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Master Thesis
Accountancy
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Does the Ohlson framework explain the dynamics between
market value and accounting numbers
Name: Petros Naziroglu Student nr: 5742560 Supervisor: dr. A. Sikalidis
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Summary
In this paper, we will empirically research if accounting information provides useful information to explain market value in the long and short runs. We address our research question by examining the Ohlson model (1995) using cointegration tests developed by Engle and Granger (1987), and Johansen (1988).
Our initial results of the Engle and Granger (1987) test do not show that there is an long run relationship between the market value and book value or residual income. However, our Johansen (1988) test results did find an relationship. These finding seem consistent with Lee (2012), who initially did not found an relationship, but after loosening the constraints found an long-run equilibrium. However, our results are conflicting with Qi (2001) who found that only an small fraction of the sample exhibit long run dynamics. Furthermore, our Granger test results did not found significant power of residual income or book value in predicting the market value and vice versa. However, our results consistently show a relation between the residual income and book value on both the long- and short run. Overall, the relationship between the market value, the book value and the residual income is a mean reverting process. Therefore, our results support the view that the Ohlson (1995) framework explains the relationship between the market value and accounting numbers in the long-run. However, our results do not provide evidence that the accounting numbers provide useful information for predicting the market value in the short-run and vice versa.
3 Table of Content 1. Introduction p. 4 2. Literature review p. 6 2.1 Valuation models p. 6 2.2 Ohlson model p. 8
2.3 User ability accounting information p.9
2.3.1 Market effiency p.9 2.3.2 Information dynamics p. 10 3. Data p. 12 3.1 Descriptive Statistics p. 12 3.2 Summary Statistics p. 12 3.2.1 Variables p. 12 3.2.2 Overview Statistics p. 13 4. Methodology p. 14
4.1 Unit Root Tests p. 15
4.2 Co-integration Tests p. 16
4.2.1 Engle and Granger p. 16
4.2.2 Johansen p. 17
4.3 Granger Causality Test p. 18
5. Results p. 20
5.1 Unit Root results p. 20
5.1.1 Augemented Dick Fuller p. 21
5.1.2 Phillip and Perron p. 21
5.2 Co-integration results p. 22 5.2.1 Engle and Granger p. 22
5.2.2 Johansen p. 23
5.3 Granger Causality results p. 25
6. Conclusion p. 26
7. Discussion p. 27
4 1. Introduction
The pioneering work of Ohlson (1995) provides a theoretical framework which explains the link between the market value and accounting variables. Prior studies primarily focused on the information perspective of accounting variables, i.e., whether or not the information reflected in financial statements was incorporated in the market value. Ohlson (1995) showed that the intrinsic value is equal to the book value of equity plus the present value of the expected (future) residual income assuming clean surplus accounting. The model underlines the relevance of abnormal (or residual) earnings when determining a firm’s value. Abnormal earnings partly capture the difference between the market value and the book value by enabling the user to incorporate additional information from a value-relevant event which impacts the financial statement but is omitted or incorporated with a delay due to the nature of the accounting data (Ohlson, 1995, p. 663). Therefore, omitted information from
value-relevant events should be reflected in future abnormal earnings. The book value and the residual income are slow in tracking value-relevant events due to the opaque nature of non-accounting information. Therefore, there is a delayed response before the omitted information is reflected in the intrinsic value of firms. Myers (1999) argued that it is impossible to control other information because the omitted information is not always driven by an event. Market prices are driven not only by information, but also market sentiment. This makes it impossible to consistently reflect the information set that drives the market price.
Prior literature includes several attempts at specifying the ‘omitted information’. Initial studies adopted a cross-sectional approach and tried to reflect only the omitted information by searching for missing variables, thereby attempting to control the other missing information. Frank and Lee (1998) suggested that analyst forecasts of next year’s earnings reflect the omitted information in conjunction with the Ohlson model. Dechow (1999) similarly
incorporated analyst forecasts and found limited improvements. Hands and Landsman (1998) used dividends; Barth (1999), research and development expenses; Callen and Morel (2005), pension liabilities; and Brow and Caylor (2006), audit fees.
Prior studies show that the market value, the residual income and the book value generally exhibit non-stationary properties. However, they primarily addressed the omitted information issues using a cross-sectional approach while ignoring the time-varying nature of the data. Therefore, the ordinary least square (OLS) approach is not optimal because it could lead to
5 spurious1 results. The Ohlson model is more suited to address these issues since it is of time-varying nature.
The Ohlson model has three main advantages. First, it avoids making assumptions about future cash flows since it emphasizes on the book value. Second, Penman and Sougiannis (1998) suggested that investments be seen as balance-sheet items and not as reducing cash flows. Third, Bernard (1995) saw that the dividend discount model undervalues security prices for a shorter time horizon than the Ohlson model since not all firms pay dividends. Prior academic literature views the Ohlson model better at explaining the security price than the discounted cash flow (DCF) or dividend discount models.
In their pioneering research, Engle and Granger (1987), and Johansen (1988) found that a non-stationary time series yields consistent estimates when an OLS regression is conducted without spurious results. The underlying assumption here is that the relationship between dependent and independent variables is cointegrated. Therefore, there could be a long-run equilibrium between the market value, the book value and the residual income even when variables are independent. Cointegration suggests that there is a stable process between non-stationary variables. Statically speaking, this implicates that errors are non-stationary in the cointegration process, while the individual dependent and independent variables are not. Therefore, a time series approach seems more appropriate because it allows the market value to be captured by the book value and the residual income in a delayed process (Lee, 2013, p. 537). In addition, Ohlson (1995) used a linear model to frame the stochastic movements of abnormal earnings. It enhances the notion that the nature of the underlying variables is non-stationary, thereby addressing the lagged effect of incorporating omitted information of relevant events in accounting.
In this paper, we will empirically research if accounting information provides useful information to explain market value in the long and short runs. We address our research question by examining the Ohlson model (1995) using cointegration tests developed by Engle and Granger (1987), and Johansen (1988). In order to do so constructively, we divided our research into three sections. The first section will focus on the individual time series properties of the book value, markets and residual income by primarily examining the
stationary. The second section will examine the long-run equilibrium between the book value,
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6 the market value and the residual income through the Engle and Granger (1987), and
Johansen (1988) tests. We use both tests to strengthen the accuracy of our results. The final section will examine if there are short-term dynamics between the book value, the market value and the residual income through a Granger causality test.
Our research contributes by studying the Ohlson model using a time series approach, which has been very rarely used in prior literature. We shift the research on the Ohlson model to a different direction focusing on a shared process of individual variables and not on specifying omitted variables. In addition, we will not only focus on the long-run equilibrium but also on the short-run dynamics which has not been done in prior literature. The contribution will be two-fold. First, we will use a statistically different approach the Ordinary least squared (OLS) method which is primarily used in prior research.. Second, it will provide useful information on the broader debate of whether or not financial statements provide significant information to help explain the security pricing.
Section 2 of this paper describes related literature and reviews the Ohlson (1995) model. Section 3 describes and analyses the data. Section 4 describes the methodology of the cointegration test. Section 5 analyses the results, while Section 6 concludes the paper. 2. Literature Review
2.1 Valuations models
There has been substantial academic research on valuations focusing on the DCF model since it is the most dominant model in practice. However, the residual income model has become the more popular alternative recently, and academic research suggests that it is superior to the DCF model although both have been derived from similar underlying assumptions of the DCF method or the dividend discount model. Past academic research2 has shown that the residual income model better reflects the stock price within finite horizons than the DCF model. Penman and Sougiannis (1998) showed that the DCF can better explain stock prices by using accruals. It provide a tool for the communication of additional information regarding non-cash value changes. Furthermore matching the costs and revenues at recognition better reflects the economic reality. Therefore, it facilitates the short-term horizon forecasting of payoffs.
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7 Furthermore, Callen and Morel (2005) contended that the Ohlson (1995) model could also value non-dividend paying firms since it uses abnormal earnings. Therefore, it is more appealing to value growth stock, especially since the fraction of dividend paying firms in the US dropped to 20.8 per cent in 2009 from 66.5 per cent in 1978 (Lee, 2012, p. 536).
Furthermore, Frank and Lee (1998) suggested that the Ohlson model better explains the stock price compared to alternative accounting-based methods.
Beaver (1999) suggested that the Ohlson model can be applied to all accounting approaches if it satisfies the clean surplus accounting condition because its only requirement is that the market value be explained by the book value and the expected residual income. Therefore, Qi (2012) suggest that if the times series relationship between the book value, market value and residual income is established it would be consistent with the validity testing. Prior academic research3 mostly focused on a cross-sectional study of the Ohlson model, thereby failing to take into account the time-varying nature of the explanatory variables (Qi, 2012, p. 538). Qi (2002) found in his sample that only 5.3 per cent of market values and 1.1 per cent of book values exhibit stationarity. Callen and Morel (2005) also found that the market value, book value and residual income are independent because they exhibit stochastic behaviour. However, Callen and Morel (2005) suggested that although there is no direct causal
connection it may be wrongly inferred that they do due to either a coincidence or the presence of a certain third unknown factor, a so-called spurious correlation. Therefore, the
non-stationary behaviour of the market value, the book value and the residual income could cause spurious regression results when conducting only an empirical test using OLS regression without first examining the statistical properties of explanatory variables (Lee, 2012). In other words, the test results will show large R2 or significant t-statistics due to the spurious results, thereby not reflecting the accurate economic correlation (Dougerthy, 2011, p. 475). Despite the reservations, Myers (1999) and Ahmed et al. (2000) examined the correlation between the market value and the book value by using OLS regression without examining the properties of explanatory variables.
Qi (2000) studied the relationship between the market value, the book value and the residual income using a cointegration test that surpasses econometric issues. He found that accounting numbers capture the time variation of the stock price in only 25 per cent of the firms studied. The low correlation between the book value and the market value can be explained by the
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8 omitted information in the Ohlson (1995) model. From that perspective, the omitted
information is seen as value-relevant events that have not been incorporated in the financial statement. The omitted information is captured by future abnormal earnings which reflect the non-accounting information independent of the current and past earnings. The book value and the residual income are lagging in adjusting to the market value while incorporating the omitted information into the intrinsic value. This happens partly due to the opaque nature of the omitted non-accounting information. In other words, the market value is more forward-looking and incorporates a broader source of information than the book value or the residual income. This will be further explained in Section 2.5.
In prior literature, several attempts to specify the ‘omitted information’ were made. The first studies implemented a cross-sectional approach by only trying to reflect the omitted
information by searching for missing variables, thereby attempting to control the other missing information. Frank and Lee (1998) suggested analysts’ forecasts of the next year’s earnings to reflect the omitted information in conjunction with the Ohlson model. Dechow (1999) incorporated an analyst forecast and found very limited improvements. Hands and Landsman (1998) used dividends; Barth (1999), research and development expenses; Callen and Morel (2005), pension liabilities; and Brow and Caylor (2006), audit fees.
In general, the discussion in prior literature regarding the Ohlson model as an accounting approach to explain the security price is primarily focused on defining the other information and the correct specifications (Qi, 2012, p. 537).
2.2 Ohlson (1995) model
The Ohlson (1995) model is a valuation function that provides a concrete and complete framework to deal with value and accounting data. The model is based on three analytical assumptions (Ohlson, 1995, p. 663). The underlying assumptions are based on the DCF method and the dividend discount model.
First, the market value is determined by the present value of expected dividends (PVED), based on the available information set.
9 where MVt I is the firm’s market value of common equity at time t, Rf is the risk-free rate, Et
is the expected value, based on the information at time t and dt is dividend at t + . The
assumption of clean surplus accounting follows:
(2)
where BVt is the book value of equity at time t, NIt is earnings for the prior period and dt is
dividend.
( ) (3) After combining equations 1 and 2, the following is obtained:
∑
) (4)
The equation 4 cannot be established unless assumption linking the realized accounting number with future residual income are made. Therefore, the forecasting horizon was limited in most prior studies. However, Ohlson (1995) assumed linear information dynamics.
(5a)
(5b)
where is the unpredictable mean-zero disturbance term and the information other than residual income.
(6) where
(7)
(8)
The models from Qi (2002) provide closed-form equations not based on assumptions in contrast to prior studies. Furthermore, equation 5b enables other omitted information to be endogenously incorporated; therefore, it is consistent with prior empirical studies.
10 2.3 Usability accounting information
2.3.1 Market efficiency
In efficient capital markets, security prices fully reflect the available information in a rapid and unbiased fashion. Therefore, investors were unable to benefit from an analysis of financial information by attempting to predict future prices and looking for undervalued companies since all the relevant information is reflected in the market price. However, historically some investors have consistently outperformed the others. This shows that one group has an information advantage over the other; this could indicate that not all information is disseminated publicly. Therefore, efficient markets are slotted into three categories— strong, semi-strong and weak. The difference lies in the amount of information made available to the public, thereby affecting the time needed to adjust the market price which fully incorporates the information. Moreover, the market price could be undervalued or overvalued when the information is known only by a small group of investors. This provides an opportunity to generate additional profits. From this perspective, the ‘strong’ form can be described as monopolistic access to the relevant information by a small group of investors. There is little academic evidence for this hypothesis. On the other side of the spectrum is the ‘weak’ form which supports the view that all relevant information is in public domain and factored into the market price. The ‘semi-strong’ form is in between the two stages and claims that all public information is reflected by the market price and private relevant information will cause adjustments in the market price when made public. The semi-strong hypothesis is widely accepted in academic literature.
2.4 Information dynamics
In academic literature, a firm’s earning number (the accounting net income) is an accrual measure of its profit or loss because, in contrast to cash flows, it allows matching and timing at recognition. Therefore, it better reflects the profit or loss. The security returns (the change in a firm’s market value over a period of time plus the dividends paid) can be seen as a measure of its earnings performance.
Ball (1968) found that that the information contained in the annual income is useful if the actual income differs from the expected, the market typically has reacted in the same direction. Most of the information contained in the reported income is anticipated by the market before the annual report is released. Nichols and Wahlen (2004) found that most extreme changes in earnings are associated with a 72.2 per cent difference in abnormal returns
11 on an average over 1988–2001. Furthermore, they found that earnings are better in explaining the security returns than the cash flow of operation because of the accruals component. Dechow (1994) argued that information asymmetries create a demand for a measurement of a firm’s performance over finite intervals. However, using realized cash flows over finite intervals creates problems of timing and matching which cause noise. Accruals are set in place to mitigate these problems to make sure that earnings reflect a firm’s performance better than cash flows. Therefore, the overall evidence suggests that accruals play an important role in improving the ability of earnings to reflect a firm’s performance.
Beaver (1998) argued that there are three theoretical links between earnings and security prices when analysing the valuation implications of earnings information in capital markets. Beaver (1998) suggested that current earnings provide relevant information due to the use of accrual accounting which contains valuable information about the earning capacity of a firm. Furthermore, it provides users with additional information to predict future earnings. Current and future earnings indicate future dividend payout potential and this enables shareholders to deduce expectations of future dividends. Moreover, the value of firms can been seen as the current value of future dividends the shareholders can expect to receive. This has significant implications on valuations of a firm. Beaver (1998) concluded that new earnings information triggers a change in investor expectations of future dividends thereby affecting the market value of the firm.
Sloan (1996) studied to see if investors correctly process the information contained in the accrual and cash component of earnings. In order to determine if the persistence of earnings is dependent on the relative magnitudes of the accrual or cash flow components of earnings. The accrual component has lower persistence than the cash flow component. However, Sloan (1996) claimed that investors do not correctly distinguish the different properties of these components. Instead, it seems that investors naively fixate on earnings and stock prices and, therefore, do not correctly reflect the information conveyed by accruals and cash flows. These results are inconsistent with the efficient market hypothesis. Kormendi and Lipe (1987), and Nichols and Wahlen (2004) studied the correlation between earnings persistence and stock returns. Both studies found that high-persistence firms tend to experience higher returns in comparison to low-persistence firms with earnings increases, while there are almost no changes during downtime.
12 Bernard and Thomas (1989), and Nichols and Wahlen (2004) noticed that markets react not fully to the new information in earnings when it is announced, and stock returns after announcements are related to the ‘old’ earnings surprise. The market is not completely efficient, especially when unexpected earnings are extreme. A large portion of the reaction to information reflected in earnings happens quickly, with a substantial portion occurring weeks before the earnings announcement and a small portion of reaction occurs after the
announcement
3 Data
3.1 Descriptive statistics
Our sample has been collected from the Compustat annual industrial file database. As mentioned in Section 2.1, we collected book values, market values and residual incomes for the time period between 2000 and 2013. Our initial data set contained 32,643 firms, but the data on stock closing prices, total book values, net incomes and common equity was missing. Therefore, our final set included 8,634 firms which met the data requirements. Although much of our sample selection is similar to Qi’s (2000), we did not divide our sample into industry classification because, in our opinion, it would have led to a biased research since our research would have focused on a certain industry based on our assumption. Qi’s research incorporates only 60 per cent of the firms listed on the New York stock exchanges, focusing on manufacturing, refining and transportation although e-commerce and retail have become more important in the past decade (Qi, 2000, p. 150). Our view is strengthened by the studies conducted by Lee (2012) which found conflicting results and incorporated all companies listed on the New York stock exchanges. Notice, that although initially all firms where included, many dropped in an later stage because they did not satisfy the data requirements.
3.2 Summary statistics
3.2.1 Variables
This part will describe the definition of variables. The market value of common equity at the end of fiscal year is defined as
13 where MVt is the market value of common equity at the end of a fiscal year and the time
period t is the end of the fiscal year. The residual income will be calculated for each year t, similar to Qi (2002), as
(10)
where rt is the cost of capital at time t composed by the estimated sum of monthly treasury
bills and industry risk premium of individual firms. Qi (2002) used treasury bills because when the time-varying components of the cost of capital are used, the value estimates track stock price more closely. Furthermore, we determine the r cost of capital by calculating the weighted average cost of capital (WACC) as
(11)
(12)
(13)
where E is common equity, D is the total debt and includes the short-term debt, is the cost of debt and Re is the cost of equity.
3.2.2 Overview statistics
The average market value of a firm in our sample is around USD 7.69 billion, which is almost three times the average book value. This is consistent with the equity and debt ratios in our sample. Furthermore, the level of residual income seems consistent with Qi’s (2000) study. However, the deviations seem very broad and, therefore, we removed the top 5 per cent of the data for the residual income to reduce the effect of extreme outliers in our research. Overall,
14 our sample seems consistent with comparable studies and the results seem congruous with expectations in comparison to the similar study by Qi (2000).
Table 1: Descriptive Statistics
Mean Std. dev Min. Max/
MV 7690,363 20051,16 0,0001 626550,4 BV 2169,606 9343,242 -85340 236956 RI 260,12 2.066,54 -96.746,01 95.769,52 WACC 0,01 1,44 -58,00 179,50 RD 0,34 5,77 -0,23 473,00 ROE 0,23 14,96 -790,61 1.099,27 Equity ratio 0,73 6,68 -408,37 700,43 Debt ratio 0,27 6,68 -699,43 409,37 Market return 0,11 0,67 -1,00 6,00 4. Methodology
The methodology in this section comprises three parts. First, the hypothesis will examine if the book value, the market value and the residual income are stationary by employing three different tests. These are the augmented Dickey-Fuller (ADF) (1979) test, the Phillips and Perron (1987) test—which is more robust than the ADF (1979) test since it controls the serial correlation similar to Qi (2000)—and the Ziwot and Andrews (1992) test, which allows for potential structural breaks (changes). Second, the hypothesis will be tested to see if the market value, the book value and the residual income are cointegrated by using two tests—the
conventional Engle and Granger (1987) test, which is similar to Qi (2000), and the Johansen (1988) test, which shifts from a traditional OLS regression to a multivariate model that has more desirable statistical properties and could improve the fitting of the data. Finally, the hypothesis will be tested if analyst forecasts, the book value and the residual income are cointegrated by using the Engle and Granger (1987) and Johansen (1988) tests. For all the
15 mentioned test methods, the optimal number of lags was found by using the Akaike
information criterion (AIC).
Overall, the set-up will be constructive, because non-stationarity needs to be established before a cointegration test is used.
4.1 Unit root tests
In the following section, we will use different unit root tests to examine relevant variables (RV), which include MV, BV, RI and AF, on non-stationarity.
Dickey and Fuller (1979) developed the first unit roots test for testing non-stationarity of a time series consisting of three stages. The first stage includes only an intercept, the second only a deterministic trend, and the third both the trend and the intercept. This is represented in the following equations
∑ (14)
∑ (15) ∑ (16)
where is the individual relevant variable, is the first difference of relevant variable, is the constant, is the trend and are the estimated residuals.
However, the ADF test has some shortcomings. It assumes that errors are independently distributed and have a constant variance. Therefore, Phillips and Perron (1987) extended the models, allowing the deviation of errors and proposing a non-parametric test which controls the serial correlation. Their test has two stages: the first includes only an intercept, and the second includes both the intercept and the trend. It is represented in the equation
(17) (18)
where is the individual relevant variable, is the first difference of the individual relevant variable, is the constant, is the trend, T is the number of observations and are the
16 However, due to the length of our time interval, potential changes could occur in our time series which could mean that the ADF and the Phillips and Perron (1987) test results falsely reject the null hypothesis while the series is integrated in the same order since they do not allow the possibility of a structural break.
Therefore, we use two versions of the Ziwot and Andrews (1992) test to allow the possibility of structural changes. The test allows changes in the constant as well as changes in the intercept and slope. It is represented by equations
∑ (19) ∑ (20)
where is individual relevant variable, is the first difference individual relevant variable, is the constant, is the trend and are the estimated residuals. Here, the dummy variables allow a change in the intercept. Next, XUt=1 if t > T, otherwise 0; or change in trend XTt= t-T
if t > T, otherwise 0.
After the time series of MV, BV, RI and AF exhibited non-stationarity in the prior section, we can continue with the cointegration test.
4.2 Cointegration tests
This section will describe and explain the Engle and Granger (1987), and Johansen (1988) tests. Two or more non-stationary series variables could have a linear combination which is called cointegration. In other words, we will examine the existence of a long-run equilibrium relationship between two stock markets. The information contained by the book value and the residual income will slowly be adjusted to the long-run equilibrium. This is in the spirit of the Ohlson model, which suggested that the information dynamics from the accounting number will slowly be fed into the intrinsic value (market price) or vice versa.
4.2.1 Engle and Granger
The Engle and Granger (1987) cointegration test has two stages. In the first stage, the residual squares are estimated by using an OLS regression. It is represented in the equations
(21)
17 where both and are individual relevant variables. The estimated residual are
temporary deviations from the long-run equilibrium and p is the number of variables in the equation.
Next, the ADF test will be conducted on the estimated residual . using the model ∑ (23)
where is the estimated residual. The number of optimal lags for k is determined by using AIC.
If the estimated residual is stationary, the null hypothesis will be rejected and there will be no long-run relationship between the two stock markets. The empirical T-distribution is not similar to the ADF test as described in Section 4.1 because the unit root test is now applied on the estimated residuals. By conducting an ADF test, similar problems, as mentioned in
Section 4.1, will be deemed valid. We hope to overcome these problems, especially with the choice of optimal lags by using the AIC. Overall, the test is relatively easy and sufficient for examining the cointegration between two variables. However, the test has a stringent
restriction4 which assumes a common factor in the dynamics of the model. When this restriction does not hold, it could have a severe effect on the power of the model (Sjo, 2008, p. 11).
4.2.2 Johansen
Next, we will conduct a Johansen cointegration test which has more desirable statistical properties—all variables are endogenous and there are no restrictions as in the Engle and Granger test (mentioned in Section 4.2.1).
In this study, we employ the Johansen (1988) cointegration test. We start with the following vector autoregression 5(VAR) model
(24)
Condition: = = + 5
In the VAR model each variables is treated symmetrically and each variables has equation based on his own lags and the relation with the lags of the other variables. Therefore VAR modeling does not require as much knowledge about omitted variables in contrary to OLS method. It is sufficient to only included variables which relevant literature suggest to affect each other intertemporally.
18 where is the vector of the individual relevant variable, and vector of
residuals. We assume that is integrated to the order I (1), r are linear combinations of and are stationary; therefore, the cointegration vector, 0 < r < p, than the cointegration vectors can be represented as (Sjo, 2008, p. 14)
̀ (25)
where βi represents the i cointegration vector and j represents the effect of each cointegrating
vector on . Therefore, the number of stationary relationships is similar to the number of cointegration vectors in . It implies that all rows will be zero if there are non-stationary relationships and vice versa. This means some rows will be non-zero if there is a stationary relationship. Therefore, the rank of establishes the number of independent vectors which reflects the number of cointegration vectors. However, the rank is determined by the number of significant Eigen values found in , which can be found by using two different likelihood ratio tests— and —represented in the following models
∑ (26)
) (27)
The null hypothesis , where only the first r Eigen values are non-zero, rejects the
existence of a stationary relationship. The alternative is , where more than one r Eigen values are non-zero. Next, for the null hypothesis, there exists a cointegration vector
which is tested against the alternative of r+1 vectors (Sjo, 2008, p. 15).
Sjo (2008) argued that the trace is better since it is more robust to skewness and excess kurtosis.
4.3 Granger causality test
The previous section described the methodology which examines the long-run dynamics between variables. However, prior academic literature suggests that short-run6 interaction also plays an essential part. Therefore, Granger introduced a causality test to see if x causes y, does x contain useful information to predict y in the short run (Stock and Watson, 2011, p. 580). The models are formulated below
6Note that the frequency of the short run is a book year which could be seen as a long-run interval.
19 ∑ ∑ (28)
̇ ∑ ∑ (29)
where is the mean of each relevant variable of individual firms, is the coefficient and the direction, denotes the constant and denotes the residual. The relevant variables are BVt,, MVt and RIt.
The Granger causality test studies the predictive usefulness of variables by conducting an F-test on the coefficient .
⁄ (30)
where RSSr denotes the constrained residual sum of squares, RSSu denotes the unconstrained
residuals sum of squares, m denotes the number of observations and k the number of parameters (Stock and Watson, 2011, p. 580).
5. Results
This section will analyse the existence of a long- and short-run equilibrium between the book value, market value and residual income derived from the Ohlson model (1995). Therefore, we use two cointegration tests—the Engle and Granger test and the Johansen test—to analyse the long-run equilibrium. In order to deploy these tests, we need to ensure that our time series is stationary by using a unit root test. Finally, we will analyse the short-run dynamics by employing a Granger causality test.
5.1 Unit root results
As mentioned in Section 5, we first used two unit root tests—ADF (1981, ADF) and Phillips and Perron (1987, PP)—to analyse the characteristics of the time series both on the first level and the difference independently.
20 Overall, the ADF test results show that the null hypothesis cannot be rejected for the level series of the residual income, the book value and the market value on a significance level of 5 per cent. However, the results show some discrepancies for the level series of the market value with the trend which reject the null hypothesis at a significance level of 10 per cent. The results for the first difference reject the null hypothesis of the unit roots for all variables. Our results show that the first difference series of the residual income, the book value and the market value are non-stationary and integrated of the first order at a significance level of 5 per cent. Our findings are consistent with prior literature that the time series of the residual
income, the book value and the market value is stochastic. More important, these results show that the individual series are independent of each other, and this has implications. First, it could lead to spurious regression results in prior studies, when it is not especially tested and corrected, when conducting an OLS regression as mentioned in Section 2.1. Furthermore, it shows that there is no deterministic relationship between the different variables since they follow a stochastic movement.
In order to enhance the strength of our results, we will conduct a Phillips and Perron (1989) test which has more desirable characteristics in the following section. The results are presented in Table 2.
21 5.1.2 Phillips and Perron test
Our Phillips and Perron test results for the level time series do not consistently reject the null hypothesis for the unit root. Moreover, only the level time series for the residual income with a trend and book value with only intercept seem to reject the null hypothesis. In contrast, our test results for the first difference seem to reject the null hypothesis at a significance level of 1 per cent. Therefore, our variables are integrated of the first order. These results are consistent with the ADF test results
Table 2: Augmented Dickey-Fuller Test
The values in the table represent the results of the ADF test on both the levels and the first difference of the independent variables. The optimal number of lags was found by using the AIC. Hence, ***, ** and * imply significance at 1%, 5% and 10%.
Test statistic
RI Level Intercept and without trend -1,274
Number of Lags: 1 With trend -3.026
Intercept and trend -1,274
First difference Intercept and without trend **-3,681
Number of Lags: 2 With trend **-3,801
Intercept and trend *-3,681
BV Level Intercept and without trend 2,562
Number of Lags: 3 With trend -1,068
Intercept and trend 2,562
First difference Intercept and without trend *-2,716
Number of Lags: 1 With trend **-3,567
Intercept and trend *-2,892
MV Level Intercept and without trend -0,63
Number of Lags: 1 With trend *-3,3
Intercept and trend -0,63
First difference Intercept and without trend *-3,722
Number of Lags: 2 With trend **-3.619
Intercept and trend *-1,63
The critical values from MacKinnon (1991), intercept: 1% (-3.43), 5% (-2.86) and 10% (-2.57); trend: 1% (3.96), 5% (- 3.41) and 10% (-3.12).
22 found in Section 5.1.1. After establishing the non-stationarity of the time series in the section, we can continue with testing the cointegration. The results from the Phillips and Perron test are shown in Table 3.
5.2 Cointegration results
5.2.1 Engle and Granger test
Our Engle and Granger test results do not show a long-run relationship between the market value and the book value or the residual income. The results conflict with prior literature, because accounting information is seen as a source of relevant information, but it is in competition with more viable sources, as shown by Ball (1968). From that perspective, Beavers (1998) and others saw that new earnings trigger a change in investor expectations for future dividends, which influence the market valuations of a firm. Therefore, it is more
Table 3: Phillips and Perron Test
The values in the table represent the results of the Phillips and Perron Test on both the levels and the first difference of independent variables. The optimal number of lags was found by using the AIC. Hence, ***, ** and * imply significance at 1%, 5% and 10%.
Test Statistic
RI Level Intercept and without trend -1,476
Number of Lags: 1 With trend **-3,63
First difference Intercept and without trend *-4,438
Number of Lags: 2 With trend **-4,22
BV Level Intercept and without trend **3,179
Number of Lags: 3 With trend -1,454
First difference Intercept and without trend *-4,858
Number of Lags: 1 With trend *-6,115
MV Level Intercept and without trend -0,876
Number of Lags: 1 With trend -2,811
First difference Intercept and without trend *-3,889
Number of Lags: 2 With trend **-3,729
RI is the residual income, BV is the book value and MV is the market value. The critical values from MacKinnon (1991), intercept: 1% (-3.43), 5% (-2.86) and 10% (-2.57); trend: 1% (3.96), 5% (- 3.41)
23 surprising that there is no cointegration between the residual income and the market value because you would intuitively expect a framework between earnings and share values from previous literature. Furthermore, there seems to be no cointegration between the book value and the market value. The results seem consistent with prior studies from Qi (2001) who found that the market value is not cointegrated with the book value or the residual income. Lee (2012) initially found similar results, but after relaxing their constraints and implementing their fractional integration framework found a long-run equilibrium between the market value, the book value and the residual income.
There seems to be a cointegrating relationship between the residual income and the book value. This can partly be explained by the use of accruals which enables users of financial statements to structure the cash flows generated by their assets in a way that they reflect the performance of the firm. This is a very interesting finding, but beyond the scope of our research topic.
5.2.2 Johansen test
In the following section, we use a bivariate cointegration test analysing the trace statistic ( ) and the maximum value statistic ( . The Johansen test will only indicate the
rank of the cointegration vectors, which would imply that there exists a vector between the variables on the long-run. Our results confirm the long-run dynamics between the BV and the RI at a significance level of 5 per cent. More surprising is the discovery of a vector between the MV and the BV at a significance level of 1 per cent. Furthermore, the results show the existence of a vector between the RI and the MV at a significance level of 1 per cent. Both results are surprising and conflict those found in the Engle and Granger test in the previous section. The explanation for these results could have two perspectives—analytical and
Table 4: Engle and Granger Cointegration Test
MV BV RI
MV -2,658 -1,849
BV -2,256 **-3,252
RI -2,14 ***-3,926
24 economic literature. The nature of the model used by Johansen7 is different. It examines a three-dimensional space using vectors, in comparison to the Engle and Granger model which uses OLS8 in a two-dimensional space. The Johansen test thereby broadens the notion of describing the relationship between different variables by analysing the individual vectors which could capture the relationship. Moreover, the test does not exclude the results of the Engle and Granger model but widens the narrative of the potential relationships it researches. Academic literature also explains the relationship by creating a framework between the book value, the earnings and the market value. First, earnings contain relevant information
regarding a firm’s performance, thereby influencing its share value. Second, earnings reflect the performance of assets. Therefore, you can expect that all three variables are independent of each other but share a long-run equilibrium. This in line with the reasoning behind the Ohlson (1995) model which can be applied to all accounting approaches provided the clean surplus accounting condition is satisfied. Furthermore, these results contradict the study by Qi (2001) who found that only 25 per cent of the accounting information explains the market value. This can be partly explained by the different set-up and time period of their sample. They divided their sample into different industry classifications using only 60 per cent of the total available data. This could lead towards a bias while choosing certain industries that exhibit a lot of uncertainty. More explicitly, their focus was on manufacturing, refining and transportation, while e-commerce and retail have become more important in the past decade. Therefore, the time period of their sample could affect their results since the composition of the New York Stock Exchange index has changed in the past decade. Their results were initially supported by Lee (2012). However, they found that after loosening the constraints there was a cointegration between the market value, the book value and the residual income. Therefore, our results are consistent with the results found by Lee (2012). Moreover, our research is more comparable as they do not make a distinction between industry
classifications.
7 See Section 4.2.2.
8
25 5.3 Granger causality results
Next, we look at the short-run dynamics between the market value, the book value and the residual income by employing the Granger causality test. One would expect a significant relationship since academic literature shows that earnings contain relevant information which can influence the market price. There are two main underlying assumptions. First, earnings provide investors with additional information regarding dividends, which enables to better forecast their future earnings, and this information will likely affect overall stock prices. Second, it will provide additional information to investors on the earnings potential of the firm. Both assumptions are very similar. However, their underlying thought fundamentals differ. The first is based on valuing the firm only on future dividends (see Section 2.2), while the second sees accounting information as one of the many sources of information at an investor’s disposal to value the firm. From both perspectives, one would expect earnings to affect the market value, but with differing magnitudes.
Our results show that the residual income contains information useful for predicting the book value in the short run. Surprisingly, one would expect, from prior academic literature, a Granger causality to exist. Since the residual income (earnings) enables users to predict the earnings potential of a firm, it can also help predict the frequency of dividends and the amount when valuing the firm. However, our results do show short run dynamics between market
Table 5: Johansen Cointegration Test
MV BV RI
Trace Max Trace Max Trace Max
r = 0 r ≥ 1 r ≤ 1 r=2 r = 0 r ≥ 1 r ≤ 1 r=2 r = 0 r ≥ 1 r ≤ 1 r=2
MV 0,97 0,01 37,58*** 0,06 0,88 0,01 23,30*** 0,07
BV 0,97 0,01 37,58*** 0,06 0,24 0,44 14,60*** 4,66
RI 0,88 0,01 23,30*** 0,07 0,24 0,44 14,60** 4,66
Statistical significance is denoted; r = 0; λ (max): 14,07 (5%)**, 18,63 (1%)***. λ (trace): 15,41 (5%)**, 20,04 (1%)***. r ≥ 1; λ (max): 3,76 (5%)**, 6,65 (1%)***. λ (trace): 3,76 (5%)**, 6,65 (1%)***.
26 value and book value or residual income. Therefore it seems that accounting numbers do not provide useful information on the predicting the market value on the short run. This views is extensively supported by academics literature. Hence, accounting numbers slowly9
incorporate new relevant information, see section 2.4. The efficient market theory suggest that the new information is already incorporated by the security price before the accounting number are released, therefore the impact on the short run is limited.
6. Conclusion
In this study, we empirically investigated if the Ohlson model is able to explain the market value, which is a function of the book value and the residual income. We used cointegration tests developed by Engle and Granger (1987), and Johansen (1988) to examine this
relationship. Most prior academic literatures focused on studying the omitted variables by using cross-sectional regression methods, such as OLS. However, our results show that the market value, the book value and the residual income exhibit non-stationary behaviour which could lead to spurious results when using OLS. Therefore, we used cointegration tests
developed by Engle and Granger (1987), and Johansen (1988) to examine this relationship to avoid potential problems with spurious results.
9 Note, that our short run time interval is annually, which is seen in practice as long run. Table 6 Granger-Causality Test (Pair Indices)
F Prob MV-BV 0,705 0,703 MV-RI 1,929 0,381 RI-BV 14,608 0,001*** RI-MV 1,155 0,561 BV-RI 6,900 0,032** BV-MV 1,168 0,558
27 Our Engle and Granger (1987) test results did not show a long-run relationship between the market value, the book value and the residual income. These results were consistent with Qi (2000) and the initial findings of Lee (2012). However, the Johansen (1988) test results exhibited a relationship between the different variables, which is consistent with the findings of Lee (2012). Therefore, the relationship between the market value, the book value and the residual income is a mean reverting process. In other words it provides evidence that the Ohlson model is able to explain the long-run equilibrium between market value and accounting numbers. However, our time periods are annual so a long run from this
perspective would be defined as multiple years. Therefore one can question how useful the information is.
To address these issues, we conducted a Granger causality test to examine the predictive value of one variable on the other. Our results show that the book value and the residual income do not provide predictive information in forecasting the market value annually. However, our results do show a predictive power of the book value in forecasting the residual income and vice versa. The reasoning could be managerial behaviour, which is beyond the scope of our research despite being a very interesting topic for further research.
Overall, our results support the view that the Ohlson framework explains the relationship between the market value, the book value and the residual income in the long run. However, it does not provide useful information on the book value and the residual income predicting the market value in the short run.
7. Discussion
In our research set-up, we chose to not divide our sample under industry classification as Qi (2000) did because it would have led to a bias. I However, it did affect the risk premium we used for calculating the WACC. Therefore, it could be overweight or underweight for some firms. In my opinion, it would have a minimal effect given the large sample but it is an issue to acknowledge. Furthermore, our results show long- and short-run dynamics between the book value and earnings. It would be interesting to see a study and understand where this relationship comes from.
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