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Evaluating an empirical evaluation of accounting income numbers

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Date added: 17-06-26

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Accounting theorists have tested the usefulness of accounting practice which had been agreed with certain analytic model which consist only a few assertions. In each case, they are using a completely analytical approach which has generally been restricted to the extent of comparing the existing practices with the more preferable .One of the major shortcomings of this method which is completely analytical approach is that it ignores the extent to which it can predict or explain the observed behavior. 

Completely analytical approach has led theorists to claim that income numbers cannot be defined substantively, they lack meaning and are therefore of doubtful utility.  The argument about income numbers argued that accountants should also consider new situations and problems such as price level changes and taxation charges instead of just concentrating on a few problem areas. However, as accounting lacks an all 'embracing theoretical framework' dissimilarities in practice occurred. So, net income becomes incomparable which have no other substantive meaning at all. Hence empirical testing becomes important and compulsory to emphasize that a lack of substantive meaning does not generally imply a lack of utility.

An empirical test tests the agreement as to what real world outcome represents an appropriate test of usefulness. Since accounting income numbers are of special interest to the investors, security prices have been used as the predictive criterion of the investment decision. If an observed revision of stock prices is related with the release of income report then it can be concluded that the information reflected in income numbers is useful. We can also say that the purpose empirical test is to test the relationship between stock price and income numbers. The content and timing if the existing annual net income will be evaluated as the lack of either one of them will vitiate the usefulness of income numbers.

Empirical Test

The reason to select the behavior of security prices to be the operational test of usefulness is based on the recent developments in Capital Theory. The Capital theory supports the proposition that if the information from income numbers is useful in forming stock prices, capital markets are efficient and unbiased. It means that the market will adjust the stock prices rapidly to the information from income numbers and will not give any chance for abnormal gain.

The authors relate the income numbers and security prices based on this theory and they are focusing on the information of a particular firm, not all firms. They construct 2 alternative models which are income regression model and naïve model to show what capital market expects the income to be. Then, they also look into the market's reaction when the expectations been identifying as wrong by using stock return model.

Conditional Expectation of Income Changes

There is a study shows that about half of the variability in a firm's earning per share (EPS) is associated with economy wide effects. So, it indicates that at least part of the change in a firm's income can be predicted in the following year. If a firm's income is related to other firm's income in particular way and there is knowledge about those other firm's present income, it can result in the conditional expectation for the firm's present income. From this, it shows the difference between the actual change in income and its conditional expectation will be the new information from a firm's present income numbers.* However, the difference may come from the policy effects. Seem these 2 effects are felt at the same time, thus their relationship must be estimated jointly.

The authors use Ordinary Least Squares (OLS) in estimating the actual change in income. The equation is as below:

∆Ij,t-r = â1jt + â2jt∆Mj,t-r + ûj,t-r …(1)

a1jt, a2jt : Coefficients from the linear regression

∆Ij,t-r : Change in income of firm j

∆Mj,t-r : Change in income of all firms in the market (other than firm j)

ûj,t-r : Forecast error / unexpected income change

r =1,2,…,t-1 : Data up to end of previous year

In income regression model, the expected change in income for firm j can be predicted by the average income change for the market.

∆Îj,t = â1jt + â2jt∆Mj,t …(2)

From equation 1 & 2, it is obviously showing that the difference is ûj,t. It is called as forecast error or unexpected income change where is actually the difference between actual income (∆Ij,t ) and expected income (∆Îj,t). This forecast error is what we assume to be the new information from a firm's present income numbers.*

The Market's Reaction

Similar as the above, there is also a study states that up to 40% of the variability in stock's monthly rate of return is associated with the market wide effect. The effect of market wide information on monthly rate of return can be estimated by its predicted value of the monthly price relatives of firm j's stock on a market index of returns.

[PRjm - 1] = ˆb1jm + ˆb2jm[Lm - 1] + ˆvjm …(3)

b1j, b2j : Parameters from the linear regression

PRjm : Monthly price relative for firm j and month j

L : Fisher's "Combination Investment Performance Index"

[Lm - 1] : Market monthly rate of return

Vjm : Stock return residual

In this stock return model, the residual, vjm is the difference between realized return and expected return. As the market has been adjust rapid and efficiently to new information, the residual must represents the impact of information, on return of firm j's stock.

Economtric Issues

In income regression model, there is an assumption that the Mj (market index of income) and uj (forecast error) are uncorrelated. This assumption is supported by its alternative model which is naïve model. However, this assumption is violated by the stock return model.

Correlation of Mj and uj can be in 2 forms which are inclusion of firm j in Mj or the presence of industry effects. In income regression model, it is obviously shown in the equation 1 that the firm j is not including in Mj. It is estimated that the industry effect just account for at most 10% of the variability in a firm's income. Thus, this model belief is that the bias in the estimates is not significant. For naïve model, it is predicted that the present year income will be the same as for last and the uj is just the change in income from prior year.

In stock return model, there are 2 violations that Mj. is correlated with residual (vj). The first violation is that return on firm j is included in the Mj. although it is just a small portion. The second violation is that vj is nonzero for certain months around the report dates. It is belief that the bias will have little effect on the result although it is low.


The rate of return over a period of a particular firm would reflect only the presence of market-wide information which pertains to all firms in the case where unlikely absence of useful/significant information about the firm over that period.

We can identify the effect of individual firms' information pertaining by abstracting from market effects.

Segregate the unexpected and expected elements of income change.

If the income forecast error is negative (actually change in income is less than its conditional expectation)

Bad news-predict that if there is some association between accounting income number and stock prices

Release of the income number would result in the return on that firm's securities being less than would otherwise have been expected. Such a result () would be evidenced by negative behavior in the stock return residuals () around the annual report announcement date. And vice versa for the case of positive forecast error.


There are 3 classes of data will be used in the empirical test in both regression model and naïve model. They are the contents of income reports (income numbers), the annual report announcement date and the stock price.

Income Numbers

The income numbers for 1946 through 1966 were obtained from the Standard and Poor's Compustat tapes which is a database of financial, statistical and market information on active and inactive companies throughout the world. First, we need to obtain the distributions if the square coefficients of correlation between the changes in the incomes of the individual frims as well as the changes in the market's income index. When estimating the association between the income for a firm and the market, the income of the particular firm should be excluded from the market. In this article, we cannot refer to the existence of autocorrelation in the disturbances when the level of net income and EPS were regressed at a proper index as what was examined in the forerunner article. It is because the method to analyze the stock market's reaction to income numbers in this article presuppose that the income forecast error cannit be predicted at minimum 12 months prior to the announcement date. When the error is auto-correlated as stated above ( forerunner article) , this presupposition is inappropriate.

Annual report Announcement Dates

There are 3 kinds of annual report announcements in the Wall Street Journal which are forecast of the income report, preliminary reports and the complete annual report. The Forecast of the income report usually is done shortly after the year end which believed to be inprecise. Therefore, the preliminary report is often become a condensed preview of the annual report. Besides, as the numbers for net income is usually same for both preliminary reports and the complete annual report, the date of the annual report become generally available was assumes to be the date when the preliminary report is published on The Wall Street Journal.

Stock price

Here, we refer stock price as movement of security prices around the announcement date. Stock price were obtained from the tapes constructed by the Centre for Research in Security Prices. In this article, monthly closing prices on the New York Stock Exchange, adjusted for dividends and capital changes for the period January 1946 to June 1966 were used.

Inclusion Criteria

However, Firm included in the study must meet the following criteria:

Firm's earning data must be available on the compustat tapes for each of the years 1946 to 1966

Firm's Fiscal year ending at December 31 on The Wall Street Journal.

Firm's price data on the CRSP tapes must be at least 100 months.

Wall Street Journal announcement dates available.

The 4 selection criteria may reduce the generality of result as firms selected do not young firms.failed firm, those who do not report on 31 Dec, those which are not presented on Compustat , CRSP tapes and the Wall Street Journal.


Abnormal Performance Index (API) is a way to study how accounting income numbers are being related to stock returns. It measures the effects of the information at the time it is being disclosed and also the anticipation in the period up to the announcement of annual reports.

Define month 0 as the month of the announcement of annual report, API tracks the return over and above the equilibrium rate (excess return) that would be generated from investing one dollar in a company at the end of the month of 12 months prior to the month of annual report announcement and hold to the end of some arbitrary holding period. These excess profits are the result of information arriving which in turn affect returns.

From Figure 1, according to 3 variables, the top half is having positive forecast error. This means actual income is more than expected income. For the bottom half, it shows negative forecast error which means actual income is less than expected income. Then, the line divide the two halves consists of all firms and years in total samples. Thus, it is approximately to 1.

Positive forecast error can consider as good news for company. Meanwhile, negative forecast error can consider as bad news for company. This is because if the forecast error is positive, it means there is much information is being anticipated and the actual signal at 0 did not contain significant information. The converse situation happens to negative forecast error. They are much information not being anticipated and the actual signal at 0 did contain significant information. Thus, API did affects on the stock returns.

Specific Result

Signs of the income forecast errors

There is some difference between the two regression model variables. From the research conducted, we know that the signs of the income forecast errors for variable (2) will directly influence the signs of the income forecast errors for the variable (1). If variable (2) is positive, most probably variable (1) is positive as well. But if there is a difference among the result for both variables, then we will take into consideration the signs of the income forecast errors for variable (2).

While there is few choices between variable (2) and variable (1), variable (3) (the naïve model) is best to show the portfolio of company with negative forecast errors.

The naïve model will show the same forecast error as regression model if the change in market income is zero and there is no drift in the income.

Bias in the drift downward in the API computed

There is a computational bias in the drift downward shown in the sample. But the bias will not affect the interpreting the values of API. This explains why the changes in the bottom panel are tend to be greater to the changes in the top panel; why top panel tend to turn down after month 0 and why the bottom panel tend to persist beyond month of the announcement of report.

Definition of income

Additional definition of income:

Operating income

Net income before the nonrecurring items

Although the meaning might be slightly different, the result will be quite close even different amount is using to calculate the forecast errors

Relationship between sign of the income forecast error and stock return residual

The relationship will ne persisted as long as 2 months before the month of announcement of annual report. There are three explanations to explain the relationship:

The market's index of income was no known until few firms had announced their income numbers

There will be random error in the announcement date

The preliminary report are not perceived by the market as final

The value of annual net income relative to other sources of information

The result shows that accounting income numbers is useful as it related to stock prices. Although annual accounting report is just only one of the many sources of information that available for investors to make their investment decision, this section is also vital in providing some insight into the timeliness of the reports.

The first conclusion is about 75 percent of the value of annual net income appears to be offsetting. This means that the 25 percent left is persists, about half of it can be associated with the information consists in the reported income reports.

The second conclusion is accounting income numbers capture about half of the net effect of all information available throughout the 12 months preceding their release.

Many other bits of information are usually released in the same month as reported income

85 to 90 percent of the net effect of information about annual income is already reflected in security prices by the month of its announcement

The period of the annual report is already one-and-one-half months into history.

Results are systematically biased against findings in favor of accounting reports due to:

The assumption that stock prices are from transactions which have taken place simultaneously at the end of the month

The assumption that there are no errors in data

The discrete nature of stock prices quotations

The presumed validity of the "errors in forecast" model

The regression estimates of the income forecast errors being random variables, which implies that some misclassifications of the "true" earnings forecast errors are inevitable.


This paper had made seminal contributions in the accounting research. In fact, this paper was the first regulated effort to study the information content of the accounting income numbers. Thus, it had led to paradigm shift in the models that were earlier analyzed by the accounting theorists

The article can be concluded that the information reflected in income numbers is useful because an observed revision of stock prices is related with the release of income report.

Besides, this study brings some other issues which can be furthered tested. For example, media by which the market able to anticipate their income need to be identified and the problem faced by the accountants to assess the cost of preparing annual income reports for the more timely interim report. Besides, the relationship between the magnitude of the unexpected income change and the associated stock price adjustment could also be further tested so that it can provide a different way to measure the value of information on income changes.

Despite from the bias which mentioned in the data part, one of the most serious limitations remains the assumption of the unidirectional relationship between income and stock prices. It would be credulous to think that only income causes changes in stock prices and not vice versa. Evidence shows that stock prices and income are endogenous in nature thus if the system of simultaneous equations is used to replace simple regression technique, it is believed to be more relevant.

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