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 momentum programs (AQR momentum mutual funds, PowerShares DWA Momentum ETFs, and iShares MSCI USA Momentum Factor ETF) all use individual stock momentum. The only public program using momentum applied to asset classes was the ALPS Goldman Sachs Momentum Builder, which recently went out of business due to lack of interest.

Yet momentum applied to individual stocks is not the ideal way to use momentum. High transaction costs can negate much of the benefit of momentum investing, and most stock momentum programs dilute the momentum effect by selecting hundreds of stocks instead of just the ones showing highest relative strength. Momentum applied to indexes or sectors, rather than individual stocks, 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 Lower Risk. 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 the Russell 1000 index and from 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 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.[2]

Table 9.3 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. But the Asness et al study used long/short momentum and long/short value. Hardly anyone actually invests that way. Long only momentum and value are highly correlated. . 

We see that value combined with momentum (rebalanced monthly) does give a higher Sharpe ratio than either value or momentum alone. But there is little or no advantage with worst drawdown, and the results still pale in comparison to simple absolute momentum used with the Russell 1000 Index [3].

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 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 a switching option and rebalanced monthly. 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 Practical Anomaly?", Israel and Moskowitz of AQR show in their 2013 paper that value based on Book-to-Price only offers a long-term premium when applied to very small stocks, such as microcaps. These are unusable by larger 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 seems challenging. 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.

Even so, researchers are nothing if not persistent and imaginative. When they 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 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 model the real world well. 

So 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 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. About value and momentum separately, the authors find:
1) 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 who used data back to 1926, and who also found it to be true of other valuation measures that had data back to at least the 1930's.

2) Despite high momentum portfolio Sharpe ratios before transaction costs, the high transaction costs associated with momentum portfolios negates much of the difference in Sharpe ratios between large momentum and large value portfolios. 

 3) Since small stocks have even higher transaction costs than large stocks, the authors incorporated 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, based on high transaction costs, individual stock momentum may not be good with either small or large stocks [4]. So all we are left with that provides above market risk-adjusted returns are small value stocks that most investors (and particularly institutional ones) will 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, and then to compute an average rank. One signal can outweigh the other this way, 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 any 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 higher Sharpe ratios when trading costs are low, and the second approach gives higher Sharpe ratios when 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 rather than with individual stocks. In our 2012 post called "Value and Momentum…Not Here" we asked if there should be just value and momentum everywhere. I didn't think so then, and I see even less reason to believe so now.

[1] http:///www.aqrindex.com
[2] The AQR mutual fund using this index (AMOMX) has an annual expense ratio of 0.40%, while the Russell 1000 ETF (IWB) has an expense ratio of 0.15%.
[3] Results of momentum combined with value are better if a quality factor, such as profitability, is added, and if momentum, value, and profitability are applied to the same portfolio.See "Quality Investing" by Novy-Marx.
[4] 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. 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 between these two. 

The above are hypothetical results, 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. One cannot invest directly in an index. Please see our Disclaimer page for more information.