U.S. stock market P/E ratios, structural breaks, and long-term stock returns

Baek, Chung; Lee, Ingyu Article U.S. stock market P/E ratios, structural breaks, and longterm stock returns Journal of Business Economics and Management (JBEM) Provided in Cooperation with: Vilnius Gediminas Technical University (VILNIUS TECH) Suggested Citation: Baek, Chung; Lee, Ingyu (2018) : U.S. stock market P/E ratios, structural breaks, and long-term stock returns, Journal of Business Economics and Management (JBEM), ISSN 2029-4433, Vilnius Gediminas Technical University, Vilnius, Vol. 19, Iss. 1, pp. 110-123, https://doi.org/10.3846/16111699.2017.1409263 This Version is available at: https://hdl.handle.net/10419/317278 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Published by VGTU Press This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons. org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. *Corresponding author. E-mail: [email protected] Journal of Business Economics and Management ISSN 1611-1699 / eISSN 2029-4433 2018 Volume 19 Issue 1: 110–123 https://doi.org/10.3846/16111699.2017.1409263 U.S. STOCK MARKET P/E RATIOS, STRUCTURAL BREAKS, AND LONG-TERM STOCK RETURNS Chung BAEK1*, Ingyu LEE2 1Department of Economics and Finance, Sorrell College of Business, Troy University, Troy, Alabama, United States 2Department of IS and QM, Sorrell College of Business, Troy University, Troy, Alabama, United States Received 21 March 2017; accepted 21 November 2017 Abstract. Our study investigates structural changes in the market P/E ratio and shows how structural changes affect long-term stock market returns. Using the cumulative sum control chart and the Bai-Perron algorithm, we identify multiple structural breakpoints in the market P/E ratio and find that those structural changes are significantly perceived over the long run. Unlike previous studies that do not consider structural changes, our study is the first one that shows how structural changes asymmetrically influence long-term stock returns depending on the high or low P/E period. This implies that structural changes in the market P/E ratio play an important role in explaining long-term stock returns. We propose that structural changes should be taken into account in some manner to establish the relationship between P/E ratios and long-term stock returns. Keywords: P/E ratio, mean-reversion, structural breakpoints, historical economic events, longterm stock returns, asymmetric returns. JEL Classification: G10, G17. Introduction Traditionally, it has been noted that the stock market P/E ratio tends to revert to its historical mean which is expected to stay constant over time. Based on this traditional view, many studies have focused on investigating the relationship between market P/E ratios and stock market returns. While most of them have found a meaningful relationship between P/E ratios and long-term market returns, they have identified a minor or trivial relationship between P/E ratios and short-term market returns. However, all those studies are based only on the traditional mean-reverting characteristic of P/E ratios without recognizing structural changes in the P/E ratio over time. Journal of Business Economics and Management, 2018, 19(1): 110–123 111 The first paper (Carlson etal. 2002) that sheds light on structural breaks in the market P/E ratio shows that the market P/E ratio significantly moves upward at a structural breakpoint rather than reverts to its long-run historical mean. If, at a point in time, the long-run mean of the P/E ratio substantially moves to a higher or lower level than its historical mean, and the new level lasts for quite a long time, we can expect market investors to perceive the new level as a long-term structural change. For example, while a P/E ratio of 20 seems to be high relative to the historical mean of the stock market P/E ratio which is around 16, it would be considered relatively low if the long-run mean substantially moves up to a high level of 25 at a point in time and stays that high level for quite a long time. Then, this structural change is likely to affect long-term stock returns in some way as long as there exists a significant relationship between P/E ratios and long-term stock returns. Basically, our study consists of two parts. First, we attempt to identify structural breakpoints in the time series of the market P/E ratio over the past 142-year time span. Second, we examine how structural changes influence future long-term stock returns. From our results, we identify multiple structural breaks in the market P/E ratio over the past 142-year time span and find that structural changes asymmetrically affect future long-term stock returns depending on the high or low P/E period. In fact, significant return premiums exist during high P/E periods. This implies that market investors properly perceive structural changes in the P/E ratios and recognize high P/E ratios less (more) significantly and low P/E ratios more (less) significantly during structurally high (low) P/E periods. Thus, structural changes in the market P/E ratio appear to play an important role in explaining long-term stock returns. Since few studies have delved into the effect of structural changes in the market P/E ratio and thus, most previous studies have shown the relationship between P/E ratios and longterm stock returns without allowing for structural changes, we argue that structural changes should be considered in some manner to establish the relationship between P/E ratios and long-term stock returns. 1. Literature review and hypotheses development Many of previous studies have supported the inverse relationship between P/E ratios and long-term stock returns (Campbell, Shiller 1988; Lakonishok etal. 1994; Siegel 2000; Wu, Wang 2000; Malkiel 2004; Estrada 2006; Weigand, Irons 2007). However, one recent study (Jones 2008) finds that market P/E ratios have no impact on long-term market returns on the basis of a supply-side model. There are also studies on short-term predictability for stock returns and they show insignificant results. Some authors discover that P/E ratios play a minor role in forecasting stock returns in emerging markets (Aras, Yilmaz 2008) while P/E ratios have no relationship with stock returns in an emerging markets (Abrokwa, Nkansah 2015). Another study (Gupta, Modise 2012) finds that P/E ratios are uncorrelated with real stock returns in the South African stock market. On the other hand, one interesting study (Carlson etal. 2002) identifies a structural breakpoint in the time series of the market P/E ratio and shows that the market P/E ratio significantly moves upward at the structural breakpoint instead of reverting to its historical mean. As a result, their argument is that the long-run mean of the market P/E ratio is not 112 C. Baek, I. Lee. U.S. stock market P/E ratios, structural breaks, and long-term stock returns constant over time, which means that the market P/E ratio is non-stationary. Although their data are relatively limited and they do not analyze or discuss any effect that the structural change may have on stock market returns, they provide a new insight on studying the structural change in the market P/E ratio. A few more studies also consider structural changes in the market P/E ratio against the traditional mean-reversion theory. They mention the possibility of a structural change in the market P/E ratio (Haubrich etal. 2015), test the P/E mean-reversion using Fourier approximation (Moghaddam, Li 2017) and confirm that the market P/E ratio can become stationary after controlling for structural changes (Becker etal. 2012). However, they focus on methodologies to test the mean reversion of the market P/E ratio rather than discussing the effect of structural changes on stock market returns and lack any further discussion about the relationship between structural changes and long-term stock returns. Actually, the most recent study (Moghaddam, Li 2017) concludes that the market P/E ratio is mean-averting rather than mean-reverting and it seems to be difficult to catch empirical evidence for the mean-reversion of the P/E ratio. From these studies, we are highly motivated to study structural changes in the market P/E ratio and their impact on long-term stock returns and develop two hypotheses. First, it seems that there exists some point in time at which the market P/E ratio significantly changes (Carlson etal. 2002) and that structural change lasts for quite a long time. Since we analyze monthly P/E data over the 142-year time span, we expect that there exist multiple structural breakpoints in the market P/E ratio. Hypothesis 1: Over the past 142-year time span, there exists multiple breakpoints in time at which the market P/E ratio significantly changes and the structural change at each breakpoint is expected to last for quite a long time. Second, previous studies support the inverse relationship between P/E ratios and longterm stock returns based on the traditional view (Campbell, Shiller 1988; Lakonishok etal. 1994; Siegel 2000; Wu, Wang 2000; Malkiel 2004; Estrada 2006; Weigand, Irons 2007). If there exist structural changes in the market P/E ratio, those changes are expected to have an impact on long-term stock returns in some predictable way because market investors are likely to perceive high P/E ratios less (more) significantly and low P/E ratios more (less) significantly during structurally high (low) P/E periods. Given the inverse relationship between P/E ratios and long-term stock returns, we expect long-term stock returns to less (more) decrease with high P/E ratios and more (less) increase with low P/E ratios during structurally high (low) P/E periods. In other words, the effect of structural changes on long-term stock returns is expected to differ depending on structurally high or low P/E periods. Hypothesis 2: If there exist structural changes in the market P/E ratio, given the inverse relationship between P/E ratios and long-term stock returns, we expect that those structural changes asymmetrically affect long-term stock returns depending on structurally high or low P/E periods. 2. Data We use 142 years of monthly stock market data downloadable from Shiller’s website. The data consist of stock market (S&P Composite Stock Price Index) real prices, the consumer Journal of Business Economics and Management, 2018, 19(1): 110–123 113 price index (CPI), real earnings, real dividends, 10-year government security (Treasury note) yields, and P/E ratios from 1871 through 2012. We analyze two different types of P/E ratio. One is the P/E1 ratio calculated using the past 12-month moving average of earnings, and the other is the P/E10 ratio calculated using the past 120-month (10-year) moving average of earnings. The latter is known as the price-smoothed-earnings ratio (Campbell, Shiller 2001). Table 1 shows the basic statistics of historical P/E1 and P/E10 ratios. Table 1. Summary statistics Basic statistics PE1 PE10 Mean 15.43 16.44 Median 14.48 15.84 Standard deviation 6.62 6.56 Maximum 86.84 44.20 Minimum 4.41 4.78 Notes: The basic statistics are calculated using monthly data from 1871 to 2012. We truncate the data at the beginning or end of the entire data period if necessary for shortor long-term calculations. Since all data are real values, the results are comparable over the whole period regardless of inflation. 3. Structural breakpoints and historical economic events We attempt to identify structural breakpoints in the market P/E ratio using 142 years of monthly stock market P/E data. To find structural breaks, we adopt purely empirical approaches relying on data. First, we employ the cumulative sum (CUSUM) control chart and the unit root test with a structural break. The CUSUM control chart is used to see systematic movements of time series data. The cumulative sum is calculated as follows. ( ) 1ttt SUM SUM PE PE − = +− for t = 1, 2, …, n, (1) where PEt is the P/E ratio at time t and PE is the historical mean of the P/E ratio. The cumulative sum ends at zero with a starting value of zero. The CUSUM control chart displays the cumulative sum of differences between P/E ratios and the historical mean over the 142-year time span. We use an average of historical monthly P/E ratios as the historical mean of each type of P/E ratio: 15.43 for P/E1 and 16.44 for P/E10. Figure 1. CUSUM control chart 114 C. Baek, I. Lee. U.S. stock market P/E ratios, structural breaks, and long-term stock returns Figure 1 shows the CUSUM control chart for both P/E1 and P/E10. The CUSUM control chart clearly shows that P/E ratios systematically move up and down relative to their historical mean. An upward (downward) slope indicates a time period during which P/E ratios stay above (below) their historical mean. In fact, the points that have maximum and minimum values in peaks and troughs of the CUSUM control chart are considered structural breakpoints because the systematic upward or downward trend goes into reverse at those points. We conduct the unit root test with two adjacent sub-periods at each breakpoint and we expect the P/E ratios to be non-stationary over two adjacent sub-periods. Even when a break has a temporary effect rather than a long-term effect, the Augmented Dickey-Fuller (ADF) unit root test often tends to fail to reject the null hypothesis of a unit root (Perron 1988). With the modified unit root test (Perron 1988; Glynn etal. 2007), we add two break dummies, D1 (P/E level dummy) and D2 (P/E crash dummy), to the Dickey-Fuller unit root test. 0 11 2 2 3 1 1 p t t i ti t i PE D D t PE PE −− = ∆ =β +β +β +β +ρ + γ ∆ +ε ∑ , (2) where D1 equals 1 if t > breakpoint and 0 otherwise and D2 equals 1 if t = breakpoint + 1 and 0 otherwise. Lag terms are also added to allow for serial correlation. Table 2. Modified unit root test for structural breaks identified by the CUSUM method Panel A: P/E1 First period Breakpoint Second period λ t-statistic for the null hypothesis of a unit root (ρ=0) 1st Test Period 1/1872–7/1885 7/1885 8/1885–8/1899 0.5 –3.68 2nd Test Period 8/1885–8/1899 8/1899 9/1899–9/1958 0.2 –3.85 3rd Test Period 9/1899–9/1958 9/1958 10/1958–7/1973 0.8 –3.81 4th Test Period 10/1958–7/1973 7/1973 8/1973–3/1986 0.5 –3.37 5th Test Period 8/1973–3/1986 3/1986 4/1986–6/2012 0.3 –3.99 Panel B: P/E10 First period Breakpoint Second period λ t-statistic for the null hypothesis of a unit root (ρ=0) 1st Test Period 1/1881–1/1907 1/1907 2/1907–3/1955 0.4 –3.70 2nd Test Period 2/1907–3/1955 3/1955 4/1955–4/1973 0.7 –3.65 3rd Test Period 4/1955–4/1973 4/1973 5/1973–5/1989 0.5 –2.65 4th Test Period 5/1973–5/1989 5/1989 6/1989–6/2012 0.3 –2.38 Notes: **, * indicate statistical significance at the 0.01 and 0.05 level respectively based on the asymptotic t-distribution developed by Perron (1988). In Table 2, based on the asymptotic t-distribution with time of break relative to total sample size, λ (Perron 1988), we fail to reject the null hypothesis of a unit root (ρ=0) for all test periods at both the 1% and 5% significance levels. This means that the P/E1 and P/E10 Journal of Business Economics and Management, 2018, 19(1): 110–123 115 ratios with structural breaks turn out to be non-stationary, with long-term effects in each test period. As a result, we identify five structural breakpoints in the time series of the P/E1 and four structural breakpoints in the time series of the P/E10. We also employ the Bai-Perron algorithm run in the R Package Strucchange with the same 142 years of monthly data and a break fraction of 10%. Figure2 and Figure3 show breakpoints in the P/E1 and P/E10 respectively with the Bai-Perron algorithm. These breakpoints are slightly different from those identified by the CUSUM method. With structural breakpoints, the whole period can be divided into six different sub-periods for the P/E1 and five different sub-periods for the P/E10. In summary, both CUSUM and Bai-Perron methods identify similar breakpoints. Unlike the previous study (Carlson etal. 2002) that finds one breakpoint (fourth quarter of 1992) with limited quarterly data from 1945 to 2000, our tests show multiple structural breakpoints in the P/E1 and P/E10. These results are aligned with our Hypothesis 1. Table 3 summarizes the basic statistics for these sub-periods identified by the CUSUM method and the Bai-Perron algorithm. We categorize all sub-periods into two structurally different periods on the basis of their means and medians: High P/E period (H) and Low P/E period (L). We use the median as the long-run mean of each sub-period instead of the mean because the median is more representative of the central tendency of the sample data. However, as shown in Table3, the mean and median of each sub-period are very close to each other.For sub-periods of the P/E1 with the CUSUM method in Panel A, low P/E periods have relatively low medians, which range from 9.61 to 12.80 whereas high P/E periods have relatively high medians, which range from 17.70 to 19.96. The sub-periods of the P/E10 in Panel B have parallel ranges as well. Figure2. Structural breakpoints of PE1– Bai-Perron algorithm Figure 3. Structural breakpoints of PE10– Bai-Perron algorithm 116 C. Baek, I. Lee. U.S. stock market P/E ratios, structural breaks, and long-term stock returns Table 3. Summary statistics for structurally different sub-periods Panel A: P/E1– CUSUM Subperiod Year range Duration P/E range Mean Median Standard deviation 1 (L) 1/1872–7/1885 13 years 9.61–14.91 12.17 12.22 1.23 2 (H) 8/1885–8/1899 14 years 12.45–25.61 17.79 17.70 2.41 3 (L) 9/1899–9/1958 59 years 4.41–25.71 12.85 12.80 3.87 4 (H) 10/1958–7/1973 15 years 12.71–23.02 17.92 18.13 1.93 5 (L) 8/1973–3/1986 13 years 6.57–15.19 9.84 9.61 2.02 6 (H) 4/1986–6/2012 26 years 12.85–86.84 22.99 19.96 9.68 Panel B: P/E10– CUSUM 1 (H) 1/1881–1/1907 26 years 12.91–25.24 17.54 17.22 2.36 2 (L) 2/1907–3/1955 48 years 4.78–32.56 12.50 11.96 4.37 3 (H) 4/1955–4/1973 18 years 13.67–24.06 18.98 18.59 2.59 4 (L) 5/1973–5/1989 16 years 6.64–18.33 10.97 10.67 2.62 5 (H) 6/1989–6/2012 23 years 13.32–44.20 25.25 23.69 7.19 Panel C: P/E1– Bai-Perron 1 (L) 1/1872–12/1885 15 years 9.61–18.05 12.31 12.24 1.47 2 (H) 1/1886–12/1899 15 years 12.45–25.61 17.74 17.69 2.46 3 (L) 1/1900–9/1958 58 years 4.41–25.71 12.84 12.78 3.88 4 (H) 10/1958–10/1973 15 years 12.71–23.02 17.88 18.13 1.95 5 (L) 11/1973–7/1991 18 years 6.57–21.78 11.51 11.07 3.36 6 (H) 8/1991–6/2012 21 years 14.42–86.84 24.87 22.58 9.95 Panel D: P/E10– Bai-Perron 1 (H) 1/1881–2/1907 26 years 12.91–25.24 17.54 17.22 2.36 2 (L) 3/1907–11/1953 46 years 4.78–32.56 12.45 11.87 4.42 3 (H) 12/1953–10/1973 20 years 11.75–24.06 18.57 18.34 2.83 4 (L) 11/1973–12/1991 18 years 6.64–18.51 11.73 10.51 3.26 5 (H) 1/1992–6/2012 20 years 13.32–44.20 26.26 25.20 7.00 Notes: (L)– The P/E period that has relatively low mean and median. (H)– The P/E period that has relatively high mean and median. The duration of each sub-period extends from a minimum of 13 years to a maximum of 59 years. The starting date of the P/E10 is 9 years later than that of the P/E1 because the P/ E10 is based on 10 years of past earnings. When we take into account all of these factors, the structural breakpoints in both the P/E1 and P/E10 do not seem to be very different. Both Panel C and Panel D with the Bai-Perron algorithm also show similar statistics. In summary, since sub-periods have a minimum duration of 13 years (15 years with the Bai-Perron algorithm) which is quite a long time, it seems to make more sense to analyze the relationship between P/E ratios and stock market returns with structural breaks. This is different from the traditional standpoint which does not consider any structural change in the market P/E ratio. Journal of Business Economics and Management, 2018, 19(1): 110–123 117 There may be several possible explanations about structural changes in the P/E ratio but it is not easy to get a clear-cut answer. First, we consider the Gordon model (Constant growth model) which attempts to explain stock price movements (Balke, Wohar 2001). According to the Gordon model, the P/E ratio can be determined by three factors: dividend payout, dividend growth, and required rate of return. It can be expressed as follows: ( ) ( ) / /,P E DE r g=⁄− (3) where P and E are the price and earnings, D is the dividend, r is the required rate of return, and g is the dividend growth. Figure4 and Figure5 show growth (change) in the dividend payout ratio and growth (change) in real dividends respectively. Their averages are close to zero. We expect their growth rates to consistently stay positive or negative during each high or low P/E period. Loosely speaking, we expect to observe approximately similar patterns during high P/E or low P/E periods. However, as we see in Figure4 and Figure5, it is hard to find any similar pattern for high or low P/E periods. Even when we examine the time trend of these two factors for each sub-period by conducting a simple linear time trend regression, we do not find a consistent pattern for high or low P/E periods. Figure 4. Growth in dividend payout ratio Figure 5. Growth in real dividends While dividend payout and dividend growth are expected to be affected by firms’ policies, the required rate of return would be determined by market participants’ expectations. Basically, the required rate of return is composed of the risk-free rate of return and the risk premium. Considering that dividend payout and dividend growth do not show a consistent pattern for high or low P/E periods, we naturally expect the required rate of return to be low during high P/E periods and high during low P/E periods. However, there are several different arguments about change in the required rate of return and it is hard to find statistical evidence for stock market movements based on fundamental factors such as dividends, earnings, and interest rates (Balke, Wohar 2001).