The aim of this report is to analysis the share price and firm size with statistics tools (SPSS) between manufacture and service sector.

1. Display the data distribution for price and size variables (revenue, profit and employee) with graphs in two sectors. Graphs show as following:

1. Manufacture Sector:

2. Service Sector:

v

2. It can be seen that all graphs have a hump, the distributions are unimodal.
3. Both the share price and profit in two sectors show symmetric curves.

      4.   Further test of normality(SPSS) show only share prices in two sectors are normal distribution. (Kolmogorov-Smirnov Sig value are more than  .o5)

With these analyses, it can be seen that only share prices are normal distribution while three size variables are not normal distribution although they show approximate curves.

Testing and Presentation of Finding

One of the purposes of research is to assess if there is difference in share price between two sectors. This can transform to statistic question: Is there a significant difference in the mean share prices for manufacture and service sectors. Through the above analyses, the independent-samples t-test can be used with the suitable conditions as follows:

1. The variables are continuous scale.
2. Random sampling.
3. Independent observations
4. The distribution of scores for each sector is normal.

Meanwhile, some assumptions are violated. Firstly, assumption that the population are normally distributed is not assured. Secondly, sample size is not sufficiently large(around 30). Lastly, sample variances are unequal (eg., largest/smallest=115). However, the t test is a robust test. This means that it can b appropriately performed even when an underlying assumption is violated. (Grimm.1993)

There are seven steps for test using the independent-samples t test:

Step 1: Define the null and alternative hypotheses:

H0:   m1=m2       (The share prices means between sectors are the same, there is not a significant difference in the mean share prices for two sectors)

H1:    m1 m2        (The share prices mean between sectors are not the same, there is a significant difference in the mean share prices for two sedtors)

Step 2: Set alpha. Alpha is set at 0.05.

For some companies may influence other companies, such as earn the amount of shares of others, the assumption of independence of observations can not be guaranteed absolutely. A more stringent alpha value is acceptable.(Stevens.1996)

Step 3: Computer t score (using SPSS, show the table Figure 4)

Figure 4:

ur

Step 5: Checking assumption.

The Sig.value in Levene’s test is 0.389, larger than 0.05.This means that the assumption of equal variances of share prices has not been violated, the first line of table can be used to report t-value.

Step 6: Assessing differences between two sectors.

The value in the Sig.( 2-tailed) column is above 0.05(0.739), then the null hypothesis can not be rejected. There is not a statistically significant difference in the mean share prices between two sectors.

Step 7: Calculating the effect size

Eta squared=t*t/(t*t+n1+n2-2)=3.36*3.36/(3.36*3.36+20+20-2)=0.229.

It means 22 per cent (>14 per cent, large effect) of the variance in share price is explained by sectors.

Relationship Analysis

---Chi-Square test

In most time, investors care more about the share price and factors that effect it. Many researchers also have explored the effects of share price and firm size. Beedles et al.(1988) who reported that both size and price effects are statistically significant to average return. While           found that 1 per cent change in share price will have a greater impact on average return than a 1 per cent change in firm size. These opinions illustrate some relationship may be existed between the share price and firm size.

Firstly, it is suitable to use Chi-Square test to determine if there is a relationship between the price and size. It includes six steps:

Step 1: Changing the share price and size variables into z-scores, this can make it easy for test samples with standard.

Step 2: Sorting the z-scores in share price with one’s score above 0, another below 0 while the three size variables are sorted into three groups equally.

Step 3: Caculating  in SPSS software. Table is showed as following:

29

INTRODUCTION

The finance literature on market efficiency presents the size effect as an anomaly in which small firms stocks

tend to earn higher returns than large firms stocks even after adjusting for the higher risks associated with small

stocks. Several research papers attempted to explain this phenomenon but to no avail. In presence of this

unexplained anomaly, the question remains whether other variables were not accounted for in prior analysis.

In this context, several studies tried to explain the size effect proposing several hypotheses. These explanations

include return measurement error [Roll, 1981], tax-loss selling effect [Reinganum, 1983], transaction costs [Lustig

and Leinbach, 1983; Schultz, 1983; and Stoll and Whaley, 1983], macro economic risk factors in an APT framework

[Chen and Hsieh, 1985], skewness preference [Booth and Smith, 1987], share price level [Kross, 1985; and

Bhardwaj and Brooks, 1992a], and the differential information effect [Barry and Brown, 1984; and Elfakhani and

Zabos, 1992]. None of these studies, however, provided a complete explanation of the firm size effect.

This paper proposes an alternative explanation for the documented size effect. It postulates that small firms

suffer from excessive lack of public information and therefore are neglected. Neglect is defined as professional

informed investors expressing less, or no, interests in some stocks, particularly small stocks. Neglect occurs when

there is less professional analysis available on the stock, and therefore less public information. As such, small

(uninformed) investors require additional returns for holding small-neglected stocks.

Thus, we examine the linear relationship between the size effect and the differential information among small

and large stocks as symbolized by analysts’ neglect. Analysts’ neglect is measured twice, (1) by the number of

financial analysts pursuing information and making forecasts about the stock, and (2) by a dummy interaction

variable that relates size effect to firm neglect. Our methodology differs from that of Bhardwaj and Brooks (1992b)

in at least three ways: First we study month to month variation in the size-neglect group, second we provide a

*University of Saskatchewan,

**Indiana State University

The first author acknowledges partial financial support from the Board of Governors and the Dean of the College of Commerce, University of

Saskatchewan. The second author recognizes the financial support of Indiana State University in getting research data. The authors gratefully

acknowledge the contribution of I/B/E/S Inc. for providing forecast data as a broad academic program to encourage earnings expectations

research. The authors also thank the participants of the seventh annual meeting of the Academy of Financial Services for helpful comments. All

remaining errors are the authors’.

Journal of Financial and Strategic Decisions 30

broader examination of these size-neglect groups (10 versus 4), and third we avoid any cross-sectional

heteroscedasticity or any autocorrelation that may have existed in their two-stage regression.

In this context, we inspect the existence of size effect by using White’s time series cross-sectional regression

corrected for heteroscedasticity and autocorrelation.

Our results support the existence of size effect in January, but only for portfolios of large stocks. Interestingly,

the size-January effect is often dominated by neglect effect; i.e., large firms that are less popular among financial

analysts are found to earn higher return premiums than other more popular large firms. This finding suggests that the

market discounts stocks of larger firms when neglected by financial analysts. The results also show that individual

investors could still earn higher returns on stocks that are less pursued by financial analysts during the 1986-1990

period.

The rest of the paper is organized as follows. Next section reviews previous literature on the subject. Section II

presents the research design, hypotheses to be tested, and data sources. Section III describes the results, followed by

conclusions in section IV.

LITERATURE REVIEW

Banz (1981) finds that risk-adjusted stock returns are a monotone decreasing function of firm size. This finding

implies that CAPM is misspecified. Following this evidence, some studies focus on the interaction between size

effect and other anomalies, e.g., P/E ratio effect.1 Other studies emphasize the magnitude of the size effect.2 These

studies, however, fail to explain size effect month-to-month instability (for example, in January), or its existence.

Other studies referred to earlier also attempt to explain the size effect, but no hypothesis provided a satisfactory

explanation of the firm size effect.

Of these hypotheses, the differential information effect seems the most acceptable theory. Using the period of

listing (as a proxy for information availability), Barry and Brown (1984) find no evidence of an independent size

effect.

Another proxy for differential information is the neglected-firm effect. Under this hypothesis, firms neglected by

analysts’ investors, financial analysts, and other investment agencies suffer from lack of information or asymmetric

information [Arbel and Strebel, 1983]. Thus, neglected stocks should earn substantially higher returns to compensate

for this gap of equal access to firm information. This notion is reinforced by Ajinkya and Gift (1985) in that there

may be a connection between analysts’ forecasts, firm size, and stock returns.

The neglect hypothesis is further tested by Arbel (1985). Using the coefficient of variation of the financial

analysts’ forecasts and the number of institutions holding the stock, Arbel reports a strong January effect associated

with neglected firms. On the other hand, Dowen and Bauman (1986) argue that the size effect dominates neglect

(defined as institutional popularity when stocks are less widely held by institutions). Nevertheless, Amihud and

Mendelson (1986 and 1991) report a confounded size-neglected firm effect; i.e., stocks with low liquidity, as

measured by bid-ask spreads, are usually small and less researched, and therefore earn abnormal returns. However,

they could not explain the interaction that exists between size effect and January.

More recently, Bhardwaj and Brooks (1992b) test the neglected firm effect (proxied by the number of financial

analysts following the stock at the end of each year). They find that the neglect effect is strong in January; however,

it is weakened after controlling for share price. Outside January (all 11 months lumped together), they show that

there is a strong neglect effect in the lowest-price group in the 1977-82 period, and in the highest-price group during

1983-88. Thus, neither the neglect effect nor the share price effect is stable over all the sampling periods. Bhardwaj

and Brooks also report a confounded size-neglect effect in January, which results in a no clear dominance of either

effect. Also, they do not completely rule out an independent neglect effect.

In brief, the literature predicts there maybe a possible relationship between firm neglect and size effect.

Therefore, there maybe profit opportunities for individual investors to seek by pursuing news about financial

analysts’ neglect of small stocks.

RESEARCH METHODOLOGY

The testing methodology is implemented in taking two steps. First, a test of the firm size effect is conducted to

verify the superior performance of small stocks in January and non-January months. This step is tested using the

conventional pooled time series regression analysis (in line with Fama and MacBeth [1973]). Second, analysts’

Differential Information Hypothesis, Firm Neglect and The Small Firm Size Effect 31

neglect effect is tested as a possible explanation of the size effect, and as an inducement to individual investors to

benefit from this strategy.

The Proposed Hypotheses

Findings by Jaffe et al. (1989) and Ritter and Chopra (1989) show that the size effect is restricted to January.

Using our methodology, the null Hypothesis 1 is constructed to examine whether size-portfolios formed in January

would display any different behavior from non-January months or from the overall sample.

Hypothesis 1: For each month of the year, there are no excess return premiums related to firm size.

The next step is to investigate whether the size effect is simply a proxy for the lack of information on small

firms. At the same time, we test the ability of individual investors to realize return premiums one month following

the reports of financial analysts’ forecasts. For that purpose, the following hypotheses are formulated:

Hypothesis 2: After controlling for neglect by financial analysts, there are no excess return premiums

related to size effect.

Hypothesis 3 combines the first two hypotheses to examine any seasonality in the joint size-neglect effects.

Hypothesis 3: After controlling for neglect by financial analysts, and regardless of what month of the

year, there are no excess return premiums related to size effect.

The intuition behind the testable hypotheses is that one would suspect less publicized-small stocks to be more

sensitive to negative information, and therefore would be more volatile. Thus, firms with fewer specialized analysts

are expected to observe gradual market adjustment to unexpected corporate news (neglect effect), and therefore

abnormal returns may be realized by informed investors.

Data Sources

The sample includes all firms trading on the New York (NYSE) or American Stock Exchanges (AMEX) that

have the number of financial analysts following the sampled stocks reported on the Institutional Brokers Estimate

System Tape (IBES). Data on stock prices, returns, and number of shares outstanding are obtained from the Centre

for Research in Security Prices (CRSP) tape. Following other size studies (e.g., Fama and French [1992]), financial

institutions such as banks and insurance companies are considered to have their returns generating behavior

influenced by regulations, and therefore can confound the size effect. Thus, these firms are separated from the

sample for future research. The sampling period in this study is five years, extending from January 1, 1986, to

December 31, 1990.3 However, we exclude October 1987 from the sample to avoid any noise caused by the stock

market crash.4

All remaining CRSP firms are ranked in ascending order based on their market values. The monthly market value

of the firm (Sizet) is defined as the number of shares outstanding multiplied by month-end share price. Shares

outstanding are considered the same from one month to another until a change occurs. At the beginning of each

month, we form ten portfolios, with portfolio 1 has the 10% smallest stocks, and portfolio 10 makes up the 10%

largest stocks.5

The monthly mean return (Rt,ip) and the 90-day risk-free rate for the month (RFt) are used to calculate the mean

risk premium for each stock (Rt - RFt) for each stock in portfolio p (p=1, ..., 10). As a result of merging these data

bases, the final number of sampled firms is 972, and the sample points are 47,629 observations in 59 months (1986-

1990). To simplify the hypothesis testing procedure, the overall mean of the monthly risk premiums is calculated for

each of the ten portfolios.

Testing the Hypotheses

We test Hypothesis 1 using the conventional pooled time series cross-sectional regression. The regression model

examines the relationship between size and return premiums after controlling for January:

Journal of Financial and Strategic Decisions 32

Model 1

Yt, i p = a + b1 Size t -1, i p + b2 Dt-1 + b3 (Size t-1, i p ´ Dt-1)

where:

Yt,i p = natural log of one plus monthly return premiums of stock i in portfolio p (p=1, ..., 10)

for month t (t=1, ...,59). Return premiums are defined as Yt,ip = Rt,ip- RFt, where Rt,ip is

the return on stock i in portfolio p during month t, RFt is the 90-day risk free rate for

the same month.

Dt-1 = lagged dummy variable equals to 0 for all eleven months of the year except January,

and 1 for January.

Size t-1, i p × Dt-1 = lagged interaction dummy variable that is equal to 0 for all eleven months of the year

except January, and the product of size t-1, i p and Dt-1 for January.

where the market value of firm i assigned to portfolio p in month t-1 (Size t-1, i p) is calculated as the number of shares

outstanding multiplied by month-end share price.

The lag operator on the explanatory variables is used because portfolios are formulated at the beginning of each

month, and are then liquidated at the end of month t when returns are actually realized. It must be noted that in

January the coefficient for size is the sum of b1 and b3. A significant total coefficient (b1 + b3) would support the

notion that return premiums are high for small stocks in January.

The following regression with the proposed explanatory variables being lagged one month (as in Model 1) is run

in order to indirectly test the neglect effect as to create profit opportunities to individual investors, thus testing

Hypothesis 2:

Model 2

Yt, i p = a + b1Size t-1, i p + b2N t-1,i p + b3I t-1,i p + εt

where:

Yt, i p = natural logarithm of one plus monthly return premiums of stock i in portfolio p for month t (t=1,

...,59) as defined earlier in Model 1.

Size t-1, i p = lagged monthly natural logarithm of market value of stock i for the previous month t-1.

N t-1, i p = lagged monthly number of financial analysts tracing stock i.

I t-1, i p = lagged interaction dummy variable. The dummy variable is equal to 0 if the number of financial

analysts specializing in stock i during the previous month (N t-1, i p) is larger than the median, and is

equal to firm size (Size t-1, i p) otherwise.

In Model 2, neglect effect is tested twice; first, by the number of financial analysts (N t-1, i p), and second by the

interaction term (I t-1, i p) that connects size effect to firm neglect. We run the regression Model 2 twice. The first run

includes all data. The second regression is performed, this time after grouping the data by size, in order to examine

whether there is any seasonal interaction between size effect and the number of financial analysts pursuing the stock.

The interaction between size and seasonality is also reexamined using regression Model 2. For that purpose, the

sample is reclassified by the month of the year. For example, January includes data from January of each year of the

sampling period, 1986-1990.

Implications of the Proposed Model

Under the proposed models, and given the specified dummy variables, the hypothesized signs of the regression

coefficients in Model 2 are: b2<0 (if the neglect effect exists and significant), and b3<0 (if the size effect is restricted

to neglected firms). Statistically significant coefficient estimates on the number of financial analysts would confirm

the notion that stock performance relates to information availability. Note that if differential information exists

among large and small firms, the size effect in Model 2 should disappear. In this case, b1 must have positive sign.

The constant term, a, would capture factors other than neglect effect.

Differential Information Hypothesis, Firm Neglect and The Small Firm Size Effect 33

Econometric Concerns

Since the regression data is time series and cross-sectional, heteroscedasticity and autocorrelation can present

some serious problems. When heteroscedasticity exists, the estimators may diverge. White’s (1980)

heteroscedasticity-consistent covariance matrix estimates are used to correct the estimates for any unknown form of

heteroscedasticity. This technique also picks up a mis-specified mean or any correlation between the error term and

independent variables. Since the residual effect of stock trading is unlikely to disappear and therefore it may affect

later trading, autocorrelation can also be a problem. Furthermore, to improve parsimony and avoid collinearity,

Akaike’s (1969) Final Prediction Error (FPE), also called Amemiya Prediction Criterion, and Schwarz’s (1978)

Criterion (SC) are used to find the best descriptive model.6 The lower FPE or the higher SC, the more parsimonious

the model. Moreover, a violation of normality may make the regression analysis unreliable. Hence, normality is

tested measuring skewness and kurtosis, and by conducting Kolmogorov (D normal statistics) and non-parametric

sign rank tests.7

FINDINGS AND INTERPRETATIONS

Table 1 reports descriptive statistics for each of the ten-size portfolios. In particular, the table shows the portfolio

mean and median return premiums (portfolio return - risk free rate), and portfolio total risk (σ). The results show

that the mean return premiums are negative for all ten portfolios. In fact, only 23,019 of the 47,629 sample points

have monthly returns higher than monthly risk-free rates (which is about 48.33% of the total sample). Of the 24,610

observations that had negative premiums, 22,371 had negative returns (less than zero) over the sampling period. This

pattern can be partially explained by the observation that 54% of return premiums were negative after the October

1987 crash. Moreover, the table reveals that the smallest stocks (portfolios 1-5) had the most negative mean (and

median) premiums, while the largest stocks (portfolios 6, 8, 9, and 10) had least negative (or even positive) return

premiums over the entire sampling period. This evidence suggests that, contrary to the prediction of the size-effect

literature, smaller stocks underperformed larger stocks during our sampling period (1986-1990). Also, smaller

stocks had higher average total risk than larger stocks.