HE RUSSELL EQUITY INDEXES ARE reformulated once a year. By the end of the twelve months, the Russell 2000 has about 1750 remaining constituents while the Russell 1000 Large Cap Index has a number of stocks that will soon be in the Small Cap Index. With such a volatile market, is a full year too long to go without review?

And if a year's too long for an index, what about a trading portfolio? Our quantitative Portfolio 4 is only reformulated annually, and then turnover is high. So far, annual turnover has averaged 70%. Is one year too long a holding period?

Perhaps the mix grows stale by the end of the twelve months and maybe it could benefit from more frequent review. After all, in a volatile market, the fundamental factors that recommend a stock for inclusion could change dramatically. If that change occurs in the first few months, P4 is left holding it for the remainder of the period.

Partial Periods

When we created P4, we wanted to make sure it was tested over a meaningful period of time and that it wasn't subject to the market's swings of momentum. To assure this, we chose to only be reformulate it once a year at the end of June.

Which brings us back to the question of the holding period. If one year is too long but the model is viable, you'd expect performance to fade as time goes by. In other words, the model would do better in the first part of the period and worse in the latter.

To check this, we broke P4's 30-month history through December 2002 into five different six month periods. From each 12-month period, we lumped the first six months together and the last six months together. In other words, since P4 is reviewed every June, there were three six-month periods from July 1 through December 31, and two six-month periods from January 1 through June 30. Not a lot of data points, but enough to see a pattern.

For each of these series we looked at two things: Performance vs. the benchmark S&P 500 and correlation with the index. If the portfolio is getting long in the tooth by the end of the holding period you'd expect to see performance and correlation both fall off in the January to June period.

Halves and Quarters

Interestingly, that's exactly what we found. P4 tracked amazingly closely with the index in the July-December period, actually beating it by 0.07%. Correlation was remarkably high at .9828. (Perfect correlation between two series is +1.0 and perfect negative correlation -- movement to the exact opposite degree -- is -1.0.)

The story is quite different in the January-June period. Here correlation falls to .7908 and P4 trails the index by 1.6%. Indeed, all of P4's performance deficit with the S&P 500 is attributable to its second-half underperformance.

Still, with only five data points, it's hard to draw a valid conclusion. To test further, we divided P4's year into quarters. Why? Well if the mix was growing stale as time passed, you'd expect to see a decline in performance and correlation over each quarter. While it may be too simplistic to assume a linear progression (in plain English: The same fall-off in each quarter), it's not unreasonable to expect to see evidence of the pattern.

And, in the words of Gomer Pyle, "Surprise, surprise, surprise", that's exactly what we found. In both the July-December and the January-June period, the first three months had a higher correlation with the index than the last. In fact, correlations fell in each quarter although not in a linear fashion.

So maybe a year is too long a holding period. Maybe P4 really does start to get stale after a few months. Would shorter be better?

Tried But Not True

In fact, P3 seems to have a number of stocks that come, go, and then come back again (see Return Engagement). This strongly suggests that either two months is too short a holding period or stocks already in the portfolio must be given greater latitude before being removed.

So if twelve months is too long and two months is too short, what's just right? This is one of those questions where there's no definitive answer, yet we do have the grounds for an educated guess.

Clearly P3's two-month holding period is problematic -- that's one of the issues we'll address when we make some major changes in July. On the other hand, P4's quarterly and semi-annual breakdown suggest it would benefit from more frequent rebalancing.

At this point it's our sense that P3 should probably go to quarterly review with liberalized limits for retaining existing holdings. That way, a stock could have a bad month or two without being booted only to return to the portfolio a month later when it recovers.

P4 probably needs semi-annual revision. The correlation with the index and relative performance are high enough over the first six months of each year to suggest this is a more appropriate holding period.

Turnover may still approximate 70% on an annual basis, but with half of it coming in each half of the year. There's nothing inherently wrong with turnover, especially if it helps maintain or add to overall performance.

June 30 will mark the three-year anniversary of quantitative portfolios 3 and 4. It also marks the end of the original test period in which no major changes were to be made to the models.

In July 2003, we plan to tweak the models, but not the underlying regression equations. After three years, we've had the opportunity to gather some evidence of how the models work and where they fail. (For other studies, see Work in Progress, in the Archives.) Holding period is one of these factors, and one certainly in need of attention.

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