Cumulative market gains are zero across ‘even years’

Mkt-RF returns in ‘even years’ sum to zero over the last 50+ years (data from Ken French’s library).  This could be a spurious result although the stats suggest otherwise.


Is this result statistically significant?

Applying Student’s t-test gives a statistic of 2.3, i.e. mean returns of even versus odd years are different at the 5% significance level.

Factor Relative Momentum: surprising finding on ranking

A Value or Momentum portfolio is selected each month, based on the highest previous 12 month return (R).  Data are from Ken French’s library from 1950 to 2015.  I use the large momentum portfolio and small value portfolio (the HML anomaly does not exist in large cap stocks).

I found two surprises:

1) Ranking on squared returns (n=2) consistently outperforms ranking by return alone (n=1). In other words, the magnitude of return is important, positive or negative.  Mean reversion probably accounts for the improvement but this needs more detailed investigation.  Annual returns exceed 20% over the last 4 decades.

The table shows that the n=2 strategy performs much better than the component portfolios, particularly this century: 17% compared to 13% and 8% for Value (V) and Momentum (M) respectively.

2) Overlaying an absolute momentum filter (hold cash when return < 0) degrades returns.  The margin widens with recency: to 3.6% annually since 1999!  Sharpe ratio is not materially reduced as deviation shrinks proportionally. R1-R2 tableR1-R2 plot

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 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.