As the advantages of momentum investing become more widely known, there is naturally more research being done to explore its potential. Some of that research, such as the Moskowitz, Ooi, and Pedersen paper "Time Series Momentum," has been excellent. We prefer to point out and discuss positive things like that, but since this is a blog about momentum, we feel an obligation to also talk about momentum products and research that may be a bit off base (See "Here Comes Market Neutral Momentum…sort of").

At the end of last year, Keller and van Putten issued a paper called "Generalized Momentum and Flexible Asset Allocation." The authors applied absolute and relative momentum to the top 3 of 7 assets using data from 1998 through 2012. They developed their parameters on 8 years of data from 2005 through 2012, and indicate they validated their results on 7 years of additional data from 1998 through 2004.They call this an out-of-sample validation, yet they mention elsewhere in their paper that they determined the look back period and number of funds to invest in by looking at a longer span of data that includes the entire 1998 through 2012 period. To split a modest amount of data in half and call part of it an out-of-sample test is not correct. Data snooping bias and model over-fitting are also common practices among practitioners.

With respect to their results, eight years of data is a very small sample size for determining investment model parameters. Their results on 7 more years of data may look decent because momentum is so robust that most parameters over a certain range work out OK. However, back testing on eight years of data may not give what are really the best parameter values.

Elsewhere, the authors' paper can be rather confusing. Here is an example, "Sometimes our relative momentum is called relative strength (RS, see Faber 2010) or time series momentum (see Thomas 2012). We will also use the term return momentum to contrast better with volatility and correlation momentum."

Time series momentum is different from relative momentum (See my post Whatchmacallit). Furthermore, what they call volatility and correlation momentum has nothing to do with momentum. Momentum is about selecting assets based on persistence in their performance, either against their peers (relative momentum) or against themselves over time (absolute momentum). This makes no sense with respect to volatility or correlation.

The authors actually use volatility and correlation as ranking factors. They do the same with returns, but after they select them using relative and absolute momentum.

The authors end up ranking assets using arbitrary weights of 1.0, 0.5, and 0.5 for return momentum, volatility, and correlation, respectively. They do not explain how they came up with these weightings. I would be cautious about using the information in this paper without doing considerably more analysis and back testing.

"Time Series Momentum Versus Moving Average Trading Rules," by Marshall, Nguyen, and Visaltanachoti is an academic paper that attempts to determine if long-only momentum trading rules beat comparable moving average trading rules. They do this by comparing absolute momentum (which they call time series momentum) to comparable (according to them) moving averages of size based quintiles of US stocks using 10, 50, 100, and 200 trading day look-back periods. They have confidence in their comparisons because their correlations between momentum and moving average returns are generally in excess of .8. However, this may have something to do with their use of daily, rather than monthly, return data. Since momentum is an intermediate term anomaly, most researchers study it using monthly returns.

We get correlations ranging from .45 to .47 when comparing 12-month absolute momentum monthly returns to a range of 4 to 32 month moving average monthly returns of the US stock market for the past 38 years. We use a range of moving average lengths because one cannot just use the same look-back period for momentum and moving averages and expect comparable results. The authors hint at this themselves when they say that moving averages enter and exit stocks sooner. Their paper also identifies the average holding periods for look-back intervals of 10, 50, 100 and 200 trading days as 8, 22, 31 and 47 days for moving average rules, and 10, 32, 46 and 83 days for momentum rules. Quicker entries and exits with moving averages means that their lengths should be longer if one expects their performance to match up with the performance of absolute momentum. Choosing the same look-back period does not make absolute momentum and moving averages comparable.

An old investment adage is that moving averages should be plotted half their length behind the current price on a stock chart. A half-span lag means that the look-back period for a moving average would be twice as long as the look-back period for momentum in order for the two to be roughly comparable. The following chart should make this clear.

Let's measure absolute momentum from the midpoint of this line at 30 to the endpoint at 50. Absolute momentum measures the difference between the start and end value, which in this case is 20. The computed moving average value from the start of 30 to the end of 50 is 40. The difference between the moving average value of 40 and the end value of 50 is only 10, indicating a weaker trend than was identified using absolute momentum.

However, if we start our moving average twice as far back at the point of 10, the computed moving average value becomes 30 instead of 40, and the difference between it and our end value is now 20, the same as with absolute momentum. The numbers do not always work out exactly this way. The equivalent moving average look-back period depends on the price action along the length of the moving average. However, it is safe to say that using twice the absolute momentum look-back period gives us a better equivalent moving average length. We can see that in Panel D from Table 2 of the paper:

Stocks are in size-based quintiles from Q1 (small) to Q5 (large). Look-back periods from 10 to 200 days are in the first column. Reading across the rows, the Sharpe ratios are for moving average (MA) and absolute momentum (TSMOM) strategies using the same look-back period. We see, that except for Q5 (large), if we shift the MA strategies up one level so that their look-back periods are twice as long (or longer when going from 50 to 10) as the TSMOM look-back periods, we get an almost exact match of the Sharpe ratios. Based on using such shifted look-back periods that make MA and TSMOM strategies roughly equivalent, one can no longer say that portfolio-timing rules based on moving averages clearly outperform their absolute momentum counterparts.

To compare absolute momentum to moving average trading rules, one should examine a range of values for each. We did this and found that the best performing momentum parameters applied to different assets and different time periods have less dispersion than the best performing moving average parameters.

At the end of last year, Keller and van Putten issued a paper called "Generalized Momentum and Flexible Asset Allocation." The authors applied absolute and relative momentum to the top 3 of 7 assets using data from 1998 through 2012. They developed their parameters on 8 years of data from 2005 through 2012, and indicate they validated their results on 7 years of additional data from 1998 through 2004.They call this an out-of-sample validation, yet they mention elsewhere in their paper that they determined the look back period and number of funds to invest in by looking at a longer span of data that includes the entire 1998 through 2012 period. To split a modest amount of data in half and call part of it an out-of-sample test is not correct. Data snooping bias and model over-fitting are also common practices among practitioners.

With respect to their results, eight years of data is a very small sample size for determining investment model parameters. Their results on 7 more years of data may look decent because momentum is so robust that most parameters over a certain range work out OK. However, back testing on eight years of data may not give what are really the best parameter values.

Elsewhere, the authors' paper can be rather confusing. Here is an example, "Sometimes our relative momentum is called relative strength (RS, see Faber 2010) or time series momentum (see Thomas 2012). We will also use the term return momentum to contrast better with volatility and correlation momentum."

Time series momentum is different from relative momentum (See my post Whatchmacallit). Furthermore, what they call volatility and correlation momentum has nothing to do with momentum. Momentum is about selecting assets based on persistence in their performance, either against their peers (relative momentum) or against themselves over time (absolute momentum). This makes no sense with respect to volatility or correlation.

The authors actually use volatility and correlation as ranking factors. They do the same with returns, but after they select them using relative and absolute momentum.

The authors end up ranking assets using arbitrary weights of 1.0, 0.5, and 0.5 for return momentum, volatility, and correlation, respectively. They do not explain how they came up with these weightings. I would be cautious about using the information in this paper without doing considerably more analysis and back testing.

"Time Series Momentum Versus Moving Average Trading Rules," by Marshall, Nguyen, and Visaltanachoti is an academic paper that attempts to determine if long-only momentum trading rules beat comparable moving average trading rules. They do this by comparing absolute momentum (which they call time series momentum) to comparable (according to them) moving averages of size based quintiles of US stocks using 10, 50, 100, and 200 trading day look-back periods. They have confidence in their comparisons because their correlations between momentum and moving average returns are generally in excess of .8. However, this may have something to do with their use of daily, rather than monthly, return data. Since momentum is an intermediate term anomaly, most researchers study it using monthly returns.

We get correlations ranging from .45 to .47 when comparing 12-month absolute momentum monthly returns to a range of 4 to 32 month moving average monthly returns of the US stock market for the past 38 years. We use a range of moving average lengths because one cannot just use the same look-back period for momentum and moving averages and expect comparable results. The authors hint at this themselves when they say that moving averages enter and exit stocks sooner. Their paper also identifies the average holding periods for look-back intervals of 10, 50, 100 and 200 trading days as 8, 22, 31 and 47 days for moving average rules, and 10, 32, 46 and 83 days for momentum rules. Quicker entries and exits with moving averages means that their lengths should be longer if one expects their performance to match up with the performance of absolute momentum. Choosing the same look-back period does not make absolute momentum and moving averages comparable.

An old investment adage is that moving averages should be plotted half their length behind the current price on a stock chart. A half-span lag means that the look-back period for a moving average would be twice as long as the look-back period for momentum in order for the two to be roughly comparable. The following chart should make this clear.

However, if we start our moving average twice as far back at the point of 10, the computed moving average value becomes 30 instead of 40, and the difference between it and our end value is now 20, the same as with absolute momentum. The numbers do not always work out exactly this way. The equivalent moving average look-back period depends on the price action along the length of the moving average. However, it is safe to say that using twice the absolute momentum look-back period gives us a better equivalent moving average length. We can see that in Panel D from Table 2 of the paper:

**Table 2**

**Time-Series Momentum and Technical Analysis Performance and Comparison**

Q1
(Small) Q2 Q3 Q4 Q5 (Large)

MA TSMOM MA
TSMOM MA TSMOM MA TSMOM MA TSMOM

*Panel D: Sharpe Ratios*

10 0.47 0.38 0.41 0.31 0.42 0.28 0.37 0.25 0.16 0.04

50 0.37 0.26 0.30 0.21 0.28 0.22 0.25 0.19 0.12 0.08

100 0.27 0.19 0.22 0.15 0.21 0.18 0.19 0.16 0.12
0.11

200 0.20 0.13 0.17
0.12 0.17 0.15 0.19 0.14 0.13
0.10

Stocks are in size-based quintiles from Q1 (small) to Q5 (large). Look-back periods from 10 to 200 days are in the first column. Reading across the rows, the Sharpe ratios are for moving average (MA) and absolute momentum (TSMOM) strategies using the same look-back period. We see, that except for Q5 (large), if we shift the MA strategies up one level so that their look-back periods are twice as long (or longer when going from 50 to 10) as the TSMOM look-back periods, we get an almost exact match of the Sharpe ratios. Based on using such shifted look-back periods that make MA and TSMOM strategies roughly equivalent, one can no longer say that portfolio-timing rules based on moving averages clearly outperform their absolute momentum counterparts.

To compare absolute momentum to moving average trading rules, one should examine a range of values for each. We did this and found that the best performing momentum parameters applied to different assets and different time periods have less dispersion than the best performing moving average parameters.