**The Response of Stock Pr ices to Per manent and Tr ansitor y **

**Shocks to Accounting Ear nings**

**Chiawen Liu**

*****

Assistant Professor, Department of Accounting Yuan Ze University

**Taychang Wang**

Professor, Department of Accounting National Taiwan University

**ABSTRACT**

The purpose of this research is to use stock return and price-earnings ratio to study the impacts of earnings shocks on stock prices. We assume that the stochastic process of earnings and stock price consist of a permanent and a transitory components. What distinguishes this paper from most accounting and finance research is that the permanent part of stock price or earnings need not be random walk. The stock valuation model in Miller and Modigliani (1961) and Miller and Rock (1985) helps link a company’s earnings and stock price. Since we do not assume that the permanent part of earnings is random walk, there will be an identification problem with building a bivariate time series model, which can be handled by invoking the aforementioned theoretical relation. Through variance decomposition and impulse response analysis, we are able to see how stock return and price-earnings ratio dynamically respond to the permanent and temporary shocks to accounting earnings, which tells us how stock returns are determined. The results of the analysis show that a considerable part of the variation in stock returns can be explained by the transitory shocks to earnings, which suggests that the investors fail to distinguish between the permanent and transitory parts of earnings unmistakably. The mean-reverting behavior of stock returns can also be explained by the existence of a significant temporary component in the stock returns. The price-earnings ratios are mainly explained by the temporary shocks to earnings. This signifies that, induced by the temporary component of earnings, stock prices respond excessively to earnings.

**Keywor ds: Permanent earnings; Transitory earnings; Stock prices; Bivariate time **

series model

**1. INTRODUCTION**

It is clear that all the events that may create or destroy a company’s value will eventually reflect in earnings. The market value of a company approximately equals the book value during the start-up and the liquidating periods. In the long run there must be a fundamental connection between the changes in market value (stock return)

*

We are grateful for the support from National Science Council (Grant No. NSC 88-2416-H-002-010). pp. 35-54

and changes in book equity (earnings) on a per-share basis.1 However, in the short run, the relationship between stock returns and earnings is not as clear-cut, which is affected by how accountants measure short-run earnings. In addition, different components of earnings will have different value implications. Compared to the transitory component, the permanent component of unexpected earnings generally has a greater effect on stock return. However, it is not clear how we should slice up the unexpected earnings into these two components. It has been suggested that we could choose a bifurcation on the income statement, such as income from continuing operations, and all the items above this are classified as permanent and below it transitory. A finer approach is to examine the time-series property of earnings. One purpose of our analysis is to use the multiple time series model to estimate the permanent and transitory components of the accounting earnings.

The relationship between earnings and stock prices can be dated back to Benston (1966) and Ball and Brown (1968). They studied the relationship between changes in stock prices and changes in accounting earnings. Ball and Brown found out that the sign of stock price changes is positively related to that of the earnings changes. Beaver, Clark, and Wright (1979) extended Ball and Brown (1968) by considering the magnitude of the changes in earnings. They divided their sample into 25 portfolios according to the residual percentage changes in price and noticed that the residual percentage changes in earnings was positively related to the residual percentage changes in price. Judging from the magnitude of the changes in stock prices, it appeared the investors thought that some of the unexpected earnings was enduring and related to the dividend-paying ability in the future. However, the relationship between the changes in stock price and the changes in earnings is not constant across the portfolios. For the extreme portfolios, the percentage change in stock prices is less than that of the earnings, suggesting part of the unexpected earnings is temporary. The temporary part will affect only the current earnings, not the expected future earnings. Kothari and Sloan (1992) found that the lagged earnings have additional power. Beaver, Lambert, and Morse (1980) assumed ungarbled earnings is a first-order integrated moving average process. In this case, the regression coefficient of the price changes on earnings changes is related to the coefficient of the moving average process. Easton, Harris, and Ohlson (1992) extended the measuring horizon of the earnings and price changes and showed that, the longer this horizon, the greater the relationship between the price and earnings changes. These studies are dubbed as the information content of earnings research.

Beaver, Lambert, and Morse (1980), Beaver, Lambert, and Ryan (1987), and Kothari and Sloan (1992) studied the information content of prices. Basically, they reversed the role of dependent and independent variables in the information content of earnings studies, which is the so-called reverse regression. Price could help explaining current and expected future earnings. The reason that prices might lead earnings had to do with the historical nature of earnings and the accrual accounting system. The recognition of the value changes in assets and liabilities is delayed in the current accounting system, while the response of stock price is instantaneous. Beaver, NcAnally, and Stinson (1997) used simultaneous equation model to estimate the endogenous relationship between stock return and unexpected earnings. The errors

1

from a single equation model can be eliminated by simultaneous estimation.

Beaver and Morse (1978) found out that stock with high price-earnings ratio in the year-end often had low earnings growth during the year and had a high earnings growth in the years thereafter. Similarly, low price-earnings ratio stocks were associated with high earnings-growth during the year and low earning-growth afterward. If a fraction of the earnings was temporary and the investors knew this, the above phenomenon is explicable.

Kormendi and Lipe (1987) indicated that the extent to which the stock return was affected by the unexpected earnings was linked to the present value of the revisions in future expected earnings. They used univariate time series model to describe the changes in earnings and studied the implication of time-series property on stock valuation equation. They also indicated that the reaction of stock return to unexpected earnings was not strong. Basing on Kormendi and Lipe (1987), Lipe (1990) assumed there existed another information besides accounting earnings and examined the connection between stock return and accounting earnings. He showed that stock return is a function of the persistence of earnings time series, the required rate used to discount expected future earnings, and the relative ability of earnings to forecast future earnings.

The earnings-price relation research has tried to work on the association between the abnormal return and unexpected earnings and has also examined how the persistence of earnings affected stock returns. Some even incorporated the theoretical relationship between earnings and price (e.g., Kormendi and Lipe, 1987). However, seldom did the researchers explore the issue from a bivariate time series framework. In this paper, we use bivariate time series analysis to study the joint behavior of earnings and stock price. We also incorporate the fundamental relationship between stock price and earnings into the estimation of the empirical model. By using the method proposed by Blanchard and Quah (1989), we are able to investigate how the permanent and transitory shocks to earnings affect stock prices and the price-earnings ratio. Another feature of our research is that we use the aggregate monthly data (1871:1-1998:12), instead of the firm-specific data.2 One reason is that it is not possible to get firm-specific data from such a long period. For another, firm-specific earnings data are easily affected by the accounting methods used and the aggregate accounting earnings may be a better proxy for aggregate economic earnings. Furthermore, the present value relation in Miller and Modigliani (1961) is expressed in terms of economic earnings and stock prices.

On the other hand, although the early finance research led by Fama (1970) indicated that the stochastic process of stock price could be described as a random walk, yet studies in the past 15 years showed that the stock return was predictable (e.g., Keim and Stambaugh, 1986; Fama and French, 1988, and Lo and Mackinlay, 1988; Fama, 1991), which means that there exists a transitory component in stock prices so that it was possible to forecast future return by using only the past returns. Fama and French (1988) expressed the logarithm of stock price as the sum of a random walk, the permanent component, and a first-order autoregressive part, the transitory component. Wang (1989) also pointed out that the existence of the uninformed investors would cause excess volatility in stock prices. This is because

2

they erroneously treat the transitory part of dividends as permanent. These studies showed that dividing both the stock price and dividends into permanent and transitory components could help us understanding the behavior of stock prices.

Since both earnings and price series could be nonstationary and cointegrated and our preliminary analysis confirms this, in this paper, we focus on the return series and price-earnings spread series following the treatment in Campbell and Shiller (1987). The returns are computed as the first difference of logarithms of prices and the earnings-price spreads as the logarithms of price-earnings ratio. We use these two series to study the reaction of stock price to permanent and transitory shocks to earnings. We first assume that the stochastic processes of stock price and earnings consist of a permanent and transitory parts. Using the bivariate moving average model and the fundamental relation between stock price and earnings, we can separate the shocks to stock price and earnings into a permanent and a transitory components. By employing variance decomposition and impulse response analysis, we can further analyze the impacts of the permanent and transitory shocks to earnings on the changes in stock prices (stock returns) and price-earnings ratio. This will help us understand the factors that affect stock prices and the way they work. The result in our analysis can be used to explain the mean-reverting phenomenon. In addition, we can show how the degree of stock market efficiency is affected by the permanent and transitory shocks to earnings.

The paper is organized as follows. Section 2 briefly discusses the research method. Section 3 describes the data set and preliminary statistical analysis. Section 4 contains the main empirical findings and Section 5 concludes this paper.

**2. METHODOLOGY**

We use bivariate time series model to investigate the issue of separating the stock price and earnings into a permanent and a transitory components. How the permanent and transitory shocks to earnings affect stock prices and earnings price ratio is the focus of the empirical analysis. The method employed follows from Blanchard and Quah (1989), Quah (1992), and Lee (1995, 1996, 1998). In contrast to other research, permanent earnings need not be a random walk process and the permanent and transitory shocks to earnings need not be statistically independent.3 Since previous research indicated that price and earnings series may be nonstationary and cointegrated, it will not be appropriate to entertain a bivariate time series model of the price and earnings series directly.4 Following Campbell and Shiller (1987) and Lee (1995), we consider continuously compounded stock return and price-earnings spread instead. The former is computed by taking the fist difference of the logarithms of stock prices and the latter by taking the logarithm of price-earnings ratio. These two series are found to stationary empirically. Employing a bivariate time series

3

Kormendi and Lipe (1987) tried to link stock price and earnings. They also intended to separate stock price and earnings into a permanent and a transitory components. However, they used the differenced series and did not take cointegration into consideration and their model may be misspecified.

4_{According to the accounting and finance literature, it seems that stock price, and earnings series are }

nonstationary process. Please see Ball and Watts (1972), Albrecht, Lookabill, and Mckeown (1977), Watts and Leftwich (1977), Kleidon (1986), Marsh and Merton (1986, 1987), Campbell and Shiller (1987), Lee and Wang (1994), Lee (1995) and Lee (1996) for some examples.

model for these two series also takes care of the cointegration problem.5 This model can be regarded as a variation of the error correction model (Engle and Granger, 1987).

The equity valuation model in Miller and Modigliani (1961) and Miller and Rock (1985) connects a company’s stock price with its accounting earnings:

## ∑

∞ = + + + Θ = 1 (1 ) ) | (*i*

*i*

*i*

*t*

*t*

*i*

*t*

*t*

*r*

*I*

*E*

*P*,

where *P _{t}* is the stock price at time

*t*,

*It*+

*i*is the economic earnings at time

*t*+

*i*,

*rt*+

*i*is the investors’ required rate of return for the economic earnings at time

*t*+

*i*, Θ

*is the investors’ information at time*

_{t}*t*, and

*E*(⋅)is the expectation operator.

The above theoretical relation imposes a restriction on the coefficients in the bivariate autoregressive and moving average models on stock returns and earnings-price spread.6 Since our model relaxes the assumption that permanent earnings must be a random walk as long as its first difference is stationary, we need one more restriction for identification. The above theoretical relation helps identify the permanent and transitory components in the stock price and earnings series.

The estimation process is carried out by estimating a bivariate autoregressive model first. The empirical bivariate moving-average model is then obtained with the restriction imposed. This is done by factoring the variance-covariance matrix

### Σ

into*T*

ΛΛ where Λ≡ −1Η

) 1 (

*C* and H is the LT Cholski decomposition of *T*

*C*

*C*(1)Σ (1) and
)

1 (

*C* is the sum of the oo-order VMA coefficients from the Wold decomposition of
the VAR. This will yield impulse response coefficients such that the first variable
may have long run effects on all variables and the second may have long run effects
on all but the first variable. In our paper, the shocks are assigned as the permanent and
transitory shocks. Finally the variance decomposition analysis and the impulse
response analysis are done to explain how the two shocks will affect return and
price-earnings spread differently.

**3. DATA AND PRIMARY ANALYSIS**

We use monthly data for the empirical analysis. Our sample period starts from January 1871 till December 1998. For an explanation of the data set, please see Professor R. Shiller’s homepage.7 The price and earnings series we use are deflated by the price index level.

We first apply the unit-root tests in Dickey and Fuller (1979) and Phillips and
Perron (1988) to the two series to examine if they are stationary. According to the
results in Table 1, the ADF, *Z _{α}* , or

*Z*statistics are all greater than the

_{t}5

If earnings and stock price are cointegrated with no intercept, then it is clear that the difference of logarithm of prices and logarithm of earnings will be a stationary series (see Campbell and Shiller, 1989).

6_{ The implication of this restriction is discussed in Lee (1995), in which the relationship between }

dividends and price are investigated in a bivariate time series model. The relation between earnings and price in our paper is similar.

7

corresponding critical values for the two series, whether the nonzero-mean or the time-trend model is entertained. When the analysis is applied to the two differenced series, almost all the statistics are less than the corresponding critical values, as shown in Table 2. This means that the both price and earnings are integrated of order one, i.e., they are both nonstationary. We then employ the cointegration tests constructed by Engle-Granger (1987) and Johanson (1988) to test if the price and earnings series have long-run equilibrium relationship. The test result shown in Table 3 rejects the null hypothesis that these two series are not cointegrated.

**4. THE MAIN FINDINGS**

Since the analysis in the previous section shows that the price and earnings series are cointegrated, it is not appropriate to use the original series in estimating a usual bivariate autoregressive model. We thus substitute with the two stationary series: the continuously compounded stock return and the logarithm of price-earnings ratio.8 A bivariate autoregressive model is then estimated for these two series. The number of lags used is determined by the AIC and FPE criteria. According to Portmanteau test,

2

*χ* (56) value is 0.632, with p-value 1.000, suggesting there is no autocorrelation in
the residuals. The results in the Lagrange Multiplier test shows the LM (16) value for
the stock price change series is 14.389 with a p-value of 0.5698, and the LM (16)
value for the spread series is 14.295 with a p-value of 0.5768, also indicating that
autocorrelation is not a problem here. In addition, the results shown in Figures 1 and
2 signify that the fitting is good.

The estimated bivariate autoregressive model is then transformed to a bivariate moving-average model with the theoretical restriction imposed. This equivalent to the orthogonalization method proposed by Blanchard and Quah (1989). The next step is to perform a variance decomposition to learn how the forecast error variance of stock price changes can be explained by the permanent and transitory shocks to earnings.

**Table 1: Unit Root Tests of the Stock Pr ices and Ear nings**

We use nonzero-mean and time-trend model for the ADF test. The test statistic used is
the usual t statistic. The critical value is from Fuller (1976, p. 373) and Dickey and Fuller
(1979). Under the nonzero-mean model, the calculation of *Z _{α}* and

*Z*statistics follows from Phillips (1987) and Phillips and Perron (1988). In an ARIMA (1,0,0) model,

_{t}*Z*has the same asymptotic distribution (Fuller 1976, Table 8.5.1, Part 2) as the

_{α}*T*(

*ρ*−1) statistic in Dickey and Fuller (1979), while

*Z*has the same asymptotic distribution (Fuller 1976, Table 8.5.2, Part 2) as the

_{t}*τ*statistic in Dickey and Fuller (1979). Under the time-trend model, the

_{µ}*Z*in an ARIMA (1,0,0) model has the same asymptotic distribution (Fuller 1976, Table 8.5.1, Part 2) as the

_{α}*T*(

*ρ*−1) statistic in Dickey and Fuller (1979), while

_{τ}*Z*has the same asymptotic distribution (Fuller 1976, Table 8.5.2, Part 2) as the

_{t}*τ*statistic in Dickey and Fuller (1979).

_{τ}8

Even though this could be done in a bivariate time series framework, the statistical properties of the estimated coefficients will be complicated.

Series Nonzero-mean model Time-trend model

ADF *Zα* *Zt* ADF *Zα* *Zt*

Price -1.104 -3.006 -1.061 -2.445 -7.659 -2.542

Earnings -0.782 -2.348 -0.202 -2.820 -25.914 -3.096

Critical values (ADF and

*t*

*Z )* Critical values (ADF and

*t*

*Z )*

Nonzero-mean model Time-trend model

T 1% 5% T 1% 5%

100 -3.51 -2.89 100 -4.04 -3.45

250 -3.46 -2.88 250 -3.99 -3.43

Critical values (*Z _{α}*) Critical values (

*Z*)

_{α}Nonzero-mean model Time-trend model

T 1% 5% T 1% 5%

100 -19.8 -13.7 100 -27.4 -20.7

250 -20.3 -14.0 250 -28.4 -21.3

**Table 2: Unit Root Tests of the Differ enced Ser ies **
**of Stock Pr ices and Ear nings**

We use nonzero-mean and time-trend model for the ADF test. The test statistic used is
the usual t statistic. The critical value is from Fuller (1976, p. 373) and Dickey and Fuller
(1979). Under the nonzero-mean model, the calculation of *Z _{α}* and

*Z*statistics follows from Phillips (1987) and Phillips and Perron (1988). In an ARIMA (1,0,0) model,

_{t}*Z*has the same asymptotic distribution (Fuller 1976, Table 8.5.1, Part 2) as the

_{α}*T*(

*ρ*−1) statistic in Dickey and Fuller (1979), while

*Z*has the same asymptotic distribution (Fuller 1976, Table 8.5.2, Part 2) as the

_{t}*τ*statistic in Dickey and Fuller (1979). Under the time-trend model, the

_{µ}*Z*in an ARIMA (1,0,0) model has the same asymptotic distribution (Fuller 1976, Table 8.5.1, Part 2) as the

_{α}*T*(

*ρ*−1) statistic in Dickey and Fuller (1979), while

_{τ}*Z*has the same asymptotic distribution (Fuller 1976, Table 8.5.2, Part 2) as the

_{t}*τ*statistic in Dickey and Fuller (1979).

_{τ}Series Zero-mean Model Nonzero-mean Model

ADF *Zα* *Zt* ADF *Zα* *Zt*

Price -3.916 -77.179 -3.881 -3.875 -101.540 -9.074

Earnings -6.893 -95.526 -5.537 -6.862 -89.149 -7.721

Critical values (ADF and *Z ) _{t}* Critical values (ADF and

*Z )*

_{t}Nonzero-mean model Time-trend model

T 1% 5% T 1% 5%

100 -2.60 -1.95 100 -3.51 -2.89

250 -2.58 -1.95 250 -3.46 -2.88

Critical values (* _{Z}_{α}*) Critical values (

*)*

_{Z}_{α}Nonzero-mean model Time-trend model

T 1% 5% T 1% 5%

100 -13.3 -7.90 100 -19.8 -13.7

250 -13.6 -8.0 250 -20.3 -14.0

**Table 3: Cointegr ation Tests of the Stock Pr ices and Ear nings**

The following table contains the results from the Engle-Granger and Johanson cointegration test. The calculation of the statistics is based on a bivariate autoregressive model with an order of 36, consistent with the order used in the unit root test.

Engle-Granger test

Price Earnings

-4.01 -4.12

5% critical value -3.93 -3.93

Johanson test Nonzero-mean model Time-trend model

Number of common trends Number of common trends

Nonzero-mean *k*=0 *k*=1 *k*=0 *k*=1

34.92 7.56 30.23 4.87

5% critical value 35.07 20.17 29.51 15.20

Through forecast error variance decomposition, we are able to determine the
proportion of the *k*-step ahead forecast error variance of the two variables attributable
to the permanent and transitory shocks to earnings. Take three periods as an example.
If the corresponding numbers indicate that the 3-step ahead forecast mean squared
errors (MSE) are 0.0396 and 0.0965 for stock return and price-earnings spread
respectively. For stock return, 72.76% of the 3-step ahead MSE is attributable to the
permanent shock to earnings and 27.24% to the transitory shock to earnings. For
price-earnings spread, 39.26% of the 3-step ahead MSE is attributable to the
permanent shock to earnings and 60.74% to the transitory shock to earnings.

Figure 3 depicts the results from variance decomposition. The dark (light) part is the stock price changes that can be explained by the permanent (transitory) shock to earnings. It can be seen that most of the stock returns can be explained by the permanent shocks to earnings. However, the part that is explained by the transitory shocks to earnings is also significant compared to what could be observed in an efficient market. It appears that the investors cannot distinguish between the permanent and the transitory shocks. The stock price changes are still affected even for several months after the transitory shock to earnings in one month.

The dark (light) part in Figure 4 is the variance of the price-earnings spread that can be explained by the permanent (transitory) shocks to earnings. It is easily seen that the variation in price-earnings spread is mainly due to the transitory shocks to earnings. This implies that the changes in price-earnings ratio are mostly contributed by the transitory shocks to earnings rather than the permanent shocks. This is consistent with what Beaver and Morse (1978) has found.

We can use impulse response analysis to learn the dynamic effects of the permanent and transitory shocks to earnings. As in the variance decomposition analysis, we also considered 36 periods. Table 4 shows the estimation results of the impulse response analysis.

**Figur e 1: The Residual Analysis of the Stock Retur n Ser ies**

The upper half of the figure depicts the plot of the residuals of the bivariate autoregressive model for the first difference of the logarithm of stock prices (DNLP), i.e., stock returns. The lower half displays the autocorrelation and the partial autocorrelation coefficients of the residuals. The red lines are the two standard deviation boundaries.

**VAR Residuals for **

**DLNP**

**1874 1883 1892 1901 1910 1919 1928 1937 1946 1955 1964 1973 1982 1991**

**-0.27**

**-0.27**

**-0.18**

**-0.18**

**-0.09**

**-0.09**

**-0.00**

**-0.00**

**0.09**

**0.09**

**0.18**

**0.18**

**0.27**

**0.27**

**0.36**

**0.36**

**Autocorrs** **Partial Autocorr** **UP** **DOWN**

**0** **1** **2** **3** **4** **5** **6** **7** **8** **9** **10** **11** **12** **13** **14** **15** **16**
**-0.2**
**0.0**
**0.2**
**0.4**
**0.6**
**0.8**
**1.0**
**-0.2**
**0.0**
**0.2**
**0.4**
**0.6**
**0.8**
**1.0**

**Figur e 2: The Residual Analysis of the Pr ice-Ear nings Spr eads Ser ies**

The upper half of the figure depicts the plot of the residuals of the bivariate autoregressive model for the price-earnings spread (logarithm of price-earnings ratio). The lower half displays the autocorrelation and the partial autocorrelation coefficients of the residuals. The red lines are the two standard deviation boundaries.

**VAR Residuals for **
**LNPE**
**1874 1883 1892 1901 1910 1919 1928 1937 1946 1955 1964 1973 1982 1991**
**-0.3** **-0.3**
**-0.2** **-0.2**
**-0.1** **-0.1**
**-0.0** **-0.0**
**0.1** **0.1**
**0.2** **0.2**
**0.3** **0.3**
**0.4** **0.4**

**Autocorrs** **Partial Autocorr** **UP** **DOWN**

**0** **1** **2** **3** **4** **5** **6** **7** **8** **9** **10** **11** **12** **13** **14** **15** **16**
**-0.2**
**0.0**
**0.2**
**0.4**
**0.6**
**0.8**
**1.0**
**-0.2**
**0.0**
**0.2**
**0.4**
**0.6**
**0.8**
**1.0**

**Figur e 3: The Var iance Decomposition of Stock Retur ns**

The dark and light parts on the figure represents the variance of stock returns that can be explained by the permanent and transitory shocks to earnings respectively.

**DLNP** **LNPE**
**FEVD for DLNP**
**5** **10** **15** **20** **25** **30** **35**
**0.00**
**0.25**
**0.50**
**0.75**
**1.00**

**Figur e 4: The Var iance Decomposition of Pr ice-Ear nings Spr eads**

The dark and light parts on the figure represents the variance of price-earnings spreads that can be explained by the permanent and transitory shocks to earnings respectively.

**DLNP** **LNPE**
**FEVD for LNPE**

**5** **10** **15** **20** **25** **30** **35**
**0.00**
**0.25**
**0.50**
**0.75**
**1.00**

**Table 4: Impulse Response Analysis**

The following table lists the response of the two variables to the permanent shocks to earnings. 0 1.00000 0.84153 1 0.31519 1.00872 2 0.03420 0.91457 3 -0.01836 0.77139 4 0.01981 0.66859 5 0.05922 0.61140 6 0.08683 0.58163 7 0.06571 0.52871 8 0.04101 0.46674 9 0.03701 0.39921 10 0.03643 0.32748 11 0.04657 0.27768 12 -0.00809 0.21689 13 -0.06569 0.08474 14 -0.05069 -0.02314 15 -0.10292 -0.18125 16 -0.00957 -0.22628 17 0.01424 -0.24903 18 0.08109 -0.19925 19 -0.02158 -0.24771 20 -0.09608 -0.36243 21 -0.07998 -0.45367 22 -0.02279 -0.47198 23 0.01710 -0.46012 24 -0.00258 -0.43261 25 -0.01869 -0.42082 26 -0.04252 -0.43011 27 0.00814 -0.37651 28 0.01723 -0.31380 29 0.03560 -0.23417 30 -0.02599 -0.21563 31 -0.03963 -0.21653 32 0.00940 -0.17221 33 -0.01814 -0.15156 34 -0.03570 -0.14729 35 0.02372 -0.08727 36 0.04431 -0.02554

The following table lists the response of the two variables to the transitory shocks to earnings

0 0.71845 1.00000 1 0.14138 1.38176 2 -0.04061 1.55339 3 -0.12604 1.58683 4 -0.04722 1.67259 5 0.00852 1.79405 6 -0.04098 1.83876 7 -0.04092 1.86516 8 0.01590 1.94082 9 0.04676 2.03293 10 0.03475 2.09469 11 0.00147 2.12122 12 -0.00996 2.04028 13 -0.04173 1.92459 14 -0.03167 1.83402 15 -0.00521 1.78538 16 -0.00555 1.75250 17 0.02016 1.74834 18 -0.00291 1.72883 19 -0.07999 1.63710 20 -0.06065 1.57010 21 -0.10817 1.46272 22 -0.05089 1.42087 23 -0.04949 1.37165 24 0.00971 1.36241 25 0.01473 1.35922 26 -0.05603 1.28667 27 -0.02215 1.25860 28 -0.04415 1.20765 29 0.01566 1.21412 30 0.03991 1.24512 31 0.03126 1.26200 32 0.06273 1.30844 33 -0.03305 1.25998 34 -0.04042 1.20735 35 0.00433 1.19184 36 0.00088 1.19452

**Figur e 5: The Impulse Response of the Two Ser ies to **
** the Per manent Shocks to Ear nings**

The upper and lower halves respectively represent the impulse responses of stock returns and price-earnings spreads to the permanent shocks to earnings.

Effects of a Shock to DLNP DLNP 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 LNPE 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25

strong and positive effect on the stock returns in the beginning. The effects greatly decline after 3 months. The transitory shocks to earnings have similar effects as shown in the upper half of Figure 6, but with a smaller magnitude.

The lower half of Figure 5 signifies that the permanent shocks to earnings have a strong and positive effect on the changes in price-earnings spread in the beginning and the effect gets smaller later on. However, it increases after two years. The lower half of Figure 6 indicates that the transitory shocks to earnings have a strong effect for most of the time period considered.

**Figur e 6: The Impulse Response of the Two Ser ies to **
** the Tr ansitor y Shocks to Ear nings**

The upper and lower halves respectively represent the impulse responses of stock returns and price-earnings spreads to the transitory shocks to earnings.

Effects of a Shock to LNPE

DLNP 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 -0.40 0.00 0.40 0.80 1.20 1.60 2.00 2.40 LNPE 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 -0.40 0.00 0.40 0.80 1.20 1.60 2.00 2.40

It is also possible to decompose the series of stock price changes into two parts: (1) the cumulative effect of the current and past permanent shocks to earnings, and (2) the cumulative effect of the current and past transitory shocks to earnings. The results obtained in this part can be used to explain whether the mean-reverting phenomenon is caused by the permanent shock to earnings or the transitory shock to earnings.

Table 5 summaries the accumulated impulse responses of the shocks to earnings and are drawn in Figures 7 and 8. From the upper half of Figure 7, we can see that the cumulative effects of the permanent shocks to earnings on stock price changes have been rather steady. While the cumulative effects of the transitory shocks to earnings on stock return has been decreasing and the magnitude is smaller.

The lower half of Figure 7 shows that the cumulative effect of the permanent shocks to earnings on the changes in price-earnings spread is strong and attains its maximum in about one year. The lower half of Figure 8 shows that the cumulative effect of the transitory shocks to earnings on the changes in price-earnings spread has been increasing all the time.

**Table 5: Accumulated Impulse Response Analysis**

The following table lists the accumulated impulse response of the two variables to the permanent shocks to earnings

0 1.00000 0.84153 1 1.31519 1.85025 2 1.34938 2.76482 3 1.33102 3.53621 4 1.35083 4.20480 5 1.41005 4.81620 6 1.49688 5.39783 7 1.56258 5.92654 8 1.60360 6.39327 9 1.64061 6.79248 10 1.67704 7.11997 11 1.72361 7.39765 12 1.71551 7.61453 13 1.64982 7.69927 14 1.59913 7.67613 15 1.49621 7.49488 16 1.48664 7.26861 17 1.50088 7.01958 18 1.58197 6.82033 19 1.56039 6.57262 20 1.46430 6.21020 21 1.38432 5.75652 22 1.36153 5.28455 23 1.37863 4.82442 24 1.37605 4.39181 25 1.35737 3.97099 26 1.31484 3.54088 27 1.32298 3.16437 28 1.34021 2.85058 29 1.37581 2.61640 30 1.34982 2.40077 31 1.31019 2.18423 32 1.31959 2.01202 33 1.30146 1.86047 34 1.26575 1.71318 35 1.28947 1.62591 36 1.33379 1.60037

The following table lists the accumulated impulse response of the two variables to the transitory shocks to earnings

0 0.71845 1.00000 1 0.85983 2.38176 2 0.81921 3.93515 3 0.69318 5.52198 4 0.64595 7.19457 5 0.65448 8.98862 6 0.61349 10.82737 7 0.57258 12.69254 8 0.58848 14.63336 9 0.63524 16.66629 10 0.66999 18.76098 11 0.67146 20.88220 12 0.66150 22.92248 13 0.61976 24.84706 14 0.58809 26.68109 15 0.58288 28.46647 16 0.57733 30.21897 17 0.59748 31.96731 18 0.59457 33.69613 19 0.51458 35.33324 20 0.45393 36.90333 21 0.34576 38.36606 22 0.29488 39.78693 23 0.24539 41.15858 24 0.25510 42.52099 25 0.26983 43.88020 26 0.21380 45.16688 27 0.19165 46.42548 28 0.14750 47.63313 29 0.16316 48.84725 30 0.20307 50.09237 31 0.23433 51.35438 32 0.29706 52.66282 33 0.26400 53.92280 34 0.22358 55.13015 35 0.22790 56.32200 36 0.22878 57.51652

**to the Per manent Shocks to Ear nings**

The upper and lower halves respectively represent the accumulated impulse responses of stock returns and price-earnings spreads to the permanent shocks to earnings.

Accumulated Effects of a Shock to DLNP

DLNP 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 0 1 2 3 4 5 6 7 8 LNPE 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 0 1 2 3 4 5 6 7 8

**5. CONCLUSION**

The association between earnings and price has always been the focus of the research in financial accounting. The dynamic relation between the two series has great implications not only on the analytical and empirical research in accounting but also on the formulation of investment strategy. If the investors are rational, stock prices should be affected by permanent shock to earnings, i.e., permanent earnings. Whether this is true needs to be explored empirically. The purpose of this research is to examine the response of stock returns and price-earnings spreads (the logarithm of price-earnings ratio) to the permanent and transitory shocks to earnings. Starting from Campbell and Shiller (1987), most variables considered in the long-duration time series analysis are measured in an aggregate level. Instead of doing firm-specific analysis, this approach reduces the problem associated with measurement error associated with the accounting earnings in a single firm and the aggregate accounting earnings may be a better proxy for aggregate economic

**the Tr ansitor y Shocks to Ear nings**

The upper and lower halves respectively represent the accumulated impulse responses of stock returns and price-earnings spreads to the transitory shocks to earnings.

Accumulated Effects of a Shock to LNPE

DLNP 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 0 10 20 30 40 50 60 LNPE 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 0 10 20 30 40 50 60

earnings, which allows us to link the earnings to stock price.

The empirical results show that, although a great portion of the stock return can be explained by the permanent shocks to earnings, the part that can be justified by the transitory shocks to earnings is not insignificant. This suggests that the investors may not be able to differentiate the permanent part from the transitory part of accounting earnings. Stock price is responsive to the transitory shock to earnings occurred earlier, even after three years. Another finding is that the variation in the price-earnings ratio is mainly due to the transitory shocks to earnings.

As to the impulse response analysis, the permanent shock to earnings has a strong and positive on the stock return, but the effect reduces after three months. Same remark can be said about the transitory shock except that the magnitude is smaller. The effect of permanent shock to earnings on the price-earnings ratio is also significant, but has a U shape in our estimation period. While the effect of the transitory shock to earnings on the price-earnings ratio has been large and steady all the time.

very high. It seems that they are unable to tell apart the difference between the permanent and transitory shocks to earnings. This is consistent with the mean-reverting phenomenon, indicating that a great portion of the variation in stock return is temporary. The change in price-earnings ratio is largely caused by the transitory shock to earnings. In addition, we can also use the price-earnings ratio to predict the future stock return.

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**股票價格對於會計盈餘永久性及暫時性衝擊的反應**

**劉嘉雯 **

元智大學會計學系助理教授
**王泰昌**

臺灣大學會計學系教授
**摘 要**

研究的目的在於以股票價格的變動及股價盈餘差數（price-earnings spread，
本益比的自然對數值）來研究股價對盈餘衝擊(earnings shock)的反應。首先假
設盈餘的隨機過程(stochastic process)為一永久性部份(permanent component)與
暫時性部份(transitory component)的總和，和許多文獻不同的是：永久性部份不
一 定 需 假 設 為 隨 機 漫 步 (random walk) ， 此 係 一 過 於 強烈的假設。 利用如
Modigliani & Miller(1961) 及 Miller & Rock (1985)的股票評價模型可以將一公司
之盈餘與股價連結在一起。由於本研究假設永久性盈餘不一定是隨機漫步，在
分解為永久性及暫時性部分時會有認定(identification)的問題，前述的理論關係
可以幫助我們在為股價變動及股價盈餘差數設立二元時間序列模型時做認
定。納入股價盈餘差數的理由在於股價及盈餘之間可能有共積的現象，因此可
採用類似 Engle and Granger (1987)中提及的誤差修正模型 (error correction
model, ECM) 方法。本研究利用二元的移動平均模型 (bivariate moving average
model, BMAR)及二元自我相關模型 (bivariate auto-regressive model, BVAR) 配
合著前述的理論關係將股價及盈餘的衝擊分解為永久性及暫時性的部份，透過
變異數分解 (variance decomposition) 及脈衝反應分析 (impulse response analysis)
進一步瞭解股票價格及其變動與本益比對永久性及暫時性的盈餘衝擊的動態
反應，有助於我們了解股價變動的影響因素及影響方式。本研究的結果指出投
資人並無法區分盈餘中的永久性及暫時性部份，這可以解釋股票平均數復歸
(mean-reverting) 現象造成的可能原因為股票報酬率中有很大一部份的性質為
暫時的。股價盈餘差數的變動主要源於盈餘暫時性的衝擊，這也顯示股價相對
於盈餘在盈餘有暫時性的衝擊時會有較劇烈的反應。
**關鍵字：永久性盈餘、暫時性盈餘、股票價格、二元時間序列模式。**