Value investing is perhaps the oldest and most popular

A Framework for Value Investing∗ Seungmin Chee Assistant Professor, University of Oregon

Richard Sloan L. H. Penney Professor of Accounting, UC Berkeley

Aydin Uysal Ph.D. Candidate, UC Berkeley

This version: September 2011 (Preliminary and Incomplete)

Abstract: This paper provides a framework for defining, formulating and evaluating value investment strategies. We define the relative value of an investment in terms of the prospective yield implied by the investment’s current price and expected future cash flows. We develop an intuitive and parsimonious approach for estimating the prospective yield by aggregating expected earnings over a suitable forecast horizon. We then adapt our approach to construct a realized yield metric that can be used as a more direct alternative to realized security returns in evaluating value strategies. Finally, we show how our framework can be used to evaluate competing measures of value, construct improved measures of value, and attribute the returns to an investment strategy to value versus other sources.

∗

We are grateful for the comments of workshop participants and the University of Pennsylvania, Bob Holthausen and Jim Ohlson. All errors and shortcomings are our own.

1.

Introduction Value investing is perhaps the oldest and most popular style of investing. Yet, despite its

popularity in practice, the theoretical underpinnings of value investing have developed little since the pioneering work of Graham and Dodd (1934). In this paper, we propose a definition of the relative value of an investment that is both theoretically rigorous and practically appealing. We then develop an associated framework to evaluate competing measures of value, construct improved measures of value, and attribute the returns to an investment strategy to value versus other sources. We define the relative value of an investment in terms of the prospective yield implied by the current price of the investment and the expected future cash distributions to be received on the investment. We are obviously not the first to propose evaluating investments on their prospective yields. For example, there is a large body of literature investigating the prospective yields on common stocks, which are variously referred to as implied costs of capital, implied expected returns and implied discount rates (e.g., Gebhardt, Lee and Swaminathan, 2001; Claus and Thomas, 2001). We build on this literature by using the prospective yield as a starting point for our analysis of value investing. We begin by providing a new approach for the estimation of the prospective yield. Our approach is based on Ohlson’s (1995) analysis of earnings-based valuation. Ohlson shows that the prospective yield can be approximated by the aggregate expected cum-dividend earnings yield over sufficiently long horizons. Analysts frequently provide earnings forecasts for 3 or more years into the future and our empirical analysis suggests that aggregation periods of 2 years are usually sufficiently long for reasonable convergence in prospective yield approximations. Our approach builds on Easton, Harris and Ohlson (1992) who introduce the approach of aggregating realized earnings in order to mitigate errors in annual earnings. At a conceptual level, the main advantage of our approach is that it does not require arbitrary assumptions about terminal values. At a practical level, it is based on the expected ‘earnings power’ of a security, which is a primary focus of sell-side security analysts and a basic tenet of value investing. We derive a number of insights from our framework. First, we show that our closed form solution for the prospective yield has a natural interpretation when computed using realizations of past earnings rather than expectations of future earnings. We refer to the thus-computed construct as the ‘realized yield’. Computed over a suitable horizon, the realized yield provides an effective diagnostic for the expost evaluation of value strategies. We show that it provides a more efficient alternative to realized stock

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returns, because realized stock returns are affected by a broader set of new information arriving during the period. This new information represents noise from the perspective of evaluating value strategies. Second, armed with estimates of the market-consensus earnings expectations, we can use our framework to decompose realized stock returns into components attributable to (i) the market-implied prospective yield at the beginning of the period, (ii) earnings surprises relative to the consensus, and (iii) the change in the market-implied prospective yield. Our approach is more direct, intuitive and parsimonious than previous approaches based on predictive regressions for expected returns (e.g., Vuolteenaho, 2002). Our empirical analysis examines various implications of our framework using consensus analysts’ forecasts to proxy for expected earnings. Our analysis produces several significant insights. First, we demonstrate that variation in long-horizon security returns is dominated by fundamentals. Second, we show that our approach to estimating the prospective yield by aggregating expected earnings over several future years dominates existing value metrics in terms of predicting future realized yields and future realized stock returns. Thus, our analysis highlights significant opportunities for improvement in the relative value metrics used by academics and index providers. Third, we use our framework to determine the source of variation in future stock returns to various value metrics. Our evaluation produces several insights. For example, we find that value metrics using earnings and dividend yields tend to identify firms that deliver persistently high yields. Thus, variation in the returns to these metrics is primarily attributable to the realization of high expected returns. In contrast, value metrics using book values and cash flows tend to identify stocks with temporarily high yields. Thus, variation in returns to these metrics is primarily attributable to mean reversion in expected returns. Fourth, we show that the staleness in the consensus analysts’ forecasts that we use to compute market-implied yields results in significantly biased yield estimates. The remainder of the paper proceeds as follow. In the next section, we provide a brief overview of value investing, develop our framework for the construction and evaluation of value strategies and discuss the relation of our framework with previous research. Section 3 describes data and variable measurement. Section 4 presents our empirical results and section 5 concludes.

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2.

Development of Hypotheses

2.1

Overview of Value Investing Value investing is perhaps the oldest and most popular style of investing. Yet, despite its

popularity, the theoretical underpinnings of value investing are not well defined. The seminal treatise on value investing is Graham and Dodd (1934). They advise value investors to focus their attention on securities “which are selling below the levels apparently justified by careful analysis of the relevant facts” (see p. 13). They further encourage value investors to concern themselves with “the intrinsic value of the security and more particularly with the discovery of discrepancies between the intrinsic value and the market price” (see p. 17). Graham and Dodd argue that speculative factors cause market prices to deviate from intrinsic values and that there is an inherent tendency for the resulting disparities to correct themselves through the adjustment of price to value (see pp. 22-23). Thus, securities selling below intrinsic value are expected to generate superior long-term investment performance. Graham and Dodd recognize that intrinsic value is an elusive concept. In providing broad guidance for the determination of intrinsic value, they note that: “In general terms it is understood to be the value which is justified by the facts, e.g., the assets, earnings, dividends, definite prospects, as distinct, let us say, from market quotations established by artificial manipulation or distorted by psychological excesses. But it is a great mistake to imagine that intrinsic value is as definite and as determinable as is the market price. Some time ago intrinsic value (in the case of common stock) was thought to be about the same thing as “book value,” i.e., it was equal to the net assets of the business fairly priced. This view of intrinsic value was quite definite, but it proved almost worthless as a practical matter because neither the average earnings nor the average market price evinced any tendency to be governed by the book value. Hence this idea was superseded by a newer view, viz., that the intrinsic value of a business was determined by its earnings power. But the phrase ‘earnings power’ must imply a fairly confident expectation of certain future results. It is not sufficient to know what the past earnings have averaged, or even that they disclose a separate line of growth or decline. There must be plausible grounds for believing that this average or this trend is a dependable guide to the future.” [Graham and Dodd (1934, p. 17)]

Both academic research on value investing and common practical approaches to value investing have evolved relatively little since the pioneering work of Graham and Dodd. For example, Fama and French (1992) popularized the use of the book-to-market ratio as a measure of relative value and Lakonishok, Shleifer and Vishny (1994) use both the book-to-market ratio and the trailing annual earnings to price ratio as measures of relative value. Providers of value indices also use similar ratios in value index construction. Russell uses the book-to-market ratio, S&P use a weighted combination of the

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book-to-market, trailing annual dividend-to-price, trailing annual sales-to-price and trailing annual cash flow-to-price ratios and Dow Jones uses a weighted average of the book-to-market, consensus forecast of next year’s annual earnings-to-price, trailing annual earnings-to-price and dividend-to-price ratios. The fundamentals in the numerators in each of the above ratios represent naïve estimates of the intrinsic value of the security and are then divided by market prices to arrive at measures of relative value, with higher ratios signifying greater relative values. The fundamentals used by both academics and practitioners closely follow Graham and Dodd’s guidance of estimating intrinsic value using either current book value or proxies for earnings power (e.g., past earnings, past dividends, past sales and consensus forecast of future earnings). This approach for identifying the relative value of a security ignores many valuerelevant attributes including the timing of the future cash distributions, the risks associated with the cash distributions and the liquidity and scale of the investment. Graham and Dodd (1934) acknowledge the existence of these other attributes and suggest either making relative value comparisons across a class of investments with similar attributes (pp. 57-63) or incorporating an appropriate ‘margin of safety’ in the yields of more risky and illiquid securities (p. 231). Value investing can therefore be summarized by the following three steps: 1.

Forecast the future earnings power on each security using existing data pertaining to the security and underlying business (e.g., dividends, book value, earnings).

2.

Estimate the expected yield on the security implied by its earnings power and the current market price. Henceforth, we refer to this as the ‘prospective yield’.

3.

Determine the relative value of each security by ranking on the prospective yield (with higher yields indicating greater value) and either: a. Classifying investments into groups with similar attributes; or b. Incorporating an appropriate ‘margin of safety’ in the yields of more risky and illiquid investments.

The first two steps involve an objective forecasting exercise with observable outcomes. The third step is inherently more subjective in nature. There is widespread disagreement about both the other attributes that are value relevant and the appropriate technology for incorporating these attributes into the valuation. The remainder of the paper therefore focuses on the prospective yield with specific application to common stocks.

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2.2

A Framework for Value Investing We accomplish several tasks in this section. First, we formally define the prospective yield over

the life of an investment. Second, we derive a simple closed form solution for estimating the prospective yield using earnings expectations. Third, we introduce an ex post version of our prospective yield, which we refer to as the realized yield. We propose the realized yield as a more direct alternative to the realized stock return for the ex post evaluation of value strategies. Fourth, we show how our framework can be used to decompose realized stock returns into a component attributable to the prospective yield, a component attributable to unexpected earnings and a component attributable to changes in the prospective yield. Our framework closely follows Ohlson (1995) and begins with the familiar dividend discounting valuation model:

1 where Vt = the intrinsic value of the investment at the end of period t dt = the net cash distribution paid by the investment at the end of period t r = the appropriate discount rate Et [.] = the expected value operator conditioned on information available at the end of period t. The major issue in the implementation of the dividend-discounting model is the specification of the appropriate discount rate. As described in the previous section, the value investor addresses this issue by substituting the market price at the end of period t (denoted Pt) for Vt and then solving for the prospective yield,

:

1

While this formula mirrors the standard dividend-discounting model, Pt replaces Vt and we solve for the prospective yield,

, that sets the discounted value of the expected future cash distributions equal to the

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market price at the end of period t. The prospective yield is analogous to the implied cost of capital construct developed in previous research (e.g., Gebhardt, Lee and Swaminathan, 2001) 1. The major challenge in estimating

is in forecasting the expected future cash distributions.

Practitioners typically frame their cash flow forecasts as earnings forecasts. Ohlson (1995) formalizes this substitution by noting cash distributions on equity securities are paid out of the undistributed contributed capital and accumulated past undistributed earnings of the firm. This substitution is embodied by the accounting ‘clean surplus’ relation: dt = BV t-1 + X t - BVt where BVt = accounting book value of the security at the end of period t Xt = accounting earnings generated during period t A firm’s accounting earnings is an estimate of the additional capital generated by its operations during over the course of a period. Since firms typically reinvest a substantial portion of internally generated capital, accounting earnings provides a more timely measure of the new capital that has been generated by a firm’s operations and will ultimately be distributed to investors. Substitution of the clean surplus relation into the dividend discounting model allows the prospective yield to be expressed in terms of current price and expected earnings. In particular, Ohlson (1995, p. 674) shows that if we define: 1

1

where 1

then

as

∞, and so for sufficiently large T, the prospective yield can be approximated as:

1

1

1

We discuss the relation of our approach to the implied cost of capital literature in more detail in the next section. 7

This provides a parsimonious closed form solution for the prospective yield. Note that

is the

expected aggregate cum-dividend earnings over the next T periods. The expression therefore formalizes Graham and Dodd’s intuition that the key input required for the assessment of the relative value of a security is the indicated earnings power. 2 There are two important issues associated with the implementation of this solution. First, for finite T, it is only an approximation. It therefore becomes an empirical matter as to whether this approximation proves useful for practical values of T. Second, explicitly incorporates forecasts of future dividends. This begs the question of why we benefit from recasting the dividend discounting valuation model in terms of accounting earnings. To understand why, first note that

only includes an adjustment for the opportunity cost of the cumulative earnings

at time t+T on dividends paid between t and t+T. If the security is not expected to pay a dividend during the next T-1 periods, then no forecast of future dividends is required. Intuitively, recasting the valuation model in terms of earnings is helpful when most earnings are expected to be reinvested for the foreseeable future. Since most firms reinvest the majority of their earnings, recasting the valuation model in terms of earnings allows for more of the information about the present value of future dividends to be captured in a finite forecast horizon. We are now in a position to use our closed form solution for the prospective yield to develop some tools for evaluating value investing. To simplify notation, we begin by assuming that T=1 and that our closed form solution is an equality. With these assumptions, the task of the value investor is to forecast:

This suggests that the performance of a value strategy can be directly evaluated using the realized yield, , where:

Note that the realized yield provides a practical alternative to the realized stock return for evaluating value strategies, because it only focuses on that part of the realized return that the value investor set out to forecast. The realized stock return is also influenced by the end of period stock price, which may also be impacted by changing expectations of earnings beyond period t+1 and by changes in the prospective yield. 2

See Graham and Dodd (1934) p. 354 and p. 429. 8

To better understand the determinants of realized stock returns, we can extend the framework to decompose realized stock returns into the prospective yield, an unexpected return attributable to news about future fundamentals and an unexpected return attributable to changes in the prospective yield. The market price at the beginning of period t+1 can be expressed as:

While the market price at the end of period t+1 can be expressed as:

If we define ∆ and ∆ Then it follows that the realized return between period t and period t+1 is: 1

∆

∆

∆

∆

And if we further define the realized fundamental return, F, as: ∆ Then the realized stock return can be decomposed as follows: ∆

∆

∆

This final expression reveals the three key drivers of the period t+1 realized stock return. First, we have the prospective yield or expected return, y. Second, we have the unexpected fundamental return, F-y. Note that the realized fundamental return equals the sum of realized earnings growth plus realized dividend yield. In the absence of a dividend payout, earnings are expected to grow at a rate equal to the prospective yield. Conversely, with a 100% payout ratio, earnings are not expected to grow at all. The third driver of the return is the change in the prospective yield, Δy, with increases in yields driving returns down, There is also a fourth term reflecting the interaction of earnings growth and the change in the

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prospective yield. This framework allows an investor who is armed with expectations of future earnings to decompose realized returns into 3 key drivers. The preceding analysis hinges critically on our assumptions that T=1 and that no dividends are paid during the period. The framework is readily extended to cases where T>1 and dividends are paid in the interim. For T>1, we simply replace

, where

with

In cases where the security is expected to pay dividends, we must forecast the earnings that would have been generated from the reinvestment of dividends paid during the intervening periods between the time of their payment and the end of period T. This approach has been previously applied by Easton, Harris and Ohlson (1992). We follow Easton et al. in assuming that dividends are reinvested at the risk free rate. 3 The T period aggregate cum-dividend earnings ending in period t, denoted 1

, is approximated as: 1

,

where ,

= the risk free rate for period t

Substituting

for

in our expression for

gives the following expression for the one

period prospective yield using T periods of aggregate earnings: 1

We can also measure realizations of

1

by substituting

for

. This provides a

corresponding measure of the realized yield based on aggregating over T periods: 1

1

3

A natural alternative is to assume that dividends are reinvested at the prospective yield. This alternative has two limitations. First, we no longer have a closed form solution for and must use an iterative search procedure to the resulting polynomial. Second, and perhaps more importantly, this alternative does not represent an implementable investment strategy, since it essentially assumes that dividends can be reinvested at the hypothetical intrinsic value of the security rather than the actual market price. 10

Similarly, we can decompose the realized stock return over any T period interval into the prospective yield, the unexpected fundamental return and the change in the prospective yield by substituting for

in our preceding analysis. Our framework also hinges on the assumption that T is sufficiently large to summarize

information about the prospective yield. Formally stated, this requires that: ,0

∞

Intuitively, expected cum-dividend earnings for the next T periods must exhaust available information pertaining to the present value of expected future cash distributions. T=one year is clearly insufficient. For example, earnings can display predictable multi-year cycles and new product innovations can take more than one year to be reflected in earnings. For this reason, sell-side analysts often forecast earnings for several years into the future. But earnings are very rarely forecast beyond 5 years into the future, suggesting that in the majority of cases, T=5 years will be sufficient for reasonable convergence. But this is ultimately an empirical issue and so we defer further discussion until our empirical tests.

2.3

Summary and Implications Our framework has a number of implications for both research and practice. We summarize the

implications in this section and provide a more detailed comparison with existing literature in the next section. (i)

The prospective yield provides a theoretical basis for measuring the relative value of competing investments. Note that the prospective yield only considers the expected return implied by the current price and expected future cash distributions. It ignores other potentially value-relevant attributes including the risk, the timing of the expected cash distributions and the liquidity of the investment. The value investor can either directly compare the prospective yields on investments that are similar with respect to these other attributes or use the prospective yield as one input in comparing investments that differ with respect to these attributes.

(ii)

We provide a simple closed-form solution for estimating the prospective yield over finite forecasting horizon: 1

1

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This solution relies only on the clean surplus relation and the assumption that T is sufficiently large to summarize information about the prospective yield. We therefore predict that the thusderived estimates of the prospective yield improve with the earnings aggregation period, but at a decreasing rate. (iii)

We propose a new diagnostic for the ex post evaluation of competing measures of relative value. We refer to this diagnostic as the realized yield, 1

, where: 1

We show that for finite T, the realized yield allows for more direct evaluations of a value strategy than the corresponding realized market return, because the realized security return is also impacted by new information about future fundamentals and expected returns. T must again be sufficiently large for (iv)

to summarize information available at time t about the prospective yield.

The realized market return and the realized yield must converge over the life of a security, so these two types of return are predicted to be more highly correlated over longer investment horizons.

(v)

We provide a parsimonious decomposition of the realized stock return into the prospective yield, the unexpected fundamental return and the change in the prospective yield. This decomposition allows the returns of specific investment strategies to be decomposed and attributed to these three sources. For example, if we use the consensus sell-side analysts’ forecasts of future earnings to perform the decomposition, we can attribute the returns on any investment strategy to (i) consensus-implied prospective yield at the beginning of the period, (ii) consensus earnings surprise over the period, and (iii) consensus-implied discount rate changes over the period.

2.4

Relation to Prior Work Our framework for value investing and the associated empirical implications are related to several

areas of existing work. First, many of the insights from our framework are anticipated by the classic works on value investing. This is no coincidence, as our framework is designed to formalize such insights. Second, our analysis of the prospective yield is closely related to the large body of academic research on the implied cost of capital. Third, our decomposition of the realized market return into the fundamental return and the speculative return is related to a large body of research that attempts to decompose realized market returns into cash flow news and discount rate news. We discuss the relation with these other areas of research in more detail below. 12

2.4.1

Classic Works on Value Investing Our framework is inspired by and formalizes some of the key intuition expressed in Graham and

Dodd (1934). First, our approach to estimating the prospective yield parallels Graham and Dodd’s approach to estimating the intrinsic value based on the indicated ‘earnings power’ (p. 17). Graham and Dodd define earnings power as “what the company might be expected year after year” (p. 354). Our approach of cumulating forecast earnings over multiple future years parallels closely with their concept of forecasting long-run earnings power. Our framework also distinguishes between fundamentals versus speculation in the market’s pricing of securities and demonstrates that news about fundamentals is the long-run determinant of investment returns. This mirrors Graham’s (2003, p. 477) view that ‘in the short run, the market is a voting machine, but in the long run it is a weighing machine”. Graham and Dodd explicitly recognize the role of non-fundamental sources of stock price movement as follows “the market is a voting machine, whereupon countless individuals register choices which are the product partly of reason and partly of emotion” (1934, p. 23). Our fundamental return measure, F, captures the portion of the realized stock return that is the product of ‘reason’, thus allowing us to extract and analyze the portion of the stock return that is driven by emotion. Our framework also formalizes Keynes’ (1953) arguments that while the long-run valuation of a security depends on its prospective yield, the short run price is ‘liable to change violently as a result of the sudden fluctuation of opinion due to factors which do not really make much difference to the prospective yield’ (p. 154). Keynes therefore distinguishes between ‘the term speculation for the activity of forecasting the psychology of the market, and the term enterprise for the activity of forecasting the prospective yield of assets over their whole life’ (p. 158). Finally, our framework formalizes and extends Bogle and Swensen’s (2009) decomposition of realized stock returns into a fundamental component and a speculative component. Bogle and Swensen apply their decomposition to aggregate market indices and identify three determinants of realized returns (p. 53): 1. The dividend yield at the beginning of the period 2. The earnings growth rate over the period 3. The change in the price earnings ratio during the period. They identify the first two determinants as the drivers of the fundamental component of returns and the third determinant as the speculative component of returns. If the payout ratio, earnings growth rate and P/E ratio are constant, then the realized return will equal the sum of the dividend yield and the earnings 13

growth rate. Note that this is just a more restricted version of our framework and their fundamental component of returns corresponds closely to ours. Their framework, however, is more restrictive in that it requires fixed payout ratios and earnings growth rates. Bogle and Swensen apply their analysis to aggregate market indices, where the assumptions of stable payout ratios and earnings growth rates are reasonable. Our framework instead relies simply on earnings aggregation, making it more suitable for application to individual stocks, where their assumptions are often more troublesome. Bogle and Swensen’s main conclusion also mirrors a key implication of our framework: ‘As the time frame increases from a single year to a 25-year period, the powerful influence of short-term speculation recedes, and investment returns conform much more closely, if not precisely, to the investment fundamentals: dividend yields and earnings growth. This corresponds with the dual implications of our analysis that (i) the long-run expected stock return is equal to the prospective yield and (ii) the long-run realized stock return converges to the realized yield. 2.4.2

Implied Cost of Capital Literature Our analysis is also closely related to the large body of previous research on the implied cost of

capital (e.g., Gebhardt, Lee and Swaminathan, 2001; Claus and Thomas, 2001). At a theoretical level, our prospective yield measure is equivalent to the implied cost of capital measure. Where our analysis differs is in the approach for estimating this measure. The implied cost of capital literature employs discrete estimates of ‘flows’ (dividends, free cash flows or abnormal earnings) for several future annual periods and assumes a terminal growth rate for the final period’s flow. A numerical search procedure is often used to solve the resulting polynomial for the implied cost of capital. We, in contrast, cumulate estimates of cum-dividend earnings over several future annual periods. Our approach differs from previous research in that we don’t apply an arbitrary terminal assumption to the terminal period flow. Instead, we rely on the process of earnings aggregation over the entire forecast horizon. This approach makes more efficient use of information from the entire forecast horizon and is less susceptible to forecasting errors in the terminal period flow. The existing literature has had limited success in coming up with measures of the implied cost of capital that can forecast realized returns, and this has been attributed to the naïve reliance on analysts’ inefficient and biased earnings forecasts in the computation of terminal values (e.g., Easton and Monahan, 2005). Since our approach is less susceptible to these problems, we expect that the resulting estimates of the prospective yield will better forecast realized returns. 2.4.3

Return Decomposition Literature

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Our analysis is also related to the large body of research that attempts to decompose stock returns into cash flow news and discount rate news. Shiller (1981) pioneered this literature by documenting that the variability of stock price indices cannot be accounted for by information about future dividends, because dividends do not vary enough to justify price movement. Shiller assumed a constant discount factor and so subsequent research explored whether variability in stock prices can also be attributed to news about discount factors. The most common approach to return decomposition was originally proposed by Campbell and Shiller (1988) and Campbell (1991) and extended by Vuolteenaho (2002). This approach selects and handful of state variables to predict expected returns. The usual approach involves estimating a first order vector autoregression using a small number of predictive variables and monthly/annual data. Vuolteenaho, for example, uses realized returns, book-to-market ratio and return on equity as predictive variables. The expected return forecasts and associated persistence parameters are used to infer discount rate news and the residual is assigned to cash flow news. While theoretically appealing, this approach hinges critically on the specification of the predictive model. Chen and Zhao (2009) show that it is sensitive to the state variables chosen and can yield counterintuitive results. For example, they demonstrate that a seemingly reasonable implementation of this approach leads to the unappealing conclusion that variation in US Treasury bond returns is driven primarily by cash flow news. Our approach differs from the above approach in several respects. First and foremost, we directly estimate the future cash distributions and hence cash flow news. Second, we incorporate explicit forecasts of future cash flows for several years into the future, thus avoiding the reliance on a first order VAR using annual data. Third, our approach requires fewer subjective assumptions regarding model specification. In our empirical work, we simply use analyst consensus forecasts to estimate cash flow news. Our approach to return decomposition is also closely related to Chen and Zhao (2008). They also directly estimate cash flow news from analysts’ forecasts. Their approach parallels the approach used in the implied cost of capital literature and suffers from the same limitations as mentioned in the previous subsection. In particular, their approach is very dependent on the assumed terminal year flow. Our approach to return decomposition is also related to Daniel and Titman (2006). They decompose the 5-year stock return into a component that can be attributed to tangible information and a component that can be attributed to intangible information. Their approach for estimating tangible information involves regressions of the realized stock return on the cum-dividend growth in book value over the same period. They find that future stock returns are unrelated to the tangible component of the return and negatively related to the intangible component of the return. Their decomposition of returns 15

into a tangible component corresponds to our decomposition of returns into a fundamental component. The key difference between the two studies is that we use a more structured valuation model and a larger information set for estimating the fundamental component. Finally, our study builds on the research of Easton, Harris and Ohlson (1992). They pioneer the approach of aggregating earnings over multiple years for the purpose of reducing measurement errors in earnings and they demonstrate that aggregating realized earnings and returns over longer periods increases their contemporaneous correlation. We build on their work by embedding their idea of earnings aggregation into a structured valuation framework and applying it to value investing.

3.

Data and Variable Measurement We use three main sources of data for this study. Historical accounting data are obtained from the

COMPUSTAT files, stock return data are obtained from the CRSP daily files and analyst forecast data is obtained from I/B/E/S files. Our empirical analysis uses annual financial data from 1962 to 2007 if the analysis does not require analyst forecasts. If the analysis calls for analyst forecast data, we use annual financial data from 1983 to 2007. Since we use all available observations with the necessary data for each analysis, our sample size differs across analyses depending on the measurement interval and variable availability. Hence, we report sample sizes separately for each of our analyses. Financial firms are excluded from our sample. Table 1 summarizes the measurement of each variable and we provide detailed information on variable measurement below.

3.1

Realized Yield Estimates and Earnings Measured over Horizons beyond One Year We measure all variables on a per-share basis, adjusted for stock splits and stock dividends as of

the end of our sample period. Our tests use earnings measured before extraordinary items. To estimate the realized yield measured over T periods ending in period t, denoted periods ending in period t

, we first cumulate earnings over T

, where T varies from one to five years.

When dividend payments occur during the earnings measurement interval, we calculate the cumulative cum-dividend earnings

by adding the hypothetical earnings that would have been

generated on these dividends between the time of the dividend payment and the end of the measurement interval. We assume that the reinvested dividends earn the risk-free rate and use the realized one month T-

16

bill rate as the risk-free rate. 4 Additionally, we assume that any dividends paid during fiscal year τ (

are paid half way through each fiscal year. For example, the dividends paid out during

fiscal year τ are assumed to be reinvested for (t – τ) years and six months. The weighted average common shares outstanding over the measurement interval are used as a deflator for the T period cumulative cumdividend earnings.

3.2

Prospective Yield Estimates and Analyst Consensus Forecasts of Future Earnings We construct our prospective yield estimates using analyst consensus forecasts of future earnings.

We do not claim that these forecasts represent efficient forecasts of future earnings. As a practical matter, we simply follow previous research in using these forecasts as proxies for earnings expectations. To the extent these forecasts are inefficient, our prospective yield estimates will be compromised. To estimate the prospective yield at time t, denoted consensus forecasts of future earnings,

, we first aggregate T years of analyst

. We select the I/B/E/S consensus forecasts of earnings 3

months after the fiscal year end of year t. For years without an explicit consensus forecast of earnings, we estimate future earnings using the consensus analyst long-term earnings growth forecast. We calculate aggregate T-year of cum-dividend forecast earnings,

by adding earnings

that would be generated from the reinvestment of future dividends during T years of forecasting period. We forecast future dividends by applying the time t dividend payout ratio to the forecasts of earnings from year t+1 through t+T. The dividend payout ratio is computed as dividends paid during year t deflated by the I/B/E/S actual earnings of year t. If the dividend payout ratio is negative due to negative earnings, we use a payout ratio of zero. Dividends are assumed to be reinvested to earn 3 months T-bill rate at time t and are assumed to be paid half way through the year. 5

3.3

Realized Stock Returns Realized stock returns are computed as raw buy-hold returns inclusive of dividends and any

liquidating distributions. The return cumulation period begins three months after the fiscal year-end. If a stock is delisted during the return window, the CRSP delisting return is included in the buy-hold return. Missing delisting returns are replaced with -.55 for stocks traded on NASDAQ and -.3 for stocks traded on NYSE/AMEX prior to delisting as suggested by (Shumway and Warther, 1999). 4 5

Similar results are obtained if the one-month T-bill rate is replaced with three-month T-bill rate or a 5% fixed annual rate. Results are similar if we use one-year T-bill rate as a replacement of 3 month T-bill rate. 17

4.

Results We present our results in 3 subsections. In the first subsection, we examine the properties of the

prospective yield and its underlying components. This analysis provides evidence on the reasonableness of the assumptions underlying our approach. The second section employs our realized yield metric to evaluate competing measures of value. The third subsection uses our return decomposition to explore the sources of the returns to a variety of value metrics and related return predictors.

4.1

Properties of the Prospective Yield We begin this section by reporting descriptive statistics on aggregate cum-dividend earnings

construct underlying the prospective yield. Table 2 reports descriptive statistics on aggregate realized exdividend earnings (

), earnings on dividends ( d · r ) and cum-dividend earnings (

) for aggregation

periods ranging from 1 to 5 years. Note that all of the amounts are computed on a per share basis. There are two important points to note from table 2. First, earnings on dividends constitute an insignificant part of aggregate cum-dividend earnings at the 1 year measurement interval, but become progressively more important at longer intervals. Nevertheless, the median values indicate that earnings on dividends constitute only 1% of aggregate cum-dividend earnings even over a 5 year interval. Thus, as a purely practical matter, the dividend adjustment is not significant. Second, the median values of aggregate cumdividend earnings grow in approximate proportion to the length of the measurement interval, but the mean values grow at a much faster rate. In particular, mean cum-dividend earnings grow from 0.142 at the 1 year interval to 1.843 at the 5 year interval. The difference between the mean and median results likely reflects the presence of a small number of firms with strong and persistent earnings growth rates. The presence of such firms highlights the importance of using an earnings aggregation interval that is sufficient to exhaust opportunities for predictable earnings growth. Table 3 replicates the analysis in table 2 using analysts’ forecasts of earnings and dividends in place of actual realizations of earnings and dividends. Note that the analysis in table 3 can only be performed on the subsample of firms for which analysts’ forecasts are available. It is therefore restricted to the period from 1983 to 2007 and covers a subsample of the larger and more liquid firms. The mean and median values of the per-share earnings and dividend numbers are therefore much larger than in table 2. The standard deviations of the earning numbers in table 3, in contrast, tend to be smaller. There are at 18

least two explanations for this result. First, much of the ex post variation in realized earnings is unpredictable. Second, analysts often exclude what they perceive to be ‘transitory’ components from their earnings forecasts (e.g., special items). The other point of note from table 3 is that there is stronger evidence of earnings growth using the forecasts in table 3 compared to the realizations in table 2. For example, median aggregate cum-dividend earnings grow from 0.862 over the one year interval to 1.950 over the two year interval, implying an annualized growth rate of 26%. This result can be attributed to the well-documented optimistic bias in sell-side analysts’ longer-term earnings forecasts (e.g., Bradshaw, Richardson and Sloan, 2006). These results highlight a shortcoming of using sell-side earnings long-term earnings forecasts to construct estimates of the prospective yield. To the extent that the underlying forecasts are optimistic, the corresponding estimates of the prospective yield will be upwardly biased. Table 4 presents descriptive statistics on the estimates of the prospective yield computed by deflating the aggregate cum-dividend earnings estimates from table 3 by beginning of period price. The prospective yield estimates are annualized to facilitate comparability across different aggregation periods. Panel A of table 4 reports statistics on the distribution of the prospective yield estimates. The distributions are reasonably symmetrical and stable across aggregation periods. Using a 1-year measurement interval, the mean (median) prospective yield is 6.2% (6.3%). As the aggregation interval increases, the prospective yield estimates gradually increase until they reach 8.0% (7.9%) using the 5 year measurement interval. The increases in the prospective yield estimates as we move to longer horizons are likely a consequence of the previously discussed optimism in analysts’ longer-term earnings forecasts. The interquartile range for the prospective yield spans an economically plausible range of values for expected equity returns. For example, using a one-year aggregation period, the lower quartile is 4.2% and the upper quartile is 8.5%. The corresponding interquartile range for the annualized 3 month T-bill rate over our sample period was 3.3% to 5.7%. Thus, this range allows for a positive but modest equity premium. The extreme tails of the distribution, however, look more implausible. The 1st percentile is 9.78%, while the 99th percentile 17.8%. The former implies an excessively negative equity premium, while the latter implies an excessively large equity premium. These extreme tails likely reflect a small number of cases where analysts’ short-term earnings forecasts deviate significantly from investors’ expectations of long-run earnings power that are reflected in security prices. Consistent with this explanation the range of prospective yield estimates narrows as we move to longer aggregation periods. It is also noteworthy that the mean and median prospective yield is only around 7% over the sample period. The corresponding mean (median) realized return over this period is 19% (12%) (see table 19

8). Figure 1 provides a likely explanation for this discrepancy. Panel A (B) plots the mean (median) prospective yield estimates using 1 and 5 year aggregation periods by calendar year over our sample period. The prospective yield estimates for the intermediate aggregation periods lay between these two extremes, and so we omit them for clarity. Figure 1 also plots the corresponding risk free rate, proxied by the 3 month T-Bill yield. Both the mean prospective yields and the risk free rate decline over our sample period as the economy moves from the high yield environment of the early 1980s to the low yield environment of the 2000s. For example, the mean prospective yield declines from around 12% in 1983 to around 6% in 2007. This significant reduction in expected equity returns over our sample period explains why the average realized return is greater than the average expected return for the period. Realized returns have exceeded expectations as expected returns have unexpectedly declined. Panel B of table 4 provides an analysis of how our prospective yield estimates change as we lengthen the aggregation period. If analysts’ short-term earnings’ forecasts do a poor job of capturing their expectations of long-run earnings power, then we should observe significant changes in prospective yields as the earnings aggregation period is extended. In contrast, however, we observe that changes in annualized prospective yield from extending the aggregation period are very small. The mean change in going from a one to a two year aggregation is about 5 basis points. This likely reflects the optimism in longer-term forecast discussed earlier. But the interquartile range is only 2 to 6 basis points and the standard deviation is only 9 basis points. The changes get even smaller as we move to longer aggregation periods. In short, there is no evidence that using aggregation periods beyond 2 years leads to significantly different prospective yield estimates. There are two possible explanations for this finding. First, investors have little ability to forecast long-run earnings power over and above what is reflected in shortterm earnings expectations. Second, analysts’ forecasts of longer-term earnings may be simple extrapolations of their short-term earnings forecasts and are poor proxies for investors’ actual long-term earnings expectations. Regardless of the explanation, we do not have access to investors’ actual expectations and so we simply note that the use of longer-term aggregation periods is unlikely to make much difference to the accuracy of our implied yields estimated using analysts’ forecasts.

4.2

Value Investing and the Realized Yield We begin this section by providing statistics on the properties of the realized yield, Y. Table 5

provides statistics for the realized yield and the realized stock return (R) for various aggregation periods. Recall that the realized yield is measured as the realized cum dividend earnings for the period divided by 20

the stock price at the beginning of the period. It can be contrasted with the realized stock return, which also reflects non-fundamental factors and changing expectations of fundamentals in future periods. In order to examine the behavior of these other factors, we also look at the difference between the realized and fundamental yields (R-Y). Note that all 3 metrics are reported on an annualized basis to facilitate comparison. The first point of interest in table 5 is that the mean and median realized yields tend to be lower than the corresponding realized stock returns. For example, with 5 years of aggregation the mean (median) realized yield is 5.5% (6.2%) versus a mean (median) realized return of 7.1% (7.7%). Following from our discussion of the prospective yields in table 4, this is most likely attributable to the fact that expected returns dropped over the sample period. Consistent with this, the median realized yields in table 5 are all around 6%, which corresponds closely to the corresponding median prospective yields reported in table 4. The second point of interest from table 5 is that the ranges and standard deviations of the realized yields are substantially smaller than for the corresponding realized returns. This highlights the importance of factors other than realized fundamentals in driving variation in realized security returns. This effect is strongest at short horizons and weakens at longer horizons. For example, the ratio of the standard deviation of Y to R is 27% using 1 year aggregation and rises to 47% using 5 year aggregation. Figure 2 illustrates temporal variation in this relation, plotting the cross-sectional variance of realized yields and realized stock returns for each year in our sample period. Panel A uses annual aggregation periods. The higher volatility of realized stock returns is evident. The height of the technology bubble in 1999 is particularly recognizable. Panel B uses 5-year aggregation periods and each calendar year reports the cross-sectional variance for the previous 5 years. It is immediately clear that the relatively higher variability of realized returns is muted over longer aggregation periods. The correlation matrices reported in the final columns of table 5 provide further insights into the relation between realized stock returns and realized yields. The diagonals in these correlation matrices report first-order autocorrelations for the corresponding variable. Realized yields tend to be strongly positively serially correlated, while realized returns tend to be weakly negatively serially correlated. The latter effect is attributable to negative serial correlation in the impact of non-fundamental factors on realized returns. These correlations indicate that fundamentals have predictable and persistent impacts on stock returns, but that these effects tend to be swamped by less predictable and more transitory nonfundamental influences. Finally, the correlations between R and Y indicate that the relative role of

21

realized fundamentals in driving realized security returns is small at short horizons (correlation=0.197), but becomes much more significant at longer horizons (correlation=0.619). The statistics reported in table 5 have two important takeaways for value investing. First, even the perfect prediction of future fundamentals and hence future realized yields does not help very much in the prediction of future stock returns. This is because variation in stock returns is dominated by nonfundamental factors and changing expectations of future fundamentals rather than by the realization of expected fundamentals. Second, the prediction of future fundamentals is relatively more effective in the prediction of realized stock returns over longer horizons. This is because fundamentals tend to persist, while non-fundamental factors tend to be more transitory in nature. These two takeaways highlight the importance of long investment horizons for successful value investing. We next evaluate several popular measures of relative value using our framework. We first look at the relation of each of the measures with realized returns over the next 5 years, relation of the measures with the realized yield over the next 5 years,

. We then look at the

. Finally, we look at the relation

between each of the measures and the portion of realized stock returns that is unrelated to the fundamental yield,

. A measure of relative value should forecast the

component of

possible that some existing measures of relative value could incidentally forecast case, looking at their relation with

. But it is also . In this latter

alone overstates their effectiveness as a measure of relative value.

Table 6 reports descriptive statistics for the components of the realized stock return and the measures of relative value. Note that since our tests use five years of future returns data and employ analysts’ earnings forecasts, the sample used in these tests is restricted to firm-years from 1987 to 2002 for which analysts’ earnings forecasts are available, a total of 25,833 firm years. The measures of relative value we use are the prospective yield metric developed in this paper (y) book-to-market ratio (B/M), the trailing annual earnings-to-price ratio (E/P), the trailing annual dividend-to-price ratio (Div/P), the trailing annual sales-to-price ratio (Sales/P) and the trailing annual cash flow to price ratio (CF/P). We also include 2 additional measures that are well known to predict future stock returns but are not traditional measures of relative value. The first is the accounting accruals variable from Sloan (1996), Accrual, measured as the ratio of the change in non-cash working capital over the past year to average total assets. Accrual is interesting in our context, because the numerator is an important component of earnings, suggesting that it should be positively related to traditional measures of value. Yet at the same time, Sloan (1996) demonstrates that Accrual is negatively related to future stock returns because it is negatively related to predictable changes in future earnings that are not anticipated by investors. The 22

second additional variable is the past 5 year stock return,

, motivated by the evidence of long-term

return reversals in De Bondt and Thaler (1985). While this is a contrarian measure, it does not contain any fundamental information, and so it would be surprising to find that it has a relatively strong relation with the future realized yield. Panel B of table 6 reports correlations between the various measures. We include measures of the prospective yield employing forecast earnings aggregation periods from 1 year (

) to 5 years (

,

). The presence of ‘ltg’ as a superscript in the prospective yield signifies the use of

the analyst long-term earnings growth forecast to substitute for the lack of explicit earnings forecasts. The correlations between the prospective yield measures using different forecast horizons are all extremely high. This follows from the finding in table 4 that using longer aggregation periods to estimate the prospective yield makes little difference. All of the prospective yield measures are also strongly positively correlated with both future realized yields and future realized stock returns. In theory, we would expect the measures of the prospective yield to improve as we aggregate earnings expectations further into the future. As a practical matter, however, the correlations with both future realized returns and future realized yields are highest for

. This is the measure of the prospective yield that aggregates

explicit forecasts of earnings for the next two years, but does not use the long-term growth rate forecast. As discussed earlier, this likely reflects the fact that analysts’ longer-term forecasts tend to be optimistic and inaccurate (see Bradshaw, Drake , Myers and Myers, 2011). For brevity, we therefore report subsequent results using only

.

The correlations between the all other measures of relative value are all significantly positive, but below 0.6. It is also interesting to see that Accrual is positively correlated E/P even though it is negatively related to future stock returns. Finally, we see that

is negatively related to all the

traditional measure of value, but is particularly strongly negatively related to B/M. This is interesting in that these two variables are the most difficult to motivate as yield proxies on ex ante grounds. Instead, they both seem to capture temporary overreactions in stock returns. Panel A of table 7 reports results for regressions of the five year ahead cumulative stock return, on the measures of relative value computed as of the beginning of the 5-year return measurement interval. We first report regressions for each measure and we then report multiple regressions using combinations of measures. All measures of relative value load with the predicted positive sign and are statistically significant. Considered individually,

, B/M and CF/P have the greatest predictive ability with respect

to future realized returns (r-squares all exceeding 2.5%). Accrual and

are both negatively related to

future stock returns, as documented by prior research. The final row considers all measures together. 23

continues to load with a significantly positive coefficient and both Accrual and

continue to load

with significant negative coefficients. All other variables are insignificant. Panel A of table 7 also reports results using combinations of value measures employed by 3 value index providers, Russell, S&P and Dow Jones. The Russell construct is the most parsimonious, simply relying on book value. The S&P construct incorporates three additional metrics (Div/P, Sales/P and CF/P) as does the Dow Jones construct (E/P, FY1/P and Div/P). While the exact methodologies used by the index providers vary, they can be approximated by standardizing and equal weighting across the selected measures of relative value. We therefore report two regressions. The first regression simply incorporates the measures of value that are used to construct the index. The second regression first standardizes the measures and then constrains the regression to coefficients to be equal across the standardized measures to approximate the methodologies used by the index providers. 6 The Dow Jones value construct has the highest association with future returns, with an adjusted R-square of 3.6% in the constrained regression. The Russell value construct, which is the simplest, has the weakest association with future stock returns. Panel B of table 7 replicates the analysis in panel A after substituting variable. Recall that

for

as the dependent

represents the future realized yield, thus providing a more direct evaluation of

relative value signals. Consistent with this, we see that all of the relative value signals load with the predicted significantly positive coefficients and their adjusted R-squares are all uniformly higher. For example, the R-square for E/P increases from 1.1% in panel A to 10.7% in panel B. Moreover, Accruals and

, the two signals that are not traditional measures of relative value, load either insignificantly or

with the wrong sign in panel B.

has the greatest explanatory power in both the simple and multiple

regression setting. B/M is a noteworthy poor performer in panel B. It is the weakest of the value signals on a standalone basis and it loads significantly negatively in the multiple regression. It is also interesting to note that the statistical and economic significance of Accrual increases in the multiple regression. Sloan (1996) shows that accruals capture the least persistent component of earnings and Bradshaw, Richardson and Sloan (2001) show that analysts’ earnings forecast fail to incorporate this information. Thus, the negative weighting on accruals in the multiple regression serves to aid in the prediction of future realized earnings by lowering the implicit weight on the accrual component of earnings in other value signals. We also see improvements in the relative explanatory power of the index provider value 6

We emphasize that these are our own imperfect approximations of the methodologies employed by the value index providers and so should not be used to evaluate the relative performance of the underlying indices. 24

constructs relative to panel A, with the Dow Jones construct continuing to have the highest explanatory power. Panel C of table 7 replicates the analysis in panel A using the component of realized stock returns that is not reflected in the realized yield,

. Recall that this component of stock returns reflects

both non-fundamental factors and changes in expectations about fundamentals beyond the return measurement interval. The results indicate that the traditional value measures have a mixed relation with this component of returns. Consistent with this component of returns not relating to value investing, the rsquares on the value measures are generally much lower than they were in panels A and B of table 7. The coefficient on E/P even becomes negative and insignificant. B/M, however, is the one striking exception to this general result. The magnitude, significance and explanatory power of B/M is significantly greater in panel C relative to panel B. This suggests that B/M is negatively related to future changes in expected returns rather than positively related to the level of future expected returns. With respect to the non-value measures, both Accrual and

load more significantly negatively in panel C than they do in panels A

of B. This corroborates prior research suggesting that they are not measures of relative value. Instead, Accrual identifies situations where investors have overestimated the persistence of earnings (see Sloan, 1996) and

identifies situations where investors have overreacted to information (see Debondt and

Thaler, 1985). It is also noteworthy that in the multiple regression, the only relative value measure to load significantly is B/M and its statistical significance is greatly reduced.

is by far and away the most

important determinant of this component of realized returns. Finally, the explanatory power of each of the index provider constructs is lower than in panels A and B. However, since each of the constructs includes B/M, they still achieve statistical significance. To summarize, the results in this section demonstrate that most traditional value metrics forecast future stock returns via their ability to forecast the realized future yield. These results support the use of the realized yield as a metric for evaluating value strategies. B/M, however, is an important exception to this general result. In particular, the explanatory power of the B/M is concentrated in the unrealized yield component of stock returns, suggesting that it captures transitory shocks to expected returns that are perhaps due to investor overreaction to information. Consistent with this explanation, the explanatory power of B/M is largely subsumed by

. Finally, the non-value metrics, Accrual and

, both derive

their ability to predict future realized returns through their ability to forecast the unrealized rather than the realized yield component of returns. These results show that, unlike the realized stock return, the realized yield helps distinguish between value and non-value sources of return predictability. 25

4.3

Decomposing the returns to investment strategies This section illustrates how we can use our framework to decompose stock returns into expected

returns, fundamental (i.e., cash flow) news and non-fundamental (i.e., expected return) news. One key requirement of our decomposition is that we have a suitable proxy for investors’ consensus expectations of future earnings (as reflected in prices). Our empirical tests use analysts’ consensus forecasts of earnings to proxy for the investors’ expectations. We know that analysts’ forecasts are a noisy proxy for the market’s expectations (see Hughes, Liu and Su, 2008). We therefore discuss the limitations of using analysts’ forecasts in the interpretation of our results. More generally, we seek to illustrate the merits of our approach to decomposing returns while simultaneously acknowledging that our use of analysts’ forecasts to proxy for the investors’ earnings expectations is problematic. Table 8 provides descriptive statistics and correlations for our return decomposition using various return measurement intervals. All variables are annualized to ease comparability. Recall that captures expected returns using the forecasted earnings yield over the next two years, the component of returns attributable to fundamental news and ∆

captures

captures the component of returns

attributable to changes in expected returns. Focusing first on the one-year return measurement interval, variation in realized returns is driven by a roughly equal combination of

and ∆

, with

running a distant third place. As we increase the return measurement interval, the relative importance of and

increases. For example, using a 5-year return measurement, the correlations between

realized returns and

,

and ∆

are 0.224, 0.652 and 0.250 respectively. Thus, as the

return measurement interval increases, fundamentals explain a greater proportion of the variation in stock is

returns. The serial correlations in the measures help provide the intuition behind this result. strongly positively serially correlated, while ∆

is strongly negatively serially correlated (i.e., expected

returns are slowly mean-reverting). Finally, the strong negative correlations between and ∆

and both

are noteworthy. They are suggestive of noise in analysts’ forecasts as a proxy for the

market’s earnings expectations. For example, if negative information about future earnings arrives and is reflected in price, but not analyst earnings forecasts, expected return will be overstated, understated and ∆

will be

will be overstated.

Figure 3 plots the relative contributions of expected returns and fundamental news to realized returns by calendar year. Panel A uses a one year return measurement interval. The spike in non26

fundamental variance during the peak of the technology bubble in 1999 is clearly evident. Panel B uses a trailing 5-year measurement interval. It is clear that fundamentals explain a much greater proportion of the variance in realized stock returns over the longer measurement interval. The sharp increase in fundamental news in the aftermath of the technology bubble in 2001 and 2002 is notable. This likely reflects the asset write-downs that took place during these years. Table 9 provides further insight into the absolute and relative contribution of each component to variation in realized returns. This table regresses realized returns on each of the return components individually and jointly. Again, the increasing importance of fundamentals over longer measurement intervals is evident. For example, using a 5-year return measurement interval results in an r-square of 76% with most of the explanatory power deriving from fundamental news. We next regress each of the components of realized returns on the predictive variables underlying various investment strategies. Our objective is to determine the source of the returns to the different strategies. In particular, does their predictive ability with respect to future realized returns arise from predictive ability with respect to expected returns, fundamental news or changes in expected returns? Table 10 provides descriptive statistics for the variables employed in these regressions. Note that we measure each of the return components over the subsequent 5 years. The predictive variables used are similar to those employed in the previous section. Note that we don’t include the prospective yield,

,

as a predictive variable, since it now plays the role of one of the return components that comprise our dependent variables. Instead, we add the one-year forward earnings yield , FY1/P as an additional explanatory variable since this is frequently encountered as a measure of relative value in practice. Note that

and FY1/P are very similar by construction and table 10 of panel B confirms that the two are

very highly correlated. Table 11 provides the results from regressing each of the return components on the investment strategy variables. We start in panel A by regressing the expected return,

, on each of the variables.

Recall that this is the component of realized returns that we attribute to value investing. All of the relative value measures load with the predicted positive sign and are highly statistically significant. FY1/P is, not surprisingly, the most highly significant. In the multiple regression B/M is also incrementally significant. It is also noteworthy that Accrual loads with a significantly positive coefficient. While accrual is negatively related to realized returns, this predictive ability clearly doesn’t arise from value investing, because Accrual is actually positively related to expected returns. The relative rankings of the index

27

provider constructs mirror those in the realized yield regressions from table 7, with the Dow Jones index ranking highest. , on each of the

Panel B of table 11 provides results from regressing unexpected returns,

variables. Within our framework, this component of returns is unrelated to value investing. The relative value measures have mixed results in these regressions. B/M is the only variable to have a highly significant relation with future unexpected returns. But this relation becomes insignificant in the multiple regression, primarily due to the inclusion of

. The negative relation between accruals and future

stock returns is also evident in these regressions, consistent with Sloan’s (1996) hypothesis that accruals is negatively related to future earnings news. Finally, none of the index provider constructs have a robust positive relation with future unexpected returns. The Russell index has the strongest positive relation due to its sole reliance on B/M. Panel C of table 11 provides results from regressing

on each of the variables. The

value variables all load with significantly negative coefficients. This is consistent with each of these measures capturing investors’ consensus expectations of future earnings with a lag. For example, negative fundamental news that is reflected in price but not yet reflected in the fundamental measures will result in temporarily high valuation ratios and negative future revisions in the fundamental measures. Thus, the observed negative relations are consistent with stale fundamentals. Note, however, that Accrual loads with a significantly negative coefficient, which is consistent with Sloan’s hypothesis that accruals are negatively related to future fundamental news. Panel D of table 11 provides results from regressing ∆

on each of the variables. The value

variables all load with significantly positive coefficients. But this is just a consequence of the stale fundamental problem described in the previous paragraph. Stale fundamentals lead to errors in value measures that subsequently reverse, causing a positive relation between the value measures and Overall, the use of stale fundamentals in our value measures and our measures of both ∆

causes a mechanical negative relation between value measures and

positive relation between value measures and ∆

∆

.

and

and a mechanical

. These two effects cancel out when predicting future

realized returns and simply reflect a limitation in the use of analyst earnings forecasts to proxy for the market’s earnings expectations.

28

5.

Conclusions This paper provides a framework for defining, formulating and evaluating value investment

strategies. We define the relative value of an investment in terms of the prospective yield implied by the ratio of the investment’s expected cum-dividend aggregate earnings to its price. We then adapt our approach to construct a realized yield metric that can be used as a more direct alternative to realized security market returns in evaluating value strategies. We also show that our approach can be used to decompose realized security market returns into a ‘fundamental’ component (i.e., related to the investment’s underlying cash distributions) and a ’speculative’ component (i.e., related to changes in the prospective yield implied by the market price) and demonstrate the growing importance of the fundamental component over longer investment horizons. Finally, we use our approach to evaluate popular value metrics from academia and practice. We find that the forward earnings yield provides the best measure of relative value, while the book-to-market ratio identifies transitory fluctuations in expected returns. A key shortcoming of our analysis is that analysts’ forecasts are often untimely and inefficient forecasts of future earnings. Prior research shows that analysts forecasts are less timely than the forecasts embedded in stock returns (see Hughes, Liu and Su, 2008) and incorporate predictable biases that are also reflected in stock returns (see Bradshaw, Richardson and Sloan, 2001). We show that these limitations of analysts’ forecasts are also present in our data. Consequently, forecasts of the prospective yield using analysts’ earnings forecasts are noisy and our attempts to use analysts’ forecasts to decompose stock returns are also noisy. The use of improved forecasts of earnings should improve the practical application of our framework.

29

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Table 1 Variable Measurements Each variable is measured on a per-share basis, and adjusted for stock splits and stock dividends as of the end of sample period. Each variable except for stock return is truncated at 1% and 99%. Variable

Formula and Detailed Definition

Realized yield:

1

1

1

,

1

Annualized realized yield measured over T periods ending in period t+T using cumulative cum-dividend earnings over T periods. T period cumulative earnings before extraordinary item ending in period t+T, where T varies from one to five years. Deflated by common shares averaged over the earnings measurement interval. T period cumulative cum-dividend earnings ending in period t+T. Dividends are assumed to be reinvested and earn the risk free rate, . Realized one-month T-bill rates over the measurement period are used as . 7 Resulting cumulative cum-dividend earnings are deflated by common shares averaged over the earnings measurement period.

Prospective yield:

,

1

1

1

1

Annualized prospective yield measured at t using explicit earnings forecasts over the next T periods. Annualized prospective yield measured at t using earnings forecasts over the next T periods.. If explicit earnings forecasts are not available, future earnings are estimated based on analyst longterm earnings growth forecast.

7

Similar results are obtained if the one-month T-bill rate is replaced with three-month T-bill rate or a 5% fixed annual rate. 32

Variable

Formula and Detailed Definition All I/B/E/S consensus forecasts of earnings are collected for year t+1 through t+T, measured in the period following the announcement of prior earnings through the 3 months after the fiscal year end of year t. For years without consensus forecast of earnings, we estimate future earnings based on analyst long-term earnings growth forecast. T period cumulative forecast cumdividend earnings ending in period t+T. Dividend payout ratio is computed as dividends paid at time t deflated by the I/B/E/S actual earnings of the corresponding 1 1 , period. Dividends are assumed to be reinvested and earn the rate equivalent to the yield on 3 months T-bill at time t. We also assume that dividends are paid half way through each fiscal year.

Components of realized stock return: Annualized stock return measured over T periods ending in period t. Raw buy-hold returns inclusive of dividends and delisting returns. The return calculation period begins from 3 months after the fiscal year-end of t-T and extending for T periods. Missing delisting returns are replaced with -.55 for NASDAQ firms and -.3 for NYSE/AMEX firms.

∆

∑

Fundamental return

Unexpected fundamental return Change in the prospective yield measured using T periods of data

∆ Relative value measures: B/Mt E/P t

Book to market ratio at time t. Earnings before interests and taxes to price ratio at time t.

FY1/Pt

Forecast EPS for year t+1 to price ratio at time t.

Div/Pt

Dividend to price ratio at time t.

Sales/Pt

Sales to price ratio at time t.

CF/Pt Accrual t

Cash flow to price ratio at time t. Accruals at time t measured as net income minus cash flow from operations deflated by average total assets.

33

Table 2 Descriptive statistics for realized earnings

Aggregation Period, T

·

, and cum-dividend earnings

Variable

Mean

Std. Dev

P1

Q1

Median

Q3

P99

d·r

0.136 0.006 0.142

4.626 0.014 4.629

-10.251 0.000 -10.244

-0.012 0.000 -0.011

0.350 0.000 0.352

1.011 0.006 1.019

4.785 0.067 4.817

d·r

0.341 0.026 0.366

8.048 0.057 8.059

-18.850 0.000 -18.836

-0.060 0.000 -0.058

0.686 0.000 0.696

1.971 0.025 2.003

8.9914 0.2781 9.1543

d·r

0.662 0.061 0.722

10.285 0.133 10.317

-25.593 0.000 -25.579

-0.070 0.000 -0.064

1.030 0.001 1.051

2.933 0.061 3.007

13.009 0.639 13.443

d·r

1.110 0.114 1.224

11.799 0.248 11.867

-30.683 0.000 -30.550

-0.022 0.000 -0.010

1.416 0.006 1.460

3.918 0.119 4.054

16.911 1.176 17.608

d·r

1.653 0.189 1.843

12.915 0.409 13.045

-34.362 0.000 -34.138

0.055 0.000 0.070

1.826 0.018 1.900

4.900 0.202 5.137

20.739 1.885 22.106

1 year

    2 years

    3 years

    4 years

    5 years

 

, reinvestment return on dividends

All variables are defined in Table 1. Each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers. Sample consists of 158,845 observations from 1962 to 2007 (t) for annual earnings, 147,510 observations from 1963 to 2007 (t) for 2 year aggregation period, 136,156 observations from 1964 to 2007 (t) for 3 year aggregation period, 124,190 observations from 1965 to 2007 (t) for 4 year aggregation period, and 113,344 observations from 1966 to 2007 (t) for 5 year aggregation period.

34

Table 3 Descriptive statistics for expected earnings earnings Aggregation Period, T

Variable

1 year

d·r     2 years

d·r     3 years

d·r     4 years

d·r     5 years

d·r  

, reinvestment return on dividends

·

, and cum-dividend

Mean

Std. Dev

P1

Q1

Median

Q3

P99

1.050 0.007 1.057

1.167 0.015 1.173

-1.570 0.000 -1.570

0.400 0.000 0.400

0.860 0.000 0.862

1.530 0.007 1.540

4.890 0.067 4.920

 

 

 

 

 

 

 

2.356 0.028 2.384

2.387 0.063 2.413

-2.640 0.000 -2.640

0.940 0.000 0.950

1.930 0.000 1.950

3.326 0.028 3.370

10.430 0.2787 10.483

 

 

 

 

 

 

 

3.884 0.067 3.951

3.779 0.151 3.839

-3.538 0.000 -3.538

1.614 0.000 1.632

3.200 0.000 3.247

5.390 0.067 5.491

16.67 0.662 16.817

 

 

 

 

 

 

 

5.665 0.126 5.791

5.404 0.285 5.513

-4.380 0.000 -4.380

2.433 0.000 2.469

4.704 0.000 4.794

7.750 0.126 7.956

24.057 1.249 24.458

 

 

 

 

 

 

 

7.746 0.208 7.955

7.359 0.474 7.530

-5.270 0.000 -5.270

3.415 0.000 3.478

6.490 0.000 6.637

10.507 0.210 10.836

32.748 2.079 33.294

All variables are defined in Table 1. Each of the variables is truncated at 1% and 99% to mitigate outliers. Sample consists of 49,756 observations from 1983 to 2007 (t) for each aggregation period.

35

Table 4 Descriptive statistics for annualized prospective yield and increases in prospective yield as T increases. The sample consists of 49,373 observations from 1983 to 2007(t). Panel A: Descriptive statistics for prospective yield Aggregation Period, T

Mean

Std. Dev

P1

Q1

Median

Q3

P99

1 year

0.062

0.046

-0.097

0.042

0.063

0.085

0.178

2 years

0.068

0.042

-0.067

0.047

0.068

0.090

0.179

3 years

0.073

0.041

-0.053

0.052

0.072

0.094

0.181

4 years

0.076

0.040

-0.047

0.056

0.075

0.097

0.183

5 years

0.080

0.040

-0.043

0.060

0.079

0.101

0.185

Panel B: Descriptive statistics for increases in annualized prospective yield as forecasting period, T increases. Aggregation Period, T 1 to 2 years 2 to 3 years 3 to 4 years 4 to 5 years

Mean

Std. Dev

P1

Q1

Median

Q3

P99

0.005

0.009

-0.012

0.002

0.004

0.006

0.044

0.004

0.005

-0.009

0.002

0.003

0.005

0.024

0.003

0.005

-0.008

0.001

0.003

0.005

0.019

0.003

0.005

-0.007

0.001

0.003

0.005

0.018

All variables are defined in Table 1. Each of the variables is truncated at 1% and 99% to mitigate outliers.

36

Table 5 Descriptive statistics and correlations— and Pearson correlations—autocorrelation (diagonal) for the realized stock return and the realized yield. Realized stock return and realized yield are annualized. Common observations across different measurement periods are included. Aggregation Period, T 1 year

2 years

3 years

4 years

5 years

Sample Period, t

Variable

Mean

Std. Dev

Q1

Median

Q3

1963 - 2007

0.147

0.590

-0.199

0.059

0.359

N=136,288

0.035

0.162

0.005

0.058

0.105

0.113

0.581

-0.223

0.006

0.296

1964 - 2007

0.088

0.336

-0.122

0.068

0.266

N=124,216

0.047

0.119

0.005

0.059

0.105

0.044

0.313

-0.159

0.007

0.198

1966 - 2007

0.076

0.265

-0.086

0.071

0.228

N=113,689

0.050

0.108

0.007

0.060

0.105

0.030

0.243

-0.130

0.008

0.162

1966 - 2007

0.074

0.224

-0.063

0.075

0.208

N=101,136

0.054

0.099

0.010

0.061

0.106

0.026

0.203

-0.110

0.010

0.142

1967 - 2007

0.071

0.199

-0.047

0.077

0.194

N=93,586

0.055

0.093

0.012

0.062

0.106

0.023

0.181

-0.096

0.012

0.129

-0.080

0.197

0.962

0.517

-0.079 -0.104

-0.044

0.407

0.936

0.474

0.076 -0.106

-0.049

0.498

0.906

0.420

0.131 -0.116

-0.056

0.579

0.880

0.366

0.195 -0.120

-0.107

0.619

0.856

0.299

0.223 -0.151

All the correlation coefficient estimates are significant at a less than 1% level. All variables are defined in Table 1. Each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers.

37

Table 6 Panel A Descriptive statistics and correlations for R, Y, R-Y and relative value measures. Each variable is annualized. The sample period is from 1993 to 2007 (t). Panel A: Descriptive statistics Variable

Mean

Std. Dev

P1

Q1

Median

Q3

P99

25,833

0.071

0.176

-0.412

-0.028

0.082

0.176

0.494

25,833

0.046

0.063

-0.172

0.021

0.055

0.082

0.172

25,833

0.036

0.160

-0.323

-0.065

0.030

0.127

0.465

25,833

0.068

0.040

-0.063

0.048

0.069

0.090

0.170

22,123

0.072

0.037

-0.045

0.052

0.072

0.092

0.164

25,833

0.074

0.038

-0.042

0.054

0.074

0.095

0.170

24,673

0.079

0.035

-0.014

0.059

0.078

0.098

0.171

24,572

0.082

0.034

-0.004

0.063

0.081

0.102

0.172

24,501

0.086

0.034

0.002

0.067

0.085

0.105

0.176

25,813

0.508

0.303

0.050

0.285

0.458

0.675

1.451

E/P t-5

25,820

0.046

0.066

-0.199

0.029

0.054

0.077

0.164

Div/Pt-5

25,820

0.016

0.021

0.000

0.000

0.006

0.025

0.087

Sales/Pt-5

25,820

1.345

1.306

0.034

0.486

0.945

1.744

6.326

CF/Pt-5

23,455

0.088

0.102

-0.177

0.033

0.078

0.137

0.391

Accrualt-5

21,337

-0.043

0.080

-0.265

-0.081

-0.044

-0.006

0.185

19,682

0.152

0.163

-0.195

0.047

0.140

0.246

0.610

, , , ,

/

N

  

38

Table 6 Panel B: Correlation matrix—Pearson (above diagonal) and Spearman (below diagonal)

R

,

,

,

0.175

0.163

0.147

0.162

0.103

0.146

0.131

0.170

-0.079

-0.137

0.384

0.347

0.311

0.278

0.107

0.328

0.285

0.158

0.258

-0.009

0.062

0.053

0.049

0.059

0.060

0.057

0.139

-0.018

0.047

0.086

0.095

-0.093

-0.189

0.961

0.966

0.931

0.891

0.851

0.406

0.630

0.337

0.418

0.409

0.150

-0.009

1.000

0.985

0.957

0.926

0.457

0.566

0.355

0.449

0.426

0.133

-0.066

0.987

0.962

0.932

0.454

0.562

0.336

0.448

0.396

0.140

-0.048

0.991

0.971

0.471

0.520

0.317

0.453

0.366

0.143

-0.070

0.993

0.455

0.485

0.281

0.438

0.333

0.148

-0.069

0.425

0.454

0.239

0.411

0.296

0.159

-0.058

0.127

0.324

0.562

0.375

-0.026

-0.430

0.274

0.148

0.455

0.318

0.176

0.147

0.364

-0.029

-0.089

0.295

0.012

-0.260

-0.269

-0.147

Y

R-Y

0.620

0.914

0.181

0.193

0.182

0.324

0.406

0.411

0.038

0.667

,

B/Mt-5

E/P t-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

0.942

0.426

0.178

0.445

0.055

0.184

0.445

0.066

0.971

0.172

0.425

0.058

0.975

1.000

0.165

0.404

0.061

0.947

0.988

0.990

0.153

0.374

0.058

0.915

0.966

0.969

0.993

0.136

0.343

0.050

0.879

0.936

0.941

0.975

0.994

0.166

0.232

0.138

0.519

0.560

0.550

0.553

0.536

0.509

E/P t-5

0.171

0.430

0.046

0.768

0.723

0.720

0.682

0.645

0.606

0.374

Div/Pt-5

0.171

0.343

0.076

0.359

0.367

0.343

0.313

0.268

0.218

0.299

0.383

Sales/Pt-5

0.176

0.310

0.109

0.589

0.623

0.609

0.603

0.582

0.552

0.643

0.427

0.285

CF/Pt-5

0.216

0.348

0.138

0.448

0.470

0.437

0.411

0.376

0.336

0.442

0.507

0.424

0.409

-0.098

-0.054 -0.105

0.104

0.090

0.098

0.100

0.107

0.116

-0.024

0.191

-0.041

0.002

-0.393

-0.119

0.037 -0.178

-0.035

-0.086

-0.065

-0.079

-0.074

-0.062

-0.427

0.084

-0.060

-0.287

-0.178

, , , ,

/

Accrualt-5

All variables are defined in Table 1. Each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers.

39

Accrual

R(t-5, t)

0.138 0.122

Table 7 Panel A: Ordinary least squares regressions of stock return on relative value measures. Stock return is measured over five years and annualized. The sample period is from 1993 to 2007 (t). Associated t-statics (in italics) are adjusted for overlapping samples. = ω0 + ω1 Relative Value Measures t-5 + B/Mt-5

E/P t-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Adj. R2

Accrualt-5

N

Intercept

yt-5

22,123

0.005 0.93 0.023 4.92 0.059 19.71 0.052 17.26 0.047 13.53 0.049 14.86 0.062 19.65 0.106 30.85 0.039 3.85 Intercept

0.911 13.11

0.581 4.51 B/Mt-5

0.023 4.92

0.094 11.78

0.026

0.110 0.018 34.45 5.47 S&P/ Salomon Smith Barney Index

0.013

25,813 25,820 25,820 25,820 23,455 21,337 19,682 13,165 N

0.037 0.094 11.78

0.026 0.273 7.41

0.011 1.215 10.62

0.021 0.018 9.52

0.017 0.289 11.81

0.029 -0.180 -5.20

0.007 0.47 E/P t-5

0.083 1.11 FY1/Pt-5

0.130 0.75 Div/Pt-5

-0.001 -0.34 Sales/Pt-5

0.085 1.84 CF/Pt-5

-0.152 -2.78 Accrualt-5

0.006 -0.134 -8.66 -0.134 -6.02

0.019 0.059 Adj. R2

Russell Index 25,813

25,813

23,448

0.023 4.62

0.034 3.22

0.646 5.03

0.006 2.63

0.179 6.51

0.043

23,448

0.042 10.31

0.016 10.02

0.016 10.02

0.016 10.02

0.016 10.02

0.021

-0.001

0.050

-0.022

0.541

0.658

-0.13

5.57

-0.47

6.39

5.31

0.010

0.095

0.095

0.095

0.095

   Dow Jones Index 25,813

25,813

0.047

0.036

2.02 13.86 13.86 13.86 13.86 All variables are defined in Table 1. Each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers. 40

Table 7 Panel B: Ordinary least squares regressions of realized yield on relative value measures. Realized yield is measured over five years and annualized. The sample period is from 1993 to 2007 (t). Associated t-statics (in italics) are adjusted for overlapping samples. = ω0 + ω1 Relative Value Measures t-5 + B/Mt-5

E/P t-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Intercept

yt-5

22,123

-0.002 -1.24 0.035 20.48 0.032 31.64 0.033 31.56 0.036 28.93 0.033 28.69 0.041 37.79 0.049 39.36 0.006 1.70

0.670 29.98

0.505 12.20

-0.022 -4.45

0.093 3.90

0.376 6.76

0.001 1.21

0.027 1.81

-0.056 -3.17

Intercept

B/Mt-5

E/P t-5

FY1/Pt-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Accrualt-5

25,813 25,820 25,820 25,820 23,455 21,337 19,682 13,165 N

Adj. R2

Accrualt-5

N

0.169 0.022 7.75

0.012 0.309 24.91

0.107 0.840 21.34

0.081 0.008 11.52

0.025 0.156 18.26

0.066 -0.007 -0.59

0.000 0.022 3.91 0.003 0.45

0.004 0.171 Adj. R2

Russell Index 25,813

0.035 0.022 20.48 7.75 25,813 0.059 0.005 59.19 5.50 S&P/ Salomon Smith Barney Index

0.012 0.012

23,448

0.031 18.36

-0.026 -7.15

0.716 16.35

0.006 7.62

0.107 11.46

0.123

23,448

0.034 23.47

0.006 11.09

0.006 11.09

0.006 11.09

0.006 11.09

0.026

0.009

-0.020

0.075

0.516

0.538

5.17

-6.84

4.86

18.77

13.37

0.021

0.039

0.039

0.039

0.039

   Dow Jones Index 25,813

25,813

11.80 16.14 16.14 16.14 16.14 All variables are defined in Table 1. Each of the variables is truncated at 1% and 99% to mitigate outliers. 41

0.203

0.048

Table 7 Panel C: Ordinary least squares regressions of unrealized yield on relative value measures. Unrealized yield is measured over five years and annualized. The sample period is from 1993 to 2007 (t). Associated tstatics (in italics) are adjusted for overlapping samples. = ω0 + ω1 Relative Value Measures t-5 + B/Mt-5

E/P t-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Intercept

22,123

0.019 3.66 -0.002 -0.42 0.038 13.89 0.030 10.87 0.021 6.74 0.025 8.16 0.030 10.70 0.069 21.63 0.042 4.39

0.226 3.52

0.115 0.95

0.033 2.27

-0.004 -0.05

-0.368 -2.26

-0.003 -1.04

0.072 1.64

-0.114 -2.22

Intercept

B/Mt-5

E/P t-5

FY1/Pt-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Accrualt-5

25,813 25,820 25,820 25,820 23,455 21,337 19,682 13,165 N

Adj. R2

Accrualt-5

N

0.003 0.074 10.12

0.019 -0.043 -1.29

0.000 0.357 3.41

0.002 0.011 6.21

0.007 0.148 6.54

0.009 -0.191 -6.11

0.009 -0.174 -12.06 -0.152 -7.27

0.036 0.047 Adj. R2

Russell Index 25,813

-0.002 0.074 -0.42 10.12 25,813 0.051 0.012 18.68 4.42 S&P/ Salomon Smith Barney Index

0.019 0.009

23,448

0.001 0.11

0.061 6.24

-0.120 -1.01

0.000 0.13

0.088 3.46

0.020

23,448

0.017 4.53

0.011 7.03

0.011 7.03

0.011 7.03

0.011 7.03

0.010

0.000

0.073

-0.099

0.012

0.097

0.10

8.82

-2.25

0.15

0.85

-0.001

0.057

0.057

0.057

0.057

-0.17

9.03

9.03

9.03

9.03

   Dow Jones Index 25,813

25,813

All variables are defined in Table 1. Each of the variables is truncated at 1% and 99% to mitigate outliers. 42

0.021

0.016

Table 8 Descriptive statistics and Pearson correlations—autocorrelation (diagonal) for the components of realized stock returns (y, F-y, Δy). Common

observations across different measurement periods are included. Each variable is annualized. T 1 year

Sample Period, t

Variable

0.113

0.366

N=27,822

0.068

0.040

0.050

0.068

0.087

0.080

0.480

-0.113

0.057

0.221

0.048

0.496

-0.158

0.008

0.195

1985 - 2007

0.139

0.307

-0.040

0.111

0.275

N=24,686

0.070

0.038

0.051

0.069

0.089

0.054

0.281

-0.091

0.040

0.170

0.106

0.511

-0.172

0.031

0.262

1986 - 2007

0.125

0.234

-0.013

0.111

0.239

N=22,368

0.071

0.038

0.052

0.070

0.090

0.039

0.219

-0.079

0.029

0.143

0.132

0.555

-0.182

0.042

0.317

1987 - 2007

0.115

0.190

0.001

0.108

0.214

N=20,295

0.073

0.037

0.053

0.072

0.092

0.028

0.180

-0.073

0.022

0.120

0.156

0.600

-0.180

0.061

0.350

1988 - 2007

0.108

0.165

0.012

0.105

0.197

N=18,806

0.074

0.037

0.054

0.073

0.093

0.019

0.154

-0.068

0.015

0.101

0.188

0.655

-0.170

0.081

0.388

∆

∆

Q3

-0.115

∆ 5 years

Median

0.604

∆ 4 years

Q1

0.187

∆ 3 years

Std. Dev

1984 - 2007

∆ 2 years

Mean

-0.100

0.045

0.363

0.237

0.791

-0.139

0.213

0.094

-0.093 -0.089

-0.089

0.133

0.582

0.263

0.723

-0.238

0.235

-0.090

-0.316 -0.270

-0.148

0.162

0.628

0.264

0.662

-0.260

0.300

-0.155

-0.326 -0.300

-0.138

0.197

0.649

0.251

0.624

-0.278

0.332

-0.127

-0.327 -0.336

-0.207

0.224

0.652

0.250

0.589

-0.287

0.324

-0.132

-0.318 -0.417

All the correlation coefficient estimates are significant at a less than 1% level. All variables are defined in Table 1. Each variable is annualized and each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers.

43

Table 9 Ordinary least squares regressions of stock returns on y, F-y, Δy. Associated t-statics (in italics) are adjusted for overlapping observations. Each variable is annualized and truncated at 1% and 99% except for stock returns. T 1 year

2 years

3 years

4 years

5 years

Sample Period, t

Intercept

Adj. R2

-∆

1984 - 2007

0.140

0.687

N= 27,822

19.45

7.51

0.002

0.150

0.457

43.98

64.95

0.132

0.173

0.288

48.98

40.62

0.087 13.14

0.664 7.90

1985 - 2007

0.064

1.069

N= 24,686

11.09

14.88

0.496 72.86

0.322 48.24

0.637

45.53

79.49

0.339

0.122

0.158

44.72

30.32

-0.055

1.692

0.850

0.276

-14.44

35.36

127.60

75.49

1986 - 2007

0.054

1.002

N=22,368

9.42

14.21 0.670

46.21

69.61

0.111

0.111

41.10

23.63 1.494

0.900

0.197

-12.50

35.26

121.67

66.50

1987 - 2007

0.041

1.006

N=20,295

7.22

14.35

N=18,806

0.684

46.39

60.86 0.079

38.32

18.49 0.923 112.91

0.139 55.68

0.063 0.737 0.050

0.095

0.696

46.44

52.74

0.425

0.097

0.063

35.67

15.84

-0.041

1.512

0.944

0.106

-13.22

39.42

102.25

48.07

44

0.691

0.422

0.102

14.11

0.070

0.039

0.095

6.01

0.601

0.394

-0.042

1988 - 2007

0.069

0.026

0.099

1.506 38.04 0.993

0.207 0.018

0.104

-0.043 -13.47 0.035

0.056

0.063 0.758

Table 10 Panel A Descriptive statistics and correlations for R, y, F-y, Δy and relative value measures. Each variable is measured over 5 years and annualized. The sample period is from 1988 to 2007 (t). Panel A: Descriptive statistics Variable

N

Mean

Std. Dev

P1

Q1

Median

Q3

P99

17,168

0.106

0.152

-0.262

0.015

0.104

0.192

0.520

17,168

0.073

0.034

-0.006

0.054

0.073

0.092

0.161

17,168

0.033

0.149

-0.315

-0.057

0.027

0.115

0.445

17,168

0.018

0.147

-0.347

-0.065

0.014

0.098

0.424

∆

17,168

0.173

0.622

-0.755

-0.167

0.077

0.372

2.546

/

17,161

0.478

0.284

0.047

0.267

0.427

0.636

1.356

E/P t-5

17,161

0.051

0.051

-0.138

0.032

0.054

0.076

0.165

FY1/Pt-5

17,161

0.068

0.035

-0.024

0.048

0.067

0.087

0.161

Div/Pt-5

17,161

0.017

0.022

0.000

0.000

0.009

0.027

0.088

Sales/Pt-5

17,161

1.264

1.198

0.048

0.482

0.906

1.627

5.987

CF/Pt-5

15,649

0.094

0.091

-0.120

0.040

0.081

0.138

0.369

Accrualt-5

14,450

-0.046

0.070

-0.240

-0.081

-0.047

-0.012

0.152

13,747

0.164

0.156

-0.159

0.063

0.150

0.253

0.615

  

45

Table 10 Panel B: Correlation matrix—Pearson (above diagonal) and Spearman (below diagonal) ∆

Rt 0.220 0.205

B/M

E/P

FY1/P

Div/P

Sales/P

CF/P

0.975

0.643

0.229

0.181

0.114

0.207

0.066

0.143

0.147

-0.038

-0.165

-0.004

-0.301

0.341

0.510

0.603

0.970

0.384

0.469

0.451

0.100

-0.108

0.729

0.157

0.068

-0.022

-0.011

-0.021

0.039

0.048

-0.061

-0.144

-0.345

-0.065

-0.239

-0.312

-0.129

-0.073

-0.078

-0.116

-0.057

0.178

0.197

0.325

0.058

0.120

0.124

0.027

-0.017

0.211

0.459

0.386

0.546

0.455

-0.028

-0.424

0.678

0.334

0.190

0.460

0.262

0.103

0.388

0.434

0.456

0.110

-0.066

0.149

0.408

-0.017

-0.143

0.328

0.012

-0.267

-0.308

-0.215

0.969

-0.002

0.643

-0.319

0.739

∆

0.319

0.530

0.207

-0.282

B/M t-5

0.181

0.598

0.060

-0.122

0.272

E/P t-5

0.165

0.725

0.012

-0.255

0.407

0.417

FY1/Pt-5

0.198

0.972

-0.003

-0.321

0.522

0.553

0.779

Div/Pt-5

0.080

0.394

-0.005

-0.152

0.155

0.352

0.409

0.407

Sales/Pt-5

0.176

0.629

0.048

-0.126

0.257

0.638

0.440

0.596

0.307

CF/Pt-5

0.181

0.490

0.078

-0.096

0.246

0.507

0.530

0.494

0.448

0.440

-0.056

0.077

-0.076

-0.114

0.031

-0.024

0.185

0.087

-0.022

0.006

-0.384

-0.147

-0.112

-0.136

-0.041

-0.037

-0.426

0.026

-0.074

-0.135

-0.299

-0.242

Accrualt-5

Accrual

   All variables are defined in Table 1. Each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers.

46

0.119 0.116

Table 11 Panel A: Ordinary least squares regressions of prospective yield (annualized) on relative value measures. The sample period is from 1988 to 2007 (t). Associated t-statics (in italics) are adjusted for overlapping observations. = ω0 + ω1 Relative Value Measures t-5 + N

Intercept

B/Mt-5

17,161

0.044 44.27 0.053 80.18 0.009 31.16 0.063 90.69 0.056 74.51 0.058 74.21 0.071 96.07 0.080 90.99 0.008 15.40

0.061 34.21

0.007 9.16

Russell Index 17,161 0.044 44.27 17,161 0.073 308.29

0.061 34.21 0.014 58.55

17,161 17,168 17,161 17,161 15,649 14,450 13,747 10,657

E/P t-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Adj. R2

Accrualt-5

0.254 0.407 44.57

0.367 0.941 236.58

0.942 0.615 24.35

0.147 0.013 30.84

            -0.056 -11.73

0.009 35.26 0.008 125.64

0.217 0.168 28.21

0.203 0.047 5.34

0.936 133.39

-0.007 -0.86

0.001 4.19

0.007 2.79

0.009 3.04

0.010 -0.022 -5.68 0.000 -0.04

0.012 0.947

0.254 0.166

S&P/ Salomon Smith Barney Index 15,649 0.041 0.024 97.06 24.29 15,649 0.074 0.006 314.75 70.44 Dow Jones Index 17,161 0.007 49.54 17,161 0.073 389.94

FY1/Pt-5

       

-0.058 -37.04 0.008 125.64

0.309 27.77 0.006 70.44

0.965 387.32 0.008 125.64

-0.002 -0.61 0.008 125.64

0.007 34.62 0.006 70.44

0.071 26.06 0.006 70.44

0.386 0.241

0.951 0.479

All variables are defined in Table 1. Each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers. 47

Table 11 Panel B: Ordinary least squares regressions of (annualized) on relative value measures. The sample period is from 1988 to 2007 (t). Associated t-statics (in italics) are adjusted for overlapping observations. = ω0 + ω1 Relative Value Measures t-5 + N

Intercept

B/Mt-5

17,161

0.016

0.036

3.22

3.99

17,161 17,168 17,161 17,161 15,649 14,450 13,747 10,657

E/P t-5

FY1/Pt-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Accrual

Adj. R2

R(t-5,t)

0.005

0.036

-0.061

10.12

-1.23

0.000

0.036

-0.042

6.57

-0.59

0.000

0.036

-0.152

10.99

-1.29

0.000

0.027

0.005

7.29

2.28

0.002

0.026

0.078

6.89

2.70

0.002

0.030

-0.131

8.74

-3.24

0.004

0.056

-0.128

14.73

-7.58

0.057

0.025

0.085

-0.171

-0.570

-0.001

0.032

-0.110

-0.131

5.43

1.55

0.87

-1.18

-3.32

-0.43

0.64

-1.88

-5.74

0.016

0.036

3.22

3.99

0.033

0.006

12.86

2.49

0.020 0.031

   Russell Index 17,161 17,161

  

0.005 0.002

  

S&P/ Salomon Smith Barney Index 15,649 15,649

0.017

0.038

-0.444

-0.001

0.070

3.19

3.06

-3.20

-0.21

2.03

0.033

0.001

0.001

0.001

0.001

12.51

1.40

1.40

1.40

1.40

0.023

0.054

-0.007

-0.162

-0.310

3.89

5.16

-0.11

-1.49

-2.33

0.033

0.000

0.000

0.000

0.000

12.84

-0.40

-0.40

-0.40

-0.40

  

  

0.008 0.001

Dow Jones Index 17,161 17,161

                           All variables are defined in Table 1. Each of the variables is truncated at 1% and 99% to mitigate outliers.

0.008 0.000

  48

Table 11 Panel C: Ordinary least squares regressions of unexpected fundamental return (annualized) on relative value measures. The sample period is from 1988 to 2007 (t). Associated t-statics (in italics) are adjusted for overlapping observations. = ω0 + ω1 Relative Value Measures t-5 + N

Intercept

B/Mt-5

17,161

0.034

-0.034

7.00

-3.91

17,161 17,168 17,161 17,161 15,649 14,450 13,747 10,657

E/P t-5

FY1/Pt-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Accrual

R(t-5,t)

Adj. R2 0.004

0.052

-0.680

15.27

-14.32

0.056

0.105

-1.279

20.38

-19.09

0.096

0.033

-0.894

10.43

-7.74

0.017

0.029

-0.009

8.08

-4.37

0.006

0.028

-0.124

7.62

-4.34

0.006

0.012

-0.247

3.47

-6.16

0.013

0.022

-0.050

5.87

-2.97

0.103

0.048

-0.012

-1.704

-0.336

0.004

0.063

-0.171

-0.040

10.45

3.17

-0.13

-12.48

-2.07

1.18

1.31

-3.09

-1.87

0.034

-0.034

7.00

-3.91

0.018

-0.009

7.05

-3.58

0.003 0.133

   Russell Index 17,161 17,161

0.004 0.004

  

S&P/ Salomon Smith Barney Index 15,649 15,649

  

0.037

0.013

-0.789

-0.008

-0.034

7.16

1.08

-5.77

-2.97

-1.02

0.017

-0.005

-0.005

-0.005

-0.005

6.41

-5.79

-5.79

-5.79

-5.79

0.093

0.054

-0.079

-1.368

-0.222

16.45

5.44

-1.22

-13.37

-1.78

0.018

-0.012

-0.012

-0.012

-0.012

7.22

-13.65

-13.65

-13.65

-13.65

  

  

0.019 0.011

Dow Jones Index 17,161 17,161

0.106 0.051

                             All variables are defined in Table 1. Each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers. 49

Table 11 Panel D: Ordinary least squares regressions of changes in prospective yield (annualized) on relative value measures. The sample period is from 1988 to 2007 (t). Associated t-statics (in italics) are adjusted for overlapping observations. ∆ = ω0 + ω1 Relative Value Measures t-5 + N

Intercept

B/Mt-5

17,161

-0.014

0.391

-0.68

10.63

17,161 17,168 17,161 17,161 15,649 14,450 13,747 10,657

E/P t-5

FY1/Pt-5

Div/Pt-5

Sales/Pt-5

CF/Pt-5

Accrual

R(t-5,t)

Adj. R2 0.032

0.051

2.394

3.52

11.78

0.039

-0.216

5.725

-9.95

20.17

0.106

0.144

1.664

10.68

3.38

0.003

0.094

0.062

6.15

7.06

0.014

0.099

0.847

6.27

6.99

0.015

0.180

0.249

12.41

1.44

0.001

0.196

-0.066

11.95

-0.92

-0.331

0.199

-0.588

8.201

-3.563

-0.041

-0.078

-0.053

0.152

-7.61

2.99

-1.44

13.56

-5.00

-2.91

-0.38

-0.22

1.61

-0.014

0.391

-0.68

10.63

0.018

-0.009

7.05

-3.58

0.000 0.130

Russell Index 17,161 17,161

0.032 0.004

  

S&P/ Salomon Smith Barney Index 15,649 15,649

  

-0.015

0.323

-0.991

0.012

0.436

-0.68

6.33

-1.72

1.08

3.07

0.179

0.031

0.031

0.031

0.031

16.30

7.81

7.81

7.81

7.81

-0.248

0.128

-0.257

6.160

-2.709

-10.48

3.07

-0.94

14.33

-5.15

0.173

0.051

0.051

0.051

0.051

16.73

14.06

14.06

14.06

14.06

  

  

0.034 0.019

Dow Jones Index 17,161 17,161

0.115 0.054

                             All variables are defined in Table 1. Each of the variables except for the stock return is truncated at 1% and 99% to mitigate outliers. 50

Figure 1A:  Prospective Yields vs.  Risk Free Rate  (Means) 0.14

Rate of Return

0.12 0.1 0.08 0.06 0.04 0.02 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

0

y_1

y_5

Rf

Figure 1B:  Prospective Yields vs.  Risk Free Rate  (Medians) 0.14

Rate of  Return

0.12 0.1 0.08 0.06 0.04 0.02 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

0

y_1

y_5

Rf

Rf:

Risk-free rate of return at the end of the year.

y_T:

Prospective yield measured at the end of the year using forecasts over the next T years.

51

Figure 2A:  Variance Decompositon of Returns (1 Year) 4 3.5

Variance

3 2.5 2 1.5 1 0.5 0

R_1

Y_1

Figure 2B:  Variance Decompositon of Returns (5 Years) 0.06 0.05

Variance

0.04 0.03 0.02 0.01 0

R_5

Y_5

R_T:

Variance of realized stock return measured over trailing T years.

Y_T:

Variance of realized yield measured over trailing T years.

52

Figure 3A:  Variance Decompositon of Returns (1 Year) 1.4 1.2

Variance

1 0.8 0.6 0.4 0.2 0

R_1

F_1

y_1

Figure 3B:  Variance Decompositon of Returns (5 Years) 0.03 0.025

Variance

0.02 0.015 0.01 0.005 0

R_5

F_5

y_5

R_T : Variance of realized stock return measured over trailing T years. F_T:

Variance of fundamental return measured over trailing T years.

y_T:

Variance of prospective yield measured T years ago.

53