More ways to estimate Fama-French HML in real-time

To implement the asset allocation described in my whitepaper, the Fama-French “value factor” HML sign must be estimated in real time.  One commenter helpfully proposed RALS:

The Index takes long positions in companies with large RAFI weights relative to weightings in capitalization-weighted indices and short positions in companies with small RAFI weights relative to their weightings in cap-weighted indices.

Each company receives a weight equal to the ratio of its sales (or cash flow, dividends, book value) to the aggregate sales (or cash flow, dividends, book value) across all companies in the universe.

This sounds similar to the construction of HML.

Monthly correlation with HML is 0.65, R2 = 0.42.

Most results fall into the lower left or upper right quadrants, indicating that the sign of HML may be reliably estimated.  Only the sign is required for asset allocation using the method described in the paper.



Another option is CHEP, based on the:

Dow Jones U.S. Thematic Market Neutral Value Index

Measures the performance of an investment strategy utilizing long positions on value companies and short positions on growth companies. Value is calculated using a multi-factor ranking process based on book value to price ratio, projected earnings per share to price ratio and trailing 12-month operating cash flow to price ratio.

This also sounds similar to the construction of HML.

Monthly correlation with HML is 0.39, R2 = 0.08.


Clearly RALS is the better fit.  Unfortunately there is only a 3 year history, not enough to replicate the 30 year tests in the whitepaper.

Estimating Fama-French HML factor in real-time

A frequently asked question on my asset allocation whitepaper using the HML factor, is how to calculate HML in real time.  This can be accomplished by estimating with ETF returns (for example, Vanguard):

HML = 1/2 (Small Value + Big Value) – 1/2 (Small Growth + Big Growth).

= 1/2 (VBR + VTV – VBK – VUG)

Using Yahoo finance data gives the following results:


The trend line is at 45 degrees but scatter is significant.  I still need to recalculate the findings from the paper with estimated HML.  Of course, with a full database of stocks, actual HML could be calculated in real time but this is probably outside the resources of an individual investor.

The last 4 years looks like this:


Value outperformance over momentum is accelerating.

Asset allocation paper makes SSRN top ten downloads

Thanks for all the downloads, emails and comments!

Your paper, “EXPLOITING FACTOR AUTOCORRELATION TO IMPROVE RISK ADJUSTED RETURNS”, was recently listed on SSRN’s Top Ten download list for: Capital Markets: Asset Pricing & Valuation eJournal, Capital Markets: Asset Pricing & Valuation eJournals, ERN: Asset Pricing Models (Topic), Econometric Modeling: Capital Markets – Asset Pricing eJournal, Econometric Modeling: Financial Markets – Capital Markets eJournals and Mutual Funds, Hedge Funds, & Investment Industry eJournal.

As of 15 July 2014, your paper has been downloaded 165 times. You may view the abstract and download statistics at:

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Capital Markets: Asset Pricing & Valuation eJournal Top Ten, Capital Markets: Asset Pricing & Valuation eJournals Top Ten, ERN: Asset Pricing Models (Topic) Top Ten, Econometric Modeling: Capital Markets – Asset Pricing eJournal Top Ten, Econometric Modeling: Financial Markets – Capital Markets eJournals Top Ten and Mutual Funds, Hedge Funds, & Investment Industry eJournal Top Ten.

Asset allocation whitepaper released.

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.


Trend following + seasonality update

An update to the popular post on combining TF and seasonality.  To recap:

  1. Trend Following: Price is above 10 month average (per Faber).
  2. Seasonality: Average upcoming month return (r) over previous y cycles with m periodicity is above a threshold T.
  3. Dataset used is Fama-French “Small-Value” portfolio from 1954 to 2014.

AMIBROKER CODE (commented):


RESULTS 1984-2014 (thresholds from 0 to 1%)




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.

Practically combining trend-following and seasonality

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.