1. The studies on S&P 500 reconstitution include Arnott and Vincent (1986), Harris and Gurel (1986), Goetzmann and Garry (1986), Shleifer (1986), Jain (1987), and Lamoureux and Wansley (1987).
2. Both the pre-announcement itself and the grace period (the time between the announcement date and the effective date) allow liquidity providers to gradually accumulate inventory of the stocks the index funds need to purchase on the effective date and to gradually absorb the stocks the index funds must sell; both lessen the price impact of the trading necessary to accomplish index rebalancing.
3. This observation is far less reliably true for other asset classes, in which uneconomic players can be startlingly large players. For instance, in investment-grade and sovereign bonds, central banks often trade without a profit motive, and insurance companies and banks have reserve haircuts that proactively encourage them to hold one class of bonds over another (e.g., creating a uneconomic sale of any newly downgraded junk bonds).
4. For more information, please see our “Alice in Factorland” article series composed of Arnott, Kalesnik, and Wu (2017a, b), Arnott, Clements, and Kalesnik (2017), and Arnott et al. (2017).
5. Bill Fouse at Wells Fargo Bank is often credited with running the first index funds in 1969, but this is not correct because his funds at the time excluded any company whose debt was below investment grade on the grounds of imprudence and violation of fiduciary standards. After 1973, Wells Fargo determined these exclusions led to material underperformance and began running true index funds.
6. According to ETFdb.com (http://etfdb.com/compare/lowest-expense-ratio/), today’s most competitive index-tracking ETFs are from Charles Schwab, with fees of three bps. Large segregated accounts that track indices for institutional clients may have management fees of one to two bps.
7. The CAPM was developed independently by Jack Treynor (1961, 1962), William Sharpe (1964), John Lintner (1965a,b) and Jan Mossin (1966). Their work built on earlier research by Harry Markowitz into diversification and modern portfolio theory. For their contribution to the economic sciences, Sharpe and Markowitz received, jointly with Merton Miller, the 1990 Alfred Nobel Memorial Prize in Economic Sciences.
8. Mean-variance efficiency means that the market portfolio, leveraged up or down to the desired risk level, is unbeatable except by luck.
9. De Bondt and Thaler (1981) demonstrated that 1) in the very short term (about a month after portfolio construction), the winner stocks underperform the loser stocks (this is known as short-term mean reversion and is partially explained by the bid–ask bounce as demonstrated by Roll, 1984); 2) in the intermediate term (up to a year), the winner stocks outperform the loser stocks (this is also known as the momentum effect documented first by Jegadeesh and Titman, 1993); and 3) in the longer term (two to three years), the winner stocks underperform the losers. Although the momentum effect moves in the opposite direction of short-term and long-term mean reversion, mean reversion dominates, as demonstrated by De Bondt and Thaler.
10. Banz (1981) showed that small-cap stocks outperform large-cap stocks. This phenomenon is known as the size premium. Berk (1997) argued theoretically and demonstrated empirically that the small-cap effect is largely driven by small-cap stocks being relatively cheaper and large-cap stocks being largely more expensive.
11. This is an oversimplification, of course. A high-yield stock might fall off the list, while delivering an above-market total return during the decade, and a low-yield stock can move onto the list while underperforming. And, the threshold for the top 10 list, as a percentage of the overall market capitalization, can change. Even so, it would be rare for a company to fall off the list while outperforming the market.
12. The 12 sectors are nondurables, durables, manufacturing, energy, chemicals, business equipment, telecom, utilities, shops, healthcare, finance, and other. Arnott and Wu (2012) used SIC codes to define the 12 sectors. These definitions may vary from the GICS definitions. The G-8 countries are Australia, Canada, France, Germany, Italy, Japan, United Kingdom, and United States.
13. Here’s a fun thought experiment. Suppose the S&P Index Committee had imagined their index might be used to run money. They would likely have considered other weighting schemes. Weighting by market capitalization would likely have been dismissed as preposterous: Why weight a company more heavily just because it’s more expensive? Perhaps weighting by a company’s sales would have carried the day. Well, we would then have trillions fundamentally indexed today, with cap-weight strategies barely registering. A marketer for a cap-weight index fund might be heard to say: “Nevermind that it loses 75% in rolling five-year spans. In theory, you can’t beat cap weight on a risk-adjusted basis.”
14. According to the S&P Dow Jones Indices “Annual Survey of Assets” as of yearend 2016, $2.95 trillion in total assets were indexed to the S&P 500. According to the prior year’s survey, the yearend 2015 assets indexed to the S&P 500 totaled $2.14 trillion. Net of 12% price appreciation in 2016, this would imply $550 billion net inflows into the S&P 500 tracking funds during 2016. If we add 20% for price appreciation of the S&P 500 in 2017, and add the same flows experienced in 2016, then the $2.95 trillion should have grown to approximately $4.1 trillion by yearend 2017.
15. 2 x 4.4% x $4.1 trillion = $360 billion.
16. According to the S&P Dow Jones Indices “Annual Survey of Assets” as of yearend 2016, $5.7 trillion in assets were benchmarked to the S&P 500 (excluding directly indexed assets). According to yearend 2015 estimates, S&P 500-benchmarked assets equaled $5.4 trillion. Given the 12% price appreciation in 2016, the benchmarked assets likely experienced an outflow of $0.35 trillion. If we assume 20% price appreciation in 2017 and a similar level of outflow as in 2016, we estimate the benchmarked assets to be around $6.5 trillion.
17. The raw component change list from Siblis Research includes company names, tickers, action of the change (addition or deletion), announcement date, and effective date. We use component change data from Siblis for the period from March 1973 to March 2017, and data from Wikipedia for the remaining months of 2017.
18. The number of constituents in the S&P 500 is not always 500. Since 2015, the index has held 505 stocks following a methodology change to allow multiple share classes of S&P 500 constituent companies.
19. Additions lacking price data in the six months before the effective date will be assumed to be nondiscretionary, and deletions missing price data for the six months after the effective date will be assumed to be nondiscretionary. This rule will not pick up recent IPOs as nondiscretionary additions because, according to the S&P rule book, an IPO is required to have at least 12 months of history to be eligible for consideration for S&P inclusion. https://us.spindices.com/documents/methodologies/methodology-sp-us-indices.pdf
20. The valuation discount is defined as the valuation ratio of the stock relative to the market valuation ratio. With the exception of P/B, for which we use single-year book value, we use five-year-average fundamental values in the other price-to-fundamentals ratios: P/E, P/CF, P/S, and P/D. The average valuation discount is the exponent of the pooled average of the log of the valuation discount ratio for each individual metric. The total average is the simple average of the four.
21. This asymmetry is consistent with the findings by Chan, Kot, and Tang (2013) who found a permanent positive effect on the stock price from being included in the S&P 500. The authors attributed the effect to likely broader coverage by analysts, higher liquidity, and more institutional ownership.
22. Another reason the glamour stocks may have been added to the S&P 500 may have been to minimize order imbalances and volatility due to increased orders from index funds.
23. For periodic cross-checking, we use SPY ETF holdings from December 2010 and September 2005 (when the S&P 500 fully transitioned to float-adjusted weighting). We use Vanguard 500 holdings as of December 1999. The holdings data are from Bloomberg.
24. Arnott, Beck, and Kalesnik (2015) found that a portfolio using 20-year-old stale capitalization weights outperforms an index using current information by about 180 bps a year.
25. Attentive readers may surmise that if discretionary deletions outpace additions by over 20% in the first year after an index change takes effect, and with average turnover of over 4% a year, the lazy replication should add over 80 bps a year. Correct? Not really. Remember that additions are far larger (3½ times the valuation multiples on larger sales and profits) than deletions, so additions are over 4% a year. Deletions are far smaller, with the difference made up of lightly trimming all remaining S&P 500 constituents to complete the 4% in purchases. The additions lag the S&P 500 by 1.28% in the year after addition, which contributes 5–6 bps of the 25 bps in alpha generated from laziness. If discretionary deletions are less than half of all deletions, and if they are half the size of the additions, then they represent only about 1% of annual turnover (and a little less for the Russell 1000 and Russell 3000). If they outperform by 19% in the year after they have been deleted, this adds 19 bps of additional benefit from laziness.
26. Our test starts in 1973, the first year NASDAQ-traded stocks are captured in the CRSP/Compustat database. Thus, the turnover beginning in 1973 originates predominantly from index dynamics.
27. This approach sometimes leads to having more stocks to add than to drop, and vice versa. If, for example, we need to add 20 stocks and drop 30, we choose to drop the 20 smallest, and vice versa, so that the index remains a 500-stock index.
28. The same finding also implies that the commonly used approach of rebalancing on a single day of the year is flawed.
29. If we take the difference in performance of 22 bps between the replicated trade-on-announcement S&P 500 and the replicated S&P 500 as the measure of explicit trading costs, reducing this by 10% would translate into 2 bps a year of better performance. Adding up these 2 bps of savings from lower trading costs and the 20–21 bps of savings from removing the buy-high/sell-low dynamic translates into about 22–23 bps of savings.
30. Granted, we are venturing into the realm of data mining, but we find that when the following three strategies are combined in proportions of 1:1:3, approximately 14 bps of value is added with 25 bps of tracking error: global world ex top 10 global stocks, lazy replicated S&P 500 delayed by 3 months, and lazy replicated S&P 500 delayed by 12 months. If we add the replicated trade-on-announcement S&P 500 as the fourth driver of return (which is not easy to reliably replicate, but can be roughly approximated) and assign weights in the proportions of 1:1:3:13, with the last weight of 13 given to the replicated trade-on-announcement S&P 500 strategy—the value-add is 18 bps with tracking error of 25 bps. Giving the 18 bps a haircut to account for the fact that without private information a total replication of the replicated trade-on-announcement S&P 500 is impossible, we arrive at a value-add of 15 bps.
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