To bring the equation and concepts to life, we can use the example of a simple value portfolio. To form the portfolio, we sort stocks by their price-to-book value (P/B) ratio and assign the bottom third to our portfolio, similar to the value portfolio constituting the Fama–French high-minus-low (HML) factor. We build the portfolio at the start of the calendar year and rebalance it at the end of December. We will follow this simple value portfolio over an annual cycle.
On January 1, the portfolio, consisting of stocks with a P/B ratio ranked in the lowest third of the equity universe, has an overall P/B ratio of 1.97.4 As the year progresses, the companies held in the portfolio use profits to pay dividends (distributed earnings) and to increase book value (retained earnings). Assume the dividend yield averages 4.0% and the growth in book value is estimated at 2.4%. After experiencing this growth and the corresponding increase in valuations, many of the stocks no longer qualify for the value portfolio.
The portfolio no longer consists solely of value securities with P/B ratios ranked in the bottom third of the equity universe, but rather is composed of a rag-tag mix of value, neutral, and growth companies. The portfolio’s P/B ratio rises from 1.97 in January to 2.10 in December. Accordingly, in the annual rebalancing process, we substitute the stocks that no longer qualify for our value portfolio with replacements priced at lower valuation multiples and offering improved yields,5 which brings the portfolio’s P/B ratio back below 2.0 to 1.99.
At this point, we have all the information we need to decompose this simple portfolio’s return into the three components of revaluation, profitability, and migration. For fun, before you read on or peek at the footnote, grab a calculator or pull up Excel and try the computations. Do you get the following results? A 1.0% revaluation return, 6.4% profitability return, and 5.4% migration return that combine for a roughly 13.0% portfolio return.6 These annualised return decomposition outcomes closely match those of a US large-cap value strategy from July 1963 through December 2006, the 44-year period preceding value’s latest drawdown.
The fundamental measures of a portfolio rarely remain steady after each rebalancing cycle. In our simple example, the portfolio began the year with a P/B ratio of 1.97 and ended the year with a P/B ratio of 1.99, which implies a 1.0% revaluation return. Now imagine if our portfolio in January had a P/B ratio of 1.50 instead of 1.97. In that scenario, we would have witnessed a substantial repricing of value stocks, with a remarkable revaluation return of 28.3%! Because the portfolio’s P/B ratio reverts back below 2.0 (or 1.99 in our example) by year-end after its rebalancing, we can view the revaluation return as a one-off, unlikely to be repeated unless we witness continuous increases in price growth in excess of any growth in book value.
Having teased out the return drivers of a value portfolio, we can use the same decomposition lens on a growth portfolio. Over the same span from July 1963 through December 2006, a US large growth portfolio earned 9.4% a year, composed of a 1.1% revaluation return, –7.0% migration return, and 15.3% profitability return. In a growth portfolio, drag from the migration component is to be expected. Consistent with the results of Chaves and Arnott (2012), rebalancing or migrating away from higher-yielding value stocks into lower-yielding growth stocks reduces the potential growth of dividends in growth portfolios. Although the return from migration detracts from overall performance, a significant contribution from the profitability component more than offsets the aforementioned loss.
Given the temporary nature of revaluation changes, we focus on the structural drivers of return. In short, over the full 44-year span ending 2006, value beats growth because the pricing spread results in a migration difference of 12.4% that dwarfs the profitability difference of −8.8%.