Stock selection based on contemporaneous accounting information Oscar Scholing1
Master’s Thesis Finance2 University of Groningen Faculty of Economics and Business
MSc. Finance Date: 07-06-2018
Abstract
In this study contemporaneous accounting information is related to firm value using the Feltham Ohlson (1995) model. The perceived firm value from the model compared to the stock price in the market decides whether a stock is attractive for investment. The strategy earns excess returns of 7% in the first quarter subsequent portfolio construction, followed by an excess return of 3% in the following quarter. The excess returns cannot be explained by factors from the Fama and French (2015) five-factor model.
Key Words: Fundamental analysis, portfolio selection strategies JEL-code: G1
1 Student number: 2181916
1. Introduction
In the equilibrium of the CAPM, value equals price (Lintner, 1966). Similar (portfolios of) securities have the same expected rate of return. Investors cannot earn excess returns. In practice, price does not need to be equal to value due to costly information, transaction costs limits to arbitrage, et cetera. Each investor assigns his own value to a stock, compares this value with the price, and based on this comparison designs a trading strategy.
Bernard and Thomas (1989) and Sloan (1996) find that prices fail to immediately incorporate public available information, especially earnings news. Abarbanell and Bushee (1998) find value relevant information is captured by accounting. However, the mere association between accounting and prices is not sufficient to pronounce market efficiency with respect to this information (Abarbanell and Bushee, 1998). The practice of fundamental analysis is a tool required to improve market efficiency; to exploit mispricing (Abarbanell and Bushee, 1998). Fundamental analysists assume a fundamental value for stocks, which is known by a
subsection of the market participants (Schasfoort and Stockermans, 2017). These market participants profit from selling the stock if the firm is overpriced and vice versa. This drives the stock price back to its fundamental value.
An investor needs a model to relate accounting information to firm value. The Ohlson (1995) model better predicts and explains stock prices than models that discount short-term forecasts of dividends and cash flows according to Penman and Sougiannis (1996) and Francis et al. (1997). Bernard (1995) finds that 68% of the variation in equity value can be explained by the Ohlson (1995) model, while dividends forecasts explain only 29% of the variation in equity value.
Ohlson (1995) presents a closed form valuation function which uses abnormal earnings and book values. The Feltham Ohlson (1995) model is an extended version of the Ohlson (1995) model which takes conservative accounting into account.
I want to assess whether an investor using accounting data can earn excess returns or not. I relate value to accounting data using the Feltham Ohlson (1995) model. Finding excess returns may imply a violation of the efficient market hypothesis.
The returns are evaluated via the Fama and French (2015) five factor model to ensure that the excess returns are attributable towards its selection criteria.
The results show that investors can earn excess returns that are unexplained by the Fama and Fench (2015) five-factor model. The hedge portfolio obtains a significant alpha of 7% in the first quarter subsequent portfolio formation. The second quarter subsequent portfolio
formation results in a significant alpha of 3%.
The study tests the excess returns for 12 subsequent quarters to determine the optimal investment horizon. The excess returns of the portfolios are tested for time consistency. Lastly, the study tests the effects of an increased deviation from the perceived value to limit the number of stocks (and transaction costs).
2. Literature review
This section starts with a review of the Feltham Ohlson (1995) model. Subsequently, I discuss the relevant portfolio theory. The last subsection provides an overview of alternative
investment strategies.
2.1. Model development
The Ohlson (1995) model assumes that a firm’s value equals the present value of expected dividends: !" = %&"[(" ) *] (1 + /)* 1 *23 (1) !" = the market value of the firm’s equity at time t
(" = dividend net of capital contributions just before time t / = discount rate
&"[ ] = expected value operator conditioned on date t information
The second assumption made by Ohlson (1995) is the clean surplus accounting relation: 4!" = 4!"53+ 6"− (" (2) where,
4!" = (net) book value of equity at time t 6"= earnings for the period (t-1,t)
The clean surplus relation allows to replace dividends in equation (2) with book values and earnings. This results in:
!" = % &"[4!")*53 + 6" ) *− 4!")*] (1 + /)* 1 *23 (3)
Rewriting of equation (3) results in:
!" = 4!"+ %&"[6")* − / × 4!" ) *53] (1 + /)* − &"[4!")1] (1 + /)1 1 *23 (4)
The last term in equation (4) is assumed to be zero (Ohlson, 1995).
Ohlson (1995) makes use of abnormal earnings. Abnormal earnings are equal to earnings minus a charge for the use of capital (determined by beginning period book value of equity):
<"= 6"− / × 4!"53 (5) where,
Combining equation (4) and (5) yields in: !"= 4!"+ % &"[<" ) *] (1 + /)* 1 *23 (6)
The present value of expected dividends and the clean surplus relation imply that the market value equals the book value plus the present value of future expected abnormal earnings. Equation (6) is nothing more than a restated version of de dividend discount model.
Ohlson (1995) assumes that abnormal earnings satisfy the following autoregressive process: <")3 = ?33<"+ ?3@A"+ B3,")3 (7E)
A")3 = ?@@A"+ B@,")3 (7F) where,
A" = other value relevant information
?33 = a fixed persistence parameter that is non-negative and less than 1 ?3@ = a fixed persistence parameter that is non-negative and less than 1 ?@@ = a fixed persistence parameter that is non-negative and less than 1 B3," = the unpredictable, mean zero disturbance term at time t
B@," = the unpredictable, mean zero disturbance term at time t
Based on equation (6), (7a), and (7b) Ohlson (1995) derives the valuation function specified as:
!" = 4!"+ G3<"+ G@A" (8) where,
G3 = ?33 / (1 + / − ?33)
G@ = (?3@)(1 + /) / [(1 + / − ?@@)(1 + / − ?33)]
Ohlson (1995) assumes unbiased accounting. In contrast with Ohlson (1995), Feltham and Ohlson (1995) who take conservative accounting into account. Unbiased accounting is defined as a firm’s expected value equals book value in the long run, whereas conservative accounting firm’s expected value exceeds the book value of a firm in the long run.
Easton and Pea (2004) find that accounting is conservative and that including a term for accounting conservativism improves the explanatory power of the model.
Conservative accounting affects the measured abnormal earnings of t+1 (Feltham and Ohlson, 1995). To be consistent, I add also a term for the effects of conservative accounting on
abnormal earnings t:
The specification of abnormal earnings needs an additional term, as a result the valuation function includes an additional term. Equation (8) and (9) together demonstrate that firm value is a function of abnormal earnings, book value of equity at time t and book value of equity at time t-1. The final value function is:
!" = G36"− G3(/ × 4!"53) + G@4!"+ GK4!"53 (10) The quality of the Feltham Ohlson (1995) model depends on the inputs and assumptions of the model. Earnings quality, defined as the degree to which reported earnings capture economic reality (Krishnan and Parsons, 2008) is often disputed. Accounting research has identified circumstances (e.g. management compensation) that can impact earnings quality. Financial statements are less useful and asset allocation by stakeholders is affected if investors are ‘‘fooled’’ by reported earnings (Healy and Wahlen, 1999)
Furthermore, earnings may be compromised by the effects of one-time events. Dechow et al. (1999) argue that the inclusion of extraordinary items is unlikely to enhance the prediction of abnormal earnings. Nevertheless, exclusion of one-time events violates the clean surplus relation.
Isidro et al. (2008) explorers the relation between violation of the clean surplus accounting and valuation errors using Ohlson (1995). They find weak evidence for this relationship in the United States.
The mentioned issues may result in a biased estimate of firm value. In practice, investors may want to additional analysis of the financials before forming the (active) portfolio.
2.2. Active portfolio management
Treynor and Black (1973) state that in absence of expectations different from the market consensus, investors should hold a replica of the market portfolio. Treynor and Black (1973) assumes that security analysis, properly used, can improve portfolio performance.
Following Lintner (1965) I define excess return on a security as the actual return on the security minus the interest paid on short-term risk-free assets (for a time interval) Treynor and Black (1973) distinguish two components in excess return; the explained component and the independent component. The explained component (the risk premium) is the market
component (for a time interval). Treynor and Black (1973) assume that the independent component for the different securities are, almost, but not quite, statistically independent. Treynor and Black (1973) name the expected value of the explained component the ‘‘market premium’’ and the expected value of the independent component the ‘‘appraisal premium’’. Treynor and Black (1973) state that the optimal portfolio consists of two subportfolios. A subportfolio formed on the basis of the means and variances of the independent return of specific securities. The other subportfolio is an approximation of the market portfolio. The focus is on the first subportfolio, the active portfolio. There are no positions in the active portfolio when the appraisal premium is zero.
According to Treynor and Black (1973), only the appraisal premium (and appraisal risk) is important in selecting the securities for the optimal active portfolio. Assuming that on average half of the analyzed securities is overpriced, and the other half is underpriced. The long positions of the underpriced securities and the short positions of overpriced securities will cancel out the expected market risk (assuming market risk is randomly distributed among over and underpriced securities according to the analysis (Treynor and Black, 1973)). An investor should start with appraising the security in question. The formation of the active portfolio should be independent of expectations of the market as a whole. An investor should give a price to a security consistent with the consensus macroeconomic forecast implicit in the general level of security prices (Treynor and Black, 1973). If an investor’s appraisal value deviates from the current value in the market, the security is attractive for investment in the active portfolio. The security is mispriced according to the investor’s analysis. The next step is the correlation between an investor’s analysis and the subsequent (excess) returns. The analysist’s contribution to the performance of the active portfolio depends on how well his identified independent returns (by security analysis) correlate with the actual independent returns (Treynor and Black, 1973).
Assuming that the analysis is able to give an unbiased estimate of a company’s true value, a key issue is the process of price convergence to the true value (estimate). Do over and
underpriced securities immediately translate in positive (negative) independent returns? How long do these independent returns persist?
Spierdijk and Bikker (2012) describe the mean reversion process in stock prices as; a decline in stock prices is most likely followed up by and upward price movement, and vice versa. Poterba and Summers (1988) argue that mean reversion is due to irrational behavior of noise traders resulting in prices that deviate from their ‘‘fundamental’’ value. Balvers, Gilliland and Wu (2000) find that mean reversion in stock prices takes approximately three years.
The length of the investment horizon is critical in finding independent returns.
2.3. Return evaluation
Treynor and Black (1973) use CAPM to explain the relation between risk and the expected return of a stock. Fama and French (1992) expanded CAPM by including 2 additional factors; size and value. In 2015, Fama and French presented the five-factor model. Fama and French (2015) find the five-factor model explains better the variation in average stock returns than CAPM and the three-factor model.
The Fama and French (2015) five-factor model is specified as follows:
MN" − MO" = GN+ PNQMR"− MO"S + TNUV4"+ ℎNXVY"+ /NMVZ"+ [N\V]"+ BN"(11) where,
MN" = the return of asset i for period (t-1,t) MO" = the risk-free rate for period (t-1,t) GN = alpha (the intercept) for period (t-1,t)
MR"− MO" = the excess market return for period (t-1,t)
UV4" = the return on a portfolio of small firms minus the return on a portfolio of big firms for period (t-1,t)
XVY" = the return on a portfolio of high book-to-market firms minus the return on a portfolio of low book-to-market firms for period (t-1,t)
MVZ" = the return on a portfolio with high operating profitability minus the return on a portfolio with low operating profitability for period (t-1,t)
\V]" = the return of a low investment portfolio minus the return of a portfolio of a high investment portfolio for period (t-1,t)
PN, TN, ℎN, /N, and [N = the asset’s sensitivity to each of the factors for period (t-1,t) BN" = the error term for period (t-1,t)
The size effect can be explained by risk of smaller firms which justifies a higher risk
premium. Smaller firms are less diversified and face more problems in times of recession. The value effect is due to relative distress risk that high book-to-market firms face relative to low book-to-market firms.
Fama and French (2015) state, by reasoning from the dividend discount model, that a lower market value (meaning a higher book-to-market value) implies a higher expected return. Higher expected future earnings result in higher expected returns while higher expected growth of book value (investment) decreases the expected returns (Fama and French, 2015). Novy-Marx (2013) finds that profitable firms (measured by the ratio gross profits to assets) generate significantly higher returns than unprofitable firms. Aharoni et al. (2013) find a negative relation between expected investment and returns. The findings derived from the dividend discount model, Novy-Marx (2013) and Aharoni et al. (2013) motivated Fama and French (2015) to include a profitability and investment factor in the five-factor (2015) model.
Jensen (1968) uses alpha (the intercept in the five-factor model; see equation (1)) to determine if an investor has an ability to forecast asset prices. Lintner and Black (1973) name this
intercept the independent return. If an investor does have an ability to forecast asset prices, alpha is positive. A naïve random selection of assets can be expected to have an intercept of zero. An alpha is observed if an asset (portfolio) has a higher return than a normal risk premium for its level of risk measured according to the risk factors. In other words, alpha measures an asset’s return in excess of its risk-adjusted reward according to capital asset pricing theory.
2.4. Alternative investment strategies
Hong et al. (2000) and Jegadeesh and Titman (1993, 2001) base a profitable investment strategy on momentum. Momentum traders assume that an estimated price trend will extrapolate (Schasfoort and Stockermans, 2017). Abarbanell and Bushee (1998) have a profitable strategy based on fundamental analysis.
months. Hong et al. use the gradual diffusion of information as argument for this phenomenon. The losers in the portfolio contributes most to the strategy.
In contrast with Hong et al. (2000), Jegadeesh and Titman (1993, 2001) divide the stocks in 10 groups based on past 6 months performance. They buy the top performing 10% while they short the 10% worst performing stocks. This results in an alpha (evaluated via the Fama and French three factor model (1992)) of 1.24 % per month for the following 6-months due to overreaction of stock prices to information (Jegadeesh and Titman, 2001). The sample consists all stocks traded on the NYSE, AMEX and Nasdaq from 1965 until 1998. Alpha disappears after 12 months.
Abarbanell and Bushee (1998) use a fundamental analysis approach to find stocks attractive for investment. They use 9 accounting-based signals to predict alpha (e.g. relative changes in inventory). They obtain an alpha of 13.2% per year (cumulative) by a combination of short and long positions in securities (based on decile ranks). Alpha does not persist in the second and third year of the strategy. Abarbanell and Bushee (1998) argue that alpha is due to underreaction of market participants to accounting information. Abarbanell and Bushee (1998) found alpha is unaffected by controls for Fama and French’s (1992) risk factors. Their study uses data from 1974 until 1998.
A brief summary of the mentioned investment strategies can be found in table 1.
Table 1.1 Overview of alternative investment strategies
Study Alpha Persistence of the strategy
Momentum
Hong et al. (2000) 0.53% per month (over a
6-month holding period) 10 months to 2 years (dependent on analysts’
coverage) Jegadeesh and Titman (1993,
2001)
1.24% per month (over a 6-month holding period)
1 year
Fundamental Analysis
3. Methodology and data
This section documents and motivates the methods and data.
3.1. Regression equation
The value component in the final valuation function, equation (10), is not observable.
Therefore, I replace value with market capitalization of the firm. This adjustment implies also the replacement of book value and earnings (based on common equity). These replacements motivate the inclusion of an error term in the regression equation:
V"= P3&"− P3(/ × ]"53) + P@]"+ PK]"53+ BN" (12) where,
V" = the market capitalization of the firm’s common equity at time t ]" = the book value of a firm’s common equity at time t
&" = earnings of common equity for the period (t-1,t)
I scale the regression variables with the lagged book values because of non-stationary
properties of the data and to take differences in size of firms into account. This means that the regression equation (adjusted for panel data) is:
VN" ]N"53 = P^+ P3 &N" ]N"53+ P@ ]N" ]N"53+ BN" (13) where, P^ = PK− P3/ 3.2. Data
To estimate regression equation (14), I need a firm’s market capitalization, book value of common equity and earnings of common equity. The necessary data for the regression equation is obtained from the Compustat database.
The sample of this study consists of all firms that have been part of the S&P 500 in the period from January 1970 until December 2015. This means that the sample captures the whole economic cycle (times of periods with growth and decline of the economy). Data availability and accessibility motivates me to use S&P 500 firms as data sample.
The S&P Dow Jones Indices updates the S&P 500 index components regularly due to
The data is on a quarterly basis to expand the amount of observations. Table 3.1 presents an overview of the variables (obtained from Compustat) necessary for the regression analysis.
Table 3.1 Compustat variable description and calculation
Regression variable Compustat item Compustat definition Calculation
V" PRCCQ
CSHOQ
End share price Number of common shares outstanding
PRCCQ × CSHOQ
&" EPSPXQ Earnings per share (basis)
excl. ordinary items
EPSPXQ × CSHOQ
]" CEQQ Common equity (total) CEQQ
Following Dechow et al. (1999) and Myers (1999), I use earnings per share excluding extraordinary items as measurement for earnings. This is in conflict with the clean surplus assumption. However, ordinary items are nonrecurring, and inclusion is unlikely to improve the prediction of abnormal earnings (Dechow et al., 1999).
Following Collins et al. (1997) I delete all observations with missing variables or with negative common equity values. Furthermore, I delete the top and bottom 1.5% of the observations based on price- to-earnings (P/E) ratio and price-to-book (P/B) ratio (Collins et al., 1997). This results in a final sample with 126,268 observations. Table 3.2 presents the descriptive statistics of the sample.
Table 3.2 Descriptive statistics sample (on a quarterly basis) V"
]"53
&" ]"53
]"
]"53 P/E ratio P/B ratio
Mean 2.657 0.035 1.041 62.55 2.52 Median 1.904 0.036 1.024 52.81 1.86 Minimum 0.07 -41.70 0.02 -270.63 0.39 Maximum 527.72 62.27 141.97 537.20 14.48 St. Dev. 3.08 0.25 0.70 75.11 2.09 Observations 126,268 126,268 126,268 125,837 126,268
P/E ratio is calculated as R_
`_ and P/B ratio as
R_
a_
Return on equity is 3.5% per quarter, what means that the sample’s return on equity is 14% per year. The P/E ratio is 15.6 on a yearly basis and the P/B is 2.5. All three values are in line with historical values according to Koller et al. (2015).
The data is based on companies’ fiscal dates. However, some companies’ fiscal dates do not correspondent correctly with calendar dates (this is the case for 22.1% of the observations). I expect minor effects of this issue because the deviation is only 1 or 2 months.
The Ohlson (1995) model has been studied extensively. Most research has used the cross-sectional approach to study the Ohlson (1995) model (Chen et al., 2014). Other researchers used a time-series approach to study the relationship between market values, earnings and book values. I decide to use the panel data analysis to have enough observations per regression and to limit the amount of regressions to perform.
I split the observations in groups based on their sector according to classification of the Global Industry Classification Standard (presented in Table 3.3). I find the observations from peers of the same sector more important to estimate the regression coefficients because of similarities within the sector. Regression analysis based on sectors allows for heterogeneity in the sample. By using a sector approach instead of pooling all observations together, I expect to improve the quality and reliability of estimated regressions coefficients.
Table 3.3 Overview of sectors
Sector number Sector name Observations
10 Energy 8,401 15 Materials 9,809 20 Industrials 18,389 25 Consumer Discretionary 21,243 30 Consumer Staples 9,663 35 Health Care 10,415 40 Financials 16,793 45 Information Technology 12,555 50 Telecommunication Services 1,943 55 Utilities 10,192 60 Real Estate 2,698
The downside of this approach is the decrease of amount of observations per regression. Especially for the sectors Telecommunication Services and Real Estate, the amount of observations is limited. The limited amount of observations can decrease the accuracy of the regression coefficients.
I use 32 observations per firm to estimate the regression coefficients. Ahmed, Morton, and Schaefer (2000) require at least 15 years of data available to estimate the regression
The sample consist of observations from 1970Q2 to 2015Q4. Requiring 32 quarters of observations means that the first regression period is from 1970Q2 to 1978Q1 and results in the regression coefficients belonging to time 1978Q1. I estimate the regression coefficients from 1978Q1 until 2015Q4. This results in 152 regressions for every sector (a total of 1672 regressions).
In order to choose the correct panel data model, I employ the redundant fixed effects test and the Hausman test. The results can be found in appendix A, table A.2. The results show that the two-error component model is the adequate model (significant on the 1% level). This model allows for both entity fixed effects and time fixed effects within the same model. In other words, the intercept of the model may vary cross-sectional and over time.
The estimated regression coefficients are presented in table 3.4. More detailed summary statistics are in Appendix A, table A.3.
Table 3.4 Coefficients estimates
bcd ecd5f = gh+ gf icd ecd5f+ gj ecd ecd5f+ kcd Sector P^ P3 P@ Energy Mean -5.73 -8.49 7.79 Median -0.75 0.82 2.78 Materials Mean -0.15 15.61 1.88 Median -1.22 3.91 3.68 Industrials Mean -7.80 35.59 9.21 Median -6.82 25.65 9.33
Consumer Discretionary Mean -13.14 3.60 15.64
Median -3.18 -1.22 5.10
Consumer Staples Mean -3.50 33.16 5.61
Median 0.19 20.76 1.52
Health Care Mean -1.25 1.25 5.24
Median -1.17 1.22 4.01
Financials Mean 0.51 29.97 0.38
Median -0.02 12.42 0.96
Information Technology Mean -0.32 18.78 4.02
Median 0.00 10.08 3.99 Telecommunication Services Mean -1.58 23.20 4.08 Median -1.63 21.32 3.82 Utilities Mean -0.19 4.27 1.56 Median 0.10 0.67 1.00
Real Estate Mean -0.35 28.22 1.97
Median 0.25 9.64 1.67
Dechow et al. (1999) find positive values for P3 and P@. They find a higher value for P3 than for P@ (3.88 versus 0.40 with an intercept of 9.72). The higher weight on earnings is in line with the results of this study (this holds for 8 of 11 sectors).
3.3. Values perceived from the Feltham Ohlson (1995) model
The estimated regressions coefficients are used to determine a firm’s value according to the Feltham Ohlson (1995) model. Subsequently, I compare the perceived values with the observed market values. Companies are attractive for investment if the perceived value deviates at least 50% from the observed market value. I use a 50% cut-off percentage to be sure that a company’s stock price has a significant deviation from the market price and limit the amount of stocks in the portfolios to save transaction costs. Corporate finance
practitioners aim at a value range of ± 15% according to Koller et al. (2015). The 50% cut-off percentage provides a margin of safety.
I use long, short and hedge investment strategies. The long portfolio consists of stocks which are undervalued according to the Feltham Ohlson (1995) model. I expect these stocks to appreciate and I want to profit from the stock gain with the long position. The short portfolio consists of stocks that are overvalued according to the Feltham Ohlson (1995) model. By short-selling I bet on the expected falling prices of these stocks. The hedge portfolio combines the long and short strategy.
Every stock has an equal weight in respectively the long, short or hedge portfolio. I investigate the relation between perceived mispricing (according to the Feltham Ohlson (1995) model) and the optimal investment horizon of these assets. Every quarter I determine which stocks qualify for investment and I form the corresponding portfolios. Then, I construct series for portfolio return in the first, second, third, etc. quarter after portfolio formation for analysis. This study analyses the portfolio returns for the subsequent 12 quarters after portfolio formation to find the optimal investment horizon.
The return of each stock is calculated using logarithmic returns so that they are time consistent (on a quarterly basis):
MN" = ln nU′N" + (6UN"
U′N"53 p (14)
where,
MN" = the return of stock i for period (t-1,t)
Dividend per share for each company is obtained from the Compustat database. The portfolio return is calculated as (on a quarterly basis):
M6N" = % q MN" r"53s t N23 (15) where,
M6N" = the return of portfolio i at time t
r"53= the number of stocks that qualify for the portfolio at time t-1
3.4. Returns evaluation
To evaluate the portfolio returns, I use the Fama and French (2015) five factor model. I obtain all the necessary data for this model (including risk-free rates) from the Kenneth R. French data library. I use standard errors corrected with the Newey-West procedure to deal with heteroskedasticity and autocorrelation. Table 3.5 shows the descriptive statistics of the risk-free rate and the returns on the risk factors for the period 1978Q2 until 2015Q4.
Table 3.5 Descriptive statistics Rf and risk factors (on a quarterly basis)
Rf Rm-Rf SMB HML RMW CMA Mean 1.18% 1.99% 0.46% 0.81% 1.07% 0.88% Median 1.21% 3.10% 0.43% 0.50% 0.59% 0.50% Minimum 0.00% -24.38% -10.85% -17.22% -14.17% -7.66% Maximum 3.81% 20.67% 12.15% 26.05% 27.08% 20.05% St. Dev. 0.90% 8.37% 4.77% 5.98% 4.62% 4.05%
Data obtained from http://mba.tuck.dartmouth.edu/
To check whether the results are consistent over time, I employ the Quandt-Andrews
4. Results
Every quarter I constructed a portfolio based on the perceived value from the Feltham Ohlson (2015) model, which I compared with market value. I hold every portfolio for 12 quarters to examine the optimal investment horizon. I distinguish series of excess returns in first, second, third, etc. quarter after portfolio formation for every portfolio. The summary statistics of the excess returns for the different portfolios are presented in table 4.1.
The excess return of the short portfolio is calculated as the risk-free rate minus the return on the portfolio. The excess return of the hedge portfolio is calculated as the excess return of the long portfolio plus the excess return on the short portfolio.
Table 4.1 Summary statistics excess returns portfolios (50% cut-off) in the first, second, etc. quarter after portfolio formation
Quarter 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th Long portfolio Mean 3.81% 4.31% 4.13% 4.36% 4.36% 4.21% 3.98% 3.88% 4.00% 3.94% 3.74% 3.56 Median 3.73% 4.64% 4.62% 4.55% 5.15% 4.56% 4.65% 4.08% 4.76% 5.03% 4.85% 4.68% Min -23.1% -24.5% -26.3% -24.5% -25.3% -27.1% -27.0% -26.6% -27.0% -27.4% -26.5% -24.8% Max 24.28% 24.28% 22.97% 25.22% 24.61% 24.21% 24.99% 26.46% 25.72% 26.39% 25.61% 26.74% St. Dev. 8.60% 8.45% 8.50% 8.52% 8.51% 8.59% 8.41% 8.30% 8.56% 8.56% 8.28% 8.48% Sharpe* 0.44 0.51 0.49 0.51 0.51 0.49 0.47 0.47 0.47 0.46 0.45 0.42 Short portfolio Mean 0.09% -3.06% -2.98% -3.32% -3.26% -3.02% -3.61% -3.85% -3.58% -3.53% -3.65% -3.55% Median -0.85% -3.97% -3.65% -4.03% -4.00% -3.61% -4.36% -4.19% -3.93% -3.34% -3.21% -3.23% Min -29.3% -33.7% -33.4% -37.4% -35.6% -33.6% -31.8% -28.0% -33.0% -33.5% -35.0% -30.4% Max 38.45% 37.04% 32.04% 38.08% 32.50% 33.15% 32.23% 35.21% 34.49% 34.22% 35.61% 38.84% St. Dev. 10.34% 10.51% 10.87% 10.85% 9.96% 10.36% 9.67% 9.97% 10.30% 9.99% 9.87% 9.47% Sharpe* 0.01 -0.29 -0.27 -0.31 -0.33 -0.29 -0.37 -0.39 -0.35 -0.35 -0.37% -0.37 Hedge portfolio Mean 3.90% 1.24% 1.16% 1.04% 1.09% 1.19% 0.37% 0.03% 0.42% 0.41% 0.09% 0.01% Median 2.79% 0.94% 0.58% 0.61% 0.72% 1.20% 0.17% 0.31% 0.27% 0.44% 0.30% -0.24% Min -12.4% -20.1% -18.2% -22.4% -15.4% -16.3% -28.3% -20.9% -23.1% -16.3% -20.8% -22.9% Max 23.56% 23.47% 22.14% 24.19% 21.37% 18.47% 17.24% 16.53% 17.58% 14.33% 17.23% 15.27% St. Dev. 6.10% 6.25% 6.34% 6.11% 5.32% 6.04% 5.59% 5.57% 6.22% 5.25% 5.90% 5.53% Sharpe* 0.64 0.20 0.18 0.17 0.21 0.20 0.07 0.01 0.07 0.08 0.02 0.00
Note: *Sharpe is the Sharpe ratio which is calculated as the mean excess return divided by the standard deviation of excess return to get an indication for risk-return relationship.
Table 4.2 Statistics number of stocks in each portfolio (50% cut-off)
Long portfolio Short portfolio Hedge portfolio
Mean 238 87 325
Median 226 81 316
Min 75 9 177
Max 433 223 495
St. Dev. 79 41 67
Figure 4.1 Number of stocks in the portfolios (50% cut-off) over time
The number of stocks in the portfolios heavily depends on the cut-off percentage used. On average, 739 stocks are available for investment each quarter. Sapp and Yan (2008) show, based on empirical research under U.S. equity funds from 1984-2002, that funds hold 91 distinct stocks on average. Diversified funds (defined as funds with an average of $1.55 billion assets) hold approximately 229 distinct stocks.
The excess returns reported in table 4.1 are evaluated via the Fama and French (2015) five-factor model to test whether the excess returns can be linked to its selection criteria (table 4.3). Figure 4.1 displays the results in a graph.
0 100 200 300 400 500 600 1978Q 2 1979Q 3 1980Q 4 1982Q 1 1983Q 2 1984Q 3 1985Q 4 1987Q 1 1988Q 2 1989Q 3 1990Q 4 1992Q 1 1993Q 2 1994Q 3 1995Q 4 1997Q 1 1998Q 2 1999Q 3 2000Q 4 2002Q 1 2003Q 2 2004Q 3 2005Q 4 2007Q 1 2008Q 2 2009Q 3 2010Q 4 2012Q 1 2013Q 2 2014Q 3 2015Q 4
Table 4.3 Alpha for portfolios (50% cut-off) in the first, second, etc. quarter after portfolio formation (using Fama and French (2015) five-factor model)
Long portfolio Short portfolio Hedge portfolio
Quarter 1st 1.72%** 2.23%*** 3.95%*** 2nd 2.24%*** -1.24%** 1.00%* 3rd 2.14%*** -1.00% 1.13%** 4th 2.24%*** -1.10% 1.14%* 5th 2.23%*** -1.21%* 1.02%* 6th 2.13%*** -0.83% 1.30%** 7th 1.88%*** -1.38%*** 0.50% 8th 1.84%*** -1.66%** 0.18% 9th 1.70%*** -1.08% 0.63% 10th 1.65%*** -0.82% 0.84% 11th 1.70%*** -1.55%** 0.14% 12th 1.38%*** -1.48%** -0.10%
Notes: * indicates statistically significant at the 10% level; ** at the 5% level; *** at the 1% level. All standard errors are calculated using Newey-West robust standard errors.
Figure 4.2 Alpha for portfolios (50% cut-off) in the first, second, etc. quarter after portfolio formation (using Fama and French (2015) five-factor model)
The results show that the long portfolio obtains a significant alpha around 2% on a quarterly basis which magnitude slowly decreases over time. The short portfolio only shows a
significant result in the first quarter after portfolio formation. The hedge portfolio benefits from the long and short positions in the first quarter after portfolio construction and obtains an alpha of 4%. Investment in the hedge portfolio results in a significant positive alpha every quarter in the first 1.5 years after portfolio formation.
The results show that it takes time before the new (accounting) information is reflected in the market prices. This in line with theory by Treynor and Black (1973) that it takes time before
-2 -1 0 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 11 12
review, the time it takes to adjust prices determines the optimal investment horizon (how long do investors benefit from the investment strategy). The results show that it takes longer to process accounting information that implies a higher market value than information that implies a lower market value.
To test whether the results are consistent over time, I employ the Quant-Andrews unknown breakpoint test. I decide to check 6 excess returns series based on the significance of alpha and the economic meaningfulness. If the test finds a significant breakpoint, I divide the series in two subseries and evaluate the excess returns separately via the Fama and French (2015) five-factor model. Table 4.4 shows the results of the Quant-Andrews unknown breakpoint test and the following evaluation of the excess return series.
Table 4.4 Results Quant-Andrews unknown breakpoint test
Portfolio Alpha series (quarter) Quant-Andrews breakpoint date Alpha before breakpoint Alpha after breakpoint
Long 2nd 1984Q1*** 11.25%*** 0.83%* Long 4th 1984Q1*** 10.97%*** 0.96%** Long 8th 1984Q1*** 10.90%*** 0.88%* Long 12th 1985Q4*** 9.01%*** 0.52% Short 1st 2000Q3*** 0.20% 4.98%*** Hedge 1st 1984Q1** 8.50%*** 3.02%***
Notes: * indicates statistically significant at the 10% level; ** at the 5% level; *** at the 1% level. All standard errors are calculated using Newey-West robust standard errors.
The results clearly show that the long portfolios performed best from 1978Q2 until 1984Q1. Alpha is above 10% in the 2nd, 4th and 8th quarter after portfolio formation. In constant, after 1984Q1 alpha is below 1% and the level of significance decreases. The short portfolio (alpha 1 quarter after portfolio formation) performs better after the breakpoint in 2000, the results before are not significant. The hedge portfolio excess returns series (1st quarter after portfolio formation) also has 1984Q1 as breakpoint. The alpha is 2.5 times as high in the period before the breakpoint.
To reduce transaction costs and to assess whether the results are robust, I increase to cut-off percentage to 75% and 100%. By selecting firms with a relative higher mispricing according the Feltham Ohlson (1995) perceived value, I expect a higher alpha. The descriptive statistics of the excess returns for the portfolios are in Appendix B; table B.1 (75% cut-off) and table B.2 (100% cut-off). Table 4.5 reports the number of stocks select in the different portfolios.
Table 4.5 Statistics number of stocks in each portfolio (75% and 100% cut-off)
75% cut-off 100% cut-off
Long
portfolio Short portfolio Hedge portfolio Long portfolio Short portfolio Hedge portfolio
Mean 175 40 215 130 26 156
Median 162 40 203 118 21 146
Min 38 3 60 20 1 27
Max 370 168 418 297 153 361
St. Dev. 71 25 73 60 22 66
By increasing the cut-off percentage by 25%, the average number of stocks in the portfolios decreases approximately 20% in the long portfolio, by 50% in the short portfolio and by 30% in the hedge portfolio. Table 4.6 reports alpha for the different portfolios using a 75% and 100% cut-off percentage.
Table 4.6 Alpha for portfolios (75% and 100% cut-off) in the first, second, etc. quarter after portfolio formation (using Fama and French (2015) five-factor model)
75% cut-off 100% cut-off Long portfolio Short portfolio Hedge portfolio Long portfolio Short portfolio Hedge portfolio Quarter 1st 1.72%** 4.69%*** 6.41%*** 1.65%** 5.59%*** 7.24%*** 2nd 2.10%*** 0.34% 2.45%*** 1.91%** 1.19% 3.10%*** 3rd 1.94%** 0.15% 2.10%*** 1.50%** -0.10% 1.40% 4th 2.00%*** -0.96% 1.04% 1.77%** -0.18% 1.60% 5th 1.98%*** -0.99% 0.99% 1.70%** 0.49% 2.19%** 6th 1.98%*** -0.14% 1.84% 1.73%** 0.29% 2.02% 7th 1.80%*** -0.80% 1.00% 1.69%** -0.41% 1.28% 8th 1.59%** -1.67% -0.08% 1.58%** -4.03% -2.45% 9th 1.65%*** -1.41% 0.23% 1.55%*** -2.36% -0.81% 10th 1.51%** -1.08% 0.42% 1.37%** -0.42% 0.95% 11th 1.58%*** -0.93% 0.66% 1.53%** -0.59% 0.93% 12th 1.45%*** -1.04% 0.41% 1.28%** 0.14% 1.42%
Notes: * indicates statistically significant at the 10% level; ** at the 5% level; *** at the 1% level. All standard errors are calculated using Newey-West robust standard errors.
The short portfolio benefits from an increase in the cut-off percentage in the first quarter after portfolio formation; alpha doubles. It is still not attractive to hold the short portfolio longer than 1 quarter after portfolio construction.
Alpha for the first quarter after portfolio formation increases from 4% to 7.2% by increasing the cut-off percentage to 100%. It becomes attractive to expand the holding period of the hedge portfolio by a quarter, because of the significant alpha of 3.1% in the second quarter after portfolio formation.
Alternative investment strategies of Hong et al. (2000), Jegadeesh and Titman (2001), and Abarbanell and Bushee (1998) are all based on a hedge portfolio. The strategy described in this paper outperforms a strategy based on momentum as described by Hong et al. (2000) and Jegadeesh and Titman (2001). Both studies report an alpha for the first half year subsequent investment of respectively 0.53% per month and 1.24% per month. The hedge portfolio formed on basis of the Feltham Ohlson (2015) model obtains an alpha of 7.24% for the first quarter subsequent investment and 3.1% what clearly is higher than the momentum strategies obtain. I find the Feltham Ohlson (2015) model more suited for stock selection than
Abarbanell and Bushee (1998) model which also uses a model using accounting variables. They obtain a cumulative alpha of 13% after 1 year while the strategy described in this paper obtains an alpha of more than 10% after 6 months of investment.
5. Conclusion
Investors can estimate a company’s value based on contemporaneous accounting information using a slightly adjusted version of the Feltham Ohlson (1995) model. The model’s inputs are firm’s market value, earnings and book value. The firm value perceived from the Feltham Ohlson (2015) model are compared to observed market value to determine whether a stock is attractive for investment. If a firm’s market value deviates at least 50% (margin of safety) of the perceived value from the Feltham Ohlson (1995) model, the stock will be included in the portfolio. Every quarter I repeat this strategy to form 151 portfolios (from 1978Q1 until 2015Q4). Undervalued firms according the Feltham Ohlson (1995) are purchased for the long portfolio, while undervalued companies are shorted. The hedge portfolio combines both portfolios. Portfolio returns are 12 quarters subsequent the portfolio formation analyzed to determine the optimal investment horizon for investors. This empirical study uses S&P 500 firms.
The results show that the Feltham Ohlson (1995) model is able to obtain significant alpha for the long portfolio, short portfolio and hedge portfolio. It confirms that investors over and underreact to (accounting) information and it takes time before the market correct the stock prices accordingly. Investors can obtain alpha by detecting mispriced assets. The results show the correction takes up to three years for undervalued firms, however most of the correction takes place within the first 1.5 years. In other words, alpha decreases after 1.5 years for the long portfolio. Investors absorb accounting data that implies a lower market value much quicker. Investors who short overvalued assets, should hold the assets only for 1 quarter. The hedge portfolio combines the long and short positions and results in an alpha for 1.5 years after the portfolio formation.
The alpha obtained by the undervalued stocks is mainly due the success of the strategy from 1978Q2 until 1984Q1. In the period hereafter, alpha is lower and the level of significance decreases. In contrast, the short portfolio shows a higher alpha after its breakpoint in 2000 (this holds for the first quarter subsequent portfolio formation). Both investment strategies combined; the hedge portfolio (with only a 50% cut-off) shows significant alpha in the first quarter subsequent portfolio formation before and after its breakpoint.
In comparison to investments strategies based on momentum and another strategy based on fundamental analysis, the strategy in this paper obtains a higher alpha.
All in all, I find investment based on contemporaneous accounting information using the Feltham Ohlson (1995) model is suitable. Especially if an investor invests using the hedge portfolio. The results show that this portfolio is time consistent and an investor can lower number of the stocks to increase results. Investing in the hedge portfolio for 2 consecutive quarters results in a significant alpha of 7.2% in the first quarter and 3.1% in the second quarter prior portfolio formation.
In order to improve the results, I recommend investigating a strategy that combines fundamental analysis with momentum. The Feltham Ohlson (1995) model is able to find undervalued/overvalued firms. However, if momentum in the stock price result in a move into the opposite direction as predicted by Feltham Ohlson (1995) model, it is not attractive for investment.
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Appendix A
Table A.1 Unit root test results
The following tests are used: Levin, Lin and Chu (LLC), Im, Persaran and Shin (IMP), Augmented Dickey Fuller (ADF) and Philips and Perron (PP).
V" ]"53 6" ]"53 ]" ]"53 LLC -119.477*** -39.274*** -1,881.6*** IPS -70.909*** -119.240*** -342.833*** ADF 8,865.860*** 22,639.600*** 46,969.300*** PP 10,682.800*** 42,305.300*** 57,194.900*** Observations 116,661 120,053 116,299
Notes: *** indicates statistically significant at the 1% level. Automatic lag selection based on Schwarz info criterion.
Table A.2 Redundant fixed effects test and Hausman test results
Test Type F-statistic Chi-Square
Redundant fixed effects test
Entity-fixed effects (one way) 40.414*** 47,841.921***
Tim-fixed effects (one way) 50.490*** 9,171.153***
Entity- and time fixed effects (two
way) 48.078*** 60,895.267***
Random effects test
Hausman test 290.644***
Table A.3 Summary statistics Feltham Ohlson (1995) model regression coefficients !"# $"#%& = )*+ )& ,"# $"#%& + ) -$"# $"#%&+ ."#
Sector 10 Energy Sector 15 Materials Sector 20 Industrials
/0 /1 /2 /0 /1 /2 /0 /1 /2 Mean -5.73 -8.49 7.79 -0.15 15.61 1.88 -7.80 35.59 9.21 Median -0.75 0.82 2.78 -1.22 3.91 3.68 -6.82 25.65 9.33 Min. -36.78 -60.50 1.53 -14.67 -7.94 -81.69 -29.61 -13.70 -7.16 Max. 0.63 17.50 38.72 79.70 173.71 16.61 8.40 224.68 26.96 St. Dev. 9.81 22.57 9.90 15.14 34.65 15.80 10.78 34.57 9.68
Sector 25 Consumer Discretionary Sector 30 Consumer Staples Sector 35 Health Care
/0 /1 /2 /0 /1 /2 /0 /1 /2 Mean -13.14 3.60 15.64 -3.50 33.16 5.61 -1.25 1.25 5.24 Median -3.18 -1.22 5.10 0.19 20.76 1.52 -1.17 1.22 4.01 Min. -79.88 -15.96 -36.01 -56.94 -0.24 -19.38 -8.29 -17.63 -1.85 Max. 38.55 51.83 83.32 21.82 75.06 58.13 5.28 38.15 12.87 St. Dev. 20.77 14.12 20.52 20.23 26.76 20.13 3.65 11.22 4.28
Sector 40 Financials Sector 45 Information Technology Sector 50 Telecommunication Services
/0 /1 /2 /0 /1 /2 /0 /1 /2 Mean 0.51 29.97 0.38 -0.32 18.78 4.02 -1.58 23.20 4.08 Median -0.02 12.42 0.96 0.00 10.08 3.99 -1.63 21.32 3.82 Min. -2.06 -0.64 -4.61 -8.35 -20.10 -4.79 -7.39 -46.59 -4.22 Max. 5.02 92.20 3.15 6.34 77.61 11.56 5.89 149.01 9.56 St. Dev. 1.87 30.85 2.16 5.00 31.10 4.79 2.67 42.55 2.68
Sector 55 Utilities 60 Real Estate
Appendix B
Table B.1 Summary statistics excess returns portfolios (75% cut-off) in the first, second, etc. quarter after portfolio formation
Quarter 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th Long portfolio Mean 3.86% 4.22% 3.98% 4.18% 4.12% 4.03% 3.85% 3.64% 3.95% 3.78% 3.56% 3.50% Median 4.10% 4.53% 4.24% 4.67% 4.58% 4.44% 3.95% 3.98% 4.75% 4.74% 4.50% 4.35% Min -23.3% -24.5% -28.1% -24.8% -25.8% -27.3% -26.1% -26.5% -27.0% -30.3% -27.5% -23.6% Max 23.99% 21.73% 22.79% 25.89% 25.41% 24.12% 24.30% 26.36% 25.98% 24.47% 26.85% 26.05% St. Dev. 8.87% 8.64% 8.77% 8.78% 8.69% 8.70% 8.64% 8.51% 8.74% 8.72% 8.55% 8.61% Sharpe* 0.44 0.49 0.45 0.48 0.47 0.46 0.45 0.43 0.45 0.43 0.42 0.41 Short portfolio Mean 2.62% -1.60% -1.44% -2.17% -2.35% -1.91% -2.41% -3.30% -3.53% -3.38% -3.31% -3.28% Median 1.15% -2.40% -2.20% -3.44% -2.25% -2.67% -3.29% -4.16% -3.10% -3.44% -2.24% -3.30% Min -30.1% -37.6% -35.4% -55.3% -60.6% -47.7% -50.4% -68.6% -69.8% -59.4% -58.7% -39.0% Max 42.26% 38.29% 33.89% 41.90% 39.31% 34.49% 32.99% 35.59% 35.77% 31.71% 30.44% 43.25% St. Dev. 12.73% 13.56% 13.11% 14.31% 13.64% 13.74% 12.92% 14.75% 14.76% 13.14% 13.17% 12.50% Sharpe* 0.21 -0.12 -0.11 -0.15 -0.17 -0.14 -0.19 -0.22 -0.24 -0.26 -0.25 -0.26 Hedge portfolio Mean 6.48% 2.62% 2.54% 2.01% 1.78% 2.12% 1.44% 0.35% 0.42% 0.41% 0.25% 0.22% Median 5.13% 1.44% 1.81% 1.25% 1.70% 1.72% 1.01% 1.11% 0.97% 0.59% 1.08% 0.39% Min -25.3% -32.6% -19.1% -50.9% -50.3% -43.7% -47.8% -65.7% -67.4% -43.0% -42.3% -30.3% Max 46.16% 36.91% 37.74% 36.91% 35.10% 31.55% 31.50% 31.78% 27.25% 23.01% 22.60% 23.22% St. Dev. 9.09% 9.51% 9.08% 10.24% 9.27% 10.00% 8.83% 11.19% 10.87% 8.37% 8.93% 8.35% Sharpe* 0.71 0.28 0.28 0.20 0.19 0.21 0.16 0.03 0.04 0.05 0.03 0.03
Table B.2 Summary statistics excess returns portfolios (100% cut-off) in the first, second, etc. quarter after portfolio formation
Quarter 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th Long portfolio Mean 3.90% 4.12% 3.56% 3.97% 3.90% 3.81% 3.81% 3.56% 3.86% 3.67% 3.43% 3.20% Median 4.29% 4.62% 4.01% 4.36% 4.40% 4.26% 4.56% 3.91% 4.69% 4.91% 4.22% 3.89% Min -24.6% -24.9% -28.6% -24.2% -26.4% -26.5% -28.0% -27.8% -26.1% -29.3% -26.6% -22.3% Max 25.63% 23.89% 22.20% 23.89% 25.56% 23.86% 27.05% 25.86% 24.65% 24.49% 28.65% 25.61% St. Dev. 9.18% 8.95% 9.03% 8.95% 8.98% 8.93% 8.81% 8.76% 8.74% 8.99% 8.73% 8.78% Sharpe* 0.43 0.46 0.39 0.44 0.43 0.43 0.43 0.41 0.44 0.41 0.39 0.36 Short portfolio Mean 3.46% -0.84% -1.60% -1.65% -1.88% -1.66% -2.06% -5.65% -4.52% -3.32% -3.30% -2.78% Median 1.61% -2.09% -1.58% -2.66% -1.56% -1.66% -2.89% -2.58% -3.05% -2.51% -3.34% -2.59% Min -32% -39% -70% -126% -87% -109% -71% -482% -112% -105% -118% -111% Max 48.97% 44.30% 40.41% 48.90% 43.03% 47.90% 38.46% 52.46% 38.09% 39.98% 29.03% 50.26% St. Dev. 15.15% 15.89% 15.64% 18.50% 16.63% 17.71% 16.07% 44.17% 19.83% 16.46% 16.78% 17.80% Sharpe* 0.23 -0.05 -0.10 -0.09 -0.11 -0.09 -0.13 -0.13 -0.23 -0.20 -0.20 -0.16 Hedge portfolio Mean 7.36% 3.28% 1.95% 2.32% 2.02% 2.15% 1.75% -2.09% -0.66% 0.35% 0.13% 0.42% Median 5.74% 2.02% 2.94% 2.77% 2.23% 1.88% 1.83% 1.92% 1.89% 1.38% 1.68% 1.34% Min -18% -42% -68% -121% -76% -106% -69% -480% -110% -89% -101% -103% Max 48.21% 46.18% 44.95% 47.90% 46.33% 45.17% 45.24% 59.97% 35.36% 46.61% 24.73% 34.72% St. Dev. 11.06% 11.40% 12.07% 15.03% 12.88% 15.07% 12.66% 43.33% 17.04% 12.57% 12.94% 14.37% Sharpe* 0.67 0.29 0.16 0.15 0.16 0.14 0.14 -0.05 -0.04 0.03 0.01 0.03
