Value Investing Withmaximum Dividend to Market Ratio

Value investing withmaximum dividend to market ratio

by

Yiqing Dai*

Business School, University of Adelaide

Email:

September 2016

Abstract

The book-to-market ratio (BM) is a noisy metric for value investing because book value is a weak indicator of intrinsic value. Using the dividend discount model of Miller and Modigliani (1961), this paper proposes an alternative metric for value investing: the maximum-dividend-to-market ratio (MDM), where maximum dividend is defined as profitability minus investment. Test results show thatMDM effectively distinguishes between undervalued stocks and overvalued ones, leading to substantial economic gains. Further, MDMis a parsimonious, more efficient measure to estimate expected returns than alinear model consisting of BM, profitability and investment. An investor can increase a portfolio's Sharpe ratio by addingaMDM factor rather thana combination of the BM, profitability and investment factors.

PREFACE

PREFACE Thesis title: Value investing with maximum dividend to market ratio

Supervisors: Professor Takeshi Yamada, Dr Tariq Haque

A great deal of academic research has been published on value investing, which suggests buying undervalued stocks and avoiding overvalued ones with respect to their intrinsic value. Evidence on value investing is overwhelmingly dominated by the book-to-market ratio (BM) metric, pioneered by the findings of Rosenberg, Reid, and Lanstein (1985) and Fama and French (1992). However, because book value is a weak indicator of intrinsic value, BMis a noisy metric for value investing. Specifically, BM does not differentiate between a low-priced stock with a high intrinsic value and one whose low price is consistent withits low intrinsic value (low expectation of future cash flows). Since the second scenario is more likely in a highly competitive market, BM is rather inefficient in identifying the best value opportunities.A high BMportfolio is heavily populated by stocks that are not undervalued by the market and therefore is sub-optimal for value investing. Using the dividend discount model of Miller and Modigliani (1961), this paper proposes an alternative metric for value investing: the maximum-dividend-to-market ratio (MDM). My Test results show that:

1. MDM effectively distinguishes between undervalued stocks and overvalued ones, leading to substantial economic gains.

2. MDMis a parsimonious, more efficient measure to estimate expected returns than alinear model consisting of BM, profitability and investment. An investor can increase a portfolio's Sharpe ratio by adding a MDM factor rather than a combination of the BM, profitability and investment factors.

The paper proceeds as follows:

Section 1 introduction

Section 2 provides a simple theoretical framework for the maximum-dividend-to-market ratio.

Section 3 presents the MDMmeasure and data used in this study.

Section 4 compares MDM with a linear combination of BM, profitability and investment using firm-level FMregressions.

Section 5 presents the performance of mimic portfolios.

Section 6 conducts a horse race among the competing models to explain several prominent return anomalies.

Section 7implements robustness tests with several other measures of profitability.

Section 8 concludes.

*I am grateful to Takeshi Yamada and Tariq Haque for their invaluable advice and guidance. I thank AmitGoyal, Tom Smith, PaskalisGlabadanidis, Alex Chen and participants atthe EFA 2016 Doctoral Tutorial, the 5th Auckland Finance Meeting Doctoral Symposium and the AFAANZ Conference 2016 for helpful comments and discussions.

1. Introduction

A great deal of academic research has been published on value investing, which suggests buying undervalued stocks and avoiding overvalued oneswith respect to their intrinsic value.Evidenceon value investing is overwhelmingly dominatedby the book-to-market ratio (BM) metric, pioneered by the findings of Rosenberg, Reid, and Lanstein (1985) and Fama and French (1992). However, because book value is a weak indicator of intrinsic value, BMis a noisy metric for value investing[1].Specifically, BM does not differentiate between a low-priced stock with a high intrinsic value and one whose low price is consistent with its low intrinsic value (low expectation of future cash flows). Since the second scenario is more likely in a highly competitive market, BM is rather inefficient in identifying the best value opportunities. A high BMportfoliois heavily populated bystocks that are not undervaluedby the market and therefore is sub-optimal for value investing.

Using the dividend discount model of Miller and Modigliani (1961), this paper proposes analternative metric for value investing: themaximum-dividend-to-market ratio (MDM):

wheremaximum dividend is defined as profitability minus investment, i.e. the maximum possible dividend for a firm without outside financing. Miller and Modigliani (1961) claim that a firm's value is justified by its expected dividends –the difference between the earning power of the firm's assets and theinvestment required to maintain future earnings stream at its specified level. Given estimates of expected dividends andcurrent market value, we can solve the market discount rate on expected dividends (i.e.,long-term average expected returns)(see Fama and French 2006 and 2015a). Hence, it is a straightforward choice to use theratio of maximumdividend to market valueto estimate the cross-section of market discount rate.

Because maximum dividends are a strong indicator of intrinsic value, themaximum-dividend-to-market ratioeffectively distinguishes between undervalued stocks and overvalued ones. A high (low) MDM 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 expectation of future cash flows, the firm with highercash flows expectation must have a higher market discount rate. Likewise, if two firms are identical in cash flows expectation but different in market valuation, the firm with a 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 MDM portfolio, holdingstocks with strong fundamentals at moderate prices, as well as stocks with average fundamentals at discount prices.

Using portfolios formed by double sorts (3×3) on BM and MDM, I find that 30% of high BM stockshavelowMDM value, indicatingthat their low prices are well justified by the market for their low intrinsic values. These high-BM andlow-MDM stocks substantially underperform the market, which directly illustrates that BM is a noisy metric for value investing. Consistent with the prediction of the dividend discount model,value investing with MDM leads to substantial economic gainsin the sample period July 1963 to December 2013. For zero-cost mimicking factors formed by double sorts (2×3) on size andMDM, a $1 factor exposure delivers a cumulative profit of $28.84 for the MDM value factor, but the cumulative profit for the BM value factor is only $4.35. The Sharpe ratio improves from 0.39 for the BM value factorto 0.81 for the MDM value factor. Thus, MDM is superior to BM for value investing from both theoretical justification and empirical regularity.

This paper adds to a growing literature using the dividend discount model of Miller and Modigliani (1961) to enhance estimates of expected stock returns (see Fama and French 2006, 2015a and 2015c, and Aharoni, Grundy, and Zeng2013, and Novy-Marx 2013). The focus of those papers is to decompose the valuation equation of the dividend discount model into three component variables (BM, profitability and investment) and then combine them linearly to estimate expected returns. My work differs from those papers in one important way:I take an integrated approachusingMDM alone to estimate expected return. The dividend discount model indicates thatMDM, the interaction term between expected dividends and the reciprocal of market value, providesa closed end solution to expected return. Thus, expected return has non-linear relations with expected dividends and market value. Specifically, the marginal effect of expected dividends on expected return dependson the market value level, whereas the marginal effect of market value on expected return dependson the expected dividend level. A linear combination of BM, profitability and investmentcannot capturethisnon-linear relation; therefore,it is insufficientto provide a clean perspective on expected return.

Throughout this paper, I conduct tests to assesswhetherMDMcan outperforma linear model consisting of BM, profitability and investment measures in predicting average stock returns. In Fama-Macbeth (FM) cross-sectional regressions of stock returns on firm characteristics, MDMsimultaneously subsumes the statistical and economic explanatory powers of BM, profitability and investment. In the extreme decilespredictedto have high (low) returns by the FM regression jointly controlling for BM, profitability and investment, 27% (47%) stocks are not associated with extreme MDM value, showing no extreme returns. In time series regressions using mimicking factors, the MDM value factor generates significant alpha relative to the five-factor model (FF5) of Fama and French (2015a) that includes the market, size, BM, profitability, and investment factors. In contrast, a parsimonious model that includes only the market, size and MDM factors fully explains the BM, profitability and investment factors.In GRS tests to explain a set of prominent anomalies that are not related to the dividend discount model, the MDMfactor is better in explaining stock returns than a linear combination of the BM, profitability, and investment factors.

Since profitability is the source of dividends, I conduct a horse race between MDM and several otherprominent profitability measures for predicting average stock returns. These other profitability measures arethe earnings-to-price ratio of Ball (1978),the cash flow-to-price ratio of Lakonishok, Shleifer and Vishny(1994),the gross profitability of Novy-Marx (2013),the operating profitability of Ball, Gerakos, Linnainmaa and Nikolaev(2015), and the return-to-equity ratioof Hou, Xue and Zhang (2014). In time series spanning tests based on mimicking factors, the MDM factor dramatically outperforms the other profitability factors. In particular, none of the other profitability factors exhibits statistically reliable alpha after controlling forMDM. In contrast, the MDMfactor consistently producesa large, highly significantalphaafter controlling forother profitability factors. These results show that the MDMfactor is much closer to the efficient frontier thanother profitability factors.

The paper proceeds as follows. Section 2 provides a simple theoretical framework for the maximum-dividend-to-market ratio. Section3presents theMDM measure and data used in this study. Section 4comparesMDMwith a linear combination of BM, profitability and investmentusing firm-level FM regressions.Section 5presents the performance of mimic portfolios. Section 6 conducts a horse race among the competing models to explain several prominent return anomalies. Section 7 implements robustness tests with several other measures of profitability. Section 8 concludes.

2.Dividend discount model

The dividend discount model of Miller and Modigliani (1961), Fama and French (2006, 2008, 2015a and 2015c) and Aharoni, Grundy, and Zeng (2013) shows that the market value of a firm is the present value of its expected dividends:

(1)

where is the market value of the firm at the start of period t, are the expected dividends (expected earnings minus expected additional investment required to generate future earnings) for period t, assuming dividends are paid out at the maximum possible level without outside financing, and is the market discount rate on expected dividends or the long-term average expected return (these two terms are used interchangeably).

From the perspective of market discount rate,its relation with expected dividends and current market value can obtainedby manipulation of equation (1):

(2)

where equation (2) reveals that the expected dividend to market ratio, , provides a closed form solution for the discount factor. If themaximum possible dividends are considered in perpetuityat , by setting, we can algebraically simplify equation (2) into a much more compact equation:

, or equivalently (3)

where subscripts are dropped without leading to ambiguity in the present context. In this case, the maximum-dividend-to-market ratio provides a closed-end solution to the market discount rate. That is, given estimates of future dividends and market value, the market discount rate on dividends is uncovered to investors.

In equation (2), the expected dividend to market ratio, , can be decomposed into three component variables: BM, profitability and investment, when the expected dividends are expressed as expected earnings minus expected reinvestment of earnings:

(4)

where is expected earnings, is book equity, and is the expected change in book equity. Each of BM, expected earnings-to-book equity ratio and expected growth in book equity alone acts as an incomplete measure of expected returns because expected returns also vary with the other two variables[2]. To improve estimates of expected returns, Fama and French (2006, 2015a) linearly combineBM, profitability and investment to explain the cross section of average stock returns.

Equation (2), however, shows that the discount factor, , is given by , indicating the discount factor has economic non-linear relations with expected dividends and current market value. In this non-linear relation, a lower would indicate a higher sensitivity of the discount factor to a change of , while a lower would indicate a higher sensitivity of the discount factor to a change of . A linear combination of BM, profitability and investmentomits the non-linear relation, therefore it can work only as a noisy approach to estimate expected returns as the result of misspecification.

3. Measure of maximum-dividend-to-market ratioand data

One challenging taskinmeasuringMDMis to identify areliableproxy for expected maximum dividends. Graham and Dodd (1934) point out that the past financial record affords at least a rough guide to the future.Earlier studies find that simple proxies for expected profitability and investment provided bythe most recentrecordare powerful forecasting variables for average returns. For equity earnings, Novy-Marx (2013) finds that gross profitability (revenue minus cost of goods sold, ) has great power in predicting the cross section of average returns and interprets this as a clean accounting measure of true economic profitability. Ball, Gerakos, Linnainmaa and Nikolaev(2015) show that operating profitability (revenue less cost of goods sold less selling, general & administrative expenses excluding expenditure on research & development, ) can further improve the predictive power of profitability[3].For additionalinvestment, Aharoni, Grundy, and Zeng (2013) and Fama and French (2015a) find that the growth of total assets is negatively related to average returns[4].With equations (2) to (4),I measure the maximum-dividend-to-market ratio for each firm at the end of each June as:

(5)

Whererevenue (REVT), cost of goods sold (COGS), selling, general & administrative expenses (XSGA), research & development (XRD), interest expense (XINT) and book equity (B) are measured with accounting data for the fiscal year ending in year t-1;isthe change in total assets from the fiscal year ending in year t-2 to the fiscal year ending in year t-1, divided by t-1 total assets; M is the market capitalization at the end of December of year t-1, adjusted for changes in shares outstanding between the measurement date forB and the end of December.

I use monthly stock returns data from the Centre for Research in Security Prices (CRSP) and annual accounting data from Compustat. The asset pricing tests cover July 1963 through December 2013. I exclude financial firms and very small firms with total assets of less than $25 million or book equity of less than $12.5 million. Table 1 reports summary statistics for three sets of portfolios formed by double sorts (3×3) on MDM and one second sort variable [BM, operating profitability(OP), and investment(INV)]. At the end of each June, stocks are independently assigned to three MDM groups, and three BM, OPand INVgroups using the NYSE 30th and 70th percentiles as breakpoints. The intersections of the MDM sort and one second variable sort produce three sets of portfolios. Panel A reports portfolio (market and size) adjusted returns, which are the intercepts from time-series regressions of portfolio value-weighted returns on market value-weighted index and size factor (large minus small). Panels B, C and D report the number of firms, times series average MDM and second sort variable. Measures of BM, operating profitability (OP), investment (INV)are constructed the same way as in Fama and French (2015a) to facilitate a direct comparison.

For MDM-BM portfolios, a portfolio with high BM and low MDM substantially underperformsmost other portfolios by producing average adjusted returns of -0.10%, despite havingthe second highest average BM(0.42) in panel C. These high BM stocks are not undervalued by the market, sincethe low MDM value indicates they have low intrinsic value. Note that stocks with high BM and low MDM have an average number of firms, 315, in Panel D, accounting for 30% of high BM stocks. On the other hand, stocks with low BM and high MDM produce an impressive average adjusted return of 0.19%, the third highest among BM-MDM portfolios, despite having a very negative averaged BM of -1.24 in Panel C. These low BM and high MDM stocks are not overvalued by the market, accounting for 7.55% of low BM stocks.

Most importantly,holding MDM fixed, stocks with high BM do not significantly outperform stocks with low BM. The H-L column shows that the spread of adjusted returns between low BM and high BM stocks is only 0.10% (t = 063), 0.07% (t = 0.62) and 0.20% (t = 1.25) for the group of low, medium and high MDM stocks, respectively. In contrast, the H-L row shows that the high MDM portfolio consistently outperforms the low MDM stock by 0.39% (t = 2.46), 0.44% (t = 4.64) and 0.49% (t = 4.51)for the group of low, medium and high BM stocks, respectively. Similarly, for MDM-OP portfolios and MDM-INV portfolios, controlling for MDM invalidates the predictive power of profitability and investment, except for the group of low MDM stocks among MDM-OPportfolios. In contrast, the predictive power of MDM persists after controlling for profitability and investment.These three sets of portfolio tell a consistent story that MDM subsumes the predictive power of BM, profitability and investment.