Revival of accounting data in stock selection.

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Revival of accounting data in stock selection.

By: Sander Bos1

MSc. Thesis Finance

University of Groningen Faculty of Economics and Business

MSc. Finance

Supervisor: Dr. Ing. N. Brunia Date: 08/06/2017

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Abstract

This thesis tests an accounting based valuation model called the residual income model and uses it as a stock selection tool for portfolio formation. The model is capable of detecting undervalued equity. This study finds that there is informational content in past accounting data that is not fully incorporated by market participants. Buying stocks for a long portfolio results in significant excess returns for a period of 45 years. Most of the excess returns are obtained in the first 15 years of the sample period. The portfolios use different investment horizons. The strategy exploits mean reversion for long investment horizons and profits from noise traders in short investment horizons. It challenges the concept of semi-strong form market efficiency. The strategy is mainly applicable for hedge funds, institutional investors and wealthy individuals. ___________________________________________________________________________

Keywords: Equity valuation, efficient markets, mean reversion, portfolio selection strategies. JEL-code: G1, G2.

Word count: 13,227 (incl. abstract).

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I. Introduction

The efficient market hypothesis as described by Fama (1970) provides three categories of market efficiency that indicate how market participants process information. Various caveats in market efficiency have been found through research. Some show that excess returns can be obtained from estimating covariances and correlations from past stock data, such as that of Elton et al. (2006) and Chan et al. (1999). Some studies show that investors display bounded rational behavior, such as Hong and Stein (1999) and Lakonishok et al. (1994). Other studies show that there is informational content in accounting data that is often underestimated by investors, such as Zhang et al. (2004), Ou and Penman (1989), Holthausen and Larcker (1992) and Abarbanell and Bushee (1998). Much of previous literature finds profitable strategies that focus on momentum, investor’s sentiment perception and mean reversion. Generally, it shows that investors do not value information similar to each other and tend to over- or underreact, as Dumas et al. (2009) state.

Chan et al. (1999), Fama and French (2000) and Ou and Sepe (2002) show that accounting data, such as book values of equity, earnings, and dividends contain (future) value for a firm’s stock price and returns. These are typical ingredients for firm valuation models but are used relatively sparse in the field of portfolio investment strategies. Aforementioned studies of Zhang et al. (2004), Ou and Penman (1989), Holthausen and Larcker (1992) and Abarbanell and Bushee (1998) use earnings per share and show the informational content in valuing earnings. These studies often incorporate analysts’ forecasted earnings to value a firm or estimate its stock price. Abarbanell and Bushee (1998) note that analysts often underuse information from fundamental signals when producing these forecasts. Incorporating future earnings from analysts might therefore result in biased estimates, as Das et al. (1998) show. Dechow et al. (1999) find analyst forecasts to be overly optimistic. The authors mention that analysts often have systematic forecasting errors that tend to underestimate mean reversion in stock prices. Ou and Sepe (2002) show the value relevance of current and past accounting data and explain that market participants rely on forecasts from analysts.

3 could therefore be a profitable investment strategy. One practical valuation model capable of estimating a firm’s theoretical value is derived from the dividend discount model. This is Ohlson’s (1995) residual income model (RIM). Ohlson (1995) expresses dividends in terms of book values and (abnormal) earnings such that one can derive the theoretical value of a firm. The benefit of Ohlson’s (1995) RIM is that it can be used on a finite stream of flows, resulting in a closed form valuation model. Some previous research involves Ohlson’s (1995) forward looking RIM and its parameters, such as that of Higgins (2011), Zhang (2000a) and Dechow et al. (1999). Ou and Sepe (2002), Burgstahler and Dichev (1997) and Collins et al. (1997) use a derivation of Ohlson’s (1995) RIM that is applied to past accounting data. These studies find that there is value relevance in current- and past book values and earnings.

The RIM has, to my best knowledge, not been used as a stock selection tool to test its theoretical share prices estimates for a portfolio investment strategy. Applying the RIM to estimate theoretical share prices from past accounting data of firms is an attempt to detect under- and overvalued equity. The total of firm estimations can then be used in a portfolio setting. This study thereby hopes to add to the body of literature in stock selection strategies using accounting data and fundamental valuation by asking the following research question:

“Is accounting data in the form of Ohlson’s (1995) residual income model suited as a stock selection strategy?”

Accounting data is deemed value relevant, thereby assumed to be already reflected in the share prices from an efficient market perspective. However, if investors tend to over- or underweight accounting data then an abstract approach towards firm valuation should detect deviations in theoretical firm values. This study tests the RIM’s valuation capabilities for S&P500 firms over an extensive period from 1962 until the end of 2015 using fiscal quarter end accounting data. The analysis requires estimation of theoretical share prices using data on book values of common equity per share, earnings per share and share prices.

4 French (2015) five factor model. This study applies portfolio rebalancing horizons of one quarter and 12 quarters in order to capture mean reversion effects and excess return differences for the different holding periods. The studies of Balvers et al. (2000) and Fama and French (2000) indicate that mean reversion is present around 2.5 to 3.5 years.

The results of this study show that there are positive excess return differences between the portfolios using longer rebalancing horizons compared to short term rebalancing horizons. The empirical analysis shows profitable effects of mean reversion that can be obtained via past accounting data. I find Ohlson’s (1995) RIM able to detect undervaluation in stocks. The stock selection tool exploits the concept of semi-strong market efficiency as discussed by Fama (1970). I show that long portfolios can earn significant positive excess returns in the order of 2.65% and 3.56% per quarter. The difference between 12 quarters and quarterly rebalancing results is an average 0.91% in additional excess returns throughout the sample period. These results are robust throughout the analysis and indicate that less frequent rebalancing earns excesses in returns from mean reversion. The time of mean reversion is about three years and in line with the results of Balvers et al. (2000).

Overvalued stocks are diverging further from the theoretical estimates. The findings support the view that market participants often extrapolate firm’s expectations too far into the future, similar to Lakonishok et al. (1994). Alternatively, market participants may as well process information differently, as Dumas et al. (2009) mentions. Penman (1998b) discusses that investor’s may use different metrics, such as simple price-over-earnings ratios, in order to estimate a firm’s share price. This may imply different valuation approaches between market participants. Investors tend to prefer forward looking information, which may under- or overstate future firm prospects.

This study has set a baseline approach for the use of the RIM in stock selection. The outcomes suggest that there is information in current- and past accounting data that is not completely reflected in the market. This research thereby extends the view of value relevance in accounting data for fundamental valuation and stock investment strategies.

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II. Literature review

This section discusses the concept of efficient markets and some of its caveats. The second subsection gives a background on asset pricing models. This is followed by an explanation of alpha, the excess return source of asset pricing models. This section will explain how previous research tempts to obtain excess returns through various stock selection strategies. The last subsection will motivate accounting data valuation models. For an overview of all abbreviations, please refer to appendix A.

II.1. Efficient markets

The efficient market hypothesis as discussed by Fama (1970) involves three categories of market efficiency, knowing: weak, semi-strong and strong form efficiency and describes how markets process information. The theory assumes that there is absence of transaction costs, all information is available to all market participants and all current information is reflected in the future price of each security. The weak form of market efficiency are tests whether past price information is reflected in current security prices. Semi-strong tests are tests whether all publicly available information is fully reflected in current security prices. Strong form efficiency are tests whether markets fully reflect public and private information. In an efficient market individuals can’t obtain excess returns since everyone has the same information, although there is a lot of mixed evidence, as Elton et al. (2014) mention.

The authors mention that firm characteristics such as book values, earnings and market values have been found to be related to excess returns. This is contrasting to market efficiency since it should not be possible to earn excess returns on observable firm characteristics. Even long run returns can have prediction value.

Weak form and semi-strong form efficiency are bound to have exploitational properties due to absence of private information. Fama and French (1993) have challenged these concepts with their three factor model results. This model is one of several asset pricing models that have shed light on risk and returns. The next subsection will discuss these.

II.2. Asset pricing models

6 standard deviation of the portfolio return. According to Markowitz (1952) an investor should be indifferent between a basket of stocks in a portfolio or an individual stock as long as the mean-variance relationship is the same.

Developments in portfolio theory resulted in the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965). They find that diversification of portfolios does matter in the mean-variance space. The interrelatedness between stock mean-variances consists out of market (systematic) and idiosyncratic (non-systematic) risk factors. Each investor can set up its optimal portfolio, consisting out of a combination of a riskless asset and risky assets, depending on one’s risk appetite. The approach resulted in a construct of market equilibrium theories of asset prices.

As time progressed more sophisticated models came into existence, such as the Arbitrage Pricing Theory (APT) model by Roll and Ross (1980). The authors explain that there are three to four factors that are common in expected stock returns. These factors are referred to as risk premia and are proportional to the variance or risk measure. One of APT’s predictions is that price-earnings ratios would have explanatory power for excess returns. Fama and French (1992 and 1993) formalized APT’s underpinnings with their papers on multi-factor models. The authors find specific factors able to explain excesses in returns such as book-to-market ratios (B/M), earning-price ratios (E/P), size, leverage and market proxies. Daniel and Titman (1997) show that the return premia on small firms and high B/M stocks are not observable since these show no co-movement with any factor. Their results point out high B/M stocks and low capitalization stocks have high average returns regardless of the covariance of other similar stocks. Daniel and Titman (1997) conclude that, after controlling for size and B/M ratios, the Fama and French (1993) model fails to explain returns from size and B/M ratios. The response to some of the critique on the Fama and French (1993) three factor model resulted in a new study by Fama and French (2015). In this study they develop a five-factor asset pricing model to explain returns, motivated by the dividend discount valuation model, albeit Fama and French (2016).

7 expected returns is determined by its price-to-book ratio and expectations of its future profitability and investment. The authors refer to size and momentum as variables not explicitly linked to the decomposition of cash flows. If these two variables do help in forecasting returns then the profitability and investment factors should capture the effects. In summary the five-factor model consists out of the following variables:

- An excess market factor, return market minus risk-free rate (𝑅𝑚− 𝑟𝑓), calculated as the return on the value weighted market portfolio minus the risk-free rate,

- A size factor, small-minus-big (SMB), calculated as the average three small stock portfolio returns minus the average three big stock portfolio returns,

- A value factor, high-minus-low (HML), calculated as the average of two high B/M portfolio returns minus average low B/M portfolio returns,

- A profitability factor, robust-minus-weak (RMW), calculated similarly as the HML factor but sorted on operating profitability,

- An investment factor, conservative-minus-aggressive (CMA), calculated similarly as the HML factor but sorted on investment.

The main improvement of the five-factor model is in capturing the dynamics on portfolios with strong tilts in profitability and investment. HML is regarded to be redundant but is said to be important to understand portfolio types, as Fama and French (2015) describe. Fama and French (2015) explicitly exclude momentum from Carhart’s (1997) four-factor model due to correlation issues with the other five variables. Fama and French (2016) explain that a momentum factor will slightly improve model performance but will leave small stock momentum returns unexplained. RMW and CMA are factors assumed to be accounting for size and net share issues according to Fama and French (2015). Thus far the Fama and French (2015) note that the five-factor model is a more comprehensive model in explaining excess returns.

II.3. Stock selection strategies and seeking alpha

8 however, increasingly difficult to obtain significant alpha. Lo (2016) mentions that advancements in technology and information processing of computers results in less mispricing of securities or quicker market corrections. The imitation of stock selection strategies of investors also causes successful strategies to die out fast.

There are, broadly speaking, three categories of stock selection strategies that sometimes overlap as hybrid strategies. One involves the exploitation of historical and/or statistical data, such as the case with factor pricing models. After the rise of the CAPM, firms started to use the model to estimate betas and assess the security and portfolio towards the market. It meant that the analysis for stock selection strategies involved estimating covariances and correlations, thus primarily statistical in nature as Elton and Gruber (1997) describe. When the multi-factor models were developed the focus shifted towards estimating sensitivity of securities towards economic factors. Largely, all previous literature works with exploiting historical data to forecast correlations and covariances, such as that of Elton et al. (2006). These are most often tests of weak market efficiency. Chan et al. (1999) show that, in estimating covariances, they can select an optimal variance portfolio that gains higher returns than equal weighted portfolios on NYSE and AMEX stock exchanges. They mention that the difficulty is to predict expected returns from historical data. Chan et al. (1999) mention that the future return covariance between two stocks is predictable from a firm’s market capitalization, market beta and B/M ratios.

9 The two previous categories often use relatively short investment horizons of days, weeks or months. The last category of stock selection strategies is involved with fundamental analysis and often uses a longer investment horizon. These selection strategies use accounting data to obtain estimates of the fundamental value of a firm. The strand in literature focusing on valuation models that use accounting data for stock selection is relatively brief.

Previous mentioned literature involves variables such as B/M and earnings persistence and serve as some bridge from accounting information, to valuation to stock performance.

Some valuation research weighs heavily towards earnings per share (EPS) as the response variable, such as those of Zhang et al. (2004), Ou and Penman (1989), and Holthausen and Larcker (1992). However, when examining the value of a firm, we opt to get an estimate in which EPS is often one element of the total puzzle. Ou and Sepe (2002) find the book value of common equity per share (BVPS) to be a complementary measure for firm valuation. Frankel and Lee (1998) find similar results when using both BVPS and EPS divided by the share price of firms. The authors also show that these variables contain predictive value for three year buy-and-hold returns. Fama and French (2000) show that both BVPS and EPS can be used in terms of a ratio to show that profitability is mean reverting. Mean reversion is the tendency of assets prices to return to a trend path, as Balvers et al. (2000) describe. The rate of mean reversion is found to be about 38% per year in the paper of Fama and French (2000) but even faster when profitability is below its mean.

Much of the previous literature has found a way of exploiting the efficient market hypothesis. Accounting data can be used to exploit weak and semi-strong efficient markets since past information is interpreted differently by market participant, as Dumas et al. (2009) describe. Accounting data can be used to make an estimate of the theoretical value of a firm. Earnings and book values of common equity are found to be summary measures for firm value. The next subsection discusses some equity valuation models that can give theoretical estimates of the equity of a firm.

II.4. Equity valuation models

10 Equation (1) is the DDM: 𝑃_𝑡 = ∑ (1 + 𝑟)−𝑘_{[𝐷𝑃𝑆} 𝑡+𝑘] ∞ 𝑘=1 (1) where,

𝑃_𝑡 = the price per share at time t.

𝑟 = the constant discount rate for all future dividends at time t.

𝐷𝑃𝑆_𝑡+𝑘 = the dividend per share at the end of time t for k periods ahead.

Second, we have the discounted cash flow model (DCF), which is similar to the DDM but replaces dividends with cash flows. Lastly, we have the residual income model (RIM). This model is built on book values and dividends. All three models work for going concerns and are based on forecasting an infinite stream of cash flows and dividends, as Penman (1998a) mentions. However, practically speaking we need a model that is able to base its judgement on a finite stream of cash flows and dividends for some time horizon. The RIM lends itself for this purpose.

Dividends can be expressed in terms of book values of common equity and earnings. Ohlson (1995) formalized such a derivation for the RIM, termed the “clean surplus relation” (CSR). This is algebraically expressed as:

𝐵𝑉𝑃𝑆𝑡 = 𝐵𝑉𝑃𝑆𝑡−1+ 𝐸𝑃𝑆𝑡− 𝐷𝑃𝑆𝑡

where,

𝐵𝑉𝑃𝑆_𝑡 = the book value of common equity per share at time t. 𝐸𝑃𝑆_𝑡 = comprehensive earnings per share at time t.

The assumption of equation (2) means that the CSR allows future dividends to be expressed in terms of earnings and book values. Future earnings are, according to Ohlson (1995), expressed in terms of abnormal earnings, which is defined as:

𝐸𝑃𝑆_𝑡𝑎 = 𝐸𝑃𝑆𝑡− 𝑟 ∙ 𝐵𝑉𝑃𝑆𝑡−1 (3)

where,

𝐸𝑃𝑆𝑡𝑎 = abnormal earnings per share at time t.

11 𝑃_𝑡 = 𝐵𝑉𝑃𝑆_𝑡+ ∑∞_𝑘=1(1 + 𝑟_𝑡)−𝑘𝐸_𝑡[𝐸𝑃𝑆_𝑡+𝑘𝑎 ] (4)

This means that the price per share can be expressed as the expectation of abnormal earnings discounted at one plus the appropriate discount rate plus the book value of common equity at time t. Another assumption of Ohlson (1995) is that abnormal earnings follow a stochastic process. This assumption requires abnormal earnings to follow an autoregressive process and cause long run future abnormal earnings to cease. This assumption is what makes the RIM a closed form equation. Ohlson (1995) shows that future abnormal earnings and “other information” deemed value relevant follow an autoregressive process as:

𝐸𝑃𝑆_𝑡+1𝑎 = 𝜔𝐸𝑃𝑆_𝑡𝑎_{+ 𝑣}

𝑡+ 𝜀1,𝑡+1 (5a)

𝑣_𝑡+1 = 𝛾𝑣_𝑡+ 𝜀_2,𝑡+1 (5b)

where,

𝑣𝑡= the other value relevant information not included in financial statements at time t. 𝜔 = the constant persistence parameter of residual income, lower than one and non-negative. 𝛾 = the constant persistence parameter of other information, lower than one and non-negative. 𝜀_𝑡 = the zero-mean disturbance term at time t.

The combination of equations (5a), (5b) and (4) yield the final valuation function:

𝑃_𝑡 = 𝐵𝑉𝑃𝑆_𝑡+ 𝛼₁𝐸𝑃𝑆_𝑡𝑎+ 𝛼₂𝑣_𝑡 (6) where,

𝛼₁ = 𝜔 (1 + 𝑟 − 𝜔)⁄

𝛼2 = (1 + 𝑟) [(1 + 𝑟 − 𝜔)⁄ (1 + 𝑟 − 𝛾)]

12 Dechow et al. (1999) mention that investors often overlook mean reversion in current earnings and rely too less on book value. Frankel and Lee (1998) come to similar conclusions. These studies and that of Ou and Sepe (2002) imply that there is value relevance in past- and current accounting data which is overlooked by investors. Ou and Sepe (2002) show that past accounting data can be used for the RIM to infer the share price of a firm. Adapted for panel data, the measure for the share price of a firm then becomes:

𝑃𝑖𝑡 = 𝛽0+ 𝛽1𝐵𝑉𝑃𝑆𝑖𝑡+ 𝛽2𝐸𝑃𝑆𝑖𝑡+ 𝜀𝑖𝑡 (7) where,

𝛽₀ = the intercept

𝜀_𝑖𝑡 = the zero-mean disturbance term of firm i at time t.

The Ohlson (1995) RIM is typically estimated as in equation (7) when used with past and current accounting data, as in studies of Burgstahler and Dichev (1997) and Collins et al. (1997). Both studies show the complementary effects of BVPS and EPS. BVPS captures most of the variation in the share price when EPS are low. In other times EPS will capture most variation in the share price when earnings are high. Both studies conclude that BVPS and EPS are value relevant determinants in explaining stock prices. Penman (1998b) describes book values as the balance sheet measure of net assets generating earnings. Earnings is the income of returns from these assets. Penman (1998b) mentions that future earnings will be the same as current earnings if one adopts the assumption of a random walk process. From this perspective, future earnings are related to current book values and earnings. Dechow et al. (1999) mention that investors seem to underweight information in current earnings and book values.

13 Considering all the previous literature, Ohlson’s (1995) RIM as specified in equation (7) is capable of estimating fundamental equity values using a finite time horizon of five to ten years of past accounting data. Burgstahler and Dichev (1997) and Collins et al. (1997) show that the RIM can explain share prices via two explanatory summary measures, BVPS and EPS. Investors often under- or overweight the value relevance of current- and past accounting data, as Dechow et al. (1999) mention. If there is value relevance in current- and past accounting data that is overlooked, misinterpreted or processed differently by investors, then current share prices should eventually revert back to the mean fundamental values. Dechow et al. (1999) mention that investors often underestimate mean reversion. Analyst forecasts are often too optimistic, biased, or market participants rely too much on these forecasts, as the studies of Dechow et al. (1999), Das et al. (1998) and Ou and Sepe (2002) point out.

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III. Research methods and data

This section discusses Ohlson’s (1995) RIM specification and the sample data required to estimate the theoretical share prices of firms. Following, I explain the criteria and formation of the portfolios and calculation of returns. Lastly, I will explain how the returns are evaluated via the Fama and French (2015) five factor model.

III.1. Ohlson (1995) RIM model specification and sample data

As mentioned in section II, Ou and Sepe (2002), Burgstahler and Dichev (1997) and Collins et al. (1997) typically estimate the Ohlson (1995) RIM as in equation (7). In order to estimate the RIM, I require data on quarterly fiscal end share prices, book values of common equity per share (BVPS) and earnings per share (EPS). Earlier studies of Burgstahler and Dichev (1997), Collins et al. (1997) and Penman (1998b) find BVPS and EPS both capable to capture share price variation. Both variables are inversely related and regarded as value relevant determinants, as Penman (1998b) notes.

This study decides to use the S&P 500 firms since these share similarities in terms of size (homogeneity), data coverage and the amount of firms included in the index. One of the implications of Fama and French (2015) was that small aggressively investing firms with low profitability would remain unexplained by the model. By using the 500 largest firms I assume to overcome this issue in measuring returns.

This study uses quarterly fiscal end share price data and accounting data to have more observations, reduced variance and to overcome scaling issues, as Higgins (2011) mentions. The required data is obtained from the Compustat database. The quarterly fiscal end share price series can be obtained from January 1962 and onwards. Therefore, I decide to use a sample period from January 1962 until December 2015. To determine the index composition of the S&P 500 at any time period I obtain a list of index constituents with ticker codes from Compustat. The list contains 1,666 unique firms over the period from 1962 until the end of 2015. This list includes firms that have been delisted, gone bankrupt, are merged or acquired or have been replaced due to index component changes based on market capitalization throughout time2_.

2 _{In case of the index component changes due to market capitalization, exiting stocks remain in the analysis and}

15 Table III.1. gives an overview of the variables obtained from the Compustat database.

Table III.1. Compustat variable description and calculation

Accounting data Abbreviation Compustat Var. Name Remark

Closing share price P PRCCQ Calculated as: PRCCQ/AJEXQ

Book value of common equity per share

BVPS Calculated as:

(CEQQ-PSTKQ)/(CSHOQ*AJEXQ) Common/ordinary equity total CEQQ Preferred stock (capital) total PSTKQ Common shares outstanding CSHOQ Earnings per share

(basic) excl. ordinary items

EPS EPSPXQ Calculated as: EPSPXQ/AJEXQ

Dividends per share ex-date

DPS DVPSXQ Variable is already corrected for

adjustments. Adjustment factor

(company) cumulative by ex-date

AFC AJEXQ Adjustment factor to correct

variables for stock splits and stock dividends.

Under remarks I give the exact calculation for the variables, where needed, in accordance with Compustat variable names. The adjustment factor (AFC) is used to correct variables for stocks splits and stock dividends3. The book value of common equity per share (BVPS) is the only variable computed from other variables. Dechow et al. (1999) mention that basic earnings per share excluding extraordinary items (EPS) are preferred because these exclude nonrecurring items.

The original sample, cleaned for any missing RIM variables and negative common equity values results in 141,850 firm-quarter records. The top- and bottom 3% of outliers for BVPS are erased and 1% top- and bottom outliers based on price-to-book ratios, which is common practice in the studies of Collins et al. (1997) and Dechow et al. (1999). The final sample consists of 130,495 firm-quarter observations represented by 1,456 firms. We still deal with a few outliers in the data, as table III.2. shows.

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Table III.2. Descriptive statistics entire sample period 1962-2015

Price close BVPS EPS P/B ratio P/E ratio

Mean 258.28 167.93 1.35 2.58 66.96 Median 17.00 8.51 0.25 1.89 52.62 Maximum 585,400.00 405,027.40 16,700.00 2,098.70 11,417.50 Minimum 0.01 -333.91 -129,900.00 -545.71 -13,884.50 Std. Dev. 7,821.32 5,388.33 557.38 7.49 258.90 Observations 130,420 130,420 130,420 130,420 129,394

Closing prices and BVPS are negatively skewed, while EPS is positively skewed. In figure III.1. I show the mean and median price-to-book (P/B) and price-to-earnings (P/E) ratios through time. The long term average P/E ratio is 15 according to Koller et al. (2015). Our sample shows that mean and median P/E ratios are rather high through time. The high values are mostly the result of firms with almost no earnings in a particular quarter but with high share prices.

Figure III.1. P/B and P/E ratio through time

After 1982 the P/E ratios show a gradual upward trend. The period from 1962 until 1970 has low observations in some years, therefore the median P/E ratio could not be calculated and the mean is a little erratic. The trend in P/B ratios through time is modestly increasing. The median P/B ratios mostly lie between one and three, while the mean values lie between one and approximately four, which are both in line with historical averages.

First, I test all sample data variables from equation (7) for stationarity. The results in appendix B table B.1. show that all three variables have non-stationary properties, which is typical for financial data. To overcome stationarity issues all variables are transformed by dividing them with the lagged book value of common equity per share, similar to Burgstahler and Dichev

0 50 100 150

1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014

P/E ratio through time

Mean P/E Median P/E 0 1 2 3 4 5 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013

P/B ratio through time

17 (1997). For brevity, I denote the transformed variables with an apostrophe making the final regression equation:

𝑃′_𝑖𝑡 = 𝛽₀+ 𝛽₁𝐵𝑉𝑃𝑆′_𝑖𝑡+ 𝛽₂𝐸𝑃𝑆′_𝑖𝑡+ 𝜀_𝑖𝑡 (8)

Table III.3. presents the descriptive statistics of the transformed variables. There is some loss in observations due to the lagged variable transformation. Most variables have similar mean and median values in general. There are a few remaining outliers that won’t affect the outcome. We deal with large amounts of firm-quarter observations and many regressions that encompass the effects. Also, the outliers have relatively proportional values for all three variables, thus the RIM can estimate these observations properly. The majority of variables are not too dispersed as the standard deviations show.

Table III.3. Descriptive statistics transformed variables

𝑃′𝑖𝑡 𝐵𝑉𝑃𝑆′𝑖𝑡 𝐸𝑃𝑆′𝑖𝑡 Mean 2.65 1.03 0.03 Median 1.93 1.02 0.04 Maximum 2,112.57 875.79 30.69 Minimum -578.06 -33.68 -188.15 Std. Dev. 7.84 2.49 0.57 Observations 124,851 124,851 124,851

As Koller et al. (2015) mention, the terminal/continuing value of a firm is often estimated between five to 10 years. There are no fixed guidelines for the optimum length to determine firm values. I choose eight years or 32 quarters of data to estimate the RIM coefficients. This is an often used horizon in Koller et al. (2015) and will lead to about 20,000 observations per regression window. The rolling window regression approach starts from 1962Q1 until 1969Q4. Each subsequent rolling window regression will move one quarter ahead (t + 1) until the end of the sample period. The total of rolling window regressions to be carried out is 185. If there are any missing variables remaining for the regression then Eviews will drop these observations, as mentioned in Brooks (2014).

18 model’s intercept is varying across time and firms. Some serial correlation is present, which will be corrected with White’s period robust standard errors.

The regression coefficient estimates are all pooled in each period’s rolling window estimate, meaning they are not firm specific. This attributes to the sample size per rolling window and will lead to an increase in the accuracy of the coefficient estimation, as mentioned in Brooks (2014). The downside is that the coefficient estimates are applied generally and thereby might not represent firm characteristics. The summary results on the RIM regression variables through time are found in appendix B table B.3.

III.2. Determining theoretical share prices and portfolios

I use the pooled estimates of the RIM coefficients to make estimates of the theoretical share price of each firm at the end of each rolling window:

𝑃̂′𝑖𝑡 = 𝛽̂0+ 𝛽̂1𝐵𝑉𝑃𝑆′𝑖𝑡+ 𝛽̂2𝐸𝑃𝑆′𝑖𝑡 (9)

This results in 185 quarterly estimates of theoretical share prices for all firms included in the regressions. Not all stocks will be eligible for the portfolios. In practice one would deal with bid-ask spreads, commissions and transaction costs. Therefore, a cut-off percentage will be used such that the theoretical estimates will sufficiently deviate from the actual share prices in its specific quarter. This is common practice applied in studies such as that of Ou and Penman (1989) and Holthausen and Larcker (1992). To overcome previous mentioned issues I opt for a cut-off percentage of 15%. Theoretical estimates of stock prices that are 15% or more above the actual share price at quarter t are deemed undervalued and adopted in the long portfolio. The contrary goes for stocks estimated to be 15% or more below the actual share price at quarter t. These are deemed overvalued and will be adopted in the short portfolio. The combination of both will form the hedge portfolio.

19 quarters for the portfolios to show excess return differences through time and to test for mean reversion4.

In reality the release of accounting data and the fiscal quarters itself may not coincide with calendar years. The total sample contains 101,252 firm-quarter observations (77,60% of the total sample) that do coincide with calendar years. To allow for differences in financial statement releases, as well as realism from estimation of the theoretical share prices, portfolio formation will to take up to a quarter ahead in time. Conversely, the first sequence of returns is obtained another quarter ahead to reflect the delay. This results in 183 quarters of remaining return data for the portfolios, starting from 1970Q2 and onwards.

For each stock I calculate logarithmic total returns, such that dividend distributions are incorporated. The data is obtained from Computstat. I use the following equation:

𝑅𝑖𝑡 = ln (

𝑃𝑖𝑡+𝐷𝑉𝑃𝑆𝑖𝑡

𝑃𝑖𝑡−1 ) (10)

where,

𝑅_𝑖𝑡 = the return on stock i at quarter t.

Each portfolio’s returns is calculated as:

𝑅𝑝_𝑡= ∑ ( 𝑅𝑖𝑡

𝑁𝑡−1)

𝑁

𝑖=1 (11)

where,

𝑅𝑝𝑡 = the return on the hedge/long/short portfolio at quarter t. 𝑅_𝑖𝑡 = the total return of stock i at quarter t.

𝑁_𝑡−1= the number of stocks in the hedge/long/short portfolio, determined in quarter t-1.

III.3. Evaluating returns – five factor model

To properly evaluate the returns, it is required to calculate these in terms of excess returns. This means that I subtract the risk-free rate from the portfolio returns as follows:

𝐸𝑅𝑝𝑡 = 𝑅𝑝𝑡− 𝑟𝑓 (12)

4 _{For completeness, I show summary statistics in appendix F and G for portfolios using 2, 4 and 8 quarters of}

20 The difference between the long and short excess portfolio returns are the hedge portfolio excess returns. The interpretation is as follows, one shorts a portfolio of stocks, thereby receives an amount of cash from the sale. This cash amount can either be deposited in a bank account, receiving approximately the risk-free rate, or the proceeds can be used to purchase a portfolio of stocks. The last option results in a cancellation of the risk-free rate since we give up the right to deposit the proceeds of the sale in a bank account5.

After calculating the excess returns for the various portfolios I evaluate the excess return series via the Fama and French (2015) five factor model. I obtain the quarterly benchmark factors for the five factor model from the public library of Kenneth French6 including risk-free rates to evaluate the excess portfolio returns.

The Fama and French (2015) five factor model is specified as:

𝐸𝑅𝑝_𝑡 = 𝛼₀+ 𝛽₁(𝑀𝑘𝑡[𝑟]_𝑡− 𝑟𝑓_𝑡) + 𝛽₂𝑆𝑀𝐵_𝑡+ 𝛽₃𝐻𝑀𝐿_𝑡+ 𝛽₄𝑅𝑀𝑊_𝑡+ 𝛽₅𝐶𝑀𝐴_𝑡+ 𝜖_𝑡 (13) Where,

𝛼0 = alpha or intercept depicting the unexplained excess returns. 𝑀𝑘𝑡[𝑟]_𝑡− 𝑟𝑓_𝑡 = the excess return on the market index at quarter t. 𝑆𝑀𝐵_𝑡 = small minus big factor at quarter t.

𝐻𝑀𝐿𝑡 = high minus low factor at quarter t. 𝑅𝑀𝑊_𝑡 = robust minus weak factor at quarter t.

𝐶𝑀𝐴_𝑡= conservative minus aggressive factor at quarter t. 𝜖𝑡= the error term at quarter t.

Testing for significance of the excess returns requires that we overcome issues with autocorrelation and heteroscedasticity. This is done using Newey-West robust standard errors. The excess returns might be higher in some time periods. Due to the extensive period of evaluating returns (183 quarters) I will examine the data for break points via a Quant-Andrews and multiple breakpoint test. The Quandt-Andrews break point test can detect unknown explosiveness and is an improvement to the Chow break point test, as Brooks (2014) mentions. This tests whether potential explosiveness in returns is related to specific periods in time. If this proves to be true, I will carry out additional analysis by breaking up the returns series and evaluate the excess portfolio returns again for subperiods over the sample.

5 _{Vanguard provides some intuition on the subject of hedge strategies and the risk-free rate: https://vanguard.com/}

21

IV. Results

The results presented below in table IV.1. show the excess returns over the entire sample period from 1970Q2 until 2015Q4. I divided the results into quarterly and 12 quarter rebalancing horizons for which the returns are measured with the Fama and French (2015) five factor model. The hedge, long and short regression results are given for each rebalancing frequency.

The main finding from the table below is the concept of mean reversion. All portfolio types show improved excess returns when 12 quarters of rebalancing are used, all significant on the 1% level. The data shows that stocks revert back to their mean approximately every three years, which is in line with the results of Balvers et al. (2000) and Frankel and Lee (1998). The long portfolios are able to earn positive excess returns regardless of the rebalancing frequency. This means that Ohlson’s (1995) RIM is capable to detect undervaluation in stocks and can be used to exploit the concept of semi-strong market efficiency, as discussed by Fama (1970), using public accounting data.

Table IV.1. Fama-French 5 factor regression on excess portfolio returns with 15% cut-off

Rebalance per: Quarter 12 quarters

Portfolio: Hedge Long Short Hedge Long Short

Coefficient Excess return 0.028 2.646*** -2.618*** 1.600*** 3.564*** -1.964*** [0.400] [0.611] [0.521] [0.526] [0.747] [0.488] Rm - rf -0.034 0.685*** -0.719*** -0.125** 0.594*** -0.719*** [0.062] [0.051] [0.063] [0.055] [0.050] [0.050] SMB 0.053 0.198** -0.145* 0.049 0.120 -0.072 [0.058] [0.080] [0.076] [0.089] [0.097] [0.080] HML 0.168*** 0.312*** -0.144** 0.095* 0.282*** -0.187*** [0.063] [0.073] [0.052] [0.051] [0.067] [0.055] CMA 0.250 -0.041 0.291 0.549** 0.041 0.507** [0.350] [0.279] [0.232] [0.260] [0.282] [0.214] RMW 0.484** 0.201 0.283 0.086 0.085 0.001 [0.210] [0.189] [0.244] [0.172] [0.197] [0.209] Observations: 183 183 183 183 183 183 Adj. R2 0.131 0.682 0.759 0.105 0.548 0.771 F-statistic: 6.483*** 79.127*** 115.740*** 5.290*** 45.085*** 123.295*** ***, **, and * represents a significance level on the 1%, 5% and 10%, respectively.

22 The excess returns on the long portfolio using 12 quarters of rebalancing are 3.56% per quarter on average, which is significant on the 1% level. The quarterly rebalancing long portfolio obtains 2.65% in excess returns per quarter, also significant on the 1% level. It means that less frequent rebalancing results in a quarterly difference in excess returns of 0.91%.

The short portfolio shows less negative excess returns when 12 quarter rebalancing is applied. It obtains -1.94% on average per quarter while the quarterly rebalancing short portfolio obtains negative excess returns of -2.62% per quarter. Both excess returns are significant on the 1% level. The results of both the long and short portfolios show that 12 quarters of rebalancing leads to the best outcome in terms of excess returns.

I observe positive HML factor premia of 0.31% and 0.28% per quarter for the long portfolios using quarterly and 12 quarters of rebalancing, respectively. Both are significant on the 1% level. It shows that the selection strategy selects undervalued stocks with high book-to-market (B/M) ratios, which are value stocks said to have poor prospects according to Fama and French (1992).

The short portfolios have negative significant excess returns through time. The main finding from these portfolios is that Ohlson’s (1995) RIM is not successful in detecting overvalued equity. The significant negative loadings on HML of -0.14% and -0.19% for the short portfolios using quarterly and 12 quarters rebalancing, respectively, shows that growth stocks are shorted. These are stocks with low B/M ratios. The negative excess returns on both short portfolios show that shorting growth stocks is a bad strategy. Growth stocks diverge further from their fundamental values on either rebalancing horizon. We do observe mean reversion since the excess returns of the 12 quarter rebalancing horizon are less negative.

23

Figure IV. Cumulative excess returns portfolios with different rebalancing horizons and 15% stock deviation cut-off

-1 0 1 2 3 4 70Q 1 71 Q 4 73Q 3 75Q 2 77Q 1 78Q 4 80Q 3 82Q 2 84Q 1 85Q 4 87Q 3 89Q 2 91Q 1 92Q 4 94Q 3 96Q 2 98Q 1 99Q 4 01 Q 3 03Q 2 05Q 1 06Q 4 08Q 3 10Q 2 12Q 1 13Q 4 15Q 3 Cum. exc. re tu rn s Time period

Cumulative hedge portfolio returns 15% cut-off

Hedge Quarterly Rebalancing Hedge 12 Quarters Rebalancing S&P500 total excess returns

-2 0 2 4 6 8 10 70Q 2 72 Q 2 74Q 2 76Q 2 78Q 2 80Q 2 82Q 2 84Q 2 86Q 2 88Q 2 90Q 2 92Q 2 94Q 2 96Q 2 98Q 2 00Q 2 02Q 2 04Q 2 06 Q 2 08Q 2 10Q 2 12Q 2 14Q 2 Cum. exc. re tu rn s Time period

Cumulative long portfolio returns 15% cut-off

Long Quarterly Rebalancing Long 12 Quarters Rebalancing S&P500 total excess returns

-10 -5 0 5 70Q 1 72Q 1 74Q 1 76Q 1 78Q 1 80Q 1 82Q 1 84Q 1 86Q 1 88Q 1 90Q 1 92Q 1 94Q 1 96Q 1 98Q 1 00Q 1 02Q 1 04Q 1 06Q 1 08Q 1 10Q 1 12Q 1 14Q 1 Cum. exc. re tu rn s Time period

Cumulative short portfolio returns 15% cut-off

24 The above shows that one dollar invested in the hedge portfolio using 12 quarter of rebalancing in 1970Q2 would amount 3.11 dollars in 2015Q4. Similarly, the terminal value of the long portfolio would be 9.02 dollars in 2015Q4 if someone invested one dollar at the start of the sample. An investment in the short portfolio with 12 quarters of rebalancing would have resulted in a loss of 5.90 dollars. The quarterly rebalancing portfolios perform less than the 12 quarter rebalancing counterparts. It is also observable that most portfolios ramp up the positive and negative excess returns in the first 15 years of the sample. For example, the hedge portfolio using 12 quarters of rebalancing obtains almost twice its investment around 1974Q3. The long portfolios show the strongest increase in cumulative returns in the period from 1970Q2 until approximately 1983Q1. The short portfolios show the steepest cumulative decline in value until approximately 1986Q1.

This may imply that the effects of the Ohlson (1995) RIM stock selection strategy are not as strong in all time periods. The Quant-Andrews breakpoint test and multiple breakpoint test in table IV.2. suggest that some time periods are considered to be explosive in excess returns.

Table IV.2. Estimating data break points portfolios with 15% cut-off Break point method: Quant-Andrews Global Information Criteria Portfolio and rebalancing Break point date Break point date

Hedge portfolio 12 quarters 1977Q2*** 1977Q1 Hedge portfolio quarterly 1980Q3*** 1980Q3 Long portfolio 12 quarters 1983Q3*** 1983Q3 Long portfolio quarterly 1984Q1*** 1984Q1 Short portfolio 12 quarters 1986Q4*** 1986Q4 Short portfolio quarterly 1986Q3*** 1986Q3

*** represents significance on the 1% level. Global information criteria is based on multiple breakpoint tests using the Schwarz and LWC criterion.

The breakpoint dates in the table do approximately correspond to the periods where most of the gains and losses were realized by the different portfolios. I divide each portfolio’s excess return series in two time periods corresponding to the results in table IV.2. and report the Fama and French (2015) regression results in Table IV.3. Panel A shows the quarterly rebalancing portfolios and panel B shows the results of the portfolios using 12 quarters of rebalancing. Each portfolio regression is divided into two subperiods for ease of comparison. I will focus the remainder of the analysis on the long and hedge portfolio results since these prove most economically meaningful.

25

Table IV.3. Fama-French 5 factor regression on excess portfolio returns with 15% cut-off with varying period break points

Panel A

Rebalance

per: Quarter

Portfolio: Hedge Hedge Long Long Short Short

Period from: Until: 1970Q2 1980Q3 1980Q4 2015Q4 1970Q2 1984Q1 1984Q2 2015Q4 1970Q2 1986Q3 1986Q4 2015Q4 Coefficient Excess return 0.682 0.021 7.678*** 1.201*** -6.372*** -0.827** [0.719] [0.352] [0.798] [0.278] [0.335] [0.377] Rm - rf 0.022 -0.103* 0.607*** 0.641*** -0.604*** -0.790*** [0.089] [0.058] [0.071] [0.040] [0.050] [0.063] SMB -0.172 0.117* 0.182 0.076 -0.288*** 0.013 [0.113] [0.067] [0.116] [0.072] [0.071] [0.070] HML -0.041 0.212*** -0.014 0.321*** 0.109 -0.182*** [0.160] [0.067] [0.123] [0.058] [0.075] [0.036] CMA -0.563 0.749*** -0.754 0.100 0.781* 0.401** [1.077] [0.268] [0.790] [0.258] [0.460] [0.159] RMW 1.489 0.168 0.394 0.179* 1.147** 0.078 [1.052] [0.149] [0.637] [0.100] [0.468] [0.139] Observations: 42 141 56 127 66 117 Adj. R2 0.040 0.338 0.720 0.817 0.866 0.853 F-statistic: 1.339 15.311*** 29.299*** 113.682*** 84.83*** 135.598*** ***, **, and * represents a significance level on the 1%, 5% and 10%, respectively. Standard errors in parentheses. All standard errors are calculated using Newey-West robust standard errors

to mitigate for autocorrelation and heteroscedasticity. Break point estimates determined via Quant-Andrews and Multiple Global Information Criteria breakpoint tests.

As becomes apparent, the hedge portfolio using quarterly rebalancing still has insignificant excess returns. It confirms our earlier finding that a long and short strategy with quarterly rebalancing is not optimal. The long portfolio using quarterly rebalancing shows high excess returns of 7.68% per quarter, significant on the 1% level in the first period from 1970Q2 until 1984Q1. In the second subperiod the average quarterly excess returns are 1.20%, significant on the 1% level. This is substantially lower compared to the first subperiod and provides intuition of the excess returns over the total sample period.

26 The hedge portfolio using 12 quarters of rebalancing is significant over the first subperiod with excess returns of 6.34% per quarter on average. In the second subperiod the average excess returns of the hedge portfolio remain significantly positive but the returns are now 0.76% per quarter. The break point dates of the long portfolios using different rebalancing horizons are reasonably comparable. The difference in excess returns between the two rebalancing methods is most notable in the first subperiod, 2.26% on average per quarter (9.94%-7.68%). In the second subperiod the long portfolios with different rebalancing horizons have almost identical excess returns.

Panel B

Rebalance

per: 12 quarters

Portfolio: Hedge Hedge Long Long Short Short

Period from: Until 1970Q2 1977Q2 1977Q3 2015Q4 1970Q2 1983Q3 1983Q4 2015Q4 1970Q2 1986Q4 1987Q1 2015Q4 Coefficient Excess return 6.338*** 0.763** 9.935*** 1.194*** -5.211*** -0.356 [1.984] [0.306] [1.114] [0.256] [0.508] [0.336] Rm - rf -0.280 -0.102** 0.539*** 0.641*** -0.666*** -0.746*** [0.188] [0.048] [0.095] [0.033] [0.064] [0.046] SMB -0.147 0.140** -0.082 0.076 -0.154* 0.042 [0.229] [0.067] [0.136] [0.055] [0.080] [0.077] HML -0.033 0.083 -0.025 0.318*** 0.050 -0.230*** [0.164] [0.055] [0.098] [0.038] [0.077] [0.042] CMA -0.320 0.539** -0.589 0.117 0.686* 0.522*** [1.626] [0.256] [0.821] [0.217] [0.347] [0.174] RMW 1.521 0.092 0.913 0.174 0.394 -0.096 [1.565] [0.130] [0.779] [0.134] [0.493] [0.131] Observations: 29 154 54 129 67 116 Adj. R2 0.108 0.158 0.606 0.817 0.858 0.855 F-statistic: 1.677 6.737*** 17.32*** 114.932*** 80.518*** 136.952*** ***, **, and * represents a significance level on the 1%, 5% and 10%, respectively. Standard errors in parentheses. All standard errors are calculated using Newey-West robust standard errors

to mitigate for autocorrelation and heteroscedasticity. Break point estimates determined via Quant-Andrews and Multiple Global Information Criteria breakpoint tests.

27 Spierdijk et al. (2012) mention the possibility that economic erratic times could cause stock prices to be below their fundamental values and that they tend to overreact during recovery, causing large price swings in relatively short time intervals. The period before 1983 has known a few shocks because of increasing oil prices and interest rates. Spierdijk et al. (2012) show that between 1983 and 2009 there is almost no mean reversion in stock prices. This could explain why the long portfolios with differing rebalancing horizons in this study show both signs of relatively equal excess returns of 1.20% after 1983 and 1984 until the end of 2015. It might also be caused by irrational behavior such as overreactions to news in periods of economic uncertainty, as the studies of De Bondt and Thaler (1985 and 1987) show.

IV.1. Robustness check

Did the results show that one can exploit mean reversion and thereby show a caveat in market efficiency or was the strategy mere luck? One way of checking whether Ohlson’s (1995) RIM really is capable of detecting undervaluation is by increasing the cut-off percentage for stock selection. If the excess returns improve then this means that the model is able to detect discrepancies in stock valuation. As a robustness check I decide to use cut-off percentages of 20% and 25% to form hedge, long and short portfolios (for completeness).

Table IV.4. reports the results of the 20% cut-off portfolios with different rebalancing horizons. Compared to table IV.1., it can be seen that the long portfolio using quarterly rebalancing does mildly better with average quarterly excess returns of 2.66% (was 2.65%), significant on the 1% level. The result of the long portfolio using 12 quarters of rebalancing also improve. The excess returns are 3.71% (was 3.56%) per quarter on average, which is significant on the 1% level.

The short portfolios show larger negative significant excess returns compared to the 15% cut-off. The effect on the hedge portfolio using 12 quarters of rebalancing is a mild improvement in average quarterly excess returns of 1.70% (was 1.60%), significant on the 1% level. It shows that the RIM stock selection strategy does improve for undervalued equity but performs even worse for the estimated overvalued stocks.

28 rebalancing long portfolio shows similar increasing return effects. The difference in rebalancing leads to an average of 1.04% in excess returns per quarter. The results are again in favor of mean reversion.

Table IV.4. Fama-French 5 factor regression on excess portfolio returns with 20% cut-off

Rebalance per: Quarter 12 quarters

Portfolio: Hedge Long Short Hedge Long Short

Coefficient Excess return -0.083 2.661*** -2.744*** 1.695*** 3.705*** -2.010*** [0.416] [0.634] [0.538] [0.511] [0.783] [0.527] Rm - rf -0.053 0.680*** -0.733*** -0.146** 0.585*** -0.731*** [0.072] [0.054] [0.068] [0.059] [0.050] [0.054] SMB 0.034 0.202** -0.168** 0.072 0.119 -0.047 [0.067] [0.081] [0.080] [0.095] [0.101] [0.087] HML 0.177*** 0.316*** -0.139*** 0.107* 0.282*** -0.175*** [0.065] [0.073] [0.055] [0.058] [0.067] [0.055] CMA 0.283 -0.068 0.351 0.577** 0.049 0.528** [0.425] [0.299] [0.273] [0.256] [0.287] [0.217] RMW 0.532** 0.209 0.323 0.048 0.068 -0.020 [0.242] [0.199] [0.263] [0.163] [0.199] [0.209] Observations: 183 183 183 183 183 183 Adj. R2 0.125 0.656 0.724 0.122 0.521 0.735 F-statistic: 6.179*** 70.449*** 96.562*** 6.059*** 40.520*** 102.105*** ***, **, and * represents a significance level on the 1%, 5% and 10%, respectively.

Standard errors in parentheses. All standard errors are calculated using Newey-West robust standard errors to mitigate for autocorrelation and heteroscedasticity.

29

Table IV.5. Fama-French 5 factor regression on excess portfolio returns with 25% cut-off

Rebalance per: Quarter 12 quarters

Portfolio: Hedge Long Short Hedge Long Short

Coefficient Excess return 0.138 2.712*** -2.575*** 1.991*** 3.791*** -1.800*** [0.489] [0.671] [0.534] [0.578] [0.782] [0.489] Rm - rf -0.074 0.674*** -0.748*** -0.172*** 0.578*** -0.749*** [0.081] [0.057] [0.073] [0.059] [0.050] [0.055] SMB 0.053 0.207** -0.154* 0.040 0.125 -0.085 [0.080] [0.089] [0.083] [0.094] [0.102] [0.089] HML 0.173*** 0.316*** -0.143** 0.117** 0.283*** -0.166*** [0.070] [0.075] [0.056] [0.056] [0.066] [0.053] CMA 0.359 -0.072 0.431 0.668*** 0.079 0.588*** [0.493] [0.341] [0.283] [0.256] [0.287] [0.225] RMW 0.553** 0.192 0.361 0.011 0.037 -0.026 [0.267] [0.220] [0.261] [0.180] [0.189] [0.216] Observations: 183 183 183 183 183 183 Adj. R2 0.098 0.627 0.709 0.131 0.514 0.738 F-statistic: 4.977*** 62.234*** 89.770*** 6.493*** 39.559*** 103.597*** ***, **, and * represents a significance level on the 1%, 5% and 10%, respectively.

Standard errors in parentheses. All standard errors are calculated using Newey-West robust standard errors to mitigate for autocorrelation and heteroscedasticity.

IV.2. Result interpretation and applicability

I find Ohlson’s (1995) RIM to be a stock selection tool able to detect undervalued equity. Forming long portfolios and applying 12 quarters of rebalancing results in exploitation of mean reversion and earns significantly high excess returns. The significance of the portfolios that use 12 quarters of rebalancing provides an answer that significant excess returns are mostly attributable to mean reversion. The time to mean reversion in this study is similar to that of Balvers et al. (2000). The RIM is able to exploit semi-strong market efficiency assumptions, since past accounting data is readily available to the public. Most of the excess returns of the portfolios are obtained from 1970 until approximately 1985.

30 there is value relevance in past accounting data that is not fully reflected by market participants, possibly due to the overweighting of future firm prospects or different valuation approaches.

Lakonishok et al. (1994) find that value stocks up to April 1990 outperform growth stocks and question how such an anomaly could be exploited for such an extensive period. One explanation is extrapolation bias. This could be an explanation why our results of investing in high B/M firms is profitable for a long time period. Investors tend to extrapolate past performance too far into the future. This explanation seems plausible together with aforementioned overweighting of future prospects, causing further divergence for growth stocks and unacknowledged potential for value stocks. Another explanation of Lakonishok et al. (1994) is that systematic risks are more prevalent in value stocks. The regression results do not confirm this explanation if we interpret the systematic risk to be presented by the excess market returns beta. The market factor loadings on the long (value investing) portfolios are lower than the negative market factor loadings in the short (growth divesting) portfolios. Thus, in terms of absolute value, the response of growth stocks to the market exceeds that of value stocks. Although, one can question this interpretation of systematic risk.

Noise traders may be a possible cause as Spierdijk et al. (2012) mention. Poterba and Summers (1988) also reason that noise traders are a cause, as they find long term investment horizons to pay off. It is however arguable on what time horizon noise traders act and influence short term returns. Generally, it is said that noise traders have investment horizons of one- to three months. The results show that we can obtain significant excess returns on a quarterly basis, which is a relatively short time horizon. It may therefore imply that the selection tool exploits noise trader’s behavior on the short term and profits on the long term horizon from mean reversion. Irrational responses to news may also be a reason for exploitation of mean reversion, as De Bondt and Thaler mention (1985 and 1987).

31 uses 12 quarters of rebalancing. Abarbanell and Bushee (1998) describe that netting of portfolios requires a single trade to redecide on optimal portfolio weights. They estimate average trading costs to range between two and four percent annually if one involves commissions and bid-ask spreads. In this case, the long portfolios with various rebalancing horizons will still earn excess returns above transaction costs. Applying higher cut-off rates also increases the excess returns and decreases the amount of stocks per portfolio. However, I only tested portfolio performance up to 25% minimum cut-off rates.

I use equal stock weights to form all portfolios and calculate equal weighted excess returns. Poterba and Summers (1988) find that equal weighted excess returns are more pronounced to display mean reversion effects than value-weighted returns, specifically with long time horizons. They explain that equal weighting might result in larger return swings due to the weighted presence of less heavily traded stocks (illiquidity). Stocks might have larger relative swings in relation to fundamental stock values. They eventually discard their suggestion due to lack of evidence. I don’t find illiquidity premia plausible since we deal with (mostly) S&P500 firms.

In terms of risk, the long portfolios load positively on the HML factor and the short portfolios load negatively. According to Fama and French (1996) positive loading on HML might imply distress risk thus therefore earning risk premia for riskier stocks. The authors mention that these stocks have low P/E ratios, high B/M ratios and low sales growth. The contrary goes for the short portfolios. Fama and French (1996) also argue that positive HML slopes imply long term loser stocks with low short-term past returns. The HML factor predicts reversal of future returns. Risk, measured by the standard deviation in returns, of the long portfolios vary between 7.42% and 8.20% as shown in appendix C. The S&P 500’s standard deviation over the same sample period is 8.39% (not reported). The portfolios show less volatile than the index, and also show less co-movement in terms of market beta, reported in previous tables.

32 and come to an average excess return of 2.23% per quarter over their sample of 1871 to 1985. Abarbanell and Bushee (1998) obtain abnormal returns in accounting-based signals. They obtain size adjusted portfolio returns of 3.30% per quarter. The long portfolios in this study obtain significant excess returns between those of earlier research. The difficulty is comparing returns between studies since all studies use different methods and strategies of forming and measuring portfolios and returns. I show that accounting data can be used relatively simple to make fundamental estimates of intrinsic share prices. In terms of effort and return, the strategy possibly fits nicely as an average investment strategy. The downside of the strategy is the time it takes to form a portfolio after the release of financial statements. From estimation of theoretical share prices to portfolio formation takes up a quarter. To contrast the method, the nature of accounting data allows only for quarterly revision of the portfolios and weights due to the data releases.

Other studies, such as that of Jegadeesh and Titman (1993), found positive returns on shorter term portfolio horizons by buying past winners and selling losers. This approach only needs 12 months of previous returns (using a relative strength approach). For a holding period of one quarter, their hedge portfolios earn up to 3.93% per quarter. Their strategy also works around earnings announcement dates, but fails on longer rebalancing horizons. In that sense their strategy complements the one used in this study on the short term horizon of one quarter. It is however difficult to interpret whether their strategy will still work nowadays. The combination of the strategy in this study and possibly that of Jegadeesh and Titman (1993) may provide an investment framework that results in a top-tier strategy.

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V. Conclusion

The central question is whether the revival of accounting data in the form of the Ohlson (1995) RIM works as a stock selection tool for profitable portfolio strategies. I find the RIM able to detect undervalued equity from which one can form profitable long portfolios. The results indicate effects of mean reversion by comparing different rebalancing horizons and excess return premia. The excess returns are the highest from 1970 until approximately 1985. A possible explanation for these high returns are various economic shocks, as Spierdijk et al. (2012) explain. Market participants supposedly over- and underreact during erratic time periods, resulting in larger stock price swings. The excess returns in the period after 1985 are still significant but less than before 1985. Spierdijk et al. (2012) find similar results in excess returns from mean reversion. The time to mean reversion in this study is 12 quarters and in line with Balvers et al. (2000). The results violate the concept of semi-strong form market efficiency, as described by Fama (1970). By using past accounting data, all available to the public, the strategy earns excess returns for a period of 45 years.

The analysis started with estimating theoretical share prices using Ohlson´s (1995) RIM over the total sample period by using quarterly accounting data. The RIM variables are quarterly share prices, book values of common equity per share and earnings per share. Share price estimates are made from rolling window coefficient estimates based on 32 quarters of accounting data per rolling window. These coefficients are obtained from 1,456 firms and 216 quarters of data over a period from 1962Q1 until 2015Q4. At the end of each rolling window an estimate of the theoretical share price is made using pooled coefficients. This leads to 185 quarters of theoretical share price estimates for all firms through time. Next, I calculate the deviation of the estimated share price with the actual share price for each firm in each quarter. If a stock´s theoretical estimate deviates 15% or more in absolute value, compared to the actual share price, then I adopt it in a long (undervalued) or short (overvalued) portfolio. The combination of both long- and short positions form the hedge portfolios. All portfolios are based on equal weighting of stocks, resulting in equal weighted returns. The excess returns are then evaluated via the Fama and French (2015) five factor model.

34 RIM is persistent in its estimates I increase the minimum deviation percentages to 20% and 25%. The increase in deviation rates results in higher significant excess returns of the portfolios.

The excess returns still show signs of a profitable long portfolio strategy when one accounts for transaction costs in the order of 2% to 4%, which is a range that Abarbanell and Bushee (1998) adopt. The average excess returns from the long portfolios are in the mid-range of some other research such as those of Hong et al. (2000), Abarbanell and Bushee (1998), Chan et al. (1996) and Poterba and Summers (1988). The strategy is implementable for institutional investors, wealthy individuals and the likes.

The merit of the RIM stock selection strategy over earlier research is the simplicity of the RIM and its inputs. One needs 32 quarters of accounting data and share prices in order to estimate theoretical share prices for a sample of firms. One can determine its own cut-off percentage and conversely form its desired long portfolio. Collecting accounting variables for all firms might be an exertion but is needed in order to have sufficient observations for estimation. The amount of stocks per portfolio can lead to large sums of investments since we can’t buy fractions of shares. Applying higher deviation rates result in less stocks per portfolio but I only tested the effects up till a minimum deviation requirement of 25%.

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