As a quantitative value investor, I‘ve always struggled with the question of how long I should keep stocks in my portfolio and when I should sell these securities. Portfolio rebalancing is an important part of sticking to my game plan as a quantitative investor.

The prospect theory in behavioral finance says that people make decisions based on the potential value of losses and gains rather than the outcome and that people value gains and losses differently.

Quantitative value investors generate alpha from the process: with our systematic approach at MFIE, we avoid this problem by following a strict timetable process. We buy equities and sell them after one year. No matter what the outcome of the individual stock was during that year. This makes our life easier because selling is even more difficult than buying stocks. Emotions are simply a wrong guide to base investment decisions on.

The reason that I work with a one-year (or 12 months) buy and hold period is that most (academic) backtest studies were analyzed this way. Joel Greenblatt‘s Magic Formula, Joseph Piotroski ‘s F-score, James O’Shaughnessy ‘s ‘ What works on Wall Street ‘ tests were all based on a 1 year buy and hold strategy. After 1 year, the portfolio is ‘renewed’ with the new list of stocks pouring out of the quantitative models. The main benefit - in some countries- for having a minimum 1-year holding period; is that there is usually a lower (or no) tax rate on these investments.

I’m not a zealot on this matter, so it is interesting to have a look at whether shorter holding periods (quarterly, 6 months) generate more than enough extra alpha compared to a 1 year holding period to cover trading costs and extra taxes.

In this particular test, we analyze 3 holding periods in the “value and momentum” two-factor tests from our latest backtest study. Our primary focus is on the combination of Book to Market (BM) and 6 months price momentum.

Our backtest universe is a subset of companies in our database containing an average of about 1500 companies in the 17 countries Eurozone market during a 13-year test period (13 June 1999 to 13 June 2012). On 13 June of each year, we select a list with the 200 cheapest stocks according to their BM ratio (our value factor).

Next, we split these 200 stocks into 2 groups according to their previous 6 months performance (our momentum factor): we select the stocks that performed best in the past period and include them in the ‘winner’ portfolio. Conversely, the stocks that performed worst go into the ‘loser’ portfolio. We measure the portfolio outcomes using 3, 6, and 12 months holding period. During the year (from June to June), we are rebalancing the portfolio each quarter or every 6 months based on the 6 months momentum factor, and each year on 13 June, we also renew our list with the newest cheapest book-to-market stocks.

The results

A momentum strategy on a value portfolio delivers significant positive results. This is consistent with our intuition, and our other backtests that investors under-react to information over the short term. All three groups within, the ‘winners’ or momentum group of stocks performed better than the group of ‘losers.’--> So winners continue to win... This confirms that the screens had some ability to predict winners and losers for the next period’s momentum-driven portfolios.

The 6 months look back and 6 months holding period appears to be the optimal one of all 3 holding strategies. The quarterly rebalanced portfolio was also slightly better than the yearly. Of course, a shorter holding period may result in higher in-sample returns, but we have to contend with high trading volume, which reduces the returns due to transaction costs and may be higher taxes in some countries.