## A Better Measure Of Value

Eugene Fama and Kenneth French’s seminal 1992 paper, “The Cross-Section of Expected Stock Returns,” resulted in the development of the Fama-French three-factor model. This model added the size and value factors to the market beta factor.

One of the benefits of adding the value factor (the tendency for relatively cheap assets to outperform relatively expensive ones) to asset pricing models was that its inclusion went a long way toward explaining the superior performance of “superstar” investors from the value school of Benjamin Graham and David Dodd.

The value premium has been highly persistent; almost as persistent as the market beta premium (also known as the equity risk premium). The following table shows the persistence of the market beta and value premiums over various time frames for the period 1927 through 2015.

The value premium has also been pervasive. For example, for the period 1975 through 2015, the Fama-French International Growth Index returned 8.6% and the Fama-French International Value Index returned 13.8%, which comes to a 5.2 percentage point advantage for value. And for the period 1989 through 2015, the Fama-French Emerging Markets Growth Index returned 9.3% and the Fama-French Emerging Markets Value Index returned 13.0%, a 3.7 percentage point advantage for value.

The value premium has also been robust to various definitions. While Fama and French used the book-to-market (BtM) ratio as their measure of value, other metrics can be used to separate cheap from expensive stocks.

For example, in the United States, for the period 1952 through 2015, the annualized value premium as measured by the BtM ratio was 4.1% (t-stat = 2.4), 4.7% (t-stat = 2.9) as measured by the cash flow-to-price ratio, and 6.3% (t-stat = 3.4) as measured by the earnings-to-price ratio. Not only do we see a value premium despite the various definitions, some of the alternates have even higher returns.

**Using The Dividend-To-Market Ratio**

Yiqing Dai contributes to the literature with the July 2016 study “Value Investing with Dividend-to-Market Ratio.” Dai proposes employing the dividend-to-market (DM) ratio as a less “noisy” and more parsimonious (simpler) value metric.

With this model, dividends represent the maximum possible dividend that could be paid out as determined by profits less investment (the reinvestment of earnings required to generate future cash flows).

Dai explains: “Because expected dividends are a strong indicator of intrinsic value, the dividend-to-market ratio effectively distinguishes between undervalued stocks and overvalued ones. A high (low) DM indicates the firm’s expected future cash flows are currently discounted at a high (low) rate, hence its stocks are in the value (growth) category. If two firms are identical in market valuation but different in dividend, the firm with the larger dividend must have a higher market discount rate.”

“Likewise, if two firms are identical in dividend but different in market valuation, the firm with higher market valuation should have a lower market discount rate. Value investors could thus maximize their economic gain per dollar of investment by constructing a high DM portfolio, holding stocks with strong fundamentals at moderate prices, as well as stocks with average fundamentals at discount prices.”

Dai’s choice of DM is consistent with the latest research on factor models. In their paper, “A Five-Factor Asset Pricing Model,” which appeared in the April 2015 issue of the Journal of Financial Economics, Eugene Fama and Kenneth French took a close look at a new five-factor model.

**Fama & French Weigh In**

Their objective was to determine whether two additional factors (the same metrics Dai uses to determine the DM ratio)—profitability (RMW, or robust-minus-weak profitability) and investment (CMA, or conservative-minus-aggressive investment)—added explanatory power.

In other words, if Fama and French knew in 1992 (when they constructed the original three-factor model) what they know today, which model would they have chosen?

Following is a summary of their findings:

While a five-factor model doesn’t fully explain the cross section of returns (there are still anomalies), it provides a good description of average returns.

- The model’s main problem is its failure to explain the low average returns on small stocks that invest a lot despite low profitability. The Fama-French three-factor model, it turns out, has the same problem in explaining the poor performance of small growth stocks.
- A four-factor model that excludes the value factor (HML, or high-minus-low value) captures average returns as well as any other four-factor model they considered. A five-factor model that includes HML doesn’t improve the description of average returns relative to four-factor models because the average HML return is captured by HML’s exposure to other factors. Thus, in the five-factor model, HML is redundant for explaining average returns.

Importantly, Fama and French further found that the five-factor model performs well. They write: “Unexplained average returns for individual portfolios are almost all close to zero.”

**More On The DM Ratio**

Returning to DM as a value measure, Dai, whose study covered the period July 1963 through December 2013, found the following:

- About 30% of high BtM stocks have low DM value, indicating they are low-priced with low intrinsic value. These high-BtM/low-DM stocks substantially underperform the market, illustrating that BtM is a “noisy” metric for value investing.
- Value investing with DM leads to substantial economic gains. With zero-cost-mimicking factors formed by double sorts (2×3, with 30% and 70% as the breakpoints) on size and DM, a $1 factor exposure delivers a cumulative profit of $28.84 for the DM value factor. In contrast, the cumulative profit is only $4.35 for the BtM value factor, $3.30 for the profitability factor and $4.72 for the investment factor. The Sharpe ratio improves from 0.39 for the BtM value factor, 0.36 for the profitability factor and 0.48 for the investment factor to 0.81 for the DM value factor. The results were similar for the two roughly equal subperiods examined.
- The high-DM portfolio consistently outperforms low-DM stocks, as well as the groups of low-, medium- and high-BtM stocks by 0.39% (t-stat = 2.46), 0.44% (t-stat = 4.64) and 0.49% (t-stat = 4.51), respectively.
- DM has a strong role in explaining the cross section of average returns. For all stocks, the DM slope of 2.41 shows a t-stat of 6.99, much larger than the figures for BtM, profitability and investment.
- DM subsumes the statistical and economic explanatory powers of BtM, profitability and investment.
- DM generates significant alpha relative to the Fama-French five-factor model (which uses the market, size, value as defined by BtM, profitability and investment factors).
- DM has strong positive correlations with the BtM value (0.85) and investment (0.78) factors, and moderate correlation with the profitability factor (0.4).
- The DM value factor is better in explaining stock returns than a linear combination of the BtM value, profitability and investment factors.
- The DM value factor is superior to the Fama-French five-factor model in explaining returns of well-known anomalies (market beta, net stock issues, volatility, accruals and momentum).

Thus, Dai concluded: “DM is superior to BM for value investing from both theoretical justification and empirical regularity.”

**Focus On Profitability**

Because profitability is the source of dividends, Dai next conducted a sort of horse race between DM and several other prominent profitability measures used for predicting average stock returns: the earnings-to-price ratio, the cash flow-to-price ratio, gross profitability (revenue minus cost of goods sold), operating profitability (revenue less cost of goods sold less selling, general and administrative expenses excluding expenditure on research and development) and the return-to-equity ratio.

Dai found that the DM factor outperforms the other profitability factors: “In particular, none of the other profitability factors exhibits statistically reliable alpha after controlling for DM. In contrast, the DM factor consistently produces a large, highly significant alpha after controlling for other profitability factors. These results show that the DM factor is much closer to the efficient frontier than other profitability factors.”

Dai’s results are consistent with financial theory. However, research from Dimensional Fund Advisors suggests it is important to consider relative price and profitability separately.

In their recent paper, “Capturing Value: Why Less Can Be More,” Marlena Lee, Savina Rizova and Antonio Picca found that book-to-market and profitability, measured as profits-to-book, both contain reliable information about differences in average returns, while composite measures such as price-to-earnings, price-to-cash flow and price-to-sales did not contain reliable information about average returns once controlling for the other variables.

*This commentary originally appeared November 28 on ETF.com*

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