This blog is an adjunct to our Optimal Momentum investing website which can be found through the Website tab. It contains news and other information that may be of interest to momentum investors.

Thursday, September 11, 2014

Value and Momentum Revisited

Most academic research on momentum deals with individual stocks. Most applications of momentum are also oriented toward individual stocks. The three largest publically offered momentum programs (AQR momentum mutual funds, PowerShares DWA Momentum ETFs, and iShares MSCI USA Momentum Factor ETF) all use individual stock momentum. The only widely-available public program using momentum applied to asset classes was the ALPS Goldman Sachs Momentum Builder that recently went out of business due to lack of interest.

Yet momentum applied to individual stocks is not the ideal way to use momentum. Transaction costs due to high turnover of stock portfolios can negate much of the benefit of momentum investing. Momentum applied to broad-based indexes or sectors, on the other hand, can capture high momentum profits with much lower transaction costs.

Here is a table from my new book Dual Momentum Investing: An Innovative Approach to Higher Returns with Less Risk. (The book can be pre-ordered now from Amazon.) This table shows the performance of the AQR Momentum Index composed of the top one-third of the 1000 highest capitalization U.S. stocks based on 12-month relative strength momentum with a one-month lag. AQR weights their index positions based on market capitalization and adjusts the positions quarterly. For comparison, we show the performance of applying absolute momentum to the Russell 1000 by moving into aggregate bonds whenever 12-month absolute momentum is negative.

Table 9.2 AQR Momentum, Russell 1000, and Russell 1000 w/Absolute Momentum 1980-2013


AQR Momentum Index[1]
Russell 1000 Index
Russell 1000 w/Abs Momentum
Annual Return
15.14
13.09
15.92
Annual Std Dev
18.27
15.51
12.57
Annual Sharpe
 0.51
 0.49
 0.80
Max Drawdown
              -51.02
            -51.13
             -23.41

These figures do not account for the 0.7% per year in additional transaction costs for the AQR Momentum Index, would have put it at a disadvantage to even the Russell 1000 index on a risk-adjusted basis. 

The next table shows the AQR Momentum Index, the Russell 1000 Value Index, and a 50/50 combination of value and momentum, which was advocated in the Asness et al. (2013) paper "Value and Momentum Everywhere." This combination is supposed to be desirable due to the negative correlation between value and momentum. We see that value combined with momentum does give a slightly higher Sharpe ratio than either value or momentum alone. However, there is little or no advantage with respect to maximum drawdown, and the results still pale in comparison to simple absolute momentum used with the Russell 1000 Index.

Table 9.3 AQR Momentum, Russell 1000 Value, 50/50 AQR Momentum with Value 1980-2013


AQR Mom Index
Russell 1000 Value Index
50/50 AQR Mom with Value
Russell 1000 w/Abs Mom
 Annual Return
15.14
13.52
14.33
15.92
 Annual Std Dev
18.27
14.87
15.71
12.57
 Annual Sharpe
 0.49
 0.53
 0.55
 0.80
 Max Drawdown
          -51.02
       -55.56
          -51.47
             -23.41

As a further check on the possible worthiness of combining value with momentum, I used the Global Equity Momentum (GEM) model described and tracked on the Performance page of our website. Full disclosure of GEM and instructions on how to use it are in my new book. Using relative momentum, GEM switches between the S&P 500 and the MSCI EAFE when absolute stock momentum is positive. When absolute momentum turns negative, GEM moves into aggregate bonds. 

The table below shows GEM results from January 1974 through August 2014, as well as the results from adding the MSCI USA Value (large and mid-cap) index to GEM as an additional switching option. We see that the inclusion of value into the momentum model adds nothing to the performance of GEM.


GEM
GEM w/Value
Annual Return
17.43
17.24
Annual Std Dev
12.64
12.52
Annual Sharpe
  0.86
0.86
Max Drawdown
            -22.72
               -22.94

Furthermore, as I pointed out in a blog post last year called "Momentum…the Only Practical Anomaly?", Israel and Moskowitz of AQR, show in their 2013 paper that value, as it is commonly used, only offers a historic premium when applied to very small stocks. These stocks are generally unusable by institutional investors. How one can mix individual stock momentum (which may offer nothing special after transaction costs) with value (which may also not be all that it was once thought to be) and create something extraordinary, may be a challenging endeavor. This is especially in true in light of an earlier paper by Daniel and Titman (1999) showing that value strategies are strongest among low momentum rather than high momentum stocks, and momentum strategies are strongest among growth rather than value stocks.

Nevertheless, researchers are nothing if not persistent and imaginative. When it was found that Markowitz mean variance optimization (MVO) gave inconsistent results, researchers tried constraining the inputs, incorporating prior information to shrink the estimates, and even ignoring returns altogether to try to create portfolios that were more robust. In the end, they found that because of estimation error, equal weight portfolios were generally superior to MVO portfolios. The same overreach is true with respect to the Capital Asset Pricing Model (CAPM). This started out as a single factor model that expanded to 3 and then 4 factors. Factor fishing has now come up with more than 80 possible data-mined factors, yet the factor pricing model may still not effectively model the real world. 

Therefore, it didn't surprise me to see recent a paper by Fisher, Shaw, and Titman (2014) called "Combining Value and Momentum" that tries hard to find other ways to use value and momentum together. (Yes, this is the same Titman who co-authored the above paper that showed momentum working better with growth rather than value stocks, and who co-authored the seminal momentum papers of the 1990s with Jegadeesh.)

What is perhaps most interesting are the various findings the authors came up in the course of their research. As the saying goes, the devil is in the details. Here are some of those details.

The authors separate stocks into 2 size categories, large cap corresponding to the Russell 1000 index, and small cap corresponding to all other stocks in the CRSP database from 1975 through 2013. They base momentum on prior 12-month performance skipping the last month. With respect to value and momentum separately, the authors find:
  • Value, as measured by the price-to-book ratio, is beneficial only with small stocks and not with large stocks. This is the same conclusion reached by Israel and Moskowitz.
  • Despite high momentum portfolio Sharpe ratios before transaction costs, the high transaction costs associated with momentum portfolio turnover negates much of the difference in Sharpe ratios between large momentum and large value portfolios.
  •  Since small stocks have even higher transaction costs than large stocks, the authors incorporate higher transaction costs to conclude that none of the small momentum portfolio Sharpe ratios are higher than the Sharpe ratios of the small market portfolios.
  • In other words, depending on transaction costs, individual stock momentum may not be very good with either small or large stocks.[2] So all we are left with that provides above market risk-adjusted returns are small value stocks that most investors (and particularly institutional ones) find too expensive and difficult to trade.
The authors then look for ways to salvage momentum by combining it with value in two different ways. The first is to rank firms by momentum and value separately, and then compute an average rank. One signal can outweigh the other, and momentum still has high transaction costs with this approach. 

The authors' second approach is to use momentum as a filter for value-based portfolios. They buy stocks only when value and momentum are both favorable, and they sell stocks only when both factors are unfavorable. Momentum does not trigger trades, but instead influences the portfolios by delaying or avoiding trades. Data mining for the highest ex-post Sharpe ratios with this second approach, the authors find much greater exposure to the value factor. The optimal small cap portfolios, for example, have value allocations of 79% or more. The role of momentum with this approach is very small. 

The authors' first approach gives slightly higher Sharpe ratios when trading costs are low, and the opposite is true if trading costs are high. Of course, we do not know if these Sharpe ratios will continue out-of-sample into the future.

We can avoid the issues of high trading costs and less certain Sharpe ratios if we instead use momentum with indexes or sectors rather than with individual stocks. In our 2012 post called "Value and Momentum…Not Here" we asked if there should be value and momentum everywhere. I didn't think so then, and I see even less reason to believe that now.









[1] http:///www.aqrindex.com
[2] A study last year by Frazzini, Israel, and Moskowitz looked at large institutional trades across 19 developed markets from 1998-2013. They found the trading costs of momentum to be low, despite a higher turnover than from other factors. On the other hand, a study by Lesmond, Schill, and Zhou (2004) called "The Illusionary Nature of Momentum Profits" showed that transaction costs reduced momentum strategy returns to close to zero. Fisher et al. uses transaction cost estimates that are in between these two.

Wednesday, June 4, 2014

"Fact, Fiction, and Momentum Investing"

The AQR posse (Asness, Frazzini, Israel, and Moskowitz) recently issued a working paper that disproves many often-repeated myths about momentum investing, particularly as it applies to individual stocks. The authors back up their reasoning with results from academic papers and publicly available data. Here are the myths they address: 
  •   The momentum anomaly is small and sporadic 
  • ·It works mostly on the short side
  •   It works well only among small stocks
  •   It does not survive trading costs
  •   It does not work for a taxable investor
  •   It is best used as a screen rather than as a regular investment factor
  •   Its returns may not persist
  •   It is too volatile to rely on
  •   Different measures of momentum may give different results
  •   There is no theory or reasonable explanation to support it
 Below is a quick summary of the authors' evidence-based counter arguments:

1)  There is overwhelming evidence from scores of studies showing that momentum returns are remarkably stable and robust.

2)  There is little difference in performance between the long and short sides of momentum based on factor model regressions. Based on average returns versus the market, the long side has contributed more to momentum profits.

3)  As for working only among small caps, this is true only if you replace the word "momentum" with the word "value". Two of the authors, Israel & Moskowitz, wrote an important paper last year called "The Role of Shorting, Firm Size, and Time on Market Anomalies" that clearly showed this. That paper was the subject of my post, "Momentum...the Only Practical Anomaly?" Momentum actually works well across all size stocks.

4)  A study last year by three of these authors called "Trading Costs of Asset Pricing Anomalies" looked at large institutional trades across nineteen developed markets from 1998-2013. They found the trading costs of momentum to be low, despite a higher turnover than from other factors.

5) Several studies show that even though momentum with individual stocks has 5-6 times the annual turnover of value strategies, momentum actually has a similar tax burden. This is because momentum holds on to winners and sells losers, which avoids short-term gains in favor of long-term ones. Momentum also has a much lower dividend exposure than value.

6)   The authors point to papers showing that momentum works better as a factor-based approach than as a screen-based one.

7)  As for momentum's returns disappearing, one can say the same of any anomaly. Abnormal momentum returns have survived, however, for the past 212 years. Momentum has held up to considerable out-of-sample validation across time, geography, and asset type. The authors point out, "There is no evidence that momentum has weakened since it has become well-known and once many institutional investors embraced it and trading costs declined."

       8) Relative strength momentum is volatile, but the Sharpe ratio (which includes volatility) of momentum still comes up on top. The authors say, "Who are you calling small and sporadic?" (The authors ignore absolute momentum, which significantly reduces expected volatility and drawdown.)

9)  The authors agree that different measures of momentum can give different results, but they point out that this is true of any strategy. Different measures of momentum giving good results is a sign of robustness and not a cause for concern.

10) Momentum can be explained by either risk based or behavioral factors. As long as risks, risk preferences, biases, and/or behaviors do not change, momentum profits should continue unabated as they have for the past 200+ years. (My forthcoming book shows how behavioral biases are part of our DNA and are unlikely to change.)

The authors point out that most of the above myths can be shattered by a quick visit to Kenneth French's data library website. It is refreshing to see the authors, brought up in the Chicago efficient markets tradition, take on the challenge of those who say momentum profits cannot persist (despite plenty of evidence to the contrary) because that would contradict the theory of efficient markets. The authors point out that rejecting data because of a theory (or a one-sided view of the world) can be dangerous. They point to Columbus, Galileo, and the Salem witch trials as examples. Bravo!

The only problem I have with their paper is that the authors, perhaps keenly aware that risk-adjusted  momentum profits from individual stocks have been uninspiring over the past thirty years, repeatedly point out  that momentum works best when it is combined with value. Yet we can see in the aforementioned Israel & Moskowitz study that commonly used measures of value hold up only among the smallest stocks thar represent only 10% of total market capitalization, and these are impractical for most investors to hold. Maybe the AQR crew needs to take a closer look at the true value of the emperor's new clothes.

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