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 July 2005 All in the Timing The Effects of Turnover on Portfolio 4
But that doesn't mean turnover is always bad. Well-timed trades can capture gains before they disappear or can capitalize on mispriced securities. Everyone isn't willing to settle for "buy-and-hold" so there's got to be some sort of happy medium. Ideally, quantitative models aren't limited to coming up with optimal portfolios for one given time. Instead, they should also be capable of rebalancing, buying, and selling as conditions warrant. The trick is to determine how much turnover is enough and how much is too much. Indeed, one of the biggest criticisms of quantitative investing models is that they trade too much. Market-beating gross returns are quickly reduced by transaction costs, leaving below-market net returns. (In fact, this is a weakness of many actively managed mutual funds as well.)
We were concerned about this problem when we created our quantitative models. It wasn't much of an issue for Portfolio 6 because it only has five potential holdings. It was, however a much bigger problem for Portfolios 3 and 4 since all 500 stocks of the S&P 500 are their potential universe. By design, turnover should be more of a problem for P3. Initially, P4 was only reoptimized annually while P3 is revisited every two months. After a three-year review in July 2003, P4 is now rebalanced semi-annually in June and December. As you'd expect, annual turnover in the past two years has risen to 103% from 81%. Even so, annual turnover for the entire period (85%) is still below that of P3 (100%). That will probably reverse in the future as P3's turnover is on the decline while P4's is rising. So is this "good" turnover or "bad" turnover? Although somewhat indecisive, the evidence suggests it hasn't helped P3. In fact, it may have actually harmed performance. What about P4? History LessonP4 is a purely quantitative large cap equity model dating back to July 1, 2000. Its universe of potential holdings is limited to the current stocks of the S&P 500. All selections are derived from the model's quantitative formulas with no "qualitative" tweaking.P4 actually uses 10 different formulas, one for each of the ten S&P sectors. Each is drawn from a linear regression based on an analysis of the fundamentals of the leading S&P 500 stocks of the 1990s. The formulas rank order all of the stocks currently in their respective sectors, and only the top few are included in P4. The results are then balanced to mirror the current sector weightings of the S&P 500. This process is designed to achieve two basic goals. First, since the same fundamental factors are not equally relevant in evaluating each sector, specific formulas focusing on only salient items should produce more valid results. Presumably, these should be the top performers from each sector. The 10 formulas and current holdings for each sector are given in Stocks of P4.
Secondly, differences in model and index performance should only result from security selection and/or market timing. This is because both model and index share the same sector weightings, neutralizing its impact on performance. (For a more detailed explanation of P4's construction, please see The Starting Point.) A change in index weighting can lead to the removal of a stock, but most often this occurs at a semi-annual reoptimization when it has fallen in rank. Aside from that, stocks are only removed (or added) due to corporate actions such as mergers, sales, or bankruptcies. These, too, are relatively rare. This is as it should be since most turnover should be attributable to the working of the model, not extraneous events. Since inception (July 1, 2000), 180 different stocks have appeared in P4. The vast majority, 131, have appeared once while the remainder have been included two, three, or even four times. Chart 1 shows the frequency distribution. Once included, stocks have remained in the portfolio from 11 to 1,809 days. The average stay is 523 days, but this is mildly distorted by the few with the longest tenure. The median -- which in this case is the most representative average -- is 367 days. This distribution is illustrated in Chart 2. All of this has resulted in that 85% annual turnover rate. With this historical background, we can now return to the original question: What impact has turnover had on performance? Math LessonThis is a relative question and can only be answered by comparing P4's actual results to those that could have been obtained with no (or lesser) turnover. The best way to approach this is to use P4's methodology to construct alternative portfolios but with little or no turnover. Their results can then serve as the basis of comparison.
We went about this in two different ways. Both involved buy-and-hold portfolios with minimal turnover. Both used the model's stock rankings throughout the five-year period to create portfolios at the beginning of the period, July 1, 2000. Obviously you really couldn't have done this back in July 2000 since you wouldn't yet know how the model would rank issues over the coming five years. This, in essence, is data mining. Nevertheless, it's a workable (and simple) way to use the model's methodology to create hypothetical yardsticks. In another bit of hindsight, neither approach considered all 180 stocks that had at some point been included in P4. That's because only 161 of them are still traded today. Some (e.g. Enron, Global Crossing, and WorldCom) went through bankruptcy. Others (e.g. PeopleSoft, AT&T Wireless, and Quintiles Transnational) have been bought or taken private. The remainder (e.g. Sprint PCS, Cabletron Systems, and PE Biosystems) disappeared as the result of other corporate actions. For the most part, these were not the strongest stocks. As a result, the so-called "survivorship bias" works in favor of the hypothetical portfolios since they are derived from the 161 "stronger" issues. Their returns should have at least a slight upward bias relative to P4's actual returns. The first set of hypothetical portfolios were, like the original P4, sector weighted to the S&P 500 of June 30, 2000. They differed from P4 in two ways. First, and perhaps most critical, once created, the hypothetical portfolios had absolutely no turnover. They were therefore, simply buy-and-hold portfolios. Secondly, since all 161 stocks had passed muster at some point over the past five years, they were ordered within their respective sectors based on the number of days they actually appeared in P4. The underlying assumption was that those with longer tenures should rank above those with shorter stays. Tenure rank was then used as a means of constructing three sector-weighted portfolios. P41 has the highest rated stocks, P43 the lowest, and P42 those falling in-between.
The sector make-up of these three portfolios along with that of the current P4 are shown on the top line of Chart 3. The current S&P 500 mix is shown below P4. All weights are as of May 20, 2005. This set of hypothetical portfolios should give some insight into the effect of turnover on P4 since each, to at least some extent, shows what would have happened using the model's quantitative equity selection process without periodic reoptimization. The original sector-weighting requirement was preserved to more closely reflect P4's actual process. But what's the effect of sector weighting? Could it be that some stocks were eliminated at rebalancing not because of deteriorating fundamentals but rather because of something more arbitrary -- S&P's additions and deletions from the index and their effect on sector weights? Back in September 2000, we pointed out that turnover had increased in the S&P 500 Index. Over the course of the 1990s, through their additions and deletions, S&P converted the index into a growth index. As a result, the weightings of the growth sectors (e.g. Technology and Healthcare) increased while value sectors (e.g. Materials and Utilities) had decreased. This continues today and may have had an impact on P4. To test this, we created a second set of hypothetical portfolios. These not only eliminated turnover, but sector weighting as well. Tenure in the portfolio was again the source of ranking. This time, we simply ranked the 161 stocks by days in P4. We then took the top 54, regardless of sector, to represent P4A. The next 54 were P4B, and the bottom 53 were P4C. Not only was this a simple way to divide them, it was also in line with the 51-stock average size of P4. The resulting mixes appear on Chart 3's bottom line. Not surprisingly, the composition of the second set of hypothetical portfolios differs from that of the first, but both are derived from the same 161 stocks. The final element was return. Reading LessonTo simplify matters, we only considered price change, not total return. Under the assumption that most equity investors seek capital appreciation rather than total return, the regression analyses for both P3 and P4 were based solely on price change without regard to dividends. As a result, price change is the appropriate standard of comparison.The evaluation period runs almost five years, from July 1, 2000 through May 20, 2005. The composition of the hypothetical portfolios remained completely unchanged throughout the period. Their results as well as the actual ones for P4 and the S&P 500 appear on Chart 4.
There are no clear-cut conclusions here. P4's actual returns are some of the worst, yet they're still better than those of P41 and P4A. Since the hypothetical portfolios don't completely dominate P4, turnover is not necessarily the obvious culprit. Ideally, you'd hope that those stocks most frequently selected by P4's quantitative model would outperform those that were passed over. That doesn't appear to be the case here -- in fact the exact opposite seems to be true. In both sets of buy-and-hold models, those with stocks with the greatest tenure (P41 and P4A) greatly underperformed those with less. Results seem to increase inversely with tenure in a linear fashion. The underlying fundamentals of the various portfolios offer little help explaining the differences. Currently both P4 and the S&P 500 have betas of 1.0. This is a comparative measure of volatility with the benchmark index's beta always being set at 1.0. The hypothetical models' values range from 0.9 (P4C) to 1.2 (P41 and P4B). Neither set displays a relation between tenure and beta so volatility is apparently not a factor here. Most other fundamental factors in P4's regression model are equally unenlightening -- they have essentially the same values for the various models as well as the S&P 500. This includes P/E, Price to Book, and Return on Equity. There are two, however, that may stand out, both related to capitalization.
In both sets of hypothetical portfolios, there is a direct relation between Debt to Capitalization and return. In other words, the greater the debt as a proportion of market capitalization, the better the return. Currently P4 and the S&P 500 fall in the middle of the range, and that's essentially where their returns fall, too. Capitalization itself is inversely correlated with the models' returns. P43 and P4C have the smallest (~$19.7 billion) while P41 and P4A have the highest (~$25.0 billion). If you think back to what's been happening in the market over the past five years, this actually makes sense. Smaller stocks have handily beaten larger ones. When the economy turned up in 2003, those with more leverage -- debt to capitalization -- experienced more immediate benefits. Based on tenure, P4 was more concentrated in larger cap issues such as those in P41 and P4A. As a result, its performance lagged. Perhaps it's a good omen that P4's current average market cap is $16 billion, well below that of any of the hypothetical models. Or course, it may be too late to benefit from the small cap run since many think leadership is about to move back to larger stocks. That's the problem in trying to interpret this data. Although five years have historically represented a market cycle, no cycle is ever average. Coming off the equity bubble of the 1990s, not only have small stocks led for the past five years, value has also dominated growth. Interest rates have been abnormally low throughout the period. So without more definitive data, it's virtually impossible to draw any major conclusions about the effects of turnover on P4. Although four of the six hypothetical buy-and-hold portfolios had better results, it's still not clear this came about because of low turnover. It may just be the effect of being in the right place at the right time in regard to smaller stocks. It's unfortunate, but after all this, about the only thing you can say with any certainty is that turnover didn't help P4. For everything else, the jury is still out. Search this site! Just enter you key word or words:
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E ALL KNOW THAT TURNOVER CAN harm portfolio performance. Transaction costs and taxes on realized capital gains lower net returns. Ill-timed trading is nothing more than buying high and selling low. That's why most long-term investors try to limit turnover, leaving trading to, well, traders.
