Indexes are designed to best represent designated segments of the market. Related index series such as capitalization-based indexes and value and growth style indexes, are usually separated by ‘breakpoints’. However, in reality, the styles and sizes of securities at or near breakpoints are often not clear. Consequently, enforcing investment rules strictly based on breakpoints may both coerce securities into categories when they do not show strong characteristics and cause additional transaction costs introduced by the traffic across the breakpoints. Thus, we maintain that indexes constructed with rigid breakpoints are less representative of a market and can be costly to track. We mitigate these problems through our innovative banding and migration features.
CRSP acknowledges that in practice, fund managers may have different preferences with respect to securities and styles. The same security could be small cap to one manager but mid cap to another. And, a particular security might be considered value by certain managers, but growth by others. CRSP’s methodology helps capture this ‘grey’ area by allowing a security to split 50/50 between adjacent indexes. Those securities that remain split between the adjacent indexes are ambiguous and should defy categorization until demonstrating a more stable and dominant style or size characteristic. Allowing companies to split better represents market opinion about the opportunity set.
As mentioned in a prior piece, CRSP’s capitalization-based index breakpoints are based on cumulative capitalization while the value and growth style indexes have a breakpoint defined by average rank (AR) of value and growth scores. Banding and migration respect both these breakpoints and ‘threshold bands’ defined around breakpoints. Only when a security’s AR or capitalization moves beyond its outer band can the security begin migrating to an adjacent index. CRSP handles migration with the concept of ‘packeting’. Migrating securities are broken into two packets, each 50% of a company’s holdings. The first packet migrates when the threshold band is crossed during a ranking day, the second moves if the security stays beyond the threshold in a successive quarter.
Figure 1: Banding and Migration – a simple illustration in cap indexes
Figure 1 shows three simple scenarios to illustrate our banding and migration rules using the breakpoint and bands between mega- and mid-cap indexes. Plot a) shows a case where a security moves across the breakpoint but not the bands, and remains 100% allocated in the original, mid cap index. Plot b) shows a case where a security crosses the threshold bands once but falls back into the bands afterwards. This security would remain split 50/50 between the adjacent indexes until its cap rank score emerges from a band on either side of the breakpoint. Plot c) shows a case where the security migrates 100% from the mid-cap index to the mega-cap index over two rank periods.
CRSP maintains that an index is more useful when it better represents the designated market and is cheaper to track. Banding and migration smooth the migration process by filtering out smaller fuzzy noises and focusing on clearer signals. For scenarios illustrated in Figures 1- a) and b), banding and migration rules eliminate any unnecessary transaction costs associated with transitory fluctuations in security characteristics (whether it is cap size or value/growth score); the rules also reduce the impact and, at the same time, better represent securities that had not shown persistently dominating characteristics.
Banding and Migration in Cap Indexes
For market cap indexes, the size of a company can range from several hundred millions to several hundred billions. An appropriate bandwidth between mid- and small-cap indexes would create too much migrating activities for mega-cap securities but stagnancy for micro-cap ones. Thus, we do not apply a ‘one-size-fits-all’ approach in choosing band width. Based on the test results, CRSP assigns different band sizes around breakpoints for its mega-, mid-, small- and micro-cap indexes. As one would expect, we have a wider band around the breakpoint between mega- and mid-cap indexes than for small- and micro-cap.
CRSP considered the impact of different banding and migration strategies in terms of turnover, bad turnover (turnover that create trades more than 10% of the average daily volume) and tracking errors. In the search for the best strategy, CRSP ran more than 40 combinations of band size, packeting variations, and migration paths. Figure 2 serves as an example showing how different banding and migration strategies influenced turnover and tracking error (labeled as ‘Style Impurity’) for mid-cap securities. It depicts a clear ‘efficient frontier’ showing the general tradeoff between turnover and tracking error. CRSP performed the same test for mega-, large-, small- and micro-cap securities. While the labels are for internal usage, it is worth mentioning that CRSP’s banding and migration methodology implements the setup in ‘Threshold-Packeting 2X’. It achieves the highest average ranking based on measures of turnovers, bad turnovers and tracking errors.
Figure 2: Mid Cap Investable Index Total Turnover vs. Style Impurity
Banding and Migration in Value and Growth Indexes
Banding and migration for CRSP value and growth style indexes inherited the same concepts as for the cap-based indexes. However, CRSP acknowledged that value and growth styles are more difficult to measure than market cap. To incorporate possible additional information that had not been incorporated by our model, we also calibrate the bandwidth comparing tracking errors with Morningstar and Lipper value and growth managed funds. We evaluated bandwidth between 2% and 40% around the value and growth style average rank score breakpoint. A bandwidth of 33% accommodated maximized purity and minimized turnover without compromising either. Shown in Figure 3, bandwidth of 33% also best represents the industry practice in value and growth style investing.
Figure 3: CRSP Value/Growth Indexes Average Turnover and Tracking Error vs. Average Performance of Lipper and Morningstar Value/Growth Managed Funds
Our efforts in reducing turnover while maintaining style characteristics through banding and migration technique pay off by creating a low-cost investable index that represents the market. Figure 4 shows the comparison of turnover between Vanguard’s value and growth ETF product and the backtested CRSP value and growth indexes. CRSP’s investable indexes would have potentially generated considerable savings in transaction costs.
Figure 4: Vanguard Value/Growth ETF Product Turnover (in blue) vs. Estimated CRSP Value/Growth Index Turnover (in red); Source: CRSP, Vanguard reports available as of 03/08/13. Note: FY2009 ending 8/31/09 is first full period for Mega Cap ETFs; other ETFs have 12/31 FYE.