1. The Fundamental Index and equal-weight strategies are rebalanced annually at the beginning of January. The minimum-variance strategy simulation is based on the MSCI USA Minimum Volatility Index methodology to employ a constrained optimization on the US Large + Mid-Cap universe to minimize volatility. Constraints include minimum and maximum constituent, country, and sector weights, as well as turnover. The optimization is recomputed semi-annually.
2. Annualized average returns are measured using monthly returns from the Russell 1000 Value Total Return Index, S&P 500 Total Return Index, and FTSE RAFI US 1000 Index. All returns are measured over the period January 1, 2006, to February 28, 2017.
3. For example, a Fundamental Index portfolio based on book value will weight every stock by its book value, which is equivalent to weighting a stock by its price times its relative book-to-price ratio. Classic value indices simply throw out the growth stocks and capitalization weight the value stocks, as does the Fama–French value factor portfolio.
4. For more details, please refer to Brandhorst (2006) and Asness et al. (2015).
5. There are various ways to avoid look-ahead bias. This expanding regression methodology will eventually converge to estimating full-sample factor betas toward the end of our data sample. Alternatively, we could have used a rolling-window framework to better capture the fact that factor betas are time varying. Our goal is to replicate a smart beta strategy’s returns by constructing a factor tilt portfolio in each month based on the information available to investors at that point in time. Choosing between methodologies is a modeling choice. What we gain in capturing a more dynamic factor tilt from rolling-window regressions, we lose by estimating the betas less precisely on fewer observations. In unreported results, “dynamic” factor-tilt portfolios constructed from rolling regressions generate even higher turnover, because replicated portfolio weights move around more with the dynamic factor betas, resulting in even greater turnover and worse returns net of trading costs.
6. The expanding window regression methodology used to prevent look-ahead bias in the replicated portfolios will generate slightly different in-sample factor loadings for these portfolios, by construction. These factor loadings would be equal to the factor loadings of the smart beta strategies, and the market betas would be exactly equal to one, if they were instead estimated once in sample.
7. The discount is measured by taking the average of the ratios of the portfolio’s P/E, P/B, P/S, and P/D to the market’s respective valuation ratio. A value less than one means the portfolio is trading at a discount relative to the market.
8. Trading costs are calculated based on the Aked and Moroz (2015) trade cost model. The model assumes a 30 bp price impact per 10% of average daily volume consumed by the portfolio turnover. We appreciate and acknowledge the help of Alex Pickard in computing trading costs and capacity.
9. A reader could easily quibble with our methodology for calculating trading costs. It’s harder to contest the notion that the turnover is five times as high, with much heavier use of illiquid and thinly traded small stocks in the replicating portfolios than in the standard Fundamental Index. Do we reach the point where 100 bps of damage is done at $10 billion of AUM? Or is trading easier than we suggest, and the threshold for this magnitude of damage is $25 billion? Trading costs are squishy. The relative magnitude of the costs is probably about right; the threshold at which these costs are reached is arguable. The costs could also be worse and the capacity lower than we suggest. Ouch.
10. We report capacity assuming the portfolios are rebalanced quarterly. Monthly smoothing of trading (same trades spread over three months) should boost capacity by about 70%, and weekly rebalancing should double it again. Consequently, these figures all offer room for improvement.
11. For economy of space, we show only the full replication portfolios, with long–short replication. The long-only replication portfolios—at least for the top 10 holdings—look rather similar. None of the short positions is large enough to be included in the top 25 holdings, let alone the top 10.
12. In a recent and most amusing example, etfDB.com published a summary early in 2017 of the 25 largest smart beta ETFs. The two largest were the Russell 1000 Value and Russell 1000 Growth ETFs. Suppose a newcomer to the smart beta landscape decided to invest in the two largest just to get a “toe in the water.” Doing so they would be buying the Russell 1000—the market!
13. The term "factor" in this context usually has a specific meaning:the returns of a long–short portfolio. Although the Fundamental Index weight is not a value factor in this sense of the word, it captures the value premium.
14. Specifically, the book-to-price, sales-to-price, and cash-flow-to-price ratios and the dividend yield.