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Dimensional's Marlena Lee: How to Measure Value

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Marlena Lee, co-head of research at Dimensional Fund Advisors (DFA), recently took time to address questions by Index Fund Advisors about how best to quantify and utilize long-term premiums investors gain from tilting their globally diversified and passively managed portfolios to value-styled stocks. 

Murray Coleman: Is there a value premium?

Marlena Lee: Yes. There are many reasons one should expect differences in expected returns among securities.

Murray Coleman: How might investors identify those differences?

Marlena Lee: Valuation theory links expectations about a firm's future profits to its current price through a discount rate. It suggests the price of a stock depends on a few variables. One is the book-value of equity, which measures what a company owns minus what it owes. Another is what investors expect to receive from holding that stock (expected profits) and the discount rate applied to those profits (the investor's expected rate-of-return).

While this is an approximation, this framework provides very useful insights. One insight is that -- all other things being equal -- the lower the price paid for an investment, the higher the expected return. Another insight is that, for a given price, the higher the expected future cash flows, the higher the expected return.

Market capitalization and relative price tell us something about the prices investors pay. Profitability tells us something about the cash flows they expect to receive. Using this sensible framework, we expect: small-cap stocks to have higher expected returns than large-cap stocks (size premium); low-relative price stocks to have higher expected returns than high-relative price stocks (value premium); and high profitability stocks to have higher expected returns than low profitability stocks (profitability premium).

Murray Coleman: A wealth of academic research supports a global view of these factors driving long-term returns, doesn't it?

Marlena Lee: There are numerous academic studies documenting the existence of those premiums covering over 40 countries and nine decades of stock data. Those studies have also shown that realized premiums are volatile, which implies that there is a 'non-zero' probability that realized premiums can be negative over any investment horizon, even if in expectations they are positive every day.

That probability decreases the longer the horizon, but it never goes to zero. For instance, our research shows that, for the value premium, the probability of a 'negative' value premium decreases from 41% at one year to 14% at 10 years. (Note: See an explanation of how probability is computed in this case at end.) 

IFA US Large Indexes
As of 7/31/2018
Return: Annualized Return (%)     |     Risk: Annualized Standard Deviation (%)
Fund and Benchmarks 5 Years 10 Years 15 Years 20 years
Return Risk Return Risk Return Risk Return Risk
IFA Large Company Index 13.06% 9.72% 10.65% 14.69% 9.40% 13.16% 6.65% 14.82%
IFA Large Value Index 11.46% 11.12% 10.29% 18.78% 10.10% 16.71% 8.31% 17.74%
IFA Large Growth Index 14.72% 10.68% 11.67% 15.29% 10.06% 13.78% 6.76% 15.92%
Source: Morningstar, IFA

Murray Coleman: How do you measure it? 

Marlena Lee: Book value is a fundamental accounting variable that has been frequently used to scale a stock's price in studies that have documented value premiums. But there have been many other variables used: earnings, cash flow, sales, etc. The average return spreads produced by different fundamental variables have been similar. That is, the value premium is robust to the variable used to scale price.

The important common element across these studies is not the fundamental variable used -- it is that the studies use market price. Investors should take comfort in that.

From an investor's perspective, however, the choice of scaling variables does matter because different variables could have a different impact on portfolio diversification or turnover -- or, interact with other premiums in different ways. For instance: earnings, cash flow and sales all scaled by price (or a blend of those metrics) do not contain additional information about expected returns beyond the information contained in market capitalization, profitability and price-to-book.

This suggests that using multiple metrics to measure the value premium may add complexity to an investment process without improving our understanding of differences in expected returns among securities. And that price-to-book ratios remain a useful variable to identify value premiums.

IFA International Value Index vs Benchmark
As of 7/31/2018
Return: Annualized Return (%)     |     Risk: Annualized Standard Deviation (%)
Fund and Benchmark 5 Years 10 Years 15 Years 20 years
Return Risk Return Risk Return Risk Return Risk
IFA International Value Index 5.84% 12.81% 3.27% 21.25% 8.08% 18.87% 6.15% 18.59%
MSCI World ex USA Index (net div.) 5.64% 11.27% 3.26% 18.03% 7.32% 16.23% 4.56% 16.62%
MSCI World ex USA Growth Index (net div.) 6.59% 10.86% 3.59% 17.41% 7.55% 15.76% 3.92% 16.62%
Source: Morningstar, IFA
IFA Emerging Markets Value Index vs Benchmark
As of 7/31/2018
Return: Annualized Return (%)     |     Risk: Annualized Standard Deviation (%)
Fund and Benchmark 5 Years 10 Years 15 Years
Return Risk Return Risk Return Risk
IFA Emerging Markets Value Index 5.11% 16.49% 2.74% 25.41% 12.23% 23.76%
MSCI Emerging Markets Index (net div.) 5.25% 14.87% 2.87% 22.15% 10.42% 21.36%
MSCI Emerging Growth NR USD 7.21% 14.26% 3.74% 21.95% 10.30% 21.33%
Source: Morningstar, IFA. *MSCI Emerging Markets Index has an inception date of 1/1999

 

Murray Coleman: How do you know that P/B continues to be relevant?

Marlena Lee: Because while we generally use price-to-book ratios to identify low- and high- relative price securities, we run an ongoing test to see how the relation between price-to-book and subsequent returns has evolved over time. 

Murray Coleman: How does P/B hold up today compared to the 1990s? (That's when Fama and French wrote their seminal research paper "The Cross-Section of Expected Stock Returns."

Marlena Lee: T-statistics from these regressions have not shown any downward trend in the informational content of price-to-book, and remain well above 2 in the U.S. and in developed and emerging markets outside the U.S. In fact, in all three regions, the explanatory power of price-to-book in the past 15- to 20- years is similar to its long-term average. This suggests that book value continues to be an appropriate measure by which to scale price and obtain information about long-term differences in expected returns among securities.


Probability of outperformance is computed using one-hundred thousand simulations that bootstrap historical monthly returns from July 1926 to December 2017 for "Value Outperforms Growth." The probability of value not outperforming is calculated as 1-% probability of value outperforming. Bootstrapping is a statistical method that relies on random sampling with replacement (i.e. each random sample from a dataset is placed back into the sampling universe before the next sample is taken) to estimate properties of a sample statistic. Value Outperforms Growth: Fama/French US Value Index vs. Fama/French US Growth Index. Index descriptions are available upon request. The projections or other information generated by bootstrapped samples regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results, and are not guarantees of future results. Results will vary with each use and over time. Indices are not available for direct investment; therefore, their performance does not reflect the expenses associated with the management of an actual portfolio.