3 Factor Dual Momentum: Value, Momentum and Low Volatility (or BAB)

This post looks at Factor* Dual Momentum with 3 factors: Value, Momentum and Low Volatility (or Betting against Beta).  Previous posts covered 2 factors only.

* long portfolios from the factors, rather than the long minus short factors themselves.

Low Volatility data was kindly supplied by reader Paolo but only goes back to 1998, rather than 1950 as the previous tests.

The strategy holds the highest ranked portfolio by 12 month return, if return is greater than zero.  Results are shown for the 2 and 3 factor strategies and the underlying portfolios.

The 3 factor position is shown in the bottom trace as 4 levels:

0 = Cash, 1 = Value, 2 = Momentum, 3 = Low Volatility

Low Volatility is clearly mainly held in 2001 and 2012.



Sharpe Ratio and Annual Return are summarized above.

The strategies return similar results except for a period in 2012 when access to Low Volatility allows 3 factor to outperform.

The Value portfolio has the highest returns in some periods (and overall) but a low Sharpe Ratio.

Low Volatility has the highest Sharpe Ratio due to the smooth equity curve and smaller drawdown in 2008.

Value and the 3 factor strategy have the highest returns over the test period.

Factor Dual Momentum status and plea for data

The recent series analyzed Factor Dual Momentum.  US Value and Momentum factor portfolios were tested back to 1950, courtesy of Ken French’s data library.

Portfolios are ranked on 12 month return.  Using VBR and PDP for value and momentum, the current picture looks like this:


The strategy should be invested in PDP as relative 12 month returns are higher and absolute returns are greater than zero.


I wish to re-run the analysis with a low volatility portfolio, back to at least 1980.  This data was on betaarbitrage.com which has now disappeared.  Chris Asness’ site has factors but not portfolios.  If anyone can help, please let me know in the comments.

Dual momentum: lookback parameter

A great advantage of dual momentum is the low number of parameters (typically only a lookback length of 12 months is used).  This reduces the likelihood that results are curve-fitted or uncovered by data-mining and subsequently useless in real-time trading.

The plot below compares a 12 month lookback against 1 month and a 50:50 combination of both lookbacks:


Annual returns and sharpe ratios are listed in the chart legend and are very similar.

Of major interest though, the correlation between ’12’ and ‘1’ monthly returns is only 0.62.  Finding consistently uncorrelated strategies is difficult but rewarding.  When the two strategies are combined, standard deviation is reduced and sharpe ratio is increased to 1.3.

A zoomed plot from 2000 to present is shown below:


The larger drawdowns experienced by the individual strategies (2002, 2009 and 2011) have been reduced by combining the two relatively uncorrelated curves, without sacrificing returns.

Dual momentum: real portfolios and current status

Dual momentum with Value and Momentum factor portfolios was tested back to 1950 with 16% annual returns:


What is the tracking error of real ETFs to those portfolios?


Vanguard Small-Value (VBR) launched in 2004 and can underperform Value near market peaks but overall the 10 year return is identical.

Dorsey Wright Technical Leaders (PDP) tracks similarly to Momentum although returns lag slightly.  Note that the selection methodology is different (uses P&F not price measures) and there is an annual expense ratio of 0.6%.

The plot below shows relative 12 month momentum (Value minus Momentum).  Using this criterion, the strategy would have been invested in Momentum since June 2014 (blue line below zero).  The strategy switches are shown in red.

Momentum is currently outperforming Value more than 10% per annum therefore a large and sustained change in relative performance is needed for a switch to Value.


Dual momentum with Value and Momentum factor portfolios

Dual Momentum is a robust portfolio allocation tool.  Relative 12 month returns are used to rank assets.  Shelter is sought in a safe asset when 12 month absolute returns fall below a threshold.

Gary Antonacci describes Global Equities Momentum using US and International stock indexes with Bonds as the safe asset.  Annual returns are 17.4% since 1974.  However, my previous post showed the potential return hit when the 30 year bond bull ends and prices start to fall.

One promising solution is to use factor portfolios based on Value and Momentum and shelter in a ‘Risk-Free’ asset during downturns.  Results from this strategy are not biased by recent bull markets.  Value and Momentum are somewhat uncorrelated, enhancing returns, and supported by a vast literature showing persistent outperformance  over many decades.

As the Value effect is known to apply only to small firms, I used the small-high Value dataset from the 2×3 portfolio at Ken French’s library.  The momentum anomaly is not limited to specific market segments so the big-high Momentum portfolio was used.


Average annual compound return is 16.6% and consistent throughout the 60+ year test period (see green rolling return and red annual Risk-Free%).

Return is greater than each data series individually.  Using 6 or 4 month dual momentum gives similar results.

VBR and PDP are ETFs that can be used to mimic these portfolios.  The next post will look at tracking of these ETFs relative to the 2×3 portfolios and their current momentum status.

Dual momentum without the benefit of the bond bull market

Dual momentum, popularized by Gary Antonacci, uses 12 month returns to:

  1. rank and select the top asset (RELATIVE)
  2. shelter in a safer asset if the absolute value falls below a threshold (ABSOLUTE)

Many tactical strategies use bonds as the safer asset which enhances returns in two ways.  Firstly, returns tend to be uncorrelated with stocks and secondly, bonds have risen continuously over the past 3 decades.

Here is the result using a single risky asset (S&P 500) and Long Term Treasury Bonds (data from yahoo).  Clearly, relative momentum is not used in this case.  The lower return threshold triggering a switch into bonds is the 12 month bond return.


Equity curve is in blue and 12 month rolling return in green.  Average compound return is 9.7% since 1987 using the full dataset.

Notice the flat to negative return from 2009 through 2011.


Now, remove the underlying bond trend by subtracting the average return (0.71%) from each monthly data point and recalculate:


Compound return falls to 8.3% but the majority occurs pre-2000.

This test could be performed various ways but the result above is a possibility for this type of strategy when interest rates start to rise.

NEXT WEEK: a solution.

More ways to estimate Fama-French HML in real-time

To implement the asset allocation described in my whitepaper, the Fama-French “value factor” HML sign must be estimated in real time.  One commenter helpfully proposed RALS:

The Index takes long positions in companies with large RAFI weights relative to weightings in capitalization-weighted indices and short positions in companies with small RAFI weights relative to their weightings in cap-weighted indices.

Each company receives a weight equal to the ratio of its sales (or cash flow, dividends, book value) to the aggregate sales (or cash flow, dividends, book value) across all companies in the universe.

This sounds similar to the construction of HML.

Monthly correlation with HML is 0.65, R2 = 0.42.

Most results fall into the lower left or upper right quadrants, indicating that the sign of HML may be reliably estimated.  Only the sign is required for asset allocation using the method described in the paper.



Another option is CHEP, based on the:

Dow Jones U.S. Thematic Market Neutral Value Index

Measures the performance of an investment strategy utilizing long positions on value companies and short positions on growth companies. Value is calculated using a multi-factor ranking process based on book value to price ratio, projected earnings per share to price ratio and trailing 12-month operating cash flow to price ratio.

This also sounds similar to the construction of HML.

Monthly correlation with HML is 0.39, R2 = 0.08.


Clearly RALS is the better fit.  Unfortunately there is only a 3 year history, not enough to replicate the 30 year tests in the whitepaper.