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 May 2005 Comings and Goings The Effects of Turnover on Portfolio 3
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. Both have struggled with turnover. P4 is reoptimized twice a year, so this limits the opportunity for turnover. It's held from 45-54 stocks, but annual turnover has still averaged about 85%. [Click here for an analysis of the effects of turnover on P4.] P3 is limited to 30 stocks, but it's reoptimized six times a year. Over the past five years it's also averaged 100% annual turnover. However, after a minor tweak to its optimization formula in July 2003, annual turnover has only averaged 37% over the past two years. Since P3 has had more opportunities to see stocks come and go, we thought it would be interesting to see how its performance has been affected. Transaction costs aren't the real issue here, instead we wanted to focus on how frequently stocks entered and left the portfolio, how long they stayed, and if all that turnover really helped (or hindered) performance. Come on In and Stay AwhileP3 is a purely quantitative large cap model dating back to July 1, 2000. Based on an analysis of the fundamentals of the leading S&P 500 stocks of the 1990s, it rank orders the current index. The top 30 are selected for the portfolio. Stocks remain in the model until their ranking falls below 100 at which point they are replaced by the highest ranking stock. Prior to July 2003, the cut-off to remain in the portfolio was a rank of 40, so turnover was considerably higher.The model is reoptimized on the 15th of each even numbered month. From inception on July 1, 2000 through April 14, 2005 there have been 29 versions of this model.
Over that time, it's contained 108 different stocks. Eleven, roughly 10%, have merged or otherwise gone out of business. This is noteworthy since it introduces a degree of "survivorship bias" to the following analysis. Aside from periodically changing rankings, there's no limit to the time a stock can spend in P3 or the number of times it can come or go. Of the 108 stocks that have made an appearance, 85 have been included only once, seventeen twice, and five three times. The remaining stock, Broadcom, has appeared five times. This data is summarized in Chart 1. Without the July 2003 change that allowed stocks to remain in the model until their ranking fell to 100, more stocks would have higher numbers of appearances. Part of the reason for this change was to minimize short-term turnover as some stocks with rankings barely below 40 would leave the portfolio only to return two months later. This suggested the limit was too tight and needed to be relaxed. The current limit still assures P3 only draws from the top quintile of the index yet has resulted in substantially less turnover. Overall, once stocks arrive, they stay about 9-1/2 months. The median is 290 days. This implies a turnover rate of around 125% which is in the ballpark with the actual calculated value. The average is actually 434 days, but it's skewed upward by some outliers. Stays range anywhere from 52 days (Cabletron Systems) to 1749 days (Yahoo and Medimmune). Chart 2 shows the overall distribution. Does It Help?Unless you're a broker trying to generate commissions, the only reason for turnover is to enhance performance. P3 has certainly had its share, but has it helped?
Just looking at the raw returns, you wouldn't think so. From inception (July 1, 2003) through March 24th of this year, P3 is down 60%. Its benchmark, the S&P 500, is only off 19% over the same period. You don't need a calculator to see that's not good. At least some of P3's woes stem from the time period on which it was based. Growth led the market in the 1990s, especially in the final years. As a result, P3 has a growth bias. Unfortunately growth has trailed value in every year since -- you guessed it -- 2000. Of course understanding P3's poor performance doesn't explain it. What we're interested in here is whether turnover, P3's stock selection process, or a combination of both is the culprit. In light of the fact that growth did so poorly throughout the past five years, it's tempting to think the selection process is at fault, but actually that may not be the case. We eliminated turnover to evaluate the selection process. To do so, we created three buy-and-hold portfolios based on each stock's length of time in P3. We then compared the returns and fundamental characteristics of each portfolio to see if there was any discernable connection with return. To make the portfolios, we sorted each of the stocks by the number of days they actually spent in P3. Since P3 always has 30 stocks, we then created three 30-stock portfolios with P31 consisting of the stocks with the greatest time in P3, P32 with the next 30, and P33 with the fewest days in the model. (After eliminating the eleven stocks that were no longer trading, there were about 20 stocks left over with the lowest tenure in the model. These were not included in the study.) Returns, along with that of the S&P 500, appear in Chart 3. This isn't exactly what you'd expect.
Each of the three buy-and-hold portfolios fared better than the actual P3. In fact, none did worse than the benchmark S&P 500. This suggests P3's selection process worked well, it was just the timing -- buying high and selling too soon -- that hurt the model. P33, consisting of stocks that spent the least time in P3, was the poorest performer, matching the index. That's another vote of confidence for P3's selection process since the stocks it favored the least performed the poorest. The fact that they still outdid the actual P3 portfolio again suggests it was turnover that hurt the actual model. But this line of reasoning would also suggest that P31, the stocks the selection process favored the most, should have done better than P32. They didn't. Perhaps a look at the fundamentals will help sort this out. Chart 4 shows the fundamentals for the model, the three hypothetical portfolios, and the S&P 500. If you see a pattern, you're doing well. Few patterns emerge from the chart. Those that do don't seem to offer much insight. For example, forward P/Es decline as you look down the chart from P3 to P33, but the other fundamentals don't follow suit. Aside from return, there's little to recommend P32 over the alternatives. It does have the highest cash flow and ROE, but even that's diminished when you consider it also has the highest debt-to-capital ratio. There are, however, two things that do stand out. First, P32 has the highest market cap of the portfolios. While it falls well below that of the overall index, it does indicate that it is composed of larger stocks than the alternatives.
Secondly, and perhaps most importantly, P32 has the lowest beta. Beta is a measure of volatility, showing the portfolio's degree of sensitivity to market movement. As you'll notice from Chart 4, the index beta is 1.00. Anything over that indicates greater volatility while portfolios with betas between 1.00 and -1.00 are more stable than the benchmark. All of the portfolios have betas greater than one. P3's value of 1.73 at least partially explains why the three-year bear market hurt it much more than the S&P 500. By the same token, P32's relatively low beta helps account for its somewhat better performance. Even these two differences don't provide a fundamental reason for P32's results relative to the other alternatives. After leading the market in the late 1990s, large stocks fell harder than smaller issues. Although P32's beta is lower than the other portfolios, it's still greater than that of the index so again, this should have worked against it, not helped it. Qualified ConclusionsIt's fairly obvious from the data in Chart 4 that this analysis fails to yield much insight into the effectiveness of P3's equity selection process. P32 clearly leads the others (as well as the index) over the test period, but there's no compelling reason why.If the model was working as anticipated, P31 -- the portfolio of stocks with the longest tenure in the model -- should be expected to yield the best results. It doesn't. Neither does P33, the best bet for using the model as a contrarian stock picker.
The fact that P32 -- composed of stocks in the middle tenure of the selection process -- emerges as the strongest performer, suggests the result is random rather than systematic. Still, there's one other point worth noting: In light of the fact that P31, P32, and P33 all bested not only P3 but the S&P 500 as well, P3's model may actually be a credible means of constructing buy-and-hold portfolios. In other words, the selection process may be OK, it's the turnover that kills it. So the jury is still out on the effectiveness of the model's dynamic selection process. Maybe the market gyrations in the test period had an undue impact on the results. Perhaps if a different test period was used, the results would be more systematic. Only time and additional testing will answer these questions. One thing that doesn't seem as doubtful is the adverse affect of trading on P3. All three buy-and-hold portfolios outperformed it regardless of their stocks' actual tenure in P3. From this it would appear that the model's trading actually hurt it instead of adding value. Again, the test period may be too short to draw any definitive conclusions. Even so, the semi-monthly reoptimization is supposed to do just that: reoptimize the portfolio. From the results of the past five years, it doesn't seem to be doing so. 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.
