Does sector momentum outperform stock momentum?

A momentum strategy may be implemented at an individual stock level or sector level.

Is there an advantage to partitioning stocks into sectors and owning the strongest sector versus buying the highest momentum stocks in the market?  Stock momentum funds have been available for a few years and recently sector rotation has been packaged into an ETF.

Ken French publishes a 10 industry portfolio and momentum portfolios for US equities which may be used to investigate:


The blue curve is the top sector (ranked by 12 month return, monthly).  The red curve is top tercile stocks (ranked by 12 month return, monthly) in the largest 50% by market cap.

Sector rotation clearly outperforms stock momentum (by about 3% annually since 1950).  However, this result is for the highest ranked sector only.  It is difficult to determine the fraction of the market represented by the top sector versus top tercile large stocks but the sector slices are likely smaller.

Multiple sectors are compared below.  Top 2 and top 3 returns are comparable with the individual stock momentum strategy.


Compare the “Top 1” curve with the simple rotation between value and momentum shown on this blog.  Similar performance (17% CAR) but with only 2 instruments and fewer trades.


Finally, combine sectors with value, momentum and risk-free (RF).  The top ranked portfolio by 12 month return is selected every month:


Returns are improved about 1% annually over the entire data-set but the 4% out-performance since 2000 (from avoiding the GFC correction) accounts for the majority.

Summary stats



A rotational strategy with the top sector outperforms the large momentum FF stock portfolio.  However, this may be partially due to selecting a smaller section of the market.

These tests show that beating a simple value-momentum rotational model is tough.  Adding ten sectors to this model increases returns slightly, but at the expense of higher turnover.

This demonstrates what is possible with price-based ranking only.  Adding volatility and correlation to the scoring may give further improvement (e.g. Keller 2015 “Classical Asset Allocation”):


Markowitz portfolio optimization with VBA code

Wouter, Butler and Kipnis [2015] recently demonstrated Classical Asset Allocation (CAA) for long only portfolios, based on Markowitz’ concepts. The method uses only two parameters thus minimizing the chances of curve-fitting and data snooping.  The parameters are lookback period (12 months) and target volatility.

Main results from the paper are as follows (from 1915 to 2015):



R annual return, V volatility, TV target volatility, D max. drawdown, EW equal weight

N=8 portfolio:

SP500, EAFE, EEM, US Tech, Japan Topix, T-Bills, US Gov10y, and US High Yield.

N=39 portfolio (N=8 +):

10 Fama/French US sectors, five US bonds, US Small Caps equities, GSCI, Gold, Foreign bonds, US TIPS, US Composite REITs, US Mortgage REITs, FTSE US 1000/US 1500/Global ex US/Developed/EM, JapanGov10y, Dow Util/Transport/Industry, FX-1x/2x, and Timber

Consistent results from all datasets gives further confidence in the method.

My main interest is in factor investing.  I applied the method to the momentum and value portfolios normally used in this blog plus Mkt factor and ‘risk-free’ (all from Ken French’s data library).  Dividends are continuously re-invested and trading frictions are neglected (this strategy only trades a few times per year).

Results from two target volatilities are shown below.  The lower volatility case exhibits a remarkable 65 year Sharpe Ratio of 1.3.  The t-statistic is 10.6!

Annualized returns are 9.7% and 12.6% respectively.


The next post will cover sector portfolios and real datasets.

I used Excel’s solver to maximize 12 month trailing return with a 12 month standard deviation target.  A constraint is applied of sum of weights = 1 (no leverage).

The spreadsheet is trivial to create.  The column layout to match the VBA code is as follows.  This is for 4 datasets but may be extended as necessary.  Columns F-L start at row 13 as they require 12 months of history.

Column    Description

A                Date

B-E            Monthly return data (4 datasets)

F-I             Portfolio weights (calculated by solver)

J                 Sum of weights (F:I)

K                Weights multiplied by 12 month returns, summed

L                 Weights multiplied by 12 month stdev of returns, summed


When the solver finishes, multiply monthly returns by weights from the previous row and sum to obtain the portfolio return.

VBA code for the solver is run as a macro in the sheet containing the data:

For i = 13 To 790 ‘ monthly return data in rows 2-790

SolverAdd CellRef:=”$J$” & i, Relation:=1, FormulaText:=”1″ ‘ sum of weights = 1
SolverAdd CellRef:=”$L$” & i, Relation:=1,   FormulaText:=”3″ ‘ target stdev = 3% (10% annualized)
SolverOptions AssumeNonNeg:=True
SolverOk SetCell:=”$K$” & i, MaxMinVal:=1, ValueOf:=”0″, ByChange:=”$F$” & i & “:$I$” & i
SolverSolve userfinish:=True
SolverFinish keepfinal:=1


US recessions, the Value Factor (HML) and current status

The Fama-French value factor HML exhibits a fairly reliable 4 year cycle.  Growth and Value out-performance oscillates with a 4 year period (see my previous post on this).

Liew and Vassilou (1999), show that annual change in HML is related to future GDP change (see my blog post here).  Therefore tracking HML allows us to glean insight into upcoming economic conditions.

Where are we in the current cycle?


The black line is the 12 month moving average of HML.  St. Louis Fed recessions are in red.  HML lows clearly occur in years divisible by 4, although can lead or lag by a few months.  Lows correspond to high growth, which often (but not always) leads to recession.  One hypothesis is that the recession corrects the growth excesses in overheated parts of the economy.

HML is currently at or near the cycle low (circled).  Therefore conditions are in place for a potential recession.   Also of note is how rapidly value outperforms growth on recession exits.

Fortunately there are better recession forecasting tools than HML because the majority of market periods of extended weakness are coincident with recession.  The chart below shows the 12 month average of the Market Factor in black.

This highlights why using the sign of the 12 month return as an investment filter is so effective.  Once the return turns negative, the downturn is generally sustained.


However, the 12 month return may not provide an optimum re-entry signal.  Various oversold measures such as percentage of stocks below an N day moving average could be compared to typical recession levels to scale into value funds at low prices.

As the 12 month rolling return becomes increasingly negative, forward average annual returns rapidly rise:


Seasonality debunked (partially)

I’ve previously written about a bi-annual seasonality pattern in US equity markets:

The quarterly average market (Mkt-RF) returns from 1950 to present are shown below (data from Ken French’s library).  Quarters 1-4 are even years and 5-8 are odd years.


The table shows that mean returns of quarters 4-6 are greater than zero with high significance (t-stat > 2.3).

Except for Q8 which is marginal, all other quarterly means (including negative values) are not statistically different from zero (t-stat  < 2).  Therefore it is not possible to profit from this effect by excluding negative periods, hence the ‘partial’ debunking.

Caveats to these test results are that the dataset is small (32 points) and financial data is not normally distributed.


  1. Seasonality is a statistically significant effect:
    1. Quarters 4-6 have mean returns above zero.
    2. Other quarterly means are not statistically different from zero.
  2. A robust calendar strategy to avoid negative periods cannot be designed.

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.