1. It bears mention that the previous article in this series stirred a certain amount of controversy. While we are amused at the hyperventilating in some of the reaction, we are deeply grateful for the feedback. To us, these critics serve as surrogate journal referees. Thank you.
2. There is no generally accepted definition of “smart beta.” Our proposal, which we discuss in detail in “What ‘Smart Beta’ Means to Us” (Arnott and Kose 2014), combines one core criterion (it must overtly sever the link between the price of a stock and its weight in the portfolio) and several weaker requirements (the strategy must have most of the other advantages of conventional indexing, such as low turnover, broad market representation, liquidity, capacity, transparency, ease of testing, low fees, and so forth).
3. It bears mention that Sanjoy Basu’s seminal paper on the value effect appeared in 1977 after an extraordinary five-year run in which the value effect both delivered exceptional returns, following the collapse of the Nifty Fifty, and saw an exceptional rise in relative valuation to levels, at least on the basis of P/B, never seen since. Only about 10% of the half-century of benefits from the value effect was earned in the nearly 40 years after Basu’s paper was published; 90% predates publication. Was Basu engaged in inadvertent data mining, finding the value effect after, and because of, a surge in both relative valuation and relative performance? Probably. It assuredly wasn’t deliberate and the “wedge” between relative valuation and relative performance would suggest that the value effect has merit. Still, his was the first of many factors discovered near historical peaks of relative valuation, delivering comparatively little reward since they were first published. Caveat emptor.
4. Look-ahead modeling bias is an important issue that can render variables, even those having good in-sample correlation with subsequent returns, to be extremely weak as an out-of-sample conditioning variable. Goyal and Welch (2003) demonstrate this point using market-wide dividend yield to forecast subsequent market performance. In the third article of our series, we’ll deal with this nuance. It makes surprisingly little difference when results are as robust across markets and time spans as these. We will explore the merits of ex ante valuation-based forecasts in predicting factor returns. And we will show that factor or strategy timing is useful, if we pursue it with due caution.
5. Cheapness can be due to a higher perceived risk associated with value companies or may be associated with mispricing. Generations of academics have argued about the cause without much success in resolving the debate. Regardless of which camp is right, the value effect is still present.
6. In each of these cases our replication follows the published methodology. In the live implementation of the products based on these methodologies, investment managers may introduce significant modifications. These modifications can make live product investment characteristics quite different from published methodologies and, consequently, from our replication. We encourage potential investors interested in the products to learn the performance and the portfolio characteristics of the actual products coming from their corresponding product providers.
7. Charts plotting relative performance versus relative valuation for each of the six factors can be found in the first article “How Can ‘Smart Beta’ Go Horribly Wrong?”. Value, momentum, size, and illiquidity all show a notable wedge. Each likely has a powerful structural alpha, which can be masked by falling valuation levels or by anomalous short-term results. The same cannot be said for low beta or profitability.
8. A detail-oriented reader will notice that valuations may mean-revert due to either price changes or to portfolio turnover. When we explain the intuition behind half-life of valuation mean reversion in this article, we assume the second effect is significantly stronger.
9. A 20% correlation with monthly returns is, for example, vastly more useful than a 20% correlation with five-year returns. We divide our correlations by the square root of the time horizon, adjusting all correlations to an annualized equivalent to create an apples-to-apples comparison. An adjustment for the serial correlation of returns accomplishes much the same thing. The adjustment is an approximation using a simplified assumption that returns are not serially correlated between subperiods. This approximation breaks down for large levels of correlation; for example, if the monthly correlation is above 0.29, the annualized correlation computed using our method will be above 1.0, which is, obviously, impossible. Nevertheless, for the low levels of correlation we observe here, it is a useful approximation that allows us to make effective comparisons between disparate correlations measured on different horizons.
10. Others, such as Asness et al. (2000) and Cohen, Polk, and Vuolteenaho (2003), demonstrate this approach works for the value factor. Li and Lawton (2014) and Garcia-Feijóo et al. (2015) demonstrate that valuations are extremely important for low beta/low volatility strategies. Asness, Frazzini, and Pedersen (2013) show that valuations predict the future quality-minus-junk factor return they study in the article. Our new findings show the same principle works for almost any strategy. Recently, Dai (2016) shows that valuations can be predictive of market, value, size and profitability factor returns. Relative valuation is not the only variable demonstrated to be correlated with subsequent factor performance. Daniel and Moskowitz (2013) and Barroso and Santa-Clara (2014) show that extreme volatility tends to be predictive of subsequent momentum crashes and Granger et al. (2014) show how optionality imbedded in a rebalancing strategy is a timing mechanism that can help generate a higher return and a higher Sharpe ratio, albeit at a cost of altering higher moments.
11. We observe that P/B-based valuation does a better job of forecasting the return of the value blend factor, whereas the aggregate valuation measure does a better job of forecasting the return of the value strategy constructed based on B/P. An explanation may be that the P/B ratio has a better ability to forecast junk rallies, or those periods when recently unprofitable and highly distressed companies are valued by the market at unjustifiably low levels and sharply revert even on the slightest of positive news. The value factor formed on B/P is likely to load on low profitability/junk companies, whereas the aggregate valuation metric may be better at identifying quality and thus may do a better job of predicting the subsequent return. The value strategy constructed using a composite measure, however, has an imbedded tilt toward companies with higher profitability; that is, when the book-to-market spread is the largest, all value companies probably do well, but more profitable value companies likely do better than average. An alternative explanation may be that when the same variable is used to construct and measure the cheapness of the strategy, the valuation signal becomes noisier.
12. An example of this phenomenon, from our 1967 starting point, is when the value effect had cumulative statistical significance that was lousy at the peak of the tech bubble and the trough of the global financial crisis, but was impressive from 2004 to 2007. Did the value effect lose, then gain, then lose statistical significance? Or was a statistical estimate of its efficacy affected by our choice of end date, understated in 2000 and 2009, and overstated in 2004–2007? Was each estimate of the power of the value effect subject to its own estimation error, overlooked by much of the quant community at their peril? The lofty significance in 2004–2007 helped drive the soaring popularity of leveraged quant strategies, which “crashed” in August 2007.
13. Critics have suggested this comparison does not make sense for factors with a constantly changing composition, such as the momentum and low beta factors. In our first article, we note the turnover of these strategies, pointing out the weak relationship. Let’s not throw the baby out with the bath water. For such strategies, we show the starting valuation is a surprisingly powerful indicator of future returns, even though the portfolios change rapidly over time. In our upcoming third article, we will expand on the half-life of factors and smart beta strategies as a gauge of how quickly current relative valuations can become irrelevant.
14. Generally, we observe stronger correlations with future returns when we use aggregate relative valuation measures compared to using P/B alone.
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