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My paper on using Fama-French factors for efficient asset allocation is up on SSRN:
Downloads, comments and questions gratefully received!
The Fama-French three factor model is ubiquitous in modern finance. Returns are modeled as a linear combination of a market factor, a size factor and a book-to-market equity ratio (or “value”) factor. The success of this approach, since its introduction in 1992, has resulted in widespread adoption and a large body of related academic literature.The risk factors exhibit serial correlation at a monthly timeframe. This property is strongest in the value factor, perhaps due to its association with global funding liquidity risk.
Using thirty years of Fama-French portfolio data, I show that autocorrelation of the value factor may be exploited to efficiently allocate capital into segments of the US stock market. The strategy outperforms the underlying portfolios on an absolute and risk adjusted basis. Annual returns are 5% greater than the components and Sharpe Ratio is increased by 86%.
The results are robust to different time periods and varying composition of underlying portfolios. Finally, I show that implementation costs are much smaller than the excess return and that the strategy is accessible to the individual investor.
An update to the popular post on combining TF and seasonality. To recap:
- Trend Following: Price is above 10 month average (per Faber).
- Seasonality: Average upcoming month return (r) over previous y cycles with m periodicity is above a threshold T.
- Dataset used is Fama-French “Small-Value” portfolio from 1954 to 2014.
AMIBROKER CODE (commented):
RESULTS 1984-2014 (thresholds from 0 to 1%)
EQUITY CURVE (T = 0.8):
By increasing the threshold, annual return is almost unchanged but the time in market decreases. For the optimum threshold (0.8%), average monthly return is 2.5% when price is above its 10 month average.
One further improvement that could be made is to normalize by volatility so that the threshold is a function of standard deviation rather than an absolute value. This would allow better testing across instruments.
Here is a simple, robust method to combine trend-following and seasonality to achieve high return with low exposure and drawdown.
I use the simple filter from Faber 2007: invest when price is above its 10 month simple moving average.
Using bi-annual seasonality from my post series, I require the average return of the upcoming month over the previous 30 years to be greater than a threshold.
I use the “small-value” Fama-French portfolio “value-weighted” from 1984 – 2014 (using 1954 – 1984 for the initial averaging). This portfolio is not directly investible but funds such as Vanguard’s VBR closely approximate.
Using Amibroker for analysis, the profit distribution is positively skewed:
CAR 15%, Exposure 50%, Max. DD 9%
55 trades, average hold: 4 months, 80% winners
Sharpe 1.3, Profit Factor 16
TRADE LIST (partial: 1992 – 2014)
Note: the threshold is cumulative over 15 datapoints i.e. a threshold of 15 equates to 1% average return per month.
The complete seasonality series is here, using Fama-French data from 1984-2014.
I Daily: CAR 10% with 25% exposure.
II Annual: CAR 18% with 84% exposure.
III Fama-French factors: Fama-French HML factor over Presidential Cycle.
IV Bi-annual: excluding months 4-7 in even years, 8-10 in odd years.
- Bi-annual value: CAR 19% with 70% exposure.
- Bi-annual momentum: CAR 23% with 70% exposure.
Following my value studies I ran momentum sensitivity studies in Amibroker on trade exit dates for bi-annual seasonal trading. Data used was the daily Fama-French small momentum portfolio from 1984 to 2014. Entry date is calendar day 300 (~ Nov 1).
Annual return peaks at 23% with exposure of 70% and a stable optima.
As with the value portfolio, the highest Sharpe Ratio is achieved from selling earlier in the year: day 90 and 210 for even and odd years respectively. Annual return is reduced by 2% to achieve these higher risk-adjusted returns.
I plan to look at the addition of a trend-following filter (e.g. Faber 10 month average) and combining value and momentum to realize the portfolio benefits of negative correlation.
See previous post for Amibroker code.
I ran some sensitivity studies in Amibroker on trade exit dates for bi-annual seasonal trading. Data used was the daily Fama-French small value portfolio. Entry date is calendar day 300 (~ Nov 1).
The profit maps show smooth, stable profiles with large regions near the optima.
Maximum annual return is 19% from 1984-2014 with 70% exposure (1 trade per year). Return is less sensitive to exit date in even years relative to odd years. Holding to calendar day 260 is best in odd years, showing an average tendency to rally until August. ‘Sell in May’ reduces profits by a third!
These dates should be used as a guide only. More accurate triggers, such as an oversold condition to buy could be used. However, the average gain is 24% therefore extreme accuracy on entry and exit is not necessary.
Sharpe Ratio shows a similar and stable picture but with earlier exits: day 80 in even years and day 210 in odd years. Again, real-time triggers could be overlaid on this road map.
Note that doubling the length of these tests (back to 1954) produces very similar results, implying that the phenomena is fairly reliable although the cause is a subject of debate.
os = Optimize(“odd year sell day“,260,60,300,10);
es = Optimize(“even year sell day“,120,60,200,10);
Buy = DayOfYear() > 300;
Sell = DayOfYear() > IIf(Year()%2,os,es) && 1-Buy;
There is a marked difference in characteristics between even and odd years. To illustrate, plotting 30 years of monthly returns from Ken French’s small value portfolio against a 24 month index:
Poor performance in even years (months 1-12) starts earlier and lasts longer. The trendline exhibits a much narrower and later trough in odd years (months 13-24).
The market return, in excess of the risk-free rate, is plotted in blue. Excluding months 4-7 in even years, 8-10 in odd years and St. Louis Fed Recessions (brown) produces the red equity curve. Annual excess return is 10.2% with negligible drawdown (i.e. big losses typically occur in certain months).
Note that we are in currently in month 5 of an even year.
In the next post I will investigate the sensitivity of this simple approach to parameter changes.
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.
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.