CAPE and Excess return:
An Empirical Analysis of the Dutch Stock Market
Master Thesis Finance
Abstract
While the price to earnings ratio is a widely used measure, in cyclically adjusted for m
popularized by Robert Shiller who eventually received a Nobel Price for his empirical work in asset pricing in 2013, there is not much literature regarding the CAPE‟s effect in the Dutch Stock market. This master thesis addresses two issues: First the connection between the
cyclically adjusted price to earnings ratio and future stock returns is investigated after which the Dutch stock market is tested for the existence of a significant CAPE effect over the period from 1991 to 2013. Results show that even though it is difficult to predi ct future stock prices by means of the cyclically adjusted price to earnings ratio there is improved predictability in the long run. Furthermore it is found that while the capital asset pricing model fails to explain return differences between portfolios consisting of high versus low CAPE rated stocks, a Two Factor model including a factor for relative distress is able to capture most of the excess returns.
Keywords: P/E, CAPE, Shiller, Dutch market, Forecast, Excess return
JEL Classification: G11, G14 Word count: 14825
Supervisor: Y. Dai
Second Examiner: Prof.Dr. L.J.R. Scholtens J.D.J. Phielix
S1689967 Oosterstraat 27b 9711NP Groningen
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1 Introduction
Nicholson (1960) finds an anomaly between securities having low and high price to earnings (P/E) ratios; securities with a low price to earnings ratio (value stocks) earned significantly higher returns than their high rated counterparts (growth stocks). The efficient market hypothesis however, states that all available information is already incorporated in security prices (Fama, 1970). This found anomaly is in direct contradiction with this hypothesis. Over time, supporting evidence for this contradiction is found in research by for example Basu (1977), Bauman Conover and Miller (1998) and Anderson and Brooks (2005). Reasons for the existence of this anomaly are widely debated in several contexts; behavioural explanations are for example found by De giorgi, Hens and Post (2005) or evidence can be found of value stocks getting a premium for bearing fundamental risk as shown in research by Fama and French (1998). The value effect however seems to be persistent in all major stock markets around the world.
Researchers have found valuation measures to some extent having power to forecast long- term stock market returns. Benjamin Graham and David Dodd are considered as the founding fathers of valuation and security analysis and pioneered stock pricing comparison using earnings smoothened out over multiple years as early as in 1934 in their book „Security Analysis‟, smoothening the effect of recessions and expansions of the economic cycle.
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is provided by Adam Butler and Mike Philbrick (2013) in several valuation models over varied time- periods. The impact of the „momentum‟ component in generating bubbles or crashes in the short- to medium run is found in further research as an predictor of stock index returns by Angelini, Bormetti, Marmi and Nardini (2013) concluding that the valuation ratio however remains a good reference point of future long - run returns. Other arguments brought forward by critics include inability of the CAPE - ratio to cope with CPI- adjustments and changes in accounting rules over time as argued by Siegel (2013), effectively rendering comparison over time meaningless as concluded by Wilcox (2011). While US based literature provides evidence for the CAPE‟s predictive power (Asness, 2012) research indicates differences in CAPE‟s explanatory power for differing markets. Even though results show the CAPE ratio to be a reliable long term indicator in emerging markets as well (Klement, 2012), there is (very) little in the l iterature regarding global CAPE ratio‟s for international equity markets (Faber, 2012).
This paper analyses the CAPE effect in the Dutch stock market over the period 1991 to 2013. The following main questions are addressed:
1) Is there a connection between the CAPE- ratio and subsequent stock returns
2) Has there been a significant CAPE- effect in the Dutch market over the period 1991 to 2013?
The first question is investigated by a regression estimation of the inverse of the CAPE ratio (earnings yield) as explanatory variable and subsequent stock ret urns 1 year forward, 3 year forward and 5 year forward as dependent variables in separate regressions.
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Results show there is hardly a connection between CAPE ratios and subsequent short term future stock returns, but increasing the return horizon improves the forecasting ability of CAPE ratios, an effect strongest for the portfolios of higher ranked stocks. Portfolio building and comparison of portfolios showed evidence of an CAPE effect between 1991 and 2013. The CAPM and Fama French Three Factor Model are unable to explain return perfectly, yet a two factor model accounting for relative distress captures most of the excess returns.
2 Theoretical Background
This chapter provides the context for this thesis. Definitions of relevant ratios and related measures are provided and theory is introduced in order to outline the relevant background in which this thesis is written. After defining the price to earnings ratio, Shiller‟s cyclically adjusted price to earnings ratio and related measures the theory of efficient markets is discussed.
2.1 Measures
Several measurement methods exist to determine the value of a security. With the comparison of a stocks market traded price to it‟s fundamentals like dividends and earnings being a widely used method, the resulting ratio of Price to Earnings (P/E) is one of the most respected measurement methods in use today. Based on the methods set out by Benjamin Graham and David Dod (1934), Shiller popularized the method with earnings smoothened out over multiple years with his version of the P/E ratio: The cyclically adjusted price to earnings ratio or „CAPE‟. In the next sections the P/E ratio , CAPE ratio and other relevant valuation measures will be defined and interpreted.
2.1.1 Price- Earnings Ratio
The Price to Earnings ratio is defined as:
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where P = market price of the share EPS = earnings per share
The denominator (EPS) can be defined using different specifications depending on the specified type of P/E ratio:
1. Trailing P/E ratio: The „Earnings per share‟ definition is defined as the net income of the firm over the most recent 12- month period and divided by the total number of outstanding shares to derive the „Trailing‟‟ earnings per share. Subsequently, the P/E ratio is the current market price of the stock divided by above defined earnings per share. This definition of price to earnings ratio is the „classical‟ and most used alternative. 2. Trailing P/E from continued operations: Instead of the „net income‟ used in the classic definition, the trailing P/E from continued operations replaces this with operating earnings.
3. Forward P/E ratio: The denominator (EPS) is calculated using an estimate for the future 12 months net earnings. Subsequently the forward P/E ratio is calculated by dividing the market price of the stock by this 12 month forward estimate.
2.1.2 The Cyclically adjusted P/E ratio
The Cyclically Adjusted Price/ Earings ratio (CAPE ratio) is defined as:
CAPE ratio = P EPS10 Where P= market price of share
𝐸𝑃𝑆10 = average earnings over the past 10 years adjusted for inflation.
1. The „Raw‟ cyclically adjusted price to earnings ratio: The raw definition of the cyclically adjusted price earnings ratio was originally used for individual stocks by Benjamin Graham and David Dodd (1934). The denominator (EPS) is calculated by averaging the earnings over the past 10 years. Subsequently the raw ratio is calculated by dividing the market price by the average of the past 10 years of earnings
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cyclically adjusted price to earnings ratio or CAPE. Modified from the raw version it is calculated by correcting the past 10 years of earnings for inflation before averaging these 10 years of earnings.
2.2 Related Measures
This chapter presents a selection of the most commonly used measures related to the price to earnings (P/E) ratio.
2.2.1 Dividend yield
Dividend yield is defined as:
DY = D P where P= market price of a share
D = most recent annual dividend
The dividend yield is an easy way to compare the relative attractiveness of various dividend- paying stocks. It tells an investor the yield to be expected by purchasing a stock. It represents the annualized return a stock pays out in the form of dividends .
2.2.2 Price to Book ratio
The price to book ratio is defined as:
P B Ratio = P B
where P = market price of a share B = book value of a share
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industries (ea. retail, utilities). Contrary, higher ratios are found in industries in which intangibles are more important like pharmaceuticals and consumer products.
2.3 Capital markets
The theory around capital markets is crucial for investors and academics alike in their efforts to determine a relationship between past information and future performance in order to generate excess return, leading to several leading schools of thoughts.
2.3.1 Random Walk Theory
According to the „Random Walk Theory‟ stock prices are following independent pattern which is random and unpredictable. This implies that past movements of stock prices or market trends cannot be used to predict the future movement of stock prices. Current stock prices are considered to fully reflect available information on a firms value and profits in excess over the market are impossible to generate by using gathered information. The efficiency of the market in incorporating information in the prices is first described by Fama (1965) stating that „in an efficient market, on average, competition will cause the full effects of new information on intrinsic val ues to be reflected “ínstantaneously” in actual prices „. As concluded by Clarke, Jandik and Mandelker (2009) prices of stocks are said to follow a „Random Walk‟ because, even while prices are rationally based; changes in prices are expected to be random and unpredictable because new information, by its very nature, is unpredictable.
2.3.2 Market efficiency
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2.3.2.1 Weak Form Efficient Market
When considering the Efficient Market Hypothesis in its „weak form‟ security prices are believed to reflect all historical, public available information only. The market has no memory and forecasting future returns based on past security p rices is considered impossible. The „Weak‟ form for this version of the efficient market hypothesis comprises security prices are, arguably, the most public and most easily available piece of information. As summarized by Clarke, Jandik and Mandelker (2009) this form of the hypothesis states that, as no one should be able to profit from using som ething “ everybody else knows”. Techniques based on studying past stock price series and trading volume data, so called „technical analysis‟, is of no use under the weak form efficient market hypothesis.
2.3.2.2 Semi- Strong From Efficient Market
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2.3.2.3. Strong Form Efficient Market Hypothesis
When considering the „Strong‟ Form of the Efficient Market Hypothesis all public and private (insider) information is considered to be reflected in the current stock price. This hypothesis assumes that the market anticipates such information, and as such it is incorporated in the price- forming. It is impossible to use insider information to systemically generate profits nor can market analysis outperform a random buy- and hold strategy. Clarke, Jandik and Mandelker (2009) summarize the rationale for the strong- form market efficiency as the market anticipating, in an unbiased manner, future developments and stock prices have incorporated and evaluated information in a much more objective and informative way than insiders.
2.3.3 Mean Reversion
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3 Literature Review
3.1. The price to Earnings Effect
The first evidence of the P/E effect is found in research by Nicholson (1960). Based upon analysis of 100 major industrial stocks over the period 1939 to 1959 he formed five portfolio‟s consisting of securities with either high or low P/E ratios, rebalancing these on a five year basis. His results show the portfolio holding the lowest P/E rated stocks to earn 14.7 times the initial investments during this period while the portfolio holding the highest P/E rated stocks only earned 4.7 this investment. Following up on these results, in 1968 Nicholson continued his research on the P/E effect by testing 189 c ompanies over the period 1937 to 1962. His findings show those stocks below the threshold ratio of 10 (P/E) to earn 12.7% while those stocks above the P/E threshold ratio of 20 only earn 7.97% per annum.
Confirming results are found by Basu (1977) after analysing NYSE traded stocks over the period from 1957 to 1971 and forming equally weighted portfolio‟s consisting of high and low P/E rated stocks. Results of these tests showed the low P/E portfolio‟s outperforming the high P/E portfolio‟s by 7% per annum. Basu (1977) included the CAPM to assess how these findings deviated from the risk implied. Findings show the high P/E rated portfolio‟s to earn 2.5 to 3% less than implied by their levels of risk while the two low rated P/E portfolio‟s earned about 2 to 4.5% more. His conclusion that security prices do not fully incorporate the new P/E information is in contradiction with the efficient market hypothesis and results thus show inefficient capital markets during the investigated period.
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The explanatory power of the P/E ratio for short term future stock returns in emerging markets is analysed by Aydogan and Gursoy (2000) over the period from 1986 to 1999 by forming five portfolio‟s based upon average E/P ratios for the considered countries. After testing the three, six and twelve- month projected return for any deviations based on the P/E ratio they find evidence for the presence of a significant P/E effect. By performing regression analysis they find evidence for the E/P ratio‟s power in predicting future returns over all three horizons, while the twelve- month period shows the strongest effect.
Work by Estrada (2003) includes „Growth‟ and „Risk‟ forming two adjusted ratios. Adjusting the P/E ratio for growth (PEG) or growth and risk (PEGR) and comparing the performance of 100 US companies over the period 1975- 2002 shows that the portfolio based upon the P/E ratio adjusted for growth and risk significantly outperform s the P/E and P/E adjusted for growth based portfolio‟s.
Research by Anderson and Brooks (2005) includes business cycle effects by calculating the P/E ratio on the last two to eight years instead of only the last years earnings. While this research is very similar to the earlier research by Basu (1977) they now consider last years earnings of lesser relevance than the business cycle effects. By calculating the P/E ratio of both eight years ago and the last year they find a value premium of almost 7% higher using the last years earnings over using earnings of the eight years ago. Concluding this premium is hard to explain by standard asset pricing models they argue this is probably due to behavioral factors.
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Further research by Anderson and Brooks (2005) using UK- companies data over the period from 1975 to 2003 aims at breaking down the P/E ratio. After testing for annual market- wide P/E ratio, sector, size and idiosyncratic- effects to determine weighting factors they create a modified P/E ratio accounting for these weights. Subsequently, based upon this ratio both „normal‟ and „modified‟- ratio portfolio‟s are created and compared. Their results show P/E effects to be much stronger when using this modified ratio.
3.2 Price to Earnings effect as predictor
Following up earlier work on stock market predictability, Shiller and Campbell (1998) established that long- term stock market returns are not random walks but can be forecasted. In their research, they create an adjusted form of the P/E ratio called the „Cyclically Adjusted Price- Earnings‟, or CAPE, ratio. By taking the S&P 500 data of stock market prices and dividing by the average of the last ten years of aggreg ate earnings all measured in real terms, they established this ratio. After testing the viability of this ratio by regressing against the future ten year real returns on stocks they find the „CAPE- ratio‟ to be a significant variable in predicting long- run stock returns.
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Hansen and Tuypens (2004) used S&P 500 data over the period from 1920 to 2003 in order to show by means of the „Gordon Growth model‟ that long- run regression models based on trailing earnings over price ratio‟s to provide the predictive capacity for future returns are downward biased, claiming it is better to use a moving average of the logarithm of one plus the E/P ratio.
The predicting effect of changes in the P/E ratio to future stock returns is tested by Bartholdy (1997) as well. Based on Toronto stock exchange data over the time period from 1981 to 1996 the predictable capacity of the change in P/E effect is tested, finding a negative correlation between this change and future stock returns . Bartholdy (1997) concludes this to be caused by the tendency of investors to overreact to new information.
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4 Empirical Analysis
Methodology
The methodology is established around two parts:
1) Performing predictive regressions in order to test for a relationship between the Cyclically Adjusted Price Earnings ratio and future returns and;
2) Portfolio building to test performance differences between low and high CAPE rated stocks.
Finally, conclusions are drawn and discussed related to existing theory.
4.1 Data
The primary source of data is Datastream while secondary data sources are utilized to complement the dataset correct missing values. Furthermore, this provides a dataset to be used for verification purposes. As secondary source, acces to the Bloomberg database is provided as courtesy by IBS Capital Management. Data on interest rates is retrieved from the statistical database as provided by the Organization for Economic Co -operation and Development (OECD).
The dataset consists of stocks traded on the Dutch stock exchange. The observed period extends from 1980 to 2014. For every year, both monthly and yearly intervals are used for a total of 34 yearly or 408 monthly observations. Firms are required to fulfil at least the following criteria:
(i) The firm is traded on the Dutch stock market
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After applying these selection criteria, a total of 127 firms were considered over sample period. The inclusion of firms that went bankrupt or were delisted during the observed period is considered in order to eliminate an ex- post selection bias.
A consideration of importance is in determining the appropriate market index. While several alternatives are available (e.g. MSCI Netherlands, Aex), using these indices has a number of drawbacks for the following analyses, first of all, the data available might be limited for selected indices while a second challenge is as follows: An index weighted by market capitalization is composed of a fairly heavy concentration of the largest stocks subsequently overweighting these stocks. This bias towards large caps is removed when using an equally weighted index. These disadvantages are the foundation of my choice to construct my own equally weighted total return index, the „Dutch Index‟. The risk free rate is measured with the 3- month interbank rate, the 3-month "European Interbank Offered Rate" is used from the date the country implemented the Euro as its currency.
To perform the analysis in the following sections, the following stock information is used.
Continuously compounded yearly Total Return (1) 𝑟𝑦𝑖 = ln( 𝑅𝐼𝑦
𝑖 𝑅𝐼𝑦−1𝑖 )
where 𝑟𝑦𝑖 = continuously compounded total yearly return of stock i in year y. 𝑅𝐼𝑦𝑖 = total return index of stock i in year y
𝑅𝐼𝑦−1𝑖 = total return index of stock i in year y- 1 ln = natural logarithm
Continuously compounded monthly Total Return (2) 𝑟𝑡𝑖 = ln(
𝑅𝐼𝑡𝑖 𝑅𝐼𝑡−1𝑖 )
where 𝑟𝑡𝑖 = continuously compounded total monthly return of stock i in month t. 𝑅𝐼𝑡𝑖 = total return index of stock i in month t
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ln = natural logarithm
For this analysis we use continuously compounded returns. Using continuously compounded returns has, compared to arithmetic returns, the advantage that continuously compounded returns are symmetric. This symmetric nature is preferred from mathematical point of view. Consider for example an investment portfolio of 1000 euro. When calculating the portfolio value after a two- period structure of returns of +50% followed by -50%, the arithmetic basis yields a total value of 750 euro after two years. The same return structure on a logarithmic basis yields a total portfolio value of 1000 euro after two years, better representing the actual total absolute return after the two periods.
4.2 Descriptive data
Table 1 presents summary statistics for the „Dutch Index over the whole period from 1991 to 2013. Yearly data is considered for the constructed index. Cape ratios are calculated as of the stock price at the end of the 30th of April of each year divided by the average of past 10 (5) years of inflation adjusted earnings and the return of said year is calculated. While data is retrieved starting from 1980, the calculation method for the CAPE ratio requires 10 years of past earnings resulting in April 30th 1991 as first point of data in our sample.
Table 1: Descriptive statistics 'Dutch Index' 1991- 2013
The period 1991- 2013 refers to averages of monthly data from April 30th 1991 to April 30th 2013. The second column „Return‟
represents continuously compounded yearly returns. The CAPE5 (10) ratio is calculated by dividing the stock price of April 30th
of the year divided by the average past 5 (10) years of earnings data adjusted for inflation.
Return CAPE 5 CAPE10
Mean 0.0471 18.3247 17.8177 Median 0.0534 16.9978 15.9098 Standard Deviation 0.2638 6.8076 5.6775 Sample Variance 0.0696 46.3435 32.2338 Kurtosis 0.6791 0.1083 0.3708 Skewness -0.8799 0.7408 0.9439 Minimum -0.6102 6.6916 9.5588 Maximum 0.4156 33.6895 32.1177
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Descriptive results as averages for the entire observed period show an average return of 4.71 %. The median is 5.34%, being 0.63% higher compared to the mean implying negative (downwards) deviations from the mean. This is confirmed by the negative skewness (-0.8799). The cyclically adjusted price earnings ratios are calculated with both 5 year and 10 year averages of earnings. The mean CAPE10 ratio is 17.8177 paired with a median of 15.90. While the CAPE5 ratio is higher (18.3247 ) the standard deviation is also higher with 6.8076 compared to 5.6775. This is in line with expectations because taking the average of 10 years of earnings compared to 5 years of earnings will, everything else equal, decrease the effect of both positive and negative deviations from the mean due to its smoothening effect.. When considering the range of observed values for the „Dutch Index‟ summary statistics we can see that the CAPE5 values are observed from 6.6916 to 33.6895. The CAPE10 ran ge is smaller given values in the range between 9.5588 and 32.1177. Returns are observed in the range between a negative 61.02% and positive 41%, showing stronger deviations in the negative region.
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Table 2: Descriptive statistics 3 periods 'Dutch Index'
All periods are calculated as of April 30th of said year. For example: The period 1991- 1997 refers to monthly data starting April 30th 1991 to April 30th 1997. Column 2 „Return‟ represents the cc returns. The
CAPE5 (10) ratio is calculated by dividing the stock price of April 30th of said year by the average past 5 (10) years of earnings data adjusted for inflation.
1991-1998 Return CAPE 5 Ratio CAPE 10 Ratio
Mean 0.1257 15.9041 17.0686 Median 0.1401 13.7875 15.6631 Standard Deviation 0.1622 4.9115 4.4133 Sample Variance 0.0263 24.1230 19.4768 Kurtosis -2.2656 1.8444 4.1417 Skewness -0.0227 1.5704 1.9863 Minimum -0.0626 11.6561 13.4272 Maximum 0.3151 25.4736 26.3766 1998-2005 Mean 0.0577 18.6433 20.6469 Median 0.0644 17.8115 21.1595 Standard Deviation 0.2940 8.8041 8.0298 Sample Variance 0.0865 77.5115 64.4777 Kurtosis 0.6858 -0.7787 -1.1722 Skewness -0.6352 0.2512 -0.0133 Minimum -0.4913 6.6916 9.5588 Maximum 0.4156 32.2663 32.1177 2005-2013 Mean -0.0550 19.9595 16.2000 Median 0.0252 18.1596 15.5727 Standard Deviation 0.3209 6.5572 3.9036 Sample Variance 0.1030 42.9964 15.2382 Kurtosis -0.1058 1.4031 -0.2897 Skewness -0.7711 1.2210 0.5964 Minimum -0.6102 12.1239 10.7014 Maximum 0.3040 33.6895 23.0375
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Figure 1 presents a plot of the CAPE5 respectively CAPE10 ratio over the whole period. While the trend the line is similar for both ratios , reaching a top of approximately 33 at the end of the previous millennium and a low of approximately 7 (10) for the CAPE10 (CAPE5) ratio around 2002. A second peak is best shown by the CAPE5 ratio around the end of 2007 right before the „credit crunch‟ crisis and the subsequently following bearish markets. While the CAPE 10 ratio is a more smoothened alternative to the CAPE5 ratio, we can see that during the bullish markets of the 90‟s both ratios more or less follow the same trend. It is only in inverting markets that the effect of the previous trend effects the CAPE10 ratio longer (and thus stronger) than is the case for the CAPE5 ratio.
Source: Own investigation
Note: The CAPE5 (10) ratio is calculated by dividing the stock price of April 30th of said year by the average past 5 (10) years of earnings data adjusted for inflation. The horizontal axis represents the yearly
observation at April 30th while the corresponding CAPE ratio is specified by the vertical axis.
4.2.1 Composition ‘Dutch Index’
Table 3 presents summary statistics on the composition of the „Dutch Index‟. Full statistics are provided in the appendix. Individual firms are ranked by average continuously compounded yearly return. At first glance there no evidence of a relationship between lower CAPE ranked stocks yielding higher returns. For example, while the stock „Xeikon‟ yields the highest average return of 25.17% for an average
0 5 10 15 20 25 30 35 40
Figure 1: The 5 year and 10 year smoothened Cyclically Adjusted Price to Earnings Ratio of the ‘Dutch Index’between 1991 and 2013
CAPE5 CAPE10
Credit Crunch Dotcom Bubble
Market downturn
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CAPE10 ratio of 3.466 in line with theory that low ranked (value) stocks should on average yield higher returns, further results are mixed. The 2nd and 3rth ranked stocks are „Arcadis‟ and „Asml Holding‟ yielding return percentages of average 20.3% and 18.93% while paired with average CAPE10 ratios of 26.5074 and 47.4756. When considering the stocks delivering the lowest return percentages we can observe a negative (cc) annual return of 19.83% for a CAPE 10 ratio of 1.0098 thereby suggesting it is difficult to conclude a relationship between low CAPE rated stocks and higher subsequent stock returns. However, it must be noted that CAPE ratios can be dependent on the industry in which a firm operates.
Table 3: Summary statistics individual firms
The CAPE5 (10) ratio is calculated by dividing the stock price of April 30th of the following year divided by the average past 5
(10) years of earnings data adjusted. Column 2 „Avg yearly return‟ represents the average cc yearly return over the period from
April 30th 1991 to April 30 2013.
Rank Security Avg yearly return Mean CAPE 10 Mean CAPE 5
1 Xeikon 0.2517 3.4667 8.5656 2 Arcadis 0.2030 26.5074 21.6454 3 Asml Holding 0.1893 47.4756 44.5801 4 Vhs onroerend 0.1807 59.6073 30.7753 5 Docdata 0.1801 26.6567 21.4132 6 Hal Trust 0.1795 11.4660 11.0069
7 Smit intl. Certs 0.1752 20.3224 21.5807
8 Exact Holding 0.1733 12.8959 13.2739 9 Amsterdam Commodities 0.1578 14.3718 13.6029 10 Athlon Holding 0.1578 13.5922 12.4637 … 117 Draka Holding -0.1929 8.3465 26.3683 118 Nedsense Enterprises -0.1983 1.0098 2.9171 119 Roodmicrotec -0.2008 7.0664 13.9256
120 Nieuwe Steen Inv. -0.2097 5.2117 17.8121
121 Arcelormittal -0.2270 7.1095 6.1899
122 Kie Kinetix -0.2298 8.5340 0.0694
123 De Vries Robbe Groep -0.2939 7.4906 12.1811
124 Super de Boer -0.3074 12.8690 12.5298
125 Dico Intl. -0.3515 11.3897 23.0678
126 Lavide Holding -0.6302 9.0661 11.4829
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4.3 Predictive regressions
4.3.1 Methodology
In order to investigate the connection between the Cyclically adjusted Price Earnings ratio and future stock returns, some basic regressions are presented.
For this purpose, all stocks are ranked by their corresponding CAPE ratios from high to low. Based on this ranking, quintiles are created each consisting of 20% of the stocks in the market. Finally, forward returns for the quintiles are considered in order to test for an empirical relationship. The quintiles (and corresponding forward returns) are recalculated on a monthly basis for the period 1991- 2013. A minimum of 10 years of trading history is required for firms to qualify since past earnings over a 10 year period are required to calculate the CAPE ratio.
The following procedure is adopted:
((1) Beginning with April 1991, the CAPE 10 ratio of every sample security is computed (2) The sample securities are ranked and 5 quintiles are formed, each consisting of 20% of the securities in the sample. are created ranging from Quintile 1 (Q1) consisti ng of the 20% lowest ranked securities until Quintile 5 (Q5) which consists of the 20% highest ranked securities.
(3) For each portfolio, returns are calculated for 1 year forward (T+1), 3 year forward (T+3) and 5 year forward (T+5).
(4) Point 1 to 3 are repeated for every month until April 2013.
In order to investigate the robustness of our results, instead of quintiles a different composition is considered at the end of the analysis. For this purpose, the same procedure is followed as above and stocks and divided in a top 30%, mid 40% and bottom 30%.
The following regressions are performed in order test the connection between the CAPE ratio and subsequent future stock returns.
𝑟𝑡+𝑥𝑖 = 𝛼 + 𝛽1 𝐸𝑌5 𝑡𝑖 + 𝜀
𝑡𝑖 (1) 𝑟𝑡+𝑥𝑖 = 𝛼 + 𝛽2 𝐸𝑌10 𝑡𝑖 + 𝜀
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where
𝑟𝑡+𝑥𝑖 = Continuously compounded total return of stock i in month t + x x ranging from 1 year forward to 6 year forward from month t
𝐸𝑌5 𝑡𝑖 = Continuously compounded 5 year earnings yield of portfolio i in month t 𝐸𝑌10 𝑡𝑖= Continously compounded 10 year earnings yield of portfolio i in month t 𝛼, 𝛽1, 𝛽2 = Estimated slopes
𝜀𝑡𝑖 = Error term
The difference between regression (1) and (2) is that regression (1) uses the 10 - year smoothed (Cyclically adjusted) earnings yield. It will be tested if the explanatory power of the 5-year earnings yield (10- year respectively) increases with the return horizon. For this purpose, the range for forward returns is chosen to be one year (T+1), two year (T+2) three year (T+3) and five year (T+5)
Based on research by Hansen and Tuypens (2004) we use the logarithmic earnings yield to reduce the bias for expected future returns.
4.3.2 Descriptive statistics quintiles average CAPE rating over time
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Source: Own investigation
Note: The 10 year CAPE ratio ratio is calculated by dividing the stock price of April 30th of the following year divided by the
average past 10 years of earnings data adjusted for inflation for every year over the period 1991 - 2013. Q1 refers to the 20% (Quintile 1) of lowest CAPE rated stocks until Q5 (Quintile 5) for the 20% of highest CAPE rated stocks. The vertical axis
represents subsequent CAPE ratios. 0 10 20 30 40 50 60 70 80 90
Figure 2: 10 year Cyclically Adjusted Price to Earnings ratio for 5 quintiles and the ‘Dutch index’ during the period from 1991 to 2014
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5 Results Predictive Regressions
Table 4 presents the results of regressing both the 5 and 10 year earnings yield and 1 year forward returns. Tables 5 and 6 present the results of the same regression s for the 3 year forward and 5 year forward returns.
Table 4: Summary statistics predictive regressions one year forward returns (T+1)
The EY 5 (10) coefficient refers to the coefficient of the 5 (10) year earnings yield calculated as the inverse of the 5 (10) year CAPE ratio. Quintile 1 represents the 20% of lowest CAPE rated stocks until Quintile 5 for the 20% highest CAPE ranked stocks.
Predictive regression estimation (1) is estimated for EY5 while estimation (2) refers to the EY10 results. The following regression specifications are estimated with ordinary least squares (OLS):
(1) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽1 𝐸𝑌5𝑡𝑖+ 𝜀𝑡𝑖
(2) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽2 𝐸𝑌10 𝑡𝑖+ 𝜀𝑡𝑖
EY 5 coefficient P-value Adj. R-squared EY 10 coefficient P-value Adj. R-squared
Quintile 1 0,0009 0,1833 0.0029 0.0009 0.4910 -0.0020
Quintile 2 2.3303 0.0000** 0.1351 2.2194 0.0000** 0.0945 Quintile 3 3.7140 0.0000** 0.1521 5.8587 0.0000** 0.2135 Quintile 4 3.4771 0.0000** 0.0805 5.7054 0.0000** 0.1297 Quintile 5 6.8973 0.0000** 0.1173 6.0090 0.0000** 0.1451
*Significant at a 95% confidence interval **Significant at a 99% confidence interval
25
In order to investigate whether increasing the return horizon improves results, the same regressions are performed for the 3 year forward returns. Results are presented in table 5 below.
Table 5: Summary statistics predictive regressions three year forward returns (T+3)
The EY 5 (10) coefficient refers to the coefficient of the 5 (10) year earningsyield calculated as the inverse of the 5 (10) year CAPE ratio. Quintile 1 represents the 20% of lowest CAPE rated stocks until Quintile 5 for the 20% highest C APE ranked stocks.
Predictive regression estimation (1) is estimated for EY5 while estimation (2) refers to the EY10 results. The following regression specifications are estimated with ordinary least squares (OLS) :
(1) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽1 𝐸𝑌5𝑡𝑖+ 𝜀𝑡𝑖
(2) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽2 𝐸𝑌10 𝑡𝑖+ 𝜀𝑡𝑖
EY 5 coefficient P-value Adj. R-squared EY 10 coefficient P-value Adj. R-squared Quintile 1 -0.1124 0.0352 0.0143 -0.1061 0.0000** 0.1014 Quintile 2 4.3469 0.0000** 0.1782 3.2135 0.0000** 0.0649 Quintile 3 8.6922 0.0000** 0.3641 1.1721 0.0000** 0.3526 Quintile 4 1.2791 0.0000** 0.4016 1.6546 0.0000** 0.3986 Quintile 5 2.7728 0.0000** 0.4518 3.6476 0.0000** 0.4691
*Significant at a 95% confidence interval **Significant at a 99% confidence interval
26
To find out whether a further improvement is found by increasing the horizon another 2 years, table 6 presents the summary statistics for the 5 year return horizon.
Table 6: Summary statistics predictive regressions five year forward returns (T+5)
The EY 5 (10) coefficient refers to the coefficient of the 5 (10) year earnings yield calculated as the inverse of the 5 (10) year CAPE ratio. Quintile 1 represents the 20% of lowest CAPE rated stocks until Quintile 5 for the 20% highest CAPE ranked stocks.
Predictive regression estimation (1) is estimated for EY5 while estimation (2) refers to the EY10 results. The following regression specifications are estimated with ordinary least squares (OLS):
(1) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽1 𝐸𝑌5𝑡𝑖+ 𝜀𝑡𝑖
(2) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽2 𝐸𝑌10 𝑡𝑖+ 𝜀𝑡𝑖
EY 5 coefficient P-value Adj. R- squared EY 10 coefficient P-value Adj. R-squared Quintile 1 0.0744 0.7203 -0.0006 -0.1679 0.0023** 0.0379 Quintile 2 7.0723 0.0000** 0.3523 6.0115 0.0000** 0.1564 Quintile 3 1.1181 0.0000** 0.3915 1.2859 0.0000** 0.2675 Quintile 4 1.7864 0.0000** 0.4814 2.3474 0.0000** 0.4691 Quintile 5 4.3644 0.0000** 0.7676 5.4756 0.0000** 0.7190
*Significant at a 95% confidence interval **Significant at a 99% confidence interval
When considering the 5 year earnings yield, the results seem to become more consistent as, except for quintile 1, all R- squared values have increased. While quintile 5 now yields an impressive value for R- squared of 0.7676 when considering the 5 year earnings yield, the values for R- squared for the quintiles 2,3 and 4 have improved to 0.3523, 0.3915 and 0.4814 respectively. Remarkable is that in comparison to the 10 year yield, there are some differences; quintiles 4 and 5 show values for R- squared close to the results from the regressing the 5 year yield (0.4691 and 0.7190) while the quintiles 2 and 3 show lower values (0.1564 and 0.2675) compared to using the 5 year earnings yield. In comparison to table 5 however, the overall result show further improvement especially for the quintiles consisting of higher CAPE ranked stocks.
27
Table 7: Summary statistics CAPE regressions five year forward returns (T+5)
The CAPE5 (10) ratio is calculated by dividing the stock price of April 30th of the following year divided by the average past 5
(10) years of earnings data adjusted for inflation. Quintile 1 represents the 20% of lowest CAPE rated stocks until Quintile 5 for the 20% highest CAPE ranked stocks. Predictive regression estimation (1) is estimated for CAPE5 while est imation (2) refers to the CAPE10 results. Instead of the inverse of the CAPE ratio in both regression (1) and (2) the corresponding CAPE ratios are
estimated as explanatory variables.
The following regression specifications are estimated with ordinary least squares (OLS):
(1) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽1 𝐸𝑌5𝑡𝑖+ 𝜀𝑡𝑖
(2) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽2 𝐸𝑌10 𝑡𝑖+ 𝜀𝑡𝑖
CAPE5 Coefficient P value Adj. R squared CAPE10 Coefficient P value Adj.R squared Quintile 1 -0.0311 0.0000** 0.1190 -0.0324 0.0000** -0.0032 Quintile 2 -0.0858 0.0000** 0.5018 -0.1204 0.0000** 0.2761 Quintile 3 -0.0438 0.0000** 0.3513 -0.0860 0.0000** 0.3822 Quintile 4 -0.0493 0.0000** 0.5013 -0.0618 0.0000** 0.5514 Quintile 5 -0.0311 0.0000** 0.7747 -0.0324 0.0000** 0.8110
*Significant at a 95% confidence interval **Significant at a 99% confidence interval
28
earnings yield was 0.2675 while the result from considering the 10 year CAPE ratio was 0.3822.
Observable from regressing both the 5 year and 10 year CAPE (earnings yield) to different return horizons is a clear indication of a difference in predictability for the different quintiles. While increasing the return horizon has a positive effect for all regressions, the debate between using either 5 or 10 year horizons appears inconclusive. While the quintiles formed of higher CAPE ranked stocks show better predictable capabilities when using 10 year- historical figures there seems to be a pattern for the quintiles formed of lower ranked stocks showing better results for a CAPE basis of 5 year. We can conclude that while results are mixed, a predictive capability of the CAPE ratio is apparent en most evident for a longer return horizon.
To investigate whether these results only hold when considering extremes as tested by using quintile; table 4 presents summary statistics of the same regressions for a composition of „top 30%‟, „middle 40%‟ and „bottom 30%‟ stocks based on CAPE rating.
29
Table 8: Summary statistics 30%/40%/30% composition 5 year forward
The EY 5 (10) coefficient refers to the coefficient of the 5 (10) year earnings yield calculated as the inverse of the 5 (10) year CAPE ratio. Quintile 1 represents the 20% of lowest CAPE rated stocks until Quintile 5 for the 20% highest CAPE ranked stocks .
Predictive regression estimation (1) is estimated for EY5 while estimation (2) refers to the EY10 results The return horizon is estimated at 1 year (T+1), 3 year (T+3) and 5 year (T+5) forward returns. The following regression specifications are estimated
with ordinary least squares (OLS):
(1) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽1 𝐸𝑌5𝑡𝑖+ 𝜀𝑡𝑖
(2) 𝑟𝑡 +𝑥𝑖 = 𝛼 + 𝛽2 𝐸𝑌10 𝑡𝑖+ 𝜀𝑡𝑖
T+1 EY 5 coefficient P-value Adj. R-squared EY 10 coefficient P-value Adj. R-squared
B30 0.0006 0.4980 -0.0020 0.0003 0.8700 -0.0037
M40 3.4740 0.0000** 0.1663 4.9838 0.0000** 0,1993
T30 5.6630 0,0000** 0.1069 8.2081 0,0000** 0.1361
T+3 EY 5 coefficient P-value Adj. R-squared EY 10 coefficient P-value Adj. R-squared
B30 -0.1503 0.0357* 0.0142 -0.1446 0.0000** 0.1052
M40 8.4667 0.0000** 0.4017 1.0676 0,0000** 0.3526
T30 2.2530 0.0000** 0.4627 2.7977 0,0000** 0.4451
T+5 EY 5 coefficient P-value Adj. R-squared EY 10 coefficient P-value Adj. R-squared
B30 0.3543 0.1746 0.0039 -0.2015 0.0058** 0.030
M40 1.1569 0.0000** 0.5020 1.209 0,0000** 0.3461
T30 3.4383 0.0000** 0.7100 4.2096 0,0000** 0.6498
T+5 CAPE5 Coefficient P value Adj. R-squared CAPE10 coefficient P value Adj. R-squared
B30 -0.0709 0.0000** 0.2318 -0.0912 0.0003** 0.0541
M40 -0.0595 0.0000** 0.5749 -0.0863 0.0000** 0.4721
T30 -0.0362 0.0000** 0.7745 -0.0362 0.0000** 0.7722
*Significant at a 95% confidence interval **Significant at a 99% confidence interval
30
6 Portfolio analysis
In the following chapter low and high CAPE ranked portfolios are compared to determine if a „CAPE effect‟ exists in the Dutch stock market. The following hypothesis is formulated to investigate this relationship:
Hypothesis: Portfolios consisting of low CAPE ranked stocks outperformed portfolios consisting of high CAPE ranked stocks on a risk- adjusted basis in the Dutch stock market during the period from 1991 to 2013.
6.1 Methodology
In the second part of this analysis, Portfolios are constructed based on their CAPE - level to investigate if lower CAPE ranked stocks outperform their higher ranked counterparts. In line with the procedure followed for the predictive regressions, the following procedure is adopted:
(1) Beginning with April 1991, the CAPE ratio of every sample security is computed (2) The CAPE ratio‟s are ranked and five equally weighted portfolios (quintiles) are created. Portfolio 1 consists of the stocks with the lowest 20% CAPE ratios until portfolio 5 with the highest 20% ratios.
(3) Buy and hold strategy of 1 year
(4) Repeat point (1) to (3) for every month until April 2013.
31
After constructing the portfolios the following regressions are employed :
𝑟𝑡𝑝 − 𝑟𝑡𝑓 = 𝛼 + 𝛽 ∙ 𝑟𝑡𝑚 − 𝑟 𝑡 𝑓 + 𝜀𝑡𝑝 (1) 𝑟𝑡𝑝 − 𝑟𝑡𝑓 = 𝛼 + 𝛽 ∙ 𝑟𝑡𝑚 − 𝑟 𝑡 𝑓 + β2 ∙ 𝑆𝑀𝐵 + 𝛽𝑣 ∙ 𝐻𝑀𝐿 + 𝜀𝑡𝑝 (2) 𝑟𝑡𝑝 − 𝑟𝑡𝑓 = 𝛼 + 𝛽 ∙ 𝑟𝑡𝑚 − 𝑟𝑡𝑓 + 𝛾 ∙ 𝐿𝐶𝐴𝑃𝐸 − 𝐻𝐶𝐴𝑃𝐸 𝑡+ 𝜀𝑡𝑝 (3)
𝑟𝑡𝑝 = Continuously compounded total return of portfolio p in month t 𝑟𝑡𝑓 = Continuously compounded risk free return in month t
𝑟𝑡𝑚 = Continuously compounded total return market portfolio in month t (𝑆𝑀𝐵) = Difference in monthly (cc) returns of a portfolio consisting of
the smallest 30% minus the (cc) returns of a portfolio consisting of the largest 30% stocks
(𝐻𝑀𝐿) = Difference in monthly (cc) returns of a portfolio consisting of the 30% of stocks with the highest Book to market ratio minus the (cc) returns of a portfolio consisting of the 30% stocks with the lowest Book to Market ratio.
𝐿𝐶𝐴𝑃𝐸 − 𝐻𝐶𝐴𝑃𝐸 𝑡 = Difference between the monthly (cc) returns of a
portfolio consisting of stocks of the top 40% (quintiles 1 and 2) and bottom 40% (quintiles 4 and 5)
32
All regressions are regressed with ordinary least squares (OLS). The results for regression (1) show how much of the variation in excess returns can be explained by the model (R-squared) and the significance of the beta factor for the explanatory variable. The second regression includes the factors proposed by Fama & French (1992) after which we include a gamma factor accounting for „Cape effects‟. If this gamma factor (𝛾) is significantly different from zero it is considered helpful in explaining the dependent variable. The observed effects of including this gamma factor for the R- squared provides information whether the adapted model has superior capabilities in explaining the variation of returns and thus whether this is a „better‟ model for explaining returns.
Regression (1)
Regression (1) is the traditional capital asset pricing model (CAPM) proposed by Sharpe (1964), showing which part of an investment cannot be eliminated through diversification. It is the one- factor model where the only risk factor is the included beta representing the „ market risk‟. It implies the risk- reward trade-off where the higher the risk, the higher the return to be expected. If the CAPM would be completely „valid‟, the alpha is zero and any higher excess returns are only possible because of increased market risk. The beta- value should decrease consistently from low- CAPE- portfolios to high-CAPE- portfolios. We formulate this following:
Hypothesis 1: Portfolios based on CAPE rating that yield higher returns have a higher beta.
Regression (1) is regressed for each portfolio over the period 1991 to 2013 , testing for the presence of alpha:
𝐻0: 𝛼 = 0 𝑎𝑛𝑑 𝐻1: 𝛼 ≠ 0 (A)
33
the „market risk‟ is assumed to be positive because if a portfolio is sufficiently diversified both the market and diversified portfolio will move in the same direction.
Regression (2)
The second regression is the Three Factor model designed by Fama & French (1992) to describe stock returns. While the „traditional‟ capital asset pricing model uses only one variable, the market returns, to describe portfolio returns two additional factors are included in this model. Based on the observation that two classes of stocks outperform the market as a whole by Fama & French (1992), factors are added to reflect a portfolios exposure to these classes. The SMB factor measures the historic excess returns of small caps over big caps and the HML factor measures the historic excess returns of value over growth stocks. If the Three Factor model is able to explain all returns the alpha is zero as formulated in the following hypothesis:
𝐻0: 𝛼 = 0 and 𝐻1: 𝛼 ≠ 0 (B)
Furthermore, if the included „size‟ and „value‟ factors yield increased explanatory capabilities over the traditional CAPM model both factor betas should be significantly different from zero, as tested by:
𝐻0: 𝛽𝑠 = 0 𝑎𝑛𝑑 𝐻1: 𝛽𝑠 ≠ 0 (C)
And
H0: 𝛽𝑣 = 0 𝑎𝑛𝑑 𝐻1: 𝛽𝑣 ≠ 0 (D)
34 Regression (3)
The third regression includes a factor accounting for a „CAPE effect‟. To create this factor two portfolios are formed: The first one consisting of 40% of the stocks that have the lowest CAPE-ratios and the second consisting of the 40% stocks that have the highest CAPE ratios. Both portfolios are updated on a monthly basis. The factor is calculated by taking the difference in the returns of the low and high CAPE- portfolios each month. We interpret the formed factor (LCAPE-HCAPE) as the risk premium paid for CAPE rating or risk of relative distress. Because theory depicts that, on average, value stocks outperform growth stocks we expect a positive factor, this is formulated in the following hypothesis:
Hypothesis 2: Low CAPE- ranked portfolios are paired with positive gamma values, high CAPE- ranked portfolios are paired with negative gamma values
The model is tested by the following hypothesis:
𝐻0: 𝛼 = 0 and 𝐻1: 𝛼 ≠ 0 (E)
and
𝐻0: γ = 0 and 𝐻1: 𝛾 ≠ 0 (F)
35
7 Results Portfolio building
The summary statistics for the constructed portfolios and market for the period from April 1991 to April 2013 are presented in table 7 below. The mean CAPE ratio ranges from 5.58 (Portfolio 1) to 38.98 (Portfolio 5). Median values are slightly lower; 5.03 for portfolio 1 and 33.12 for portfolio 5. On average the one year forward return of portfolio 1 yields a negative 5.43% while the one year forward return for portfolio 5 yields 6 .9%. Going from portfolio 1 to portfolio 2, we see an increase in return with portfolio 2 yielding an 1.46% and subsequently portfolio 3 yielding 5.3%. Yet, this linear relationship between return and cape rating does not hold consistently as portfolio 4 yields an 7.61%, which is approximately 0.7% higher in comparison to portfolio 5. A first impression of related risk is provided by the portfolios volatility (measured by standard deviation); portfolio 1 has the highest volatility (0.3117) for yielding the lowest average return while portfolio 4 has the lowest volatility (0.2228) but the highest return (7.61%). Furthermore, portfolio 4 is the only portfolio which has a lower volatility in comparison to the market portfolio (0.2228 compared to 0.2293) even th ough the difference is minimal.
Table 7: Yearly summary statistics portfolios 1991 - 2013
The CAPE ratio is calculated as the stocks price of April 30th of the next year divided by the past 10 year of earnings data adjusted
for inflation. Avvg annual return refers to the (cc) yearly returns. „Avg Excess return‟ represents the average excess of returns over the risk free alternative (RF).
The risk free rate is denoted by RF, consisting of the 90 day forward short term interest rate. Volatility is measured by the standard deviation for all portfolios ranging from portfolio 1 consisting of the lowest CAPE ranked 20% of stocks until portfolio 5
consisting of the highest CAPE ranked 20% of stocks. Portfolios are rebalanced monthly. The difference between returns of portfolio 1 and 5 is denoted as „Premium‟.
Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5 Market Risk free
Mean CAPE ratio 5.5810 9.6250 13.8632 20.3083 38.9837 0.0363 Median CAPE ratio 5.0132 9.7864 12.9044 18.2144 33.1182
36
In order to gain further insight in the relationship between CAPE and returns, we consider table 7 in which the same analysis is performed for 5- year intervals. Table 7 presents the summary statistics over the period 1991 to 2013 for the constructed portfolios and market portfolio. For each portfolio, the returns are calculated if said portfolio was kept for 1 year (buy and hold strategy). Each portfolio yields 60 monthly observations per 5 year period except for the last period which only yields 24 monthly observations.
Table 7: Summary statistics portfolios 5 year intervals
The time periods provided in this table range from April 30th to April 30th of the next year. Return data for all portfolioa is
calculated as average one year forward (cc) return for the period. The risk free rate is denoted by RF, consisting of the 90 day forward short term interest rate. Volatility is measured by the standard deviation for all portfolios where Portfolio 1 is de noted as P1, Portfolio 2 as P2 until the market portfolio PM. Portfolios range from portfolio 1 consisting of the lowest CAPE ranked 20% of stocks until portfolio 5 consisting of the highest CAPE ranked 20% of stocks. Portfolios are rebalanced monthly. The difference
between returns of portfolio 1 and 5 is denoted as „Premium‟.
P1 P2 P3 P4 P5 PM RF Premium
1991-1996
Avg return 1yr forward 0.0624 0.0957 0.1529 0.1519 0.1929 0.1320 0.0671 -0.1305 Avg excess return -0.0047 0.0286 0.0859 0.0848 0.1258 0.0650
Volatility (S.D.) 0.2018 0.1839 0.1796 0.1397 0.1693 0.1561 0.0221
1996-2001
Avg return 1yr forward 0.0092 0.0283 -0.0036 0.0753 0.0330 0.0287 0.0351 -0.0238 Avg excess return -0.0259 -0.0067 -0.0387 0.0402 -0.0021 -0.0063
Volatility (S.D.) 0.1789 0.1519 0.2125 0.1546 0.2399 0.1678 0.0068
2001-2006
Avg return 1yr forward 0.0804 0.0726 0.0914 0.1069 0.0458 0.0791 0.0273 0.0346 Avg excess return 0.0530 0.0453 0.0641 0.0796 0.0184 0.0518
Volatility (S.D.) 0.2875 0.2854 0.2497 0.2413 0.2917 0.2562 0.0077
2006-2011
Avg return 1yr forward -0.3920 -0.1044 -0.0249 -0.0194 -0.0295 -0.1127 0.0273 -0.3625 Avg excess return -0.4193 -0.1317 -0.0522 -0.0467 -0.0568 -0.1400
Volatility (S.D.) 0.3110 0.3233 0.2776 0.3138 0.2573 0.2727 0.0166
2011-2013
Avg return 1yr forward 0.0010 -0.0671 0.0435 0.0511 0.1503 0.0362 0.0085 -0.1493 Avg excess return -0.0074 -0.0755 0.0351 0.0426 0.1419 0.0277
37
38
significant for the periods from 1991 to 2006 while the period from April 2006 to April 2011 was insignificant, yet only slight with a value of 0.0687.
A comparison is provided to investigate the relationship between low and high CAPE ranked stocks and subsequent stock returns. The monthly continuously compounded portfolio returns are considered for portfolio 1 and 5. Figure 3 plots the monthly returns of holding the low 20% of cape ranked stocks (Portfolio 1) versus the highest 20% of CAPE ranked stocks (Portfolio 5).
Source: Own investigation
Note: The vertical axis plots the monthly (cc) returns of portfolio 1 (lowest 20% of CAPE rated stocks) and portfolio 5 (high est
20% of CAPE rated stocks) Continuously compounded monthly returns are considered starting April 30th 1991 ranging to April
30th 2014. Both portfolios are rebalanced on a monthly basis at the last day of each month.
After plotting the monthly returns for both portfolios returns of portfolio 1 are shown to range from -42.26% to 17.33% while portfolio 5 yields returns in a range from -13.54% to 12.15%. Both portfolios yield the lowest returns (largest losses) in 2008 ; explainable through the „Credit Crunch‟ crisis which caused a worldwide decline in stocks markets. Table 8 presents the summary statistics related to figure 3.
-0,6 -0,4 -0,2 0 0,2 4 -30 -91 4 -30 -92 4 -30 -93 4 -30 -94 4 -30 -95 4 -30 -96 4 -30 -97 4 -30 -98 4 -30 -99 4 -30 -00 4 -30 -01 4 -30 -02 4 -30 -03 4 -30 -04 4 -30 -05 4 -30 -06 4 -30 -07 4 -30 -08 4 -30 -09 4 -30 -10 4 -30 -11 4 -30 -12 4 -30 -13
Figure 3: Monthly (cc) return plot portfolio 1 and portfolio 5
Portfolio 1 Portfolio 5
Credit Crunch crisis Bullish '90s
Internet bubble 'Bursting'
39
Table 8: Summary statistics monthly returns High versus Low CAPE rated portfolios
Averages are continuously compounded monthly returns ranging from April 30th 1991 to April 30th 2013 assuming a monthly rebalancing frequency. The return premium is calculated as the averaged difference
between the monthly return of portfolio 1 and 5. The „observation count‟ represents the number of monthly observations included while „Outperformance‟ counts the number of times the portfolio
outperformed its comparable (Portfolio 1 versus portfolio 5).
1991- 2013 Portfolio 1 Portfolio 5 CAPE Premium
Mean -0.0204 0.0171 -0.0375 Median -0.0122 0.0211 -0.0306 Standard Deviation 0.0720 0.0436 0.0574 Minimum -0.4226 -0.1354 -0.2872 Maximum 0.1733 0.1215 0.1151 Range 0.5959 0.2569 0.4023 Observation Count 276 276 276 Outperformance 61 215
Source: Own investigation
40
7.1 Results Regression (1)
To test whether a value premium is based on higher market risk, regression (1) is established via OLS and results are presented in table 7. CAPM theory depicts higher returns come from higher market risk (or beta). When moving from the portfolio of lowest CAPE ranked stocks (portfolio 1) to the portfolio of highest CAPE ranked stocks (portfolio 5) the beta value decreases consistently over all portfolios. This pattern is in line with the results documented in the study by Basu (1977), who finds that risk increases with decreasing P/E ratios.
Table 7: Summary statistics CAPM regression
Portfolio 1 represents a portfolio consisting of the lowest CAPE ranked 20% of stocks until portfolio 5 consisting of the highest CAPE ranked 20% of stocks. The beta coefficient represents the beta coefficient for exposure to the market risk.
The following regression is estimated:
1 𝑟𝑡 𝑝 − 𝑟𝑡 𝑓 = 𝛼 + 𝛽 ∙ 𝑟𝑡𝑚− 𝑟𝑡 𝑓 + 𝜀𝑡 𝑝
Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5 Market
Beta coefficient 1.3343 1.1019 0.8972 0.8634 0.8095 1.0000 T-statistic 2.8470 3.8597 3.4968 3.5793 2.8040 P-value 0.0000** 0.0000** 0.0000** 0.0000** 0.0000** Jensens Alpha -0.0234 -0.0026 0.0043 0.0070 0.0142 T-statistic 0.0000 0.0506 0.0004 0.0000 0.0000 P-value 0.0000** 0.0506 0.0004** 0.0000** 0.0000** R-Squared 0.7474 0.8446 0.8169 0.8238 0.7416 Adjusted 𝑅2 0.7464 0.8441 0.8163 0.8232 0.7406
*Significant at a 95% confidence interval **Significant at a 99% confidence interval
41
alpha is insignificant at a 95% confidence interval with a P- value of 0.0506 while alphas for portfolios 1, 3, 4 and 5 are highly significant.
The results imply that there is evidence of a relationship between returns and CAPE portfolios and lower ranked CAPE portfolios are paired with higher beta values. The CAPM however, is not able to perfectly explain the CAPE effect in the Dutch market since 4 out of 5 portfolios yield a significant alpha. Therefore, H0 of hypothesis (A) is rejected. If the CAPM were a perfect model in explaining differences in returns between the portfolios then all alpha values would be zero and generating alpha is not possible.
7.2 Results Regression (2)
Results from estimating the OLS estimate of regression (2) are presented in table 8.
Table 8: Summary statistics Fama French Three Factor model
Portfolio 1 represents a portfolio consisting of the lowest CAPE ranked 20% of stocks until portfolio 5 consisting of the hig hest CAPE ranked 20% of stocks. The beta coefficient represents the beta coefficient for exposure to the market risk. The return difference of small and large capitalization stocks is represented as „size‟ while the value premium ( High price to book minus
low) is represented as „Value‟.
The following regression is estimated by ordinary least squares (OLS):
(2) 𝑟𝑡 𝑝 − 𝑟𝑡 𝑓 = 𝛼 + 𝛽 ∙ 𝑟𝑡𝑚− 𝑟𝑡 𝑓 + β2 ∙ 𝑆𝑀𝐵 + 𝛽3∙ 𝐻𝑀𝐿 + 𝜀𝑡 𝑝
Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5 Market
42 *Significant at a 95% confidence interval
**Significant at a 99% confidence interval
Results how the R- squared for all portfolios hardly increases in comparison to the previously estimated CAPM regression. For example; portfolio 5 shows the largest increase in terms of R- squared from 0.7416 to 0.7444. We can conclude the overall fit of the model as indicated by R- squared hardly improves when adding the factors proposed by Fama & French (1992). This is confirmed by the coefficients of both the „Size‟ and „Value‟ factor being almost zero and insignificant at a 95% confidence interval as indicated by the corresponding P- values. This implies all coefficients are not significantly different from 0. When considering the alpha values of all portfolios we can observe that the inclusion of the factors had no observable effects as all alpha values approximately remain the same in comparison to the traditional CAPM regression. We should mention that for portfolio 2 the P- value of the alpha is slightly lower (0.0560 to 0.0439) rendering the observed alpha significant. Yet, in summary, we can conclude the Three Factor model as proposed by Fama & French holds no substantial additional explanatory power. The null hypothesis for hypothesis (B) can be rejected and we can conclude this model fails to „perfectly‟ explain returns of the CAPE portfolios. The null hypothesis for hypothesis (C) and (D) can not be rejected and we can conclude neither the „Size‟ nor the „Value‟ factor hold additional explanatory power in comparison to the CAPM.
7.3 Results Regression (3)
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at a 95% confidence interval, indicating the excess return (alpha) from the CAPM model can be explained by the included factor accounting for CAPE effects. Portfolio 5 yields a significant alpha (P- value of 0.0403) indicating there is still a portion of the returns that can not be perfectly explained after including the factor for CAPE effects. Yet, while a significant alpha still exists, the alpha value decreased from 0.0142 in the CAPM regression to 0.002 in the current Two Factor regression.
Table 9: Summary statistics OLS regression Two Factor model
Portfolio 1 represents a portfolio consisting of the lowest CAPE ranked 20% of stocks until portfolio 5 consisting of the hig hest CAPE ranked 20% of stocks. The Gamma represents the coefficient of the modified factor accounting for CAPE effect, calculated as the returns from the lowest CAPE ranked 40% of stocks minus the highest CAPE ranked 40% of stocks. The beta represents the
beta coefficient for exposure to the market risk,. The following regression is estimated:
3 𝑟𝑡 𝑝 − 𝑟𝑡 𝑓 = 𝛼 + 𝛽 ∙ 𝑟𝑡𝑚− 𝑟𝑡 𝑓 + 𝛾 ∙ 𝐿𝐶𝐴𝑃𝐸 − 𝐻𝐶𝐴𝑃𝐸 𝑡+ 𝜀𝑡 𝑝
Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5 Market
Beta 0.9983 1.0449 0.9523 0.9984 1.0044 1.0000 T-statistic 3.5775 3.3488 3.4117 4.9093 5.1488 P-value 0.0000** 0.0000** 0.0000** 0.0000** 0.0000** Gamma 0.7342 0.1245 -0.1204 -0.2949 -0.4261 T-statistic 2.6480 4.0172 -4.3411 -1.4595 -2.1984 P-value 0.0000** 0.0001** 0.0000** 0.0000** 0.0000** Jensens Alpha -0.0025 0.0009 0.0008 -0.0014 0.0020 T-statistic -1.7754 0.5961 0.5901 -1.4179 2.0603 P-value 0.0769 0.5516 0.5556 0.1573 0.0403* S.D. 0.0721 0.0560 0.0464 0.0444 0.0439 R-Squared 0.9292 0.8533 0.8288 0.9010 0.9067 Adjusted 𝑅2 0.9287 0.8522 0.8275 0.9003 0.9060
*Significant at a 95% confidence interval **Significant at a 99% confidence interval
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positive „alpha‟ opportunities still exist for the portfolio of high CAPE ranked stocks which can not be explained by this model. Hence, the 𝐻0 of hypothesis (E) can only be rejected for 4 out of the 5 portfolios. It should however be noted that for portfolio 5, the alpha would become insignificant at a 99% confidence interval.
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8 Conclusion
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earnings as the denominator of the P/E ratio in comparison to using earnings data from 8 years ago, one can argue in direct contradiction to the efficient market hypothesis that new price to earnings data is not immediately incorporated in stock prices as also concluded by Basu (1977).
To test whether positive (negative) excess return of the formed portfolios is due to higher risk, three different regression models were considered. The CAPM showed low CAPE ranked stocks indeed to yield more market risk compared to the high ranked portfolio moreover implying a negative relation between market risk and CAPE rating yet fails to capture all return differences as implied by the highly significant alphas. In an attempt to capture these opportunities for excess return the Fama & French Three Factor Model was employed adding factors accounting for excess return due to market capitalization and price to book value. Results however yielded insignificant and factors indicating these betas are not significantly different from zero. Therefore this model was no improvement in comparison to the CAPM. By adding a factor accounting for “CAPE effects” (or relative distress) to the CAPM, excess returns are captured; the alpha values for this Two Factor model are not statistically significant or close to zero , indicating excess return can hardly be generated . Therefore the main hypothesis that low CAPE ranked stocks outperformed high CAPE ranked stocks on a risk adjusted basis can be rejected if a factor accounting for relative distress is included. The values for the Adjusted R- squared show improvement in comparison to the other models considered, supporting our conclusion that the Two Factor model is superior to the other models in this thesis.
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8.1 Limitations and Further Research
