Link between HML factor and future GDP growth

The previous post explored the cyclic behaviour of the Fama French HML factor.  I proposed further work to link HML to the economy.  In fact, a literature search discovers that Liew and Vassilou (1999), document this effect:


The table contains past 12 month return of HML versus next year’s GDP growth.

The difference between ‘Bad States’ (GDP growth in bottom quartile) and other states is large in several countries.  For example, in the US, average HML growth of 2.81% led to Bad States compared to about 10% ahead of other states.

This agrees with the time series plot in the previous post showing that extreme growth (low HML) typically leads to economic recessions.


Further to the last post I ran some ‘4 year cycle’ analysis on pseudo factors.

Pseudo factors can be constructed by subtracting various Fama French portfolios:


‘High minus Up’ (Value minus Momentum) shows momentum outperforms value about 0.5% per month in the second half of the cycle, accelerating towards the end.


‘Up minus Market’ shows momentum outperforms the market at least 1% per month throughout the cycle.  Note that exits from recessions favor value due to the ‘momentum crash’ phenomena documented by Daniel and Moskowitz.

Seasonality III: Fama-French factors

The Fama French HML factor exhibits remarkable seasonality:


(This is the highest R^2 of any factor or portfolio tested over any cycle length.)

On the 4 year (Presidential Cycle) value outperforms growth 1% per month in the first 2 years.  There is an abrupt ‘flip’ at the beginning of the cycle from growth to value.


This can be seen clearly in the full time series.  The arrows show how HML decreases over the cycle and flip from low to high as the new cycle starts (after the election).

Value outperformed growth 10% per *month* in the aftermath of the Technology Bubble (2001).

The blue trace is the market factor (right axis, log scale).  The red trace is the market factor excluding summer seasonals and economic recessions (St. Louis FED model).

Interestingly, cycles with the highest growth lead to recessions.  See the lowest arrows (most negative HML) in 1980, 2000 and 2008.   One possible explanation is that the most overheated markets need to correct further, resulting in economic contraction.

Next recession 2016?  Watch for HML approaching -10.

Further work could link HML with future GDP changes.

Seasonality II: annual

Annual seasonality, also known as “Halloween Effect”.  Swinkels and Vliet (2010) investigate 5 calendar effects and find that Halloween and ‘turn of the month’ (TOM) are the strongest effects (subsuming the other 3 effects studied):

The equity premium over the sample 1963-2008 is 7.2% if there is a Halloween or TOM effect, and -2.8% in all other cases.

TOM was studied in the last post.

For size and value segments:

During Halloween and/or TOM we find a large small cap premium of 12.40%, while for other calendar effects 2.48% premium remains. For value stocks these numbers are a staggering 14.93% and 0.69% respectively.

Investigating entry and exit day of the year in Amibroker from 1984 to 2014 yields the following:

Fama-French small-value portfolio:


Annual return peaks at 18% for entries on day 300 and exits on day 250.  There is one trade per year (30 trades total).

For comparison, buy and hold return is 14%.


Sharpe Ratio is maximized at 1.9 for a later buy (day 350) and earlier sell (day 160).  Annual return at peak Sharpe is reduced to 12%, excluding return on cash during half of the time.

Fama-French small momentum portfolio:

The shapes of the surface plots are similar.  Results are compared in a table:


The momentum results exhibit a similar pattern to value but with 3% higher maximum returns.

Higher Sharpe strategies are also listed; Sharpe is 50% higher when selling 100 days earlier.  Returns are reduced by 2% to 4% and exposure by 30%.  Entry is held at day 300 as later entries limit gains, underlining the high average returns of November and December.

I also calculated the small momentum portfolio back to 1954 (60 trades) and found the same result: CAR 21%, buy day 300, sell day 260.

Finally, the portfolio is selected for each trade by 12 month momentum ranking.  Again, similar results are produced (see table), showing that fund selection could be determined in real time.


Buy = DayOfYear() > Optimize(“buy day”,350,280,350,10);

Sell = DayOfYear() > Optimize(“sell day”,160,60,270,10) && 1Buy;

PositionScore = ROC(C,252);


Next post: Factor seasonality

Seasonality I: addendum

Further to my recent post on daily seasonality near the ‘turn of the month’, I repeated the analysis for Vanguard’s large cap value fund VIVAX, excluding dividends.

The equity curve represents holding the fund during calendar days 1,2 and 25-31.  Trades are frictionless (12 per year) but the VIVAX expense ratio of 0.24% is included.


Compound annual return is 8.8% and the equity curve shape is very similar to the previous analysis using Fama-French data, as expected.

Return on cash during the 75% of days out of the market would add several percentage points to this annual return, at least until interest rates were cut in 2008.

It may also be possible to time trades to collect dividends, adding further gains.  Current yield is 2.07%.