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:

HML-GDP

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.

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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:

HMU

‘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.

UMmkt

‘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:

HML-pres

(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.

HML-trace

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:

ann-car-sv

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%.

ann-SR-sv

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:

ann-seas-tab

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.

AMIBROKER CODE:

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

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

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.

vivax

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%.

Seasonality I: day-of-the-month

This series looks at US stock market seasonality on various timeframes.  The Fama-French (FF) daily book-to-market (B/M) portfolios are used.

Marketsci has posted extensively on this topic, showing that “strong” and “weak” days tend to persist on a walk-forward basis.

This analysis is slightly different in that calendar days are used rather than trading days.  Daily return is plotted against day of the month from 1984-2014.

Capture3

The trendline shows that calendar days 1,2 and 25-31 have higher average returns than other days, irrespective of where the weekend falls.

Holding the FF large value portfolio on days 1,2 and 25-31 results in the following equity curve (frictionless).  Annual return is 10.2% with an exposure around 25% and 12 trades per year.

Capture2

It’s interesting that even during the last 2 recessions, these days perform well.  (See 2000-2002 and 2008).

This may work better with the addition of short term entry and exit triggers but I have yet to investigate.  The intent of the equity curve is only to illustrate the principle.

Next up: day-of-year seasonality.

$NAMO signal follow-up

Following the $NAMO buy signal, QQQ hit new highs today:

Capture

This signal is really only a way to measure a decent amount of selling then the beginning of a bounce.  Unfortunately I do not have the raw data to run the stats.  See the charts page for the current picture.

The $NAMO signal, and similar ones such as breadth thrusts (see Quantifiable Edges), should be more reliable when combined with seasonality and recession tracking.  Seasonality is the subject of the next few posts.

 

Fama-French momentum: absolute and relative returns

The following charts show rolling annual returns for small-cap momentum, both absolute (red) and relative to the S&P 500 (blue).  The upper trace exhibits a stable mean around 20% but annual return is negative every few years and requires fortitude, as with all long term investing.

The lower trace demonstrates that the strategy can underperform the S&P 500 in some years, notably during the tech bubble in the late 1990s.  Since then, annual underperformance has been rare and limited in magnitude.

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