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 September 2008 Just Right An Analysis of P5 and P6's Holding Periods
Ideally, a quantitative model should be based on theory grounded in fact. The theory should be tested (or as quants say, "backtested") before being finalized. When it finally goes live ("out of sample" in quant parlance), changes should be few and far between. This can be difficult when the market moves against you as it did almost immediately after quantitative models P3 and P4 were launched. As the models lost ground, it was tempting to make changes and indeed, subsequent data suggested that both P3 and P4 were negatively impacted by their holding periods. Three years into the test -- the first planned review -- we tweaked P4 and the results have subsequently improved. So what about models 5 and 6? They're quantitative, too, and their holding periods haven't been changed or even assessed. Granted, it hasn't seemed so pressing in their case because each has climbed since inception. Although there's no need to fix something that isn't broken, it is worthwhile to see if good performance would have been even better had the models employed a different holding period. It's never a good idea to be blinded by good fortune because you never know when it might turn the other way.
Original Thinking Each model has it's own algorithm: P5's for the optimal mix of domestic equities and P6's for the optimal balanced mix across domestic and foreign equity, and domestic fixed income. The S&P Super Composite 1500 is P5's benchmark while P6 has two special "blended" benchmarks. P5 is the older of the two, having been around since January 1, 2002 while P6 only dates back to January 1, 2004. Obviously these holding periods worked well, but could another have been better? One or two months between rebalancing would seem to be too short while one year is probably too long. But what about six months? A longer time between optimizations may help smooth out the effects of more frequent rebalancing in a volatile market. At the very minimum, it's at least worth a look.
P5 and P6 are both designed to be "trading portfolios". Because they are attempts to maximize equity (P5) and broad market (P6) returns, it was anticipated the optimal mix would change along with prevailing market conditions. This meant the holding periods should be short to be nimble enough to capture opportunities. By the same token, they shouldn't be too short so the models would be protected against being whipsawed by volatile markets. One month was too short, one year was too long, and three months seemed to be just about right. As a result, that's been and still is, their holding period. So far, it's served them well. On a cumulative basis through July 31, P5 is 13.1% ahead of the S&P 1500 while P6 leads its buy and hold benchmark by 2.3% and its rebalanced benchmark by 1.9%. (Keep in mind the time frames for P5 and P6 differ by two years, limiting the value of comparisons between the two.)
Go with the Flow Although it's difficult to tell, the semi-annual rebalancing would have only benefitted P5 in 2002 and 2008 (through July 31). The reason it's so hard to see this on Chart 1 is because the difference between the two is so small: .08% in 2002 and .18% in 2008. A different rounding convention would have wiped it out.
However that's not the case for the other years where semi-annual rebalancing would have significantly lagged. This is particularly true for 2004 (-3.88%), 2005 (-2.32%), and 2007 (-3.37%). Over the entire period (January 1, 2002 - July 31, 2008), semi-annual rebalancing trailed by 12.19%. This is reflected in the cumulative difference on the far right of Chart 1. It's even easier to see in Chart 2 which plots the actual difference between the quarterly and semi-annual rebalancing over time. Although the two run together for 2002, the semi-annual version quickly falls off until finally stabilizing and slightly recovering in late 2007 into 2008. Although not graphed here, Chart 2 is almost the mirror image of what was occurring in the global stock market. After a slow start due to the end of the U.S. bear market in 2001 and 2002, stocks headed off into a four-year bull run. At the same time, semi-annual rebalancing would have trailed quarterly rebalancing by about 14%. This suggests the more frequent optimization may have allowed P5 to take advantage of upward momentum in the market. The opposite occurs in the latter part of the chart. Here semi-annual rebalancing picks up some ground. This turn of events correlates with the initial shock of the credit crisis. At that point stocks turned downward and volatility increased. Semi-annual rebalancing avoided the whipsaw effects of the changing market while quarterly rebalancing was more susceptible. All of this suggests that quarterly rebalancing works better for P5 when the market is trending. More frequent optimization allows it to take advantage of existing momentum to add to return. When the market becomes directionless as it has over the past 12 months, there is no momentum and more frequent rebalancing can result in frequently buying high only to subsequently sell low. Although the test period didn't really provide an opportunity to compare the two strategies in a prolonged bear market, presumably the same would hold there: quarterly rebalancing would again outperform, having a greater opportunity to harness the (downward) market momentum. Historically the equity market has tended to trend for longer periods than not. The stagnant market of the 1970s was the clear exception, not the rule. If future markets will be like those of the past -- and there's little reason to believe they won't -- then P5 would be better served with quarterly rebalancing. It certainly has to date.
Xenophobia Although the patterns are different, the reason for the divergence is similar to that for what happened with P5. In this case, foreign equities were the key. Between 2004 and 2006, quarterly rebalancing bounced back and forth between putting 40-50% of the portfolio in foreign equities and then 0%. Semi-annual rebalancing which essentially skipped every other quarterly never allocated anything to foreign equity until 2007. As Chart 4 suggests, the fluctuation in quarterly rebalancing worked better than semi-annual's complete avoidance of foreign equity. (Arguably although not tested, P5 may have actually done even better had the foreign exposure remained constant.) The tables were turned in 2007 when quarterly rebalancing eliminated all foreign exposure and semi-annual finally allocated 50% abroad. That's when the latter recovered almost 3% against the former. Once again this clearly illustrates the benefits of being able to take advantage of changing market conditions. Quarterly rebalancing enabled P5 to better do so relative to less frequent optimization. Although the margin of outperformance declined in 2007, it still favored quarterly rebalancing at the end of the measurement period.
It's All Momentum At the other extreme, you might wonder if either or both models might be better suited to be buy-and-hold rather than trading portfolios. In that case, momentum and transaction costs wouldn't be factors at all. Despite the evidence that buy-and-hold strategies outperform more active ones over time, it's nice to be able to report that both P5 and P6 are ahead of their unmanaged indexes (SP 1500, and the "Static Benchmark", respectively) cumulatively from inception. (Click here for graphs.) It only makes sense that P5 and P6 must rely on momentum for success. By limiting potential holdings to index ETFs, we've eliminated any opportunity for outperformance from security selection or weighting. All that's left is the allocation between categories, and for that to succeed, it must depend on momentum. This was the assumption when the models were created and it's nice to see the out of sample data supporting it. Search this site! Just enter you key word or words: Get current quotes or follow your own custom portfolio,
courtesy of E-Line Financials:
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NE OF THE HARDEST PARTS OF running a quantitative model is resisting the urge to change it whenever times get tough. Sometimes the solutions seem obvious and it's hard to sit back and watch performance suffer. Yet it's the lack of knee-jerk intervention that can lead to success; arguably the strength of quantitative investing.
