-only momentum produced an annual information ratio almost three times larger than value or size. The momentum premium was positive and statistically significant in every 20-year period through 2011.[2] Going back further in time, Chabot et al. (2009) showed that abnormal stock momentum profits held up well going back to 1866 in Victorian England.

In 2013, the longest back test yet of relative strength momentum was by Geczy and Samonov in their paper “212 Years of Price Momentum - The World’s Longest Back test: 1801-2012”. The authors showed that U.S. stock momentum profits remained positive and statistically significant throughout the 212 years of their data. The equally weighted top third of stocks sorted on momentum outperformed the bottom third by 0.4% per month (t-stat 5.7).

In their most recent paper, “215 Years of Global Multi-Asset Momentum: 1800 – 2014 Equities, Sectors, Currencies, Bonds, Commodities, and Stocks”, Geczy and Samonov (2015) extended their earlier work to include a 215-year history of multi-asset momentum with six different asset classes. They found the momentum premium to be consistently significant in every asset class, across asset classes, and in combination with each other. They also found comparable results applying absolute (time-series) momentum to the same data.[3]

What It Means

During the past 25 years, there is nothing in finance that has been so extensively researched and back tested as price momentum. If academics were going to discard the EMH, they wanted a mountain of evidence before doing so.

As practitioners, we are fortunate to have this much out-of-sample validation showing the consistency and effectiveness of momentum, not to mention all the other indications of robustness. The best due diligence one can do with respect to momentum investing is to read the above referenced research papers and some of the others freely available on the Social Science Research Network (SSRN).[4] You could also read the studies referenced in my book and examine all the pages of my website.

Rigorous and extensive research has clearly shown that momentum offers superior risk-adjusted returns. It is the strongest known anomaly, and is stronger than value, buy-and-hold, and everything else that has been extensively studied. If your core investment portfolio does not utilize momentum, then you are missing the boat.

[1] See my book on Dual Momentum Investing or my research paper on absolute momentum.
[2] For more details, see my post “Momentum…the Only Practical Anomaly?”
[3] There are other studies going back 200 or more years validating absolute momentum.
[4] The word “momentum” appears in the titles of 667 SSRN papers.

↧

Value and Momentum are Correlated

July 7, 2015, 7:37 am

≫ Next: Back to Fundamentals

≪ Previous: Momentum Due Diligence

One of the most popular research papers on momentum is “Value and Momentum Everywhere” by Asness, Moskowitz, and Pedersen. In June 2013, this was published in the prestigious Journal of Finance. I have an earlier blog post which discussed that paper. However, one important item slipped by me then. It was a statement by the authors that value and momentum strategies are negatively correlated. They cited a negative monthly correlation coefficient between value and momentum of -0.24. Asness and his crew have brought up this negative correlation in subsequent writings regarding the merits of momentum and value investing.[1] Other writers and speakers have also been expounding this idea of negative correlation between value and momentum strategies.

Long/Short Versus Long Only

However, the Asness et al. study dealt only with long/short momentum and value. This is where you are long high book-to-market and high price appreciation stocks, while simultaneously short low book-to-market and low price appreciation stocks. As we will see, the correlations between long/short value and momentum are substantially different than the correlations between long-only value and momentum.

Why is this important? It is because the vast majority of the investing world uses long-only rather than long/short portfolios. This applies to both value and momentum strategies. In looking at dozens of mutual and exchange traded funds, there are few if any value/growth oriented funds (other than those from AQR using muti-assets or multi-factors) that have a balanced long/short portfolio. With momentum, I know of only a single public fund (MOM) that uses a long/short approach, and it is tiny with only $1.23 million in assets.

Therefore, correlations between value and momentum using long/short portfolios are largely irrelevant and may be misleading to many investors. We will determine the correlations between U.S. value and momentum stocks using long-only portfolios from the Kenneth French Data Library. We will use the value weighted top one- third of book-to-market value stocks and the top one-third of momentum stocks measured over their prior 2-12 month's performance during the past 87 years. We will use stocks above the median NYSE in market capitalization..These are the ones that are most commonly traded. By using only large and mid-cap stocks, we avoid the problems associated with micro-cap liquidity.

Besides looking at separate value and momentum portfolios, we will also examine a portfolio allocated 50/50 to value and momentum with monthly rebalancing. Our benchmark will be all stocks above the median NYSE market capitalization. No transaction costs or other expenses are deducted.

Correlations

Here are the monthly correlations from February 1927 to June 2015:

	MOM	VALUE	50/50	MKT
MOM	1.00	0.81	0.94	0.90
VALUE		1.00	0.96	0.92
50/50			1.00	0.96
MKT				1.00

The correlations of value and momentum to the market index are 0.92 and 0.90, respectively. As expected, these correlations are high. What may not be expected is that the correlation between long-only value and long-only momentum is also high at 0.81. This is dramatically different from the Asness et al. -0.24 monthly correlation between idiosyncratic long/short momentum and value. This difference has important implications for what long-only investors might expect if they invest in both value and momentum.

Performance Statistics

The return of any blended portfolio is a weighted average of the component returns regardless of the correlations. However, the risk exposure of a blended portfolio can differ greatly based on the correlations between the components. If those components have low or negative correlation, then there should be a substantial reduction in portfolio volatility. However, if the component correlations are strongly positive, as they are with long-only value and momentum, then there may be little reduction in risk by combining them. We see this is the case looking at results from February 1927 to June 2015:

	MOM	VALUE	50/50	MKT
ANN RTN	15.70	15.23	15.46	11.73
STD DEV	19.21	24.75	20.95	20.44
SHARPE	0.59	0.44	0.53	0.38
MAX DD	-77.4	-89.0	-83.9	-88.0

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.

The momentum portfolio has the highest return and the highest Sharpe ratio. However, a momentum portfolio of individual stocks also has very high turnover. There is some controversy as to how high the associated transaction costs may be. See Novy-Marx and Velikov (2014) for an up-to-date analysis of these costs and a review of earlier cost studies.

Value shows almost the same return as momentum and also a higher Sharpe ratio than the large/mid-cap market benchmark.We should understand that if value and momentum had a low or negative correlation, then the standard deviation of a 50/50 mix of value with momentum would likely show a lower volatility than either value or momentum individually. That is not the case here. The standard deviation of the blended portfolio is higher than the standard deviation of the momentum portfolio. It is, in fact, almost identical to the volatility of the market portfolio.

Drawdown

The same is true with respect to maximum drawdown. The market and value portfolios show around the same maximum drawdown of -88 to -89%. This is based on month-end values. Intra-month drawdowns would be higher. I cannot imagine anyone being comfortable losing more than 90% of their portfolio value. The maximum drawdown of the momentum portfolio is a little better at -77.4%, but the maximum drawdown of the value/momentum blended portfolio is back up to -83.9%.

So should there be value and momentum everywhere? We didn't think so before, and we don't think so now, at least not for long-only investors. Momentum without value shows the highest return, highest Sharpe ratio, lowest volatility, and lowest maximum drawdown. But its -77.4% maximum drawdown is still uncomfortably high, and high transaction costs may substantially reduce these momentum returns.

Summary

One way to reduce large downside exposure as well as boost expected returns in the long-run is by using dual momentum as explained in my book and throughout this blog. The absolute momentum component of dual momentum boosts the Sharpe ratios of all the above portfolios and cuts their maximum drawdown almost in half. Perhaps what we should say is, “dual momentum everywhere.”

[1]See reports by the AQR posse, “Fact, Fiction, and Momentum Investing” and “Investing with Style”.

↧

Back to Fundamentals

July 20, 2015, 11:45 am

≫ Next: Understanding Dual, Relative, and Absolute Momentum

≪ Previous: Value and Momentum are Correlated

After winning two consecutive national championships, the Green Bay Packers lost a game due to sloppy play. Coach Lombardi called a meeting the very next day to get his team back to fundamentals. When all the players were assembled, Lombardi held a football high up in the air and declared, “Gentlemen, this is a football!” From the back of the room, running back Paul Hornung shouted back, “Coach, can you slow down?”

Sometimes we all need to be reminded of fundamentals. The fundamental goal of investing should be to receive the most gain with the least pain. The question then becomes, how do we achieve this?

Asset Returns

The first step is to select the best investment assets. The following chart shows the annualized real returns of U.S. stocks, bonds, and Treasury bills since the years 2000, 1965, and 1900.

Source: Credit Suisse Global Investment Returns Yearbook2015

Over the past 100+ years, stocks have provided more than three times the real return of bonds despite the unusually strong bond market of the past 35 years. A much higher long-run return from stocks makes sense, since stocks are considerably riskier than bonds. They should therefore compensate investors with a higher risk premium.

The following chart by Wharton professor Jeremy Siegel shows the same dynamic over 200 years from the years 1802 to 2012.

Source: Stocks for the Long Run, 5th edition, Jeremy Siegel

Again we see that over the long-run, stocks have earned the highest return by a large margin. The annualized real return of U.S. stocks has been nearly twice as high as the annualized return of bonds since 1802.

Drawdowns

Even though returns are maximized, the problem with holding only stocks in one's portfolio is their high volatility and negative skewness. These create considerable left tail/drawdown risk. There have been two bear market drawdowns in U.S. stocks greater than 50% during just the past 15 years.

Not only can large equity erosions create discomfort and uncertainty in the minds of investors, but they can cause investors to react in ways that are counter to their own best interests. The yearly Dalbar studies show that investors underperformed the funds they were invested in by an average of 4% annually over the past 20 years. Poor timing by investors is often attributable to emotionally induced buying and selling.

Diversification

In order to reduce the emotional stress and poor timing decisions triggered by high stock market volatility, investors have traditionally diversified their portfolio into assets other than stocks. The main alternative has historically been bonds. However, as we saw from the above charts, our long-run expected return decreases substantially as we add bonds or assets other to an all stock portfolio.

Yet this diminished return has not stopped investors from adopting so-called balanced portfolios, such as the common one that allocates 60% to stocks and 40% to bonds. Even Harry Markowitz, the father of modern portfolio theory, split his personal investments equally between stocks and bonds.

Based on financial planning principles, some investors start off with a higher allocation to stocks in their early years and then switch to a greater allocation to bonds as they grow older. This may no longer be as prudent a strategy as it once was. The average life expectancy today of someone reaching the age of 65 is 19 years. The lengthening of retirement years and emphasis then on bond investing can aggravate the problem of portfolio under performance. Investors may need a way to keep growing their investment assets well beyond their retirement age.

Wealth Accumulation

What exactly does the old paradigm of a balanced stock and bond portfolio mean in terms of wealth accumulation over the long-run? To determine this, I looked at a rolling 40-year window comparing the performance of the S&P 500 to a portfolio invested 60% in the S&P 500 and 40% in10-year U.S. Treasuries from 1900 through 2014.

During that time, the average annual total return of the S&P 500 was 10.0%, compared with 8.3% for the 60/40 stock/bond portfolio.[1] Applying these average rates of return to a 40-year investment horizon, a $10,000 initial investment in the S&P 500 would have grown to $537,000 before expenses and taxes, while a $10,000 investment in the 60/40 stock/bond portfolio would have become only $273,500. Due to the power of compounding, an all-stock portfolio would have resulted in almost twice the accumulated wealth of a 60/40 balanced portfolio.

Many do not realize the impact over time of an extra 1-2 % per year in return and what a large difference it can have on one's accumulated wealth. (There might be far less money under active management now if investors were fully aware of this fact.)

High Costs of Diversification

In addition to lower expected risk premiums, there are substantially higher costs associated with diversification that many investors are not fully aware of. In their study “Fees Eat Diversification’s Lunch,” Jennings and Payne (2014) state that fees on diversifying assets are astonishingly high relative to their benefits. (On a real time basis, other assets have to compete with U.S. stock index funds having annual expense ratios of only 4 or 5 basis points.)

In the 1970s, U.S. investors started to look seriously at the diversifying their stock holdings internationally, despite the fact that non-U.S. stocks since 1900 have returned on average 2% less per year than U.S. stocks. Jennings and Payne found that fees reduced the benefit of international diversification by one-third for small institutional investors. Fees almost completely eliminated any diversification benefit from investing in emerging market bonds, hedge funds, and private equity. In looking at 45 different asset classes, Jennings and Payne found that fees consumed over half the expected benefit in more than 60% of those markets.

A Practical Solution

Is there anything investors can do to reduce their downside exposure during equity bear markets without giving up half their accumulated wealth in the process? Our dual momentum based Global Equities Momentum (GEM) methodology diversifies one’s portfolio in a more intelligent way.[2] GEM’s core holding is the S&P 500 in order to capture the highest long-run risk premium. GEM switches between U.S. and international stocks according to relative strength price momentum, which can improve the expected return from holding stocks. The GEM model also switches between stocks and bonds in accordance with trend-following absolute (time-series) momentum. When equities have been going up according to the rules of absolute momentum, GEM stays fully invested in stocks. When the trend of the stock market turns negative, GEM switches into low-duration aggregate bonds. Bear markets in stocks often foreshadow economic recessions with falling or flat interest rates. These are often the best times to hold bonds. Dual momentum is an adaptive approach that diversifies in a temporal way, which makes the most sense.

Here is the performance of GEM compared with the S&P 500 index and a portfolio allocated 60% to the S&P 500 and 40% to10-year Treasuries from January 1974 through June 2015. Positions are rebalanced monthly.

Performance of GEM

GEM S&P 500 60/40
Ann Rtn 17.73 12.33 10.76
Std Dev 12.36 15.43 9.74
Sharpe 0.89 0.41 0.50
Max DD -17.84 -50.95 -30.54

GEM has a considerably lower maximum drawdown than the 60/40 stock and bond portfolio. In addition to providing greater downside protection than afforded by the 60/40 portfolio, GEM returns have been significantly higher than the returns of the S&P 500 portfolio. Large losses in the S&P 500 need to be recouped before stocks can again show a net profit. For example, it takes a 100% gain to get back to even after a 50% loss. By sidestepping severe bear market losses, GEM can earn higher overall profits.

GEM remains in stocks when the trend of the stock market is positive in order to capture all it can of the high risk premium associated with stocks. GEM retreats to the safety of bonds during the 30% of the time when stocks are weak and bonds are often their strongest.

Possible Concerns

Why would anyone want to adopt a permanent stock/bond portfolio with its fixed income drag on performance when a simple dual momentum approach like GEM has shown considerably less downside exposure and substantially higher expected return than either an all-stock or a balanced stock/bond portfolio?

The first reason in some minds is that the future may not be like the past.But dual momentum is a simple model with several hundred years of out-of-sample performance to support it. The GEM look back parameter used by Cowles and Jones in 1937, has held up well back to the early 19th century and up to the present time. There are also good reasons, as described in my book, why the momentum effect should continue to persist.

The next concern may be occasional re-entry lags when a new bull market begins after dual momentum has protected your portfolio from the preceding bear market. There may also be occasionalwhipsaw tradesat other times that can cause dual momentum to temporarily lag behind the stock market. Over the past 40 years, GEM underperformed the stock market in 1979-80 and 2009-10.

No strategy can outperform all the time. Career risk associated with tracking error, long-standing aversion to market timing, and confirmation bias may keep institutional investors from ever using dual momentum.[3] As an encouraging note for the rest of us, this attitude should help keep momentum from being over exploited.

Finally, the trend-following component of GEM is slow moving so as to minimize whipsaws. This means that GEM is still subject to the volatility associated with short-term stock market fluctuation. Very conservative investors can allocate a modest portion of their portfolio permanently to bonds in order to attenuate this volatility.

Volatility Attenuated Dual Momentum

Here is what would have happened if we had allocated 75% of our investment portfolio to GEM and 25% permanently to aggregate bonds from January 1974 through June 2015.

	GEM	GEM/25	60/40
Annual Rtn	17.73	15.34	10.76
Std Dev	12.36	9.69	9.74
Sharpe	0.89	0.92	0.50
Max DD	-17.84	-11.88	-30.54

The GEM/25 allocation now has the same volatility as the 60/40 portfolio, but GEM/25 has a substantially higher annual return and Sharpe ratio. The maximum drawdown of GEM/25 is only 39% as large as the maximum drawdown of the 60/40 portfolio.

We see that dual momentum in various forms meets our fundamental goal of investing – the most gain with the least pain.

[1] Both portfolios had the same 40-year minimum average return of 5.4%. On the basis of avoiding the lowest average portfolio return, the 60/40 portfolio was not any better than the S&P 500 portfolio over a 40-year time frame.
[2] The GEM model is fully disclosed in my book, Dual Momentum Investing. It takes less than 5 minutes per month to apply it.
[3] Even those who understand and appreciate momentum can be subject to long-standing biases that keep them from using momentum in a significant way.

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Understanding Dual, Relative, and Absolute Momentum

April 13, 2015, 6:59 am

≫ Next: Momentum Back Testing

≪ Previous: Back to Fundamentals

Years ago when I first started studying momentum, two things stood out in my mind. The first was most momentum research focused on cross-sectional stock studies looking at the future performance of stocks that had been strong versus stocks that had been weak. This was what interested academics most, since abnormal profit from strong versus weak stocks was relevant to whether or not the stock market was efficient. Researchers have done extensive out-of-sample validation testing of momentum.[1] As a further check on the robustness of cross-sectional stock momentum, researchers looked at relative strength momentum applied to other assets and asset classes. They found that momentum worked well on almost everything. Past winners consistently outperformed going forward. This prompted Fama and French, two of the founders of efficient market theory, to call momentum the premier anomaly and to say that it is pervasive.

My first momentum research paper in 2011 applied relative momentum to stock market style, industry, and geographic sectors. I wanted to focus on equities because that is where risk premium and investment returns have been the highest over the long-run. I also reasoned it would be easier to apply momentum to market indexes or sectors rather than individual stocks, and that this would have much lower transaction costs and taxes than momentum applied to individual stocks. Academic research has shown that momentum applied to asset classes, market indexes, and sectors is just as strong as momentum applied to individual stocks. Broader applications of momentum would avoid the high transaction costs that could greatly reduce momentum profits.[2]

I also noticed that while relative momentum could lead to higher returns than buy-and-hold, it did little or nothing to reduce left tail risk during bear markets. In fact, bear market drawdown could be higher with relative momentum rather than without it. My first momentum paper dealt with this problem by including short and intermediate term bonds as additional asset classes. When the relative strength of stocks became less than the relative strength of short or intermediate term bonds, my model would switch into bonds. This reduced left tail risk considerably.

My next research paper in 2012, “Risk Premium Harvesting through Dual Momentum,” (winner of the 2012 NAAIM Wagner Award for Advances in Active Investment Management) expanded on what I had done earlier by clearly identifying two types of momentum: relative and absolute.[3]

Researchers had found that both types of momentum were robust across sub-sample periods, look-back periods, and holding periods. Both types of momentum gave higher risk-adjusted returns than buy-and-hold, and both held up well in extensive out-of-sample back testing. Besides comparing and utilizing relative and absolute momentum, my 2012 paper also introduced the concept of dual momentum, a synergistic approach that benefited from the enhanced returns achieved from both forms of momentum, as well as the reduced left tail risk and lower drawdown that come from including absolute momentum.

There has been a massive amount of research on relative momentum over the past 20 years. In fact, relative strength/cross-sectional momentum has been one of the most heavily researched areas in modern finance. However, until recently there has been relatively little research done on absolute momentum. My 2013 paper “Absolute Momentum: A Simple Rule-Based Strategy and Universal Trend-Following Overlay” was an attempt to help balance that mismatch. Two of my more recent blog posts have also focused on absolute momentum.

The post “And the Winner is…” described an 800 year back test of a variation of 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 during 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 trend following 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 only 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.

The “Absolute Momentum Revisited” post was my own out-of-sample research of absolute momentum on U.S. stocks back to the year 1927. Absolute momentum continued to show a higher Sharpe ratio, as well as substantially reduced volatility and maximum drawdown compared to a buy-and-hold approach. I concluded the post by saying, “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 others.”

Before returning to dual momentum, I would like to mention a new study by Zakamulin (2015) called “Market Timing with Moving Averages: Anatomy and Performance of Trading Rules.” The author looked at absolute momentum (which he called the "momentum rule") and 5 different moving average rules, including the 10-month (200 day) simple moving average often written about and used as a trend following filter. The author applied these rules to the S&P Composite stock market index from 1870 to 2010. Estimated transaction costs were accounted for, and all models were invested in U.S. Treasury bills when not in stocks. This 140 year study is now one of the longest back tests of trend following methods, including absolute momentum.

The study found that the majority of the trend following rules had better risk-adjusted out-of-sample performance than buy-and-hold. Absolute momentum was one of two trading rules that showed statistically significant outperformance. The other was a reverse exponential average. Among these rules, absolute momentum.produced the best results. Before getting too enamored with absolute momentum, we need to return to the overall theme of this blog and my book, which is dual momentum.

Here are the updated performance figures from 1974 through March 2015 for the absolute momentum part of dual momentum applied to the S&P 500 and MSCI All Country World Index ex-US (ACWX) indexes used in my Global Equities Momentum (GEM) model featured in my book and tracked on my website. The Barclays Capital U.S. Aggregate Bond Index is the safe harbor asset when absolute momentum exits equities. The GEM model is easy to implement, and its parameters have been validated in many academic papers.

	S&P500 AbsMom	S&P500	ACWX AbsMom	ACWX
Annual Return	14.3	12.3	14.0	11.6
Annual Std Dev	12.2	15.4	12.2	17.2
Sharpe Ratio	0.66	0.41	0.64	0.32
Max Drawdown	-29.6	-51.0	-23.1	-57.4

	Dual Momentum	Relative Momentum	S&P500 AbsMom	ACWX AbsMom
Annual Return	17.7	14.7	14.3	14.0
Annual Std Dev	12.4	15.8	12.2	12.2
Sharpe Ratio	0.89	0.53	0.66	0.64
Max Drawdown	-17.8	-54.6	-29.6	-23.1

Relative momentum, like absolute momentum, gave higher returns than the indexes themselves. Relative momentum, however, unlike absolute momentum, did nothing to reduce volatility or tail risk/maximum drawdown. If I were forced to choose between using relative or absolute momentum, I would choose absolute momentum. However, as I clearly point out in my book, you do not have to pick one over the other. You can use both simultaneously, and that is where the magic happens - combining absolute and relative momentum to create dual momentum.

We see that dual momentum gave us a substantial increase in average and risk-adjusted returns compared not only to the underlying indexes, but also to relative and absolute momentum individually. In addition, dual momentum's maximum drawdown is the lowest of all.

With dual momentum, the whole is greater than the sum of its parts. Dual momentum is the preferred momentum strategy here with respect to large cap U.S. and non-U.S. equity indexes.[4] That is why I call this blog “Dual Momentum,” and my book Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk.

[1] Geczy and Samonov (2012), for example, showed that momentum was highly effective on U.S. equities back to 1801.
[2] See Lesmond et al (2004), "The Illusionary Nature of Momentum Profits."
[3] Some academics refer to absolute momentum as time series or trend following momentum. However, both relative and absolute momentum are based on economic time series (asset prices), and both are trend following. Relative strength momentum looks at the trend of one asset versus other assets, while absolute momentum looks at the trend of a single asset with respect to its own past.
[4] On the Performance page of my website, I show historical returns and track the real time performance of four other dual momentum models.

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Momentum Back Testing

September 6, 2013, 3:41 pm

≫ Next: CAPE Crusaders?

≪ Previous: Understanding Dual, Relative, and Absolute Momentum

In 1937, Cowles and Jones published the first study showing that relative strength price momentum leads to abnormally high future returns. These findings are just as valid today as they were 75 years ago. Academics have been very diligent in studying momentum further, since it flies in the face of the efficient market hypothesis (EMH). EMH says you cannot beat the market using publicly available information. Hundreds of subsequent tests over the past 20 years have confirmed the veracity of momentum investing. Momentum is slowly gaining the attention it deserves as the investment world's "premier market anomaly" that is "beyond suspicion"(words of Fama & French).

Last week there was an interview of me on the MyPlanIQ blog. They asked about my work with dual momentum. I did not know at the time that MyPlanIQ intended to use my interview to promote their Tactical Asset Allocation (TAA) model. Since the details of TAA are unknown and proprietary, I cannot comment on the worthiness of their model. What I can say is I have nothing to do with any of MyPlanIQ's models and do not endorse them.

I have also noticed other advisory services, as well as some managed investment programs, that look like they have been inspired by my momentum research. I would like to make it clear that I am not involved with, nor do I endorse, any outside services.

There is a natural tendency to take others research, make a few changes to it, and hope you have created a better mousetrap. This often does not work out as expected. Here is why. High quality research is rigorous. Serious researchers subject their work to peer review and statistical significance testing. They disclose data sources and testing logic so other researchers can replicate their results. For high quality research, data is king. (I have come up with a saying: "One can never have too much money, good looks, or data.") Conscientious researchers are always trying to get as much data as they can for testing purposes. This reduces the chance of over fitting the data.

Fortunately, there has been a large amount of data available for back testing momentum. Academic researchers have consistently shown that momentum works across most markets and on out-of-sample data. Absolute momentum (trend following) has worked back to the turn of the century[i]. Relative strength momentum has worked all the way back to the beginning of the previous century![ii] This is important for two reasons. First, it leads to greater confidence in the results. Worst-case scenarios, in particular, are highly dependent on the amount of past data that is available. Second, with plenty of data, one can look at segments of the data to see how consistent and stable the results have been over time. We want to see that our overall results cover a wide range of market conditions are not dependent on just a few good periods of short-term performance. We also want to make sure our results have held up well over time and are still strong. This kind of robustness testing can reduce the chance of data snooping bias.

Another test of robustness is to look at other markets and see if your results hold up there as well. To do this in a meaningful way, you also need plenty of past data. This is why I go to the trouble of using indices instead of ETFs for my back testing. Whenever possible, I test my strategies using index data back to 1972, which is the beginning of fixed income index data. Data on a reasonable number of ETFs only goes back to 2003. There is a big difference in using forty years rather than ten years of data when you are testing strategies based on monthly price changes. In fact, one should be suspicious of any conclusions derived from using only ten or fewer years of data when evaluating intermediate term strategies like momentum. Yet that is precisely how most practitioners try to tweak and "improve" on my results, or on what they find in other momentum research papers. When working with monthly returns, ten or fifteen years is not much time. Results can easily be influenced by chance or happenstance, especially if there is not a convincing logical basis for your conclusions. What we can count on is that simple momentum works well across many different markets using a 3 to 12 month formation period. Anything else should be subject to rigorous and thorough evaluation that includes as many years as possible of past performance data, confirmation of your results in additional markets, parameter sensitivity and other robustness tests, drawdown analysis, etc.

There is another problem related to paucity of data, and that is data snooping (data dredging, data fitting) bias. Data snooping is pervasive among practitioners, and not just with respect to momentum. It can happen when you add a new parameter to a model or re-optimize existing parameters. Extensive data dredging and model over fitting can lead to spurious results and regression to the mean. A statistician friend calls this the Grim Reaper, because it can take away all or most of your expected future returns.

Data snooping often uses the same data more than once. Every data set contains patterns due entirely to chance. When you perform a large number of tests, some of them may produce false results that appear to be good. When the data itself suggests your hypotheses, it is impossible to tell whether the results are just chance patterns. If you do extensive data snooping, your evaluation criteria need to be much more stringent.

Some people think that splitting a modest amount of data into a testing set and a hold out set for cross validation will take care of this problem. However, that is not necessarily true. For example, you could split your data in half then rank your strategies based on looking at only the first half of the data. Going down your list strategies, you might find one that looks decent in both halves of the data. But it is still likely this is just due to chance, and you only have half as much data to use for back testing. Your odds go up if you use carefully constructed randomized out-of-sample tests. Otherwise, as the saying goes, "If you torture your data long enough, it will confess to anything."

About 20 years ago there was an infamous study that showed 99% of the return of the S&P500 index could be explained by a multiple regression on butter production in Bangladesh, US cheese production, and the number of sheep in the US and Bangladesh. The author of that paper still gets inquiries asking where to get data on Bangladesh butter production! More recently, a serious research paper (believe it or not) called "Exact Prediction of S&P 500 Returns" links future stock returns to the number of nine year old children in the US.

I recently came across someone offering momentum signals based on the same methodology and a very similar portfolio to the one in my first momentum paper. He water boarded the formation period parameters until the model showed an annual return of 41% over the past (guess how long) ten years. Further torturing the model's portfolio composition, he was able to come up with, and now promotes, annual returns of 73% over the past three years! If anyone thinks momentum (or anything else) can realistically provide annual returns of 73%, then I have a lovely bridge I would like to sell you.

If you cannot avoid significant data snooping bias, there is a False Discovery Rate test you can perform that will tell you if you have efficient criteria for model selection. Without something like this, you may be data snooping your way to nowhere.

Data Snoopy

[i] Moskowitz, Tobias J., Yao Hua Ooi, and Lasse Heje Pedersen, 2012, "Time Series Momentum,"Journal of Financial Economics 104, 228-250

[ii]Geczy, Christopher and Mikhail Samonov, 2013, "212 Years of Price Momentum (The World's Longest Backtest: 1801-2012)," working paper

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CAPE Crusaders?

September 24, 2013, 3:20 pm

≫ Next: Momentum...the Only Practical Anomaly?

≪ Previous: Momentum Back Testing

In their newest paper, "On the Performance of Cyclically Adjusted Performance Measures," Gray and Vogel challenge the popular belief that the Schiller P/E or Cyclically Adjusted Price Earnings (CAPE) ratio is the best way to look at value.

CAPE sounds intuitively appealing in that it inflation adjusts and averages earnings across a 10-year business cycle. Gray and Vogel take the Schiller P/E one step further and examine the 10-year inflation adjusted earnings concept with respect to other valuation metrics as well. Here is what they look at:

• 10-year average real earnings to market capitalization (CA-EM)

•10-year average real book values to market capitalization (CA-BM)

•10-year averagerealearningsbeforeinterest,taxes, depreciation, and amortization to total enterprise value (CA-EBITDA/TEV)

• 10-year average real free cash flow to total enterprise value (CA-FCF/TEV)

• 10-year average real free gross profits to total enterprise value (CA-GP/TEV)

Using NYSE, AMEX, and NASDAQ large and mid-cap data from July 1973 through December 2012, Gray and Vogel find that CA-BM was the best cyclically adjusted valuation metric relative to other valuation metrics. An annually rebalanced equal-weight portfolio of high CA-BM stocks earned 16.6 percent a year and generated the highest Sharpe (.64) and Sortino (.85) ratio among all cyclically adjusted metrics tested. Book-to-market as a valuation measure was popularized by Fama and French in the early1990's. While CA-BM is the marginal top performer over the past 40 years, all cyclically adjusted value measures have outperformed market benchmarks by large margins. Employing monthly rebalancing enhances the performance of all valuation measures. For example, the CA-BM strategy goes from a 16.6 percent compound annual growth rate (CAGR) to a 19.3 percent CAGR.

Last month, our post called Momentum Combinations showed how we can use momentum in different ways to customize portfolios and enhance performance. The Gray/Vogel dynamic duo also looks at integrating momentum with cyclically adjusted valuation measures to enhance returns. Using monthly-rebalanced portfolios, our anti-CAPE crusaders split each valuation decile into high and low momentum. Employing this additional momentum screen adds at least 100 basis points in return while decreasing maximum drawdowns modestly across the different valuation metrics. Holy Momentum, Batman!

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Momentum...the Only Practical Anomaly?

October 2, 2013, 7:52 pm

≫ Next: Momentum Hierarchy

≪ Previous: CAPE Crusaders?

Interest in momentum is growing as it gains recognition as the premier market anomaly. Our purpose here is not to report on every item or research finding related to momentum. We prefer instead to point out those that are most important or interesting because they seem exceptionally good, or, occasionally, because they seem exceptionally bad.

One exceptionally good piece of research is the working paper by Israel and Moskowitz (I&M) called "The Role of Shorting, Firm Size, and Time on Market Anomalies." This paper has important implications not only for momentum investors, but also for those who are interested in size and value based investing.

Most research papers on relative momentum present it on a long/short basis where you buy winning stocks and short losing ones. In some papers, you can find some long-only results buried in a table somewhere. Except in my papers, it can be challenging to find visual representations or detailed analyses of long-only momentum. However, I&M offer some insightful analysis of long-only momentum. It is important to look at long-only results for two reasons. First, most investors are interested only in the long side of the market. Second, in the words of I&M:

Usingdataover thelast86yearsin theU.S. stockmarket(from1926to 2011) and over the last four decadesin internationalstock marketsand other assetclasses(from1972to 2011), wefind that theimportanceofshortingisinconsequentialfor allstrategies when lookingatrawreturns. For an investor who caresonlyaboutrawreturns,thereturnpremia to size, value,andmomentumare dominatedbythe contribution fromlongpositions.

Therefore, even if you are open to shorting, it does not make much sense from a return perspective. I&M charts and tables show the top 30% of long-only momentum US stocks from 1927 through 2011 based on the past 12-month return skipping the most recent month. They also show the top 30% of value stocks using the standard book-to-market equity ratio, BE/ME, and the smallest 30% of US stocks based on market capitalization (I&M find similar results using alternative measures of value having long-term histories, such as dividend yield and long-term reversals).

Long-onlymomentum producesan annualinformation ratioalmost threetimeslarger than valueor size. Long-onlyversionsof size, value,and momentumproducepositive alphas, but thoseofsize and value arestatisticallyweak and only exist in the second half of the data. Momentum, on the other hand, delivers significant abnormalperformancerelative tothemarket and does so consistently across all the data.[1]

According to I&M:

Lookingat marketalphas across decile spreads in the table above, thereareno significantabnormalreturnsfor sizeor valuedecile spreadsover theentire1926 to 2011 timeperiod... Alphasfor momentumdecileportfolio spread returns, on theother hand, are statisticallyand economicallylarge...

Looking at these finer time slices, there is no significant size premium in any sub period after adjusting for the market. The value premium is positive in every sub period but is only statistically significant at the 5% level in one of the four 20-year periods, from 1970 to 1989. The momentum premium, however, is positive and statistically significant in every sub period, producing reliable alphas that range from 8.9 to 10.3% per year over the four sub periods.

Here is one more table from their paper that shows in more detail the influence size has on momentum and value:

In the words of I&M:

Looking across different sized firms, we find that the momentum premium is present and stable across all size groups—there is little evidence that momentum is substantially stronger among small cap stocks over the entire 86-year U.S. sample period. The value premium, on the other hand, is largely concentrated only among small stocks and is insignificant among the largest two quintiles of stocks (largest 40% of NYSE stocks). Our smallest size groupings of stocks contain mostly micro-cap stocks that may be difficult to trade and implement in a real-world portfolio. The smallest two groupings of stocks contain firms that are much smaller than firms in the Russell 2000 universe.

So there you have it. Momentum returns are strong, stable, and largely unaffected by size over the entire 86-year sample period (and in eight other markets and asset classes.) Long-only value, on the other hand, shows positive alpha only among the smallest stocks and insignificant alphas among larger stocks. Since micro-cap stocks are much more costly and difficult to trade, most investors, and particularly institutional ones, avoid this area of the market. Not only is momentum the "premier market anomaly" as per Fama & French, but, contrary to popular belief, it may be the only practical anomaly that has held up well over the past 86 years.

[1] Before reaching any definitive conclusions, it is important to consider transaction costs with individual stock momentum, since momentum portfolio turnover can be ten times larger than value and size portfolio turnover.

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Momentum Hierarchy

October 18, 2013, 5:57 am

≫ Next: Introducing Global Equities Momentum

≪ Previous: Momentum...the Only Practical Anomaly?

The chart below shows how dual momentum, absolute momentum, and relative momentum stack up against one another with our Dual Momentum Sector Rotation model. (No allowance has been made for transaction or other costs.) The light brown line at the bottom of the chart is the S&P500. The dark brown line just above it is an equally weighted average of all the sectors we use. Its shape is similar to the S&P 500, which means that volatility and drawdown are similar to the market's volatility and drawdown. Equal weighting shows modestly higher returns, due to mean reversion profits from monthly re-balancing and equal, rather than capitalization, weighting across sectors.

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.

The purple line shows relative strength momentum. It has higher profits than equal weighting, but retains the performance characteristics of the S&P500. Relative strength momentum typically boosts returns, but does little to reduce volatility or drawdown. It is the best known and most commonly used form of momentum investing.

When we get to the green line representing absolute momentum, things change. Returns are better than with relative momentum. More importantly, the dips representing larger drawdowns flatten out or disappear. Absolute momentum was out of stocks during all of the 2001-02 and most of the 2008-09 bear markets.

In the hierarchy of investment returns, equal weighting with re-balancing beats the S&P500. Relative strength momentum beats equal weighting. Absolute momentum not only beats relative strength momentum, but it is more stable and consistent. If you have to choose just one approach, then absolute momentum looks best.

However, we are not limited to just one approach. The blue line shows what happens when you combine relative and absolute momentum. Returns improve further while retaining absolute momentum's more attractive risk profile. Dual momentum is where you really want to be.

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Introducing Global Equities Momentum

January 12, 2014, 1:06 pm

≫ Next: Book Musings

≪ Previous: Momentum Hierarchy

I feature Global Equities Momentum (GEM) in my forthcoming book, so it is time to introduce it on our website. GEM is a simple but powerful model that switches between the S&P 500 Index, the MSCI All Country World Index ex-US, and the Barclays Capital US Aggregate Bond Index based on dual momentum. GEM is long just equities as long as their trend is positive based on absolute momentum. When the trend of stocks is down, GEM is only in bonds. My book will fully explore the characteristics of this model and how investors can use it.

The long run risk premium (and expected return) of bonds is substantially lower than the risk premium of stocks, so stocks are the investment vehicle of choice as long as their trend is positive. There are, however, investors who, for fiduciary or other reasons, need to keep a permanent allocation to bonds. For this reason, we also track our model that maintains 60% in stocks and 40% in bonds. We call this Global Balanced Momentum (GBM). (Formally, we called it the Global Balanced Momentum Index.) GBM applies dual momentum to both stocks and bonds.

Finally, we continue to show the performance of dual momentum applied to US equity sectors. We call this Dual Momentum Sector Rotation (DMSR). Please check out all three of these models that are now on the P erformance Page of our website.

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