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Finance Department Faculty Publications Finance Department
P/E Changes: Some New Results
Thomas S. Zorn
University of Nebraska Lincoln, firstname.lastname@example.org
Donna M. Dudney
Univ of Nebraska-Lincoln, email@example.com
Slippery Rock University of Pennsylvania
Follow this and additional works at: http://digitalcommons.unl.edu/financefacpub Part of the Finance and Financial Management Commons Zorn, Thomas S.; Dudney, Donna M.; and Jirasakuldech, Benjamas, "P/E Changes: Some New Results" (2009). Finance Department Faculty Publications. Paper 19.
http://digitalcommons.unl.edu/financefacpub/19 This Article is brought to you for free and open access by the Finance Department at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Finance Department Faculty Publications by an authorized administrator of DigitalCommons@University of Nebraska Lincoln.
Published in Journal of Forecasting 28 (2009), pp. 358–370; doi: 10.1002/for.1097 Copyright © 2008 John Wiley & Sons, Ltd. http://www.interscience.wiley.com Used by permission.
Published online December 29, 2008.
P/E Changes: Some New Results Thomas Zorn,1 Donna Dudney,1 and Benjamas Jirasakuldech 2 1 Department of Finance, University of Nebraska–Lincoln, Nebraska, USA 2 School of Business, Slippery Rock University of Pennsylvania, USA Corresponding author — Thomas Zorn, Department of Finance, University of Nebraska–Lincoln, PO Box 880490, Lincoln, NE 68588-0490, USA; e-mail firstname.lastname@example.org Abstract The P/E ratio is often used as a metric to compare individual stocks and the market as a whole relative to historical valuations. We examine the factors that affect changes in the inverse of the P/E ratio (E/P) over time in the broad market (S&P 500 Index). Our model includes variables that measure investor beliefs and changes in tax rates and shows that these variables are important factors affecting the P/E ratio. We extend prior work by correcting for the presence of a long-run relation between variables included in the model. As frequently conjectured, changes in the P/E ratio have predictive power. Our model explains a large portion of the variation in E/P and accurately predicts the future direction of E/P, particularly when predicted changes in E/P are large or provide a consistent signal over more than one quarter.
Keywords: price earnings ratio, asset pricing, relative valuation Introduction The price/earnings ratio is widely used, particularly by practitioners, as a measure of relative stock valuation. We examine the factors that explain movements in this ratio. A high absolute P/E ratio (compared to historical averages) is often cited as an indicator of overvaluation. However, if the theoretical determinants of P/E are substantially different from historical averages, a high P/E ratio can simply reflect changes in the fundamental factors that affect P/E. If interest rates are relatively low, for example, the P/E should be correspondingly higher.
There is a limit to what stock market returns alone can tell us about market valuation. The P/E ratio, with all its obvious limitations, has the merit of relating market valuation to something that investors are presumably valuing. The P/E ratio (or its reciprocal) is a natural metric for comparing market valuations over time. This paper develops a model of the fundamental determinants P/E ChangEs: somE nEw REsults of changes in the E/P ratio. Our model extends prior research by incorporating taxes and investor sentiment, and by correcting for the long-run relation between nonstationary variables in the model. The usefulness of this model is twofold. First, the model allows practitioners to evaluate changes in the market E/P and determine whether these changes are justified by changes in fundamentals. Second, the model has predictive power.
Our approach attempts to be parsimonious in the number of explanatory variables used. An aggregate E/P ratio (e.g., S&P 500 Index) is obviously affected by changes in investors’ time preferences and risk aversion. Inflationary expectations are also generally assumed to affect stock prices, as are growth prospects, the dividend payout ratio, and leverage. Our study also includes taxes, which for most investors are an important factor affecting investment decisions. We employ a novel variable to represent the effect of taxes, namely one that can be inferred from the market. Investor beliefs concerning future prospects are an important if not a dominant determinant of stock market values. We employ two variables that plausibly represent investor beliefs: the Consumer Sentiment Index and the ratio of S&P500 Index volume to population.
Our model explains a large portion of the variation in E/P, and accurately predicts the future direction of E/P, particularly when predicted changes in E/P are large or provide a consistent signal over more than one quarter.
Perhaps the simplest attempt to model the determinants of P/E is the so-called Fed Model (although this model has not been endorsed by the Federal Reserve). This model assumes that the fair value of the market P/E (calculated using 12-month forward earnings) is the reciprocal of the 10year Treasury Bond yield (Yardeni, 2003). Yardeni expands the basic Fed Model to include variables that differentiate stocks from bonds, primarily a risk measure and an expected growth measure.
Many previous studies of the determinants of P/E use the Gordon (1962) constant growth model as an expositional starting point. In this model, prices are a function of the dividend payout ratio, the required return and the growth rate in dividends. These studies generally use a regression approach and specify a linear relation between changes in these variables and changes in P/E. Most studies decompose required return into the risk-free rate and a risk premium. In time series studies using data for the S&P500 index, researchers generally document a positive relation between the risk-free rate and E/P (Loughlin, 1996; White, 2000). Results for the default risk spread (a common proxy for changes in the risk premium) are less consistent, with Kane et al. (1996) finding a significant positive relation between the spread and P/E, while Reilly et al. (1983) and Jain and Rosett (2001) find no significant relation.
Several studies examine the impact of inflation on E/P, with most empirical studies finding a positive relation between the two variables (Reilly et al., 1983; Kane et al., 1996; White, 2000). In addition to these primary determinants of P/E, researchers have also found earnings volatility (Kane et al., 1996), demographics (Geanakoplos et al., 2004), and business cycle and economic indicators (Reilly et al., 1983; Jain and Rosett, 2001; White, 2000) are related to P/E. However, results on these variables are not consistent across studies.
Jain and Rosett (2001) include the consumer sentiment index in their model, along with a set of macroeconomic variables, and find that sentiment is not a significant factor in determining E/P.
Previous time series studies generally provide empirical support for the fundamental determinants of E/P suggested by the Gordon model. However, earlier studies ignore the effect of changes in taxes on E/P and, with the exception of Jain and Rosett, ignore the impact of changes in beliefs 360 Journal forecasting 28 (2009) ZoRn, DuDnEy, & JiRasakulDECh of in on E/P. In addition, earlier studies do not recognize that several of the determinants of E/P are cointegrated (i.e., a long-run equilibrium relation exists between these variables). As a result, ordinary regression analysis can produce biased and inconsistent coefficient estimates.
Using quarterly data from 1953 to 2003, we model short-run changes in E/P as a function of changes in fundamental factors identified by previous researchers. We also include two new factors, namely changes in the implied marginal tax rate and changes in consumer optimism. Table I provides detailed descriptions of all model variable computations and data sources. Our model
variables are as follows:1
∆E/Pt = f (Dividend Payoutt, ∆Livingston Survey S&P500 Growth Forecastt, ∆One Year Nominal T-Note Yieldt, ∆Yield Curve Slopet, ∆(Baa – Aaa) Nominal Yield Spreadt, ∆(Debt/Assets)t, ∆Implied Marginal Tax Ratet, ∆(Marginal Tax Rate/Capital Gains Tax Rate)t, ∆Consumer Sentimentt, ∆ln(Volume Population)t ) (1) We employ the E/P rather than the more popular P/E ratio because the latter has the obvious defect of going to infinity as earnings go to zero. The E/P ratio also has the advantage of being directly comparable to yields on other securities such as bonds and can be viewed as the current earnings yield. Unlike the P/E, the E/P is linearly related to interest rates.
The dividend payout ratio and the growth rate have been shown by previous researchers to be negatively related to E/P. We estimate changes in growth based on expert opinion. First, we calculate the change in the forecasted growth in the S&P500 Index using the Livingston Survey of economists. The Livingston Survey participants are asked to predict the level of the S&P500 Index (excluding dividends) for a 6-month forecast horizon. We use these forecasts to construct the annualized percentage changes in the 6-month forecasts over time.
The E/P for the S&P500 index is also affected by changes in factors that influence investors’ time rate of discount. We include changes in the constant maturity 1-year Treasury note as an indicator of changes in short-term interest rates. This rate reflects the effect of changes in real interest rates and short-term inflation expectations.
Expected changes in long-term expected inflation are reflected in the slope of the yield curve.
This measure should be reasonably accurate if changes in inflation expectations are the primary cause of yield differences between risk-free assets with different maturities.
Changes in the default risk premium are used to reflect changes in the market risk premium. As an additional risk measure, we use changes in the median debt/total assets ratio calculated using the universe of Compustat firms. Increases in leverage have been viewed as a signal of greater optimism by managers, who presumably would not shoulder additional fixed payments unless they were confident that the new debt payments could be met through permanent increases in cash flow. If firms on average use leverage to signal their optimism, the relation between leverage and E/P will be negative. Alternatively, if greater leverage results in greater risk, then the opposite holds true.2
1. Along with previous researchers, we assume a linear relation between model variables. To verify the appropriateness of that model specification, we used Ramsey’s (1969) Regression Specification Error Test (RESET).
2. The increase in leverage in our empirical model cannot be due to an exogeneous decrease in stock prices because we use the book value of debt divided by the book value of total assets as our leverage measure.
P/E ChangEs: somE nEw REsults Table I. Variable definitions
We include changes in the implied marginal tax rate to control for the influence of taxes on the relative attractiveness of stocks versus alternative investments. At first glance, it appears that increases in the marginal tax rate will unambiguously increase E/P ratios by reducing after-tax cash flows to investors. This conclusion, however, assumes that changes in tax rates do not cause demand shifts across asset classes. An increase in the marginal tax rate can cause investors to shift from bonds (where interest income is taxed at ordinary income rates) to stocks, where capital gains historically have been taxed favorably.3 The effect of taxes cannot be fully captured by examining changes in top marginal individual tax rates. Investors, for example, can avoid paying the top rate through the use of tax shelters or taxavoidance/ tax-deferral strategies. In addition, not all classes of investments are equally affected by tax changes. To obtain a measure of the effective marginal tax rate in a changing tax environment, we use the change in the implied marginal tax rate. This is calculated by solving for the tax rate that equates the yields on the 10-year AAA-rated municipal and 10-year Treasury note. The primary difference between equivalent maturity AAA-rated municipals and treasuries is tax treatment, so using this method allows us to estimate the effective tax rate of the marginal investor directly from the market while controlling for other factors. We also include the change in the ratio of the top capital gains tax rate to the top marginal tax rate for individuals.