3-3-2Beta9

8/13/2019 3-3-2Beta9

1/30

Beta, size, book-to-market, and the cross-section of stock returns in Taiwan:Measurement errors and seasonalities *

I-Hsiang Huang **

Department of Finance, National University of Kaoshiung

Comments are welcome

First draft: February 3, 2004

Second draft: April 7, 2004

This draft: November 10, 2004

* The authors gratefully acknowledge constructive and helpful comments from Roger Chen, Yung-Jang Wang,and Gili Yen. The paper has also benefited from workshop at the National Chi Nan University, NationalChung Hsing University, and National Kaohsiung First University of Science and Technology. All remaining

errors are our own.** Address correspondence to I-Hsiang Huang, Department of Finance, National University of Kaoshiung,Kaohsiung, Taiwan. Tel: 886-7-5919499, Fax: 886-7-5919329, E-mail: [email protected].

8/13/2019 3-3-2Beta9

2/30

Beta, size, book-to-market, and the cross-section of stock returns in Taiwan:Measurement errors and seasonalities

Abstract

This paper investigates the explanatory power of market beta, firm size, and

book-to-market ratio, regarding the cross-sectional expected stock returns in Taiwan. In

particular, the paper proposes a simple method to correct the errors-in-variables problem in

estimating market beta in the two-pass tests of asset pricing models. The results indicate

that the explanatory power of market beta is significantly improved and successfully

captures the cross-sectional variation in expected stock returns for the full sample period

after taking the correction into account. In addition, mean stock returns appear not only a

January seasonal but also a Chinese New Year seasonal. Most interestingly, the evidences

also exhibit a January seasonal both in the beta risk premiums and in the regression

coefficient of firm size, as well as a Chinese New Year seasonal in the regression

coefficient of book-to-market ratio that is untested before.

JEL classification: G12; G14

Keywords: CAPM; Market beta; Market seasonalities; Anomalies; Taiwan Stock Market

1

8/13/2019 3-3-2Beta9

3/30

1. Introduction

One of the most important issues in finance is what factors determine expected returns

on stocks. The capital asset pricing model (CAPM) developed by Sharpe (1964), Linter

(1965), and Black (1972) is undoubtedly the most important advance in asset pricing. It

suggests a positive linear relation between market beta and expected stock returns. The

CAPM was seriously called into question by now since the publication of Fama and French

(1992), their empirical findings based on U.S. market suggest that market beta is unable to

explain the cross-section of expected stock returns. 1 To date, the central debate regarding

empirical asset pricing is whether the market beta is alive or not. The second one is whether

there are other factors on top of market beta affect stock returns. In the meantime, Black

(1993), one of the most aggressive advocators of market beta, pointed out that the test of

Fama and French (1992) leaves some important issues unsolved and strongly argues for

more empirical evidences outside the U.S. market to justify whether the market beta is still

alive or not.

In response to Black (1993), the main purpose of this paper is to investigate the

explanatory power of market beta, firm size, and book-to-market ratio, on the cross-section

of expected stock returns by using a sample of firms listed on Taiwan Stock Exchange (TSE)

and Taiwanese Over-the-counter Securities Exchange (TOTC). In recent years, Taiwanese

economy has played an important role in both Asian and world economy. Many libertarian

1 There are some studies may contradict the CAPM prior to Fama and French (1992), such as Banz (1981),Reinganum (1981), Basu (1983), Hawawini et al. (1983), Rosenberg et al. (1985) and others. However, themarket beta is alive is popularly supportive by most part of literatures, such as Black et al. (1972), Fama andMacBath (1973), Hawawini and Michel (1982), Chan and Chen (1988), Handa et al. (1989) and others. SinceFama and French (1992), the empirical evidences around the world in support of or against the market betaare coexisted. The advocators of beta alive such as Chou and Liu (2000), Clare et al. (1998), Downs andIngram (2000), Handa et al. (1993), Heston et al. (1999), Huang et al. (2003), Jagannathan and Wang (1996),Kim (1995), Kothari et al. (1995). Evidences against the beta alive like Asgharian and Hansson (2000), Chui

and Wei (1998), Daniel et al. (2001), Hu (1998), Liu et al. (1996), Sheu et al. (1998) and others. When CAPMunder such strenuous attack, there are some appealing and competitive models, including the intertemporalCAPM of Merton (1973) and Breeden (1979) and APT of Ross (1976), which are likely to replace it.

2

8/13/2019 3-3-2Beta9

4/30

policies and deregulations have been developed and implemented. In addition, the trading

activity of TSE is one of the largest security markets among Asian stock market. Foreign

institutional investors have been attracted to TSE market because of its growth potential.

Empirical evidences from Taiwanese firms may allow us to ascertain furthermore what

factors are most important in determining stock returns and may help us to understand the

seasonal behavior of risk premium from the perspective of an emerging market. According

to Bekaert and Harvey (1993), standard models are often ill suited to deal with the specific

circumstances arising in the emerging markets and the study of the emerging market has

provided impetus for both the adaptation of current models to new circumstances in these

markets and the development of new models. Therefore, this study may offer additional

insights into controversies surrounding U.S. market and others.

In generic terms, the methodology adopted in this paper is the standard two-pass test of

asset pricing model that is developed originally by Fama and MacBeth (1973). The

procedures of two-pass tests are performed as follows. Market beta of each asset with

respect to market portfolio is estimated from a first-pass separate time series regressions. In

the second-pass, the estimated betas are used in cross-sectional regressions (CSR) to

estimate the risk premium of market beta month-by-month and then through statistical tests

to examine whether estimated regression coefficients are significantly deviated from zero.

However, the errors-in-variables problem is inevitable to arises because of the true market

beta of each asset is unobservable and is estimated with errors.

Previous studies have been devoted to solving the errors-in-variables problems and

presented some support for the use of the modified estimation method as an alternative to

the traditional estimation. For example, Litzenberger and Ramaswamy (1979) proposed a

weighted least squares version of the risk premium estimator. Shanken (1992) derives an

asymptotic distribution of the CSR estimator within a multifactor framework and under the

assumption that asset returns are conditionally homoskedastic. Recently, Kim (1995)

3

8/13/2019 3-3-2Beta9

5/30

derives a modified method that is performed through a maximum-likelihood estimation

under either homoskedastic or heteroscedastic disturbance terms of the market model by

utilizing the extracted information of measurement error and idiosyncratic error.

This paper proposes a simple method that can be easily performed to correct the beta

measurement errors. In fact, the measurement error of market beta that conditional on the

market return is a function of the idiosyncratic error terms prior to each CSR. We conduct a

two-step method to correct the beta measurement errors of each asset. In the first step, the

idiosyncratic error terms for each firm during the full sample period are estimated by using

the market model adjusted nonsynchronous trading (Dimson, 1979). In the second step,

market beta for each asset at specific time is estimated and then adjusted the measure error

estimated from prior step that is a function of idiosyncratic error terms prior to each CSR.

What is the exact functional form of measurement error of market beta and how to estimate

it will be described in more detail in the next section.

Based on the findings of Fama and French (1992), the firm size effect of Banz (1981)

and book-to-market effect of Rosenberg et al. (1985) are two prominent challenges in the

contemporary asset pricing literature. 2 Given the empirical evidences in other countries

around the world, we have little knowledge about the role of market beta, firm size and

book-to-market ratio on the cross-section stock returns in Taiwan. Previous studies

presented diverse empirical results. Chui and Wei (1998) find little relationships between

expected stock returns and conditional beta, firm size, and book-to-market ratio for

Taiwanese industrial firms. Sheu et al. (1998) also present empirical evidence that

2 See Hawawini and Keim (1995) for an excellent review of this issue. There is controversy over why thefirm-specific attributes can explain the cross-section of expected stock returns. There are at least threeexplanations have been offered for the empirical findings. The first view argues that such firm-specificvariables are used to find those stocks systematically mispriced by the market (Lakonishok et al., 1994;Daniel and Titman, 1997). Alternatively, according to asset pricing theory of Merton (1973), thesefirm-specific variables may proxy for a risk factor in stock returns (Chan and Chen, 1991; Fama and French,

1993, 1996). The third view is that the observed empirical findings are largely the result of data snooping andvarious biases in the data (Black, 1993; MacKinlay, 1995; Kothari et al., 1995). There is no attempt to studywhy the firm-specific attributes can explain the cross-section of expected stock returns in this analysis.

4

8/13/2019 3-3-2Beta9

6/30

unconditional beta fail to capture the cross-sectional variation in stock returns. Surprisingly,

Huang (1997) finds an inverse relationship between returns and market beta. In contrast,

Chou and Liu (2000) show that the unconditional betas of Taiwanese industrial firms

significantly explain the cross-sectional variation in stock returns while the loadings of a

portfolio long in high book-to-market stocks and short in low book-to-market stocks and a

portfolio long in small stocks and short in big stocks, similar to Fama and French (1993),

are without explanatory capability. In addition, Ma and Shaw (1990) show that stock

returns are higher for small firms than large firms and the return difference between small

firms and large firms is higher and significantly differs from zero in January. Yet, for the

same variable, Chou and Johnson (1990) present inconsistent evidence.

Three notable differences among these studies are the method of estimating market beta,

sample selection, and the timing of firm size used. To avoid the possibility of potential data

survivorship bias, the sample of this study has included financial firms and firms listed on

Taiwanese TOTC market that are often ignored in previous studies. 3 Moreover, Fama and

French (1992) used the firm value in June of year t to explain the monthly returns from July

of year t to June of year t+1. Rather, the firm size used in this study is the market value of

equity of the firm as of the end of the second to last month. This measure has two merits.

The first is to enhance the degree of relevance of explanatory variables. Second, the firm

size variable is lagged one additional month in order to preclude the possibility that a linear

combination of stock returns, book-to-market ratio, and the product of price multiple shares

may lead to bias estimate because of bid-ask effects and thin trading. 4

The second goal of this paper is devoted to the analysis of seasonal behavior in stock

returns and in the beta risk premium. Initially, the stock return of U.S. market is on average

3 Because Fama and French (1992) were initially interested in analyzing the impact of firm leverage onstock returns, they excluded from their study all financial firms. Naturally, this treatment may subject to data

selection bias and data-snooping bias (Black, 1993).4 See Jegadeesh (1990). It is easy to show that thin trading will cause risk-adjusted returns to exhibitfirst-order negative serial correlation.

5

8/13/2019 3-3-2Beta9

7/30

higher in January than during the rest of the year is addressed by Rozeff and Kinney (1976).

Subsequently, Keim (1983) shows that most of the excess returns for small firms are

concentrated in January. 5 Furthermore, Tinic and West (1984) document that the positive

relation between beta and stock returns in U.S. market is restricted to January and the beta

risk premiums during the rest of the year are insignificantly different from zero. Corhay et

al. (1987) also find that the beta risk premium in Belgium market is significantly positive in

January. Rather, they observe a positive January beta risk premium in U.K. and France but

are not significantly different from zero. Moreover, Chui and Wei (1998) fail to find that

beta risk premiums in January are significantly different from zero for five Pacific-Basin

emerging markets. The above evidences seem to suggest that the seasonal behavior in beta

risk premium is related to the seasonal behavior in stock returns. What this paper differs

from previous studies are the data we used is firm level instead of portfolio and is more

complete than previous studies for Taiwanese firms. Moreover, there is no tax on capital

gains for individual investors in Taiwan nor is there any tax benefit for capital loss.

In addition to January seasonal in stock returns, Lee et al. (1992) find a Chinese New

Year (CNY) effect that is unique to Asian stock markets. 6 Their findings show that average

stock return of Asian markets is on average higher in the months of CNY than the rest of

the year. In light of previous evidences and arguments, if average returns can be higher in

January and in the CNY months, why isnt it possible for beta, firm size, book-to-market

5 Keim (1983) offers two possible explanations for this finding: the tax-loss-selling hypothesis and theinformation hypothesis. According to the tax-loss-selling hypothesis, toward the tax year end of December 31stockholders sell stocks that have declined in price during the year and utilize the tax benefits for capital loss.As soon as the tax year ends, the selling pressure is relieved and stocks quickly rebound to their equilibriumlevels. The above hypothesis has been tested using the stock markets outside the U.S. that without capitalgains tax. The empirical evidences are controversies. See Agrawal and Tandon (1994), Berges et al., (1984),Brown et al., (1983), Corhay et al. (1987), Gultekin and Gultekin (1983), Kato and Schallheim (1985), Lee(1992), Reinganum and Shapiro (1987), Tinic et al., (1987), and so on. The empirical experiences of U.S.market see Keim (1983), Jones et al., (1991), Roll (1983), Schultz (1985), Van de Bergh and Wessels (1985),Watchtel (1942), and so on. In addition, the information hypothesis refers to the supposition that smaller firms

have less publicly available information than do large firms. This lack of information leads to greater risk andresulting in higher returns for small firms. This hypothesis is supported such as Berry and Brown (1984).6 See also Yen et al., (2001), and Yen and Shyy (1993).

6

8/13/2019 3-3-2Beta9

8/30

ratio and stock returns to have a systematic relationship with excess returns in January and

the CNY months Until now, we have no idea about what is the effect of the CNY

seasonal in stock returns in the testing of the asset pricing. The empirical evidence of the

present study clearly shows that there exist both January seasonal and CNY seasonal in

average stock returns in Taiwan. Remarkably, the regression coefficient for beta, firm size,

and book-to-market ratio also display eminent seasonal behavior. The results show that

there is a January seasonal in beta risk premium and in the regression coefficient of firm

size, as well as a CNY seasonal in the regression coefficient of book-to-market ratio that is

untested before. Unlike the finding of Loughran (1997), we dont find a January seasonal in

book-to-market effect. The above evidences from an emerging market may have important

implications both in asset pricing test and in market efficient hypothesis.

The remainder of this paper is organized as follows. Section 2 first details the effect of

error-in-variables problem on the estimated beta risk premium and then proposes a simple

method to correct this bias. Section 3 describes the data. The empirical results are presented

and discussed in section 4. Section 5 presents conclusions.

2. Two-pass tests of asset pricing models

2.1. Effect of measurement error on estimated market risk premiums

In this section, we start with the two-pass tests originally developed by Fama and

MacBath (1973) and then examine the effect of measurement error on estimated risk

premiums of market beta in the regression analysis. Finally, a simple method of correcting

the measurement error of market beta is proposed. The relationship between expected stock

returns and market beta in the second-pass CSR for estimating the market risk premiums at

a specific time t is

ttt1t0tR ++= , t=1,,T, (1)

where and are N-vector of excess returns over risk-free rates and the market betastR t

7

8/13/2019 3-3-2Beta9

9/30

for N stocks, is a N-vector of the idiosyncratic error with mean zero and variance .

The main interest is focused on whether the regression coefficient,

t2

t1 , is indifferent from

zero or not. Hence, the ordinary least squares (OLS) CSR of on tR t can be run for each

month. By letting ],1[X N = and ]',[ 10 = , the OLS estimate of at time t is

)t,[OLSt1

OLSt0

t OLS =

OLSt1

R t1(]', GLSt1 =

GLSt

t GLS =

GLSt1

1t

=

1t

2

t

. (2)R 'X()X'X(]' t1ttOLSt ==

where denote the N-vector of ones. The test statistic of testing whether the market beta

risk premium is indifferent from zero or not is

N1

T/)(s

OLSt1

OLS1

. (3)

OLS1 is the time series mean of . Because the variance of individual stock return may

be different, then the generalized least squares (GLS) estimate of will be more efficient

than OLS estimate. The month-by-month CSR coefficient estimated from GLS at time t is

, (4))'X()X'X[ tt1t1ttGLSt0 =

where is the N N variance matrix of all firms at time t. We assume that the error terms

are serially independent and uncorrelated across stocks. Similarly, the test statistic of testing

whether the market beta risk premium is indifferent from zero or not is

t

T/)(s

GLSt1

GLS1

. (5)

GLS1 is the time series mean of . In general, the estimated beta, , is used as a proxy

for since is unobservable. Therefore, the explanatory variable is measured with

error

t

, (6)1tt +

where is a N-vector of the market beta estimated from the first-pass time series

regression by using the market model for K time series data available up to t-1, and is

a N-vector of the measurement error with mean zero and variance .

1t

1t

Consider, then, the second-pass CSR for estimating the market risk premiums at a

8

8/13/2019 3-3-2Beta9

10/30

specific time t. By substituting equation (6) into equation (1), we obtain,

, (7)t1t101tt1t1tt1t0t )(R ++=++=

Apparently, the explanatory variable in relation (7) is correlated with error term. It

hence violates one of the crucial assumptions of classical regression model. For the sake of

simplicity, the constant term is ignored and then the OLS estimator of market risk premium

is,

. (8))R '()'( t1t11t1tOLSt1 =

We insert relations (1) and (6) into relation (8) and use the Slutsky theorem to examine

whether the estimated market risk premium is consistent or not. The probability limit of the

estimated market risk premium is, 7

Q/1lim p

2t1OLS

t1+

= , (9)

where Q= )')( N/1lim( p tt . As long as the variance of measurement error of beta, , is

positive, the estimated market beta risk premium, , is inconsistent, with a persistent bias

toward zero. Obviously, the greater the variability in the measurement error of beta, the

higher the bias in the estimated market beta risk premium. This is the very reason why so

many efforts have devoted to eliminating or mitigating the error-in-variable problem in

estimating market beta.

2

t1

2.2. A simple method of correcting measurement error of beta

In what follows, we propose a simple method to correct the measurement error of

market beta. Assuming that the return-generating process at specific time t is,

tmtttt R R ++= , (10)

where is a N-vector of market return,mtR t is a N-vector of the idiosyncratic error with

mean zero and variance . The estimated market beta for the period of s, time t-k to time2

7 See Greene (1993) for a detail of demonstrating this result.

9

8/13/2019 3-3-2Beta9

11/30

t-1, is,

=

=

=

1t

k ts

2msms

1t

k tssmsms

1t

)R R (

R )R R ( , s[t-k, t-1], (11)

After substituting the relation (10) into relation (11), the estimated market beta for the

period of s, time t-k-2 to time t-1, is become,

=

=

+=

1t

k ts

2msms

1t

k tssmsms

t1t)R R (

)R R ( , s[t-k, t-1], (12)

The second term of the right side of relation (12) is the measurement error mentioned

above, . This measurement error at specific time is just a function of the idiosyncratic

error during the period of estimating beta.

1t

Naturally, the true market beta can be found only if the overall data of asset return is

collected. That is to say that the populations of all asset returns are available. However, the

stock markets continuously process through time. Therefore, we begin by assuming that

there is a common terminal data for all asset returns. The rationale of this assumption

follows the studies of Chan and Chen (1988) and Fama and French (1992). Hence, the

common terminal date for all firms is June 2002 in this paper. A simple method of

estimating the measurement error of beta is then proposed by a two-step estimation

procedure. In the first step, the idiosyncratic error for each asset during the overall period is

estimated by running regression (10). In the second step, this estimated measurement error

of market beta for each asset at specific period is computed as the second term of the right

side of relation (12) and then use it to correct the estimated beta at that time interval.

3. Data

10

8/13/2019 3-3-2Beta9

12/30

This paper uses monthly data of all firms, including financial and nonfinancial firms,

listed on Taiwan Stock Exchange (TSE) and Taiwanese Over-the-counter Securities

Exchange (TOTC) for the period from July 1982 to June 2002. As suggested by Fama and

French (1992), the following data selection criteria are applied. First, all firms must have

monthly stock returns for at least 24 months before entering the sample. Second, firms must

have a non-negative book value at the end of December each year to compute their

book-to-market ratio. Book value of equity is defined as total shareholders equity minus

book value of preferred stock. Book-to-market ratio (B/M) is equal to book value of equity

divided by the market value of equity as of the end of December of year t-1.

Fama and French (1992) use the market value of equity of the firm in June of year t to

explain the monthly returns from July of year t to June of year t+1. Rather, the firm size

used in this study is the market value of equity of the firm as of the end of the second to last

month to explain the next two monthly returns month-by-month. Firm size variable was

lagged by one additional month in order to preclude the possibility of bias estimation

because of bid-ask effects and thin trading. Conditional market betas for all firms are

estimated on 24 to 60 months as available in the five years prior to each monthly excess

returns and are the sum of the coefficients from a regression of monthly returns on the

current and prior months returns on the value-weighted portfolio of TSE and TOTC stocks.

In addition, we calculate the measurement error of estimate market beta month-by-month

discussed earlier to correct estimated market beta to derive the adjusted market beta. Both

market betas, unadjusted and adjusted beta, are estimated monthly and are used to explain

the stock returns in the next two months.

The sample consists of 63 firms in the first month and 584 firms in the final month.

There are totally 4,307 firm-years and 51,684 monthly returns observations in this analysis.

The TOTC market is called into existence in July 1994. At the inception only 3 firms are

considered; however, in the final month, there are 115 firms. Prior to the establishment of

11

8/13/2019 3-3-2Beta9

13/30

TOTC market, the mimic market portfolio is just the value-weighted index return of TSE.

We reconstruct a value-weighted stock portfolio of incorporating TSE and TOTC after July

1992. The sample this study used is more complete than previous studies for Taiwanese

firms. In addition, since there is no Taiwanese equivalent to U.S. Treasury bills, we us a

combined series of rediscount rates (before October 1984 and after July 1999) and the

91-day T-bills rate (October 1984-July 1999) as a proxy for the risk-free rate. Excess stock

returns are stock raw returns in excess of this risk-free rate.

[Insert Table 1 here]

Table 1 reports summary statistics for the explanatory variables, unadjusted and

adjusted market beta, firm size (in NT 10 million), and book-to-market ratio during the

entire period. In order to delineate the preliminary relationship among these variable, five

portfolios are formed monthly. The results of the full sample are reported in panel A, table 1.

Mean adjusted beta is 0.85 and is slightly higher than the unadjusted beta of 0.798. The

standard deviation of adjusted beta is slightly smaller than unadjusted beta. Moreover, mean

market value of equity for the full sample is NT 18950 millions. Panel B of Table 1

reports that the mean of the unadjusted betas range from 0.214 for lowest beta portfolio to

1.454 for highest beta portfolio, while the mean of the adjusted betas range from 0.358 for

lowest beta portfolio to 1.384 for highest beta portfolio. Beta spreads between highest beta

portfolio and lowest beta portfolio for the adjusted beta is 1.026 and is smaller than its

counterpart 1.24 of the unadjusted beta. The maximum standard deviations for both

adjusted and unadjusted betas occur at low beta portfolio simultaneously. Besides, there is

no systematical relationship between market beta and book-to-market ratio. We find that the

highest beta portfolio is associated with the largest firm while the lowest beta portfolio is

associated with the smallest firm. It exhibits weakly negative relationship between market

12

8/13/2019 3-3-2Beta9

14/30

beta and firm size.

Panel C of Table 1 presents the results that within a firm size, the market value of equity

ranges from NT 1890 millions for the smallest firms to NT 69960 millions for the

largest firms. There is a significantly negative relationship between firm size and

book-to-market ratio in which portfolios are formed on firm size and relationship of this

kind is also found in Panel D of Table 1 in which portfolios are formed on book-to-market

ratio. The book-to-market ratio ranges from 0.299 for the lowest group to 1.421 for the

highest group.

4. Empirical Results

4.1. Portfolio returns and seasonality

In this section, we first study whether there is seasonal behavior in Taiwan stock market.

We next turn to investigate how market beta and two important firm attributes, firm size

and book-to-market are related in pricing the underlying asset. Finally, we examine whether

there are any systematical relationships between market price and seasonal behavior in

stock returns. Seasonalities under considerations are the January effect and the CNY effect

that unique to Asian stock market. Table 2 shows that portfolios are formed on unadjusted

market beta, adjusted market beta, firm size, and book-to-market ratio. All firms are sorted

by calendar events, January and CNY, to examine the seasonal behavior in stock returns

and in return spreads. 8 To the extent that beta or firm attributes are taken into account in

8 Portfolio formation approach may either mitigate problems caused by using estimated variables asindependent variables in a two-pass methodology or, when a one-step methodology is used, allow us toestimate the covariance matrix of residual returns. However, three types of problem may occur. First, the

portfolio grouping procedure ignores the dynamic period-by-period relation between stock returns andexplanatory variables. Second, as Roll (1977) has pointed out, the portfolio formation process, by concealing

possibility return relevant security characteristics within portfolio averages, may make it difficult to reject thenull hypothesis of no effect on security returns. Third, Lo and MacKinlay (1990b) make an almost opposite

point, that if the portfolios are formed on the basis of characteristics that previous studies have found to be

related to stock return, it will be inclined to reject the null hypothesis too often due to a data-snooping bias.The third problem may be less serious than it first might appear because the number of studies of Taiwanesestock market is so smaller than U.S. market.

13

8/13/2019 3-3-2Beta9

15/30

pricing, the mean excess return spreads should be systematically positive and significantly

indifferent from zero. From Panel A of Table 2, mean excess returns for all months is 1.083

and, indeed, display pronounced seasonality. Mean excess returns are relatively higher for

the January and CNY months (9.648 and 5.662 , respectively), relatively lower, but

positive for non-January and non-CNY months (0.305 and 0.667 , respectively).


The individual firms are further partitioned into five portfolios based on their

unadjusted beta, adjusted beta, firm size, and book-to-market ratio, to examine

preliminarily whether the market beta and firm attributes are priced and their risk premiums

are related to market seasonality or not. The results show that the adjusted market beta is

priced and excess return spreads are also related to calendar seasonal. In Panel A of Table 2,

mean excess return for all firms, when portfolios formed on unadjusted beta, ranges from

1.012 for the lowest beta portfolio to 1.201 for the highest beta portfolio while mean excess

return spreads between the highest and lowest portfolio is 0.189 with a t-statistic of 0.72.

When portfolios are formed on adjusted beta, Panel B of Table 2 present that mean excess

return for all firms ranges from 1.037 for the lowest beta portfolio to 1.611 for the highest

beta portfolio. Its mean excess return spreads between the highest and lowest portfolio is

0.574 with a t-statistic of 2.19. The above result supports our prediction.

In addition to the results of all firms, mean excess return spreads for January and CNY

months are 6.217 with a t-statistic of 5.16 and 4.967 with a t-statistic of 5.68 (9.495 with a

t-statistic of 8.19 and 5.943 with a t-statistic of 6.72) when portfolios formed on unadjusted

(adjusted) beta. In contrast, mean excess return spreads for non-January and non-CNY

months are very small and are insignificant no matter how portfolios are formed on

unadjusted beta or adjusted beta. This finding indicates that there is seasonal behavior in

14

8/13/2019 3-3-2Beta9

16/30

both beta risk and returns. What this paper differs from Tinic and West (1984) is that

unadjusted beta is not priced for Taiwanese firms but adjusted beta is priced. In addition,

this paper finds a January seasonal while Chui and Wei (1998) dont find it.

We further examine whether firm size and book-to-market ratio are priced and are

related to seasonal behavior in stock returns. Panel C and Panel D of Table 2 provide

preliminary tests. The results indicate that firm size and book-to-market ratio may not be

priced in all firms because mean spreads of each quintile are not only highly volatile but

also negative some time. Instead, firm size is priced in January and book-to-market ratio is

priced in CNY months for mean return spreads of each quintile are systematically positive.

In Panel C of Table 2, mean excess return spreads for January is 7.672 with a t-statistic of

6.45 and the mean spread range from 2.92 for lowest quintile to 1.62 for the highest quintile.

Panel D of Table 2 presents the results when portfolios are formed on book-to-market ratio.

For the months of CNY excludes January, mean excess return spreads for lowest quintile is

2.586 with a t-statistic of 2.98 and the mean spreads of each quintile are also systematical

positive.

4.2. Cross-sectional regression results

In Table 3 of Fama and French (1992), they used cross-sectional regressions of expected

stock returns on market beta, firm size, and book-to-market ratio for full samples to attack

the CAPM. In this section, we use a similar approach with revisions in estimating market

beta and the timing of firm size to examine whether market beta, firm size, and

book-to-market ratio have the capability of explaining expected stock returns. In addition to

examining the samples of overall period like Fama and French (1992), this paper further

explores whether there are seasonalities in the regression coefficients of market beta, firm

size, and book-to-market ratio. The empirical evidences do show that the explanatory

power of market beta after correcting measurement error is improved and has significant

15

8/13/2019 3-3-2Beta9

17/30

capability of explaining expected returns. Besides, the results also reveal there are

distinctive seasonalities in the regression coefficients of market beta, firm size, and

book-to-market ratio.


Table 3 reports the results for the sample of the overall period. The mean OLS (GLS)

regression coefficient for the unadjusted beta is 0.202 (0197) with a t-statistics of 0.47

(0.46). When the adjusted beta is used as explanatory variable, mean OLS (GLS) regression

coefficient increases to 0.734 (0.772) and the t-statistics sharply jumps to 1.67 (1.75).

Moreover, 113 (109) of the 240 OLS (GLS) estimates of the unadjusted beta risk premiums

are positive. The positive number of coefficient is also lower than the OLS (GLS) estimates

of adjusted beta risk premiums. The above results are not altered when firm size and

book-to-market ratio are introduced. Statistically, the mean regression coefficient of firm

size and book-to-market ratio are indifferent from zero.


Table 4 presents the results for January and non-January months. In Panel A of Table 4,

the t-statistics for the regression coefficient of market beta, including unadjusted and

adjusted beta, and firm size are all significantly different from zero in January. The

t-statistics for the regression coefficient of book-to-market ratio remains insignificantly in

January. For example, the OLS regression coefficient of the unadjusted (adjusted) beta is

4.113 (5.341) with a t-statistics of 2.09 (2.65) in January. The OLS (GLS) regression

coefficient of firm size is 1.443 (-1.396) with a t-statistics of 2.15 (-2.04) in January. The

results still hold even market beta, firm size, and book-to-market ratio are considered

16

8/13/2019 3-3-2Beta9

18/30

simultaneously. In contrast, the Panel B of Table 4 indicates that market beta, firm size, and

book-to-market ratio are unable to explain stock returns in non-January months. The above

findings are consistent with previous studies such as Tinic and West (1984), but unlike the

findings of Chui and Wei (1998).


The results for the CNY effect on risk premium are presented in Table 5. Like the

results for non-January months, the Panel B of Table 5 indicates that market beta, firm size,

and book-to-market ratio are unable to explain stock returns in the non-CNY months.

Rather, the t-statistics for the regression coefficient of market beta, including unadjusted

and adjusted beta, and book-to-market ratio are all significantly different from zero in the

CNY months. For example, the OLS regression coefficient of the unadjusted (adjusted) beta

is 3.555 (3.503) with a t-statistics of 1.84 (1.76) in the CNY months. The OLS (GLS)

regression coefficient of book-to-market ratio is 1.649 (1.679) with a t-statistics of 1.67

(1.71) in the CNY months.


Because of there are 6 of 20 January months in which are also CNY months. In Table 6

we have reproduced the two-pass tests of Fama and MacBath (1973) for pure January

months and pure CNY months. The pure January (CNY) month is the January month that is

not CNY (January) month. It shows that prior findings for January months are not changed

but the results for CNY month are slightly altered. From Panel A of Table 5, beta and firm

size still have the significant capability of explaining expected returns. Rather, the market

beta has lost its significant explanatory power on excess returns in Panel B of Table 6. The

17

8/13/2019 3-3-2Beta9

19/30

t-statistics of regression coefficient for firm size become significant.

5. Conclusions

This paper proposes a simple method of correcting measurement error in beta

estimation by utilizing the idiosyncratic error of overall period tested in the two-pass tests

of asset pricing model. The empirical evidence from Taiwan stock market really show that

the explanatory power of estimated market beta after this correction is improved

significantly and successfully captures the cross-sectional variation in stock returns for the

samples of overall period even if firm size and book-to-market ratio are introduced. Unlike

the finding of Fama and French (1992), we show that firm size and book-to-market ratio

have no role in explaining the cross-section of stock returns for the samples of overall

period in Taiwan. Our findings cannot reject the hypothesis that the pricing of stock returns

on the Taiwan stock market conforms to the CAPM.

Furthermore, in reflecting on whether the risk-return relation driven by calendar

seasonal, as reported in Tinic and West (1984) and others, we think it important to recall

that the CNY effect unique to Asian stock market. Indeed, we do find that there exist both a

January seasonal and a CNY seasonal in average stock returns in Taiwan. The evidence of

an emerging market that without capital gains tax may cast doubt on the tax-loss-selling

hypothesis as an explanation of the January effect. The emergent issues are why seasonal

variations of stock returns are so popular across the national stock markets that with

different financial systems and most of what today constitutes the received concept of

modern finance are brought into question.

Remarkably, the regression coefficient for beta, firm size, and book-to-market ratio also

display distinctive seasonal behavior. The t-statistics for the regression coefficients of

market beta, including unadjusted and adjusted beta, and firm size are significantly

18

8/13/2019 3-3-2Beta9

20/30

different from zero but is insignificant for book-to-market ratio in January. Rather, the

book-to-market ratio is significantly positive related to stock returns in the months of CNY.

At the same time, our empirical findings show that beta, firm size, and book-to-market ratio

are not able to explain stock returns outside the January and the CNY months.

According to Fama and MacBeth (1973), the market efficient hypothesis and model

specification are considered simultaneously in the testing of asset pricing model. Thus, we

address a puzzle like Tinic and West (1984) that why the risk-ruturn trade-off shows up

only in certain months, such as the months of January and CNY, and why these certain

months are just the months with higher stock returns than the rest of the year. In addition,

the explanation of a proxy for risk factor and of market mispricing hypothesis for the size

effect and book-to-market effect are seemingly unable to tell us the whole story of why the

regression coefficient of firm size and book-to-market ratio are also significantly different

from zero in these certain months and are insignificantly different from zero during the rest

of the year. It seems relevant to investigate whether the intertemporal CAPM of Merton

(1973) and Breeden (1979) and APT of Ross (1976) are also subjected to certain calendar

seasonal in stock returns. However, we conjecture that some unsolved issues related to asset

pricing test should obtain valuable insights from these investigations.

19

8/13/2019 3-3-2Beta9

21/30

References

Agrawal, Anup, and Kishore Tandon, 1994, Anomalies or illusions? Evidence from stock markets in eight

countries Journal of International Money and Finance , 13, 83-106.Asgharian, Hossein, and Bjorn Hansson, 2000, Cross-sectional analysis of Swedish stock returns withtime-varying beta: The Swedish stock market 1983-96, European Financial Management , 6, 213-233.

Ball, Ray, 1978, Anomalies in relationships between securities yields and yield-surrogates, Journal of Financial Economics , 6, 103-126.

Banz, Rolf W., 1981, The relationship between return and market value of common stocks, Journal of Financial Economics , 9, 3-18.

Barry, C. B., and S. J. Brown, 1984, Differential information and the small firm effect, Journal of Financial Economics , 13, 283-294.

Basu, Sanjoy, 1983, The relationship between earnings yield, market value and return for NYSE commonstock, Journal of Financial Economics , 12, 129-156.

Bekaert, Geert, and Campbell R. Harvey, 2003, Emerging markets finance, Journal of Empirical Finance ,10, 3-55.

Berges, Angel, John J. McConnell, and Gary G. Schlarbaum, 1984, The turn-of-the-year in Canada, Journalof Finance , 39, 185-192.

Berk, Jonathan B., 2000, Sorting out sorts, Journal of Finance , 55, 407-427.Black, Fischer, 1972, Capital market equilibrium with restricted borrowing, Journal of Business , 45,

444-455.Black, Fischer, Michael C. Jensen, Myron Scholes, 1972, The capital asset pricing model: Some empirical

tests, in Michael C. Jensen, Ed.: Studies in the Theory of Capital Markets (Praeger, New York). 79-121.Black, Fischer, 1993, Beta and return, Journal of Portfolio Management , 20, 8-18.Breeden, Douglas, 1979, An intertemporal asset pricing model with stochastic consumption and investment,

Journal of Financial Economics , 7, 265-296.Brown, Philip, Donald B. Keim, Allan W. Kleidon, and Terry A. Marsh, 1983, Stock return seasonalities and

the tax-loss selling hypothesis, Journal of Financial Economics , 12, 105-127.

Chan, K. C., and Nai-Fu Chen, 1988, An unconditional asset-pricing test and the role of firm size as aninstrumental variable for risk, Journal of Finance , 43, 309-325.

Chan, K. C., and Nai-Fu Chen, 1991, Structural and return characteristics of small and large firms, Journalof Finance , 46, 1467-1484.

Chou, Pin-Huang, and Yi-Feng Liu, 2000, The cross section of expected returns in Taiwan: Characteristics,single factor, or multi factors Review of Securities and Futures Markets , 12, 1-32.

Chou, Shyan-Rong, and Keith H. Johnson, 1990, An empirical analysis of stock market anomalies: Evidencefrom the Republic of China in Taiwan, in: S.D. Rhee and R.P. Chang (eds), Pacific-basin Capital

Markets Research , Vol. 1, 283-312, North Holland, Amsterdam.Chui, Andy C.W., and K.C. John Wei, 1998, Book-to-market, firm size, and the turn-of-the-year effect:

Evidence from Pacific-Basin emerging markets, Pacific-Basin Finance Journal , 6, 275-293.Clare, A.D., R. Priestley, S.H. Thomas, 1998, Reports of betas death are premature: Evidence from the UK,

Journal of Banking and Finance , 22, 1207-1229.Corhay, Albert, Gabriel Hawawini, and Pierre Michel, 1987, Seasonality in the risk-return relationship: Some

international evidence, Journal of Finance , 42, 49-68.Daniel, Kent, and Sheridan Titman, 1997, Evidence on the characteristics of cross-sectional variation in

stock returns, Journal of Finance , 52, 1-33.Daniel, Kent, Sheridan Titman, and K.C. John Wei, 2001, Explaining the cross-section of stock returns in

Japan: Factors or Characteristics Journal of Finance , 56, 743-766.Davis, James L., 1994, The cross-section of realized stock returns: The pre-Compustat evidence, Journal of

Finance , 49, 1579-1593.Dimson, Elroy, 1979, Risk measure when shares are subject to infrequent trading, Journal of Financial

Economics , 7, 197-226.Downs, Thomas W., and Robert W. Ingram, 2000, Beta, size, risk and return, Journal of Financial Research ,

23, 245-260.Fama, Eugene F., and James D. MacBeth, 1973, Risk, return and equilibrium: Empirical tests, Journal of

Political Economy , 81, 607-636.

20

8/13/2019 3-3-2Beta9

22/30

Fama, Eugene F., and Kenneth R. French, 1992, The cross-section of expected stock returns, Journal of Finance , 47, 427-465.

Fama, Eugene F., and Kenneth, R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics , 33, 3-56.

Fama, Eugene F., and Kenneth R. French, 1996, The CAPM is wanted, dead or alive, Journal of Finance ,51, 1947-1958.

Greene, William H., 1993, Econometric analysis , 2ed, Macmillan Publishing Company, New York.Gultekin, Mustafa N., and N. Bulent Gultekin, 1983, Stock market seasonality, Journal of Financial

Economics , 12, 469-481.Hawawini, Gabriel A., and Donald B. Keim, 1995, On the predictability of common stock returns:

World-wide evidence, in Jarrow, R.A., V. Maksimovic, and W.T. Ziemba (eds), Handbooks in operationsresearch and management science: Finance, Elsevier Publisher, New York.

Hawawini, Gabriel A., Pierre A. Michel, and Claude J. Viallet, 1983, An assessment of the risk and return ofFrench common stocks, Journal of Business Finance and Accounting , 10, 333-350.

Hawawini, Gabriel A., and Pierre A. Michel, 1982, The pricing of risky assets on the Belgian stock market, Journal of Banking and Finance , 6, 161-178.

Heston, Steven L., K. Geert Rouwenhorst, and Roberto E. Wessels, 1999, The role of beta and size in thecross-section of European stock return, European Financial Management , 5, 9-27.

Hu, Shing-Yang, 1998, The effect of turnover on stock returns in Taiwan, Journal of Financial Studies , 5,1-19.Huang, I-Hsiang, Yung-Jang Wang, Chia-Cheng Ho, and Chia-Hui Hsu, 2004, On the beta estimation and

cross-sectional analysis of expected stock returns in Taiwan, Journal of Financial Studies , 11, 1-33.Huang, Yen-Sheng, 1997, An empirical test of the risk-return relationship on the Taiwan Stock Exchange,

Applied Financial Economics , 7, 229-239.Isakov, Dusan, 1999, Is beta still alive Conclusive evidence from the Swiss stock market, European

Journal of Finance , 5, 202-212.Jagannathan, Ravi, and Zhenyu Wang, 1996, The conditional CAPM and the cross-section of expected

returns,, Journal of Finance , 51, 3-53.Jones, Steven L., Winson Lee, and Rudolf Apenbrink, 1991, New evidence on the January effect before

personal income taxes, Journal of Finance , 46, 1909-1924.Kato, Kiyoshi, and James S. Schallheim, 1985, Seasonal and size anomalies in the Japanese Stock Market,

Journal of Financial and Quantitative Analysis , 20, 243-260.Keim, Donald B., 1983, Size-related anomalies and stock return seasonality, Journal of Financial

Economics , 12, 13-32.Kim, Dongcheol, 1995, The error-in-variables problem in the cross-section of expected stock returns,

Journal of Finance , 50, 1605-1634.Kim, Dongcheol, 1997, A reexamination of firm size, book-to-market, and earnings price in the cross-section

of expected stock returns, Journal of Financial and Quantitative Analysis , 32, 463-489.Kothari, S. P., Jay Shanken, and Richard G. Sloan, 1995, Another look at the cross-section of expected stock

return, Journal of Finance , 50, 185-224.Lakonishok, J., A. Shleifer, and R. Vishny, 1994, Contrarian investment, extrapolation, and risk, Journal of

Finance , 49, 1541-1578.Lee, Cheng Few, Gili Yen, and Chingfu Chang, 1992, The Chinese new year, common-stock purchasing, and

cumulative raw returns: Is Taiwans stock market informationally efficient in Klaus P. Fischer, andGeorge J. Papaioannou (eds), Business finance in less developed capital markets, Greenwood Press,Connecticut, U.S.A.

Lee, Insup, 1992, Stock market seasonality: Some evidence from the Pacific-Basin countries, Journal of Business Finance and Accounting , 19, 199-210.

Lintner, John, 1965, The valuation of risk assets and the selection of risky investments in stock portfoliosand capital budgets, Review of Economics and Statistics , 47, 13-37.

Litzenberger, Robert H., and Krishna Ramaswamy, 1979, The effect of personal taxes and dividends oncapital asset prices: Theory and empirical evidence, Journal of Financial Economics , 7, 163-195.

Liu, Y. Angela, Lee-Zer Hwang and Victor W. Liu, 1996, An analysis of systematic risk in Taiwan StockMarket, Review of Securities and Futures Markets, 8, 45-66.

Lo, Andrew W., and A. Craig MacKinlay, 1990a, When are contrarian profits due to stock market

overreaction, Review of Financial Studies , 3, 175-205.Lo, Andrew W., and A. Craig MacKinlay, 1990b, Data-snooping biases in tests of financial asset pricingmodels, Review of Financial Studies , 3, 431-468.

21

8/13/2019 3-3-2Beta9

23/30

Loughran, Tim, 1997, Book-to-market across firm size, exchange, and seasonality: Is there aneffect Journal of Financial and Quantitative Analysis , 32, 249-268.

Ma, Tai, and T.Y. Shaw, 1990, The relationships between market value, P/E ratio, trading volume and thestock return of Taiwan stock exchange, in: S.D. Rhee and R.P. Chang (eds), Pacific-basin Capital

Markets Research , Vol. 1, 313-335, North Holland, Amsterdam.MacKinlay, A. Craig, 1995, Multifactor models do not explain deviations from the CAPM, Journal of

Financial Economics , 38, 3-28.Merton, Robert C., 1973, An intertemporal capital asset pricing model, Econometrica , 41, 867-887.Reinganum, Marc R., 1981, Misspecification of capital asset pricing: Empirical anomalies based on earnings

yields and market values, Journal of Financial Economics , 9, 19-46.Reinganum, Marc R., 1983, The anomalous stock market behavior of small firms in January: Empirical tests

for year-end tax effect, Journal of Financial Economics , 12, 89-104.Reinganum, Marc R., and Alan C. Shapiro, 1987, Taxes and Stock return seasonality: Evidence from the

London Stock Exchange, Journal of Business , 60, 281-295.Ritter, J. and N. Chopra, 1989, Portfolio rebalancing and the turn-of-the-year effect, Journal of Finance , 44,

149-166..Roll, Richard, 1983, Vas ist das? The turn-of-the-year effect and the return premia of small firms, Journal of

Portfolio Management , 9, 18-28.

Roll, Richard, and Stephen A. Ross, 1994, On the cross-sectional relation between expected returns and betas, Journal of Finance , 49, 101-121.Rosenberg, Barr, Kenneth Reid, and Ronald Lanstein, 1985, Persuasive evidence of market inefficiency,

Journal of Portfolio Management , 11, 9-17.Ross, Stephen A., 1976, The arbitarge theory of capital asset pricing, Journal of Economic Theory , 13,

341-360.Rouwenhorst, K. Geert, 1999, Local return factors and turnover in emerging stock markets, Journal of

Finance , 54, 1439-1464.Rozeff, Michael S., and William R. Kinney Jr., 1976, Capital market seasonality: The case of stock returns,

Journal of Financial Economics , 3, 379-402.Shanken, Jay, 1992, On the estimation of beta-pricing models, Review of Financial Studies , 5, 1-33.Schultz, Paul, 1985, Personal income taxes and the January effect: Small firm stock returns before the War

Revenue Act of 1917: A note, Journal of Finance , 40, 333-343.Sharpe, William F., 1964, Capital asset prices: A theory of market equilibrium under conditions of risk,

Journal of Finance , 19, 425-442.Sheu, Her-Jiun, Soushan Wu, and Kuang-Ping Ku, 1998, Cross-sectional relationships between stock returns

and market beta, trading volume, and sales-to-price in Taiwan, International Review of Financial Analysis , 7, 1-18.

Taiwanese Securities and Futures Institute, 1999, Taiwan Securities and Futures Markets: 1999, TaiwaneseSecurities and Futures Institute.

Tinic, Seha M., and Richard R. West, 1984, Risk and return: January v.s. the rest of the year, Journal of Financial Economics , 13, 561-574.

Tinic, Seha M., G. Barone-Adesi, and Richard R. West, 1987, Seasonality in Canadian stock prices: A test ofthe tax-loss-selling hypothesis, Journal of Financial and Quantitative Analysis , 22, 51-63.

Van de Bergh, W., and R. Wessels, 1985, Stock market seasonality and Taxes: An examination of the

tax-loss-selling hypothesis, Journal of Business Finance and Accounting , 12, 515-530.Yen, Gili, Cheng F. Lee, Cheng-Lung Chen, and Wei-Chi Lin, 2001, On the Chinese Lunar New Year effect

in six Asian stock markets: An empirical analysis (1991-2000), Review of Pacific Basin Financial Markets and Policies , 4, 463-478.

Yen, Gili, and Gang Shyy, 1993, Chinese New Year effect in Asian stock markets, National TaiwanUniversity Management Review , 4, 417-436.

Wachtel, S. B., 1942, Certain observation on seasonal movement in stock prices, Journal of Business , 15,184-193.

22

8/13/2019 3-3-2Beta9

24/30

Table 1Summary statistics for adjusted market beta, unadjusted market beta, market value of equity,and book-to-market ratio in Taiwan: July 1982 to June 2002The sample contains all firms, including financial and nonfinancial firms, listed on Taiwan Stock Exchange(TSE) and Taiwanese Over-the-counter Securities Exchange (TOTC) for the period from July 1982 to June 2002.

It consists of 63 firms in the first month and 584 firms in the final month. There are totally 4,307 firm-years and51,684 return observations. Portfolios are formed monthly. The TOTC market is introduced in July 1994. Allfirms are allocated to five portfolios based on their market beta, firm size (ME), and book-to-market (B/M) ratio.

and denote unadjusted and adjusted market beta, respectively. The firm size used to form portfolios is themarket value of equity as of the end of the second to last month. The market beta used to sort portfolios is theestimated conditional beta as of the two months previous to stock returns. In addition, the book-to-market ratiois equal to book value of equity divided by the market value of equity as of the end of December of year t-1.Panel A, B, C, and D show the results for full samples, portfolios formed on unadjusted market beta, on firmsize, and on book-to-market ratio, respectively.

k

k ME BE/ME k ME B/M

Means Standard deviations

Panel A: Full sample

All 0.798 0.850 1895 0.754 0.534 0.524 5579 0.791

Panel B: Portfolios formed on

Low- 0.214 0.358 1306 0.740 0.439 0.530 2128 0.740

-2 0.549 0.639 1524 0.743 0.332 0.379 3456 0.686

-3 0.767 0.836 1337 0.750 0.261 0.299 2601 0.555

-4 1.004 1.032 1856 0.794 0.222 0.293 6023 0.808

High- 1.454 1.384 3449 0.744 0.360 0.413 9633 1.072

Panel C: Portfolios formed on firm size(NT 10million)

Small-ME 0.756 0.822 189 0.967 0.528 0.509 149 1.155

ME-2 0.776 0.852 389 0.856 0.497 0.483 249 0.844

ME-3 0.804 0.850 664 0.768 0.516 0.504 390 0.708

ME-4 0.794 0.833 1229 0.682 0.541 0.534 651 0.585

Big-ME 0.859 0.893 6996 0.499 0.581 0.583 11032 0.342

Panel D: Portfolios formed on B/M

Small-B/M 0.904 0.963 4519 0.299 0.589 0.585 10902 0.166

B/M-2 0.794 0.836 1759 0.499 0.544 0.550 3448 0.252

B/M-3 0.756 0.791 1258 0.669 0.523 0.509 2456 0.365

B/M-4 0.736 0.784 1057 0.882 0.491 0.466 2524 0.525

Big-B/M 0.800 0.876 888 1.421 0.503 0.483 1912 1.374

23

8/13/2019 3-3-2Beta9

25/30

Table 2Average excess monthly returns and excess return spreads for market beta, firm size, and

book-to-market ratio quintilesThe sample contains firms listed on TSE and TOTC for the period from July 1982 to June 2002. It consists of63 firms in the first month and 584 firms in the final month. There are totally 4,307 firm-years and 51,684return observations. The combined series of rediscounts rate and the 91-day T-bills rate in Taiwan as a risk-freerate. Excess returns are raw returns in excess of this risk-free rate. Portfolios are formed monthly. All firms areallocated to five portfolios based on their unadjusted beta ( ), adjusted beta ( ), size, and book-to-marketratio (B/M). Panel A, B, C and D show the results for portfolios formed on

k

, , size and B/M, respectively.The F-values are computed under the null hypothesis that the mean excess returns on portfolios lowest throughhighest are jointly equal. Significance indicators: 1 ( *** ), 2.5 ( **), and5 ( *).

k

All Low 2 3 4 High High-LowSpread

t-value(Spread)

F Value

Panel A: Portfolios sorted on

All months 1.083 1.012 1.046 1.018 1.138 1.201 0.189 0.72 0.124

January only 9.648 7.147 7.104 9.105 11.506 13.364 6.217 5.16*** 6.131

January excludes CNY 9.484 8.197 8.191 9.369 10.531 11.120 2.923 1.93* 0.860Except January 0.305 0.445 0.493 0.289 0.201 0.095 -0.350 -1.35 0.528

CNY only 5.662 3.441 3.931 5.217 7.303 8.408 4.967 5.68*** 8.649

CNY excludes January 3.531 2.674 3.436 3.561 4.255 3.728 1.054 1.26 0.754

Except CNY 0.667 0.783 0.782 0.643 0.583 0.546 -0.237 -0.87 0.200 Panel B: Portfolios sorted on k

All months 1.037 0.803 0.820 1.144 1.611 0.574 2.19** 1.995

January only 5.359 7.345 8.276 12.388 14.854 9.495 8.19*** 12.712

January excludes CNY 6.368 8.005 8.170 12.201 12.658 6.290 4.42*** 3.936

Except January 0.658 0.391 0.468 0.652 1.073 0.415 2.09** 2.174

CNY only 0.956 3.939 5.392 7.112 8.899 5.943 6.72*** 10.509

CNY excludes January 2.785 2.902 3.862 4.325 3.778 0.993 1.21 1.045

Except CNY 0.865 0.509 0.396 0.617 0.948 0.083 0.31 0.918 Panel C: Portfolios sorted on firm size

All months 2.167 0.997 0.896 0.533 0.830 -1.337 -5.11*** 10.249

January only 14.267 10.408 8.921 8.063 6.595 -7.672 -6.45*** 12.056

January excludes CNY 16.384 11.214 8.724 6.765 4.354 -12.030 -8.11*** 21.273

Except January 1.055 0.139 0.166 -0.141 0.305 -0.750 -2.88*** 5.152

CNY only 6.434 5.934 5.303 5.439 5.203 -1.231 -1.07 0.577

CNY excludes January 4.708 4.510 3.320 2.847 2.278 -2.430 -2.91*** 2.840Except CNY 1.767 0.546 0.495 0.098 0.432 -1.335 -4.88*** 9.749

Panel D: Portfolios sorted on B/M

All months 0.968 0.842 1.064 1.020 1.522 0.554 2.08** 1.211

January only 8.841 8.500 8.338 9.113 13.444 4.602 3.64*** 3.409

January excludes CNY 6.651 7.350 8.805 10.001 14.591 7.940 5.15*** 4.399

Except January 0.254 0.137 0.412 0.281 0.439 0.185 0.70 0.305

CNY only 6.053 5.515 4.759 4.919 7.066 1.013 1.07 1.671

CNY excludes January 2.494 2.878 3.458 3.739 5.080 2.586 2.98*** 2.208

Except CNY 0.507 0.408 0.738 0.662 1.018 0.511 1.85* 0.900

24

8/13/2019 3-3-2Beta9

26/30

Table 3Average slopes of monthly cross-sectional regressions of excess returns on unadjusted andadjusted market beta, firm size, and book-to-market ratio: July 1982 to June 2002Excess returns are regressed month-by-month on the explanatory variables, unadjusted and adjusted market beta,firm size, and book-to-market ratio (B/M). A combined series of the rediscounts rate and the 91-day T-bills inTaiwan is used as a risk-free rate. Excess returns are stock raw returns in excess of this risk-free rate. Market

beta is the estimated conditional beta as of the two months previous to excess returns. Firm size (ME) ismeasured as of the end of the second to last month. B/M is equal to book value of equity divided by the marketvalue of equity as of the end of December of year t-1 and used to explain the excess returns from July of year tto June of year t+1. There are totally 240 months for full samples. OLS and GLS denote that coefficients areestimated from OLS and GLS regression, respectively. Ln(.) denotes natural log operator. and denote theunadjusted and adjusted market beta, respectively. The t-statistics are in parentheses and is equal to the averageregression coefficient divided by its time-series standard error. The numbers of positive regression coefficientsare in bracket. Significance indicators: 1 (***), 2.5 (**), and 5 (*).

k

OLS estimates of average parameter values GLS estimates of average parameter valuesIntercept k ln(ME) ln(B/M) 2R Adj

Intercept k ln(ME) ln(B/M) 2R Adj

1.410

(1.83)

0.202

(0.47)[113]

0.0143 1.390

(1.79)

0.197

(0.46)[109]

0.0121

0.912

(1.44)

0.734

(1.67)*

[121]

0.0172 0.840

(1.33)

0.772

(1.75)*

[121]

0.0154

3.566

(1.71)

-0.207

(-1.11)

[117]

0.0472 3.509

(1.68)

-0.202

(-1.08)

[117]

0.0468

1.242

(1.43)

-0.073

(-0.18)

[118]

0.0394 1.223

(1.41)

-0.029

(-0.07)

[118]

0.0393

2.770

(1.50)

0.655

(1.57)[115]

-0.228

(-1.28)[116]

-0.232

(-0.67)[114]

0.0850 2.619

(1.42)

0.657

(1.58)[115]

-0.214

(-1.20)[114]

-0.229

(-0.66)[114]

0.0845

2.451

(1.34)

0.885

(2.01)**

[122]

-0.209

(-1.19)

[117]

-0.128

(-0.37)

[115]

0.0890 2.375

(1.30)

0.858

(1.97)**

[122]

-0.199

(-1.14)

[115]

-0.082

(-0.24)

[118]

0.0883

25

8/13/2019 3-3-2Beta9

27/30

Table 4Average slopes of monthly cross-sectional regressions of excess returns on market beta, firmsize, and book-to-market ratio: January versus non-January monthsExcess returns are regressed month-by-month on the explanatory variables, unadjusted and adjusted market beta,firm size, and book-to-market ratio (B/M). The market beta is the estimated conditional beta as of the two

months previous to excess returns. Firm size (ME) is measured as of the end of the second to last month.BE/ME is equal to book value of equity divided by the market value of equity as of the end of December of yeart-1 and used to explain the excess returns from July of year t to June of year t+1. There are 20 observations forJanuary months and 220 observations for non-January months. OLS and GLS denote that coefficients areestimated from OLS and GLS regression, respectively. Ln(.) denotes natural log operator. and denote theunadjusted and adjusted market beta, respectively. The t-statistics are in parentheses and is equal to the averageregression coefficient divided by its time-series standard error. The numbers of positive regression coefficientsare in bracket. Panel A shows the results for the January month only while Panel B shows the results for thenon-January months. Significance indicators: 1 (***), 2.5 (**), and 5 (*).

k



Panel A: January only (20 observations)

3.186

(1.43)

4.113

(2.09)**

[12]

0.0289 3.112

(1.40)

4.159

(2.13)**

[11]

0.0288

2.033

(1.11)

5.341

(2.65)***

[16]

00372 2.023

(1.11)

5.322

(2.63)***

[17]

0.0372

19.130

(2.59)

-1.443

(-2.15)**

[4]

0.0590 18.722

(2.50)

-1.396

(-2.04)**

[4]

0.0588

6.971

(2.42)

1.643

(1.12)

[12]

0.0407 6.959

(2.41)

1.687

(1.14)

[12]

0.0406

13.770(2.06)

4.102(1.83)*

[12]

-1.345(-1.92)*

[5]

0.810(0.63)

[12]

0.1156 13.853(2.08)

3.997(1.77)*

[12]

-1.350(1.94)*

[6]

0.788(0.60)

[11]

0.1152

12.574

(1.96)

5.419

(2.54)***

[15]

-1.334

(-2.01)**

[6]

1.035

(0.82)

[11]

0.1246 12.521

(1.90)

5.212

(2.45)***

[14]

-1.316

(-1.93)*

[6]

1.072

(0.84)

[11]

0.1239

Panel B: Except January (220 observations)1.249

1.53

-0.153

-0.36

[114]

0.0130 1.233

(1.50)

-0.163

(-0.38)

[98]

0.0127

0.810

1.20

0.315

0.72

[105]

0.0153 0.732

(1.09)

0.359

(0.82)

[104]

0.0152

2.151

1.00

-0.095

-0.49

[113]

0.0461 2.126

(0.99)

-0.094

(-0.49)

[113]

0.0459

0.721

0.79

-0.224

-0.56

[106]

0.0392 0.701

(0.77)

-0.185

(-0.46)

[106]

0.0391

1.770

0.93

0.342

0.85

[103]

-0.126

-0.69

[111]

-0.327

-0.90

[102]

0.0822 1.598

(0.84)

0.354

(0.88)

[103]

-0.110

(-0.60)

[108]

0.322

(-0.89)

[103]

0.0817

1.531

0.81

0.473

1.10

[107]

-0.106

-0.59

[111]

-0.234

-0.65

[104]

0.0858 1.452

(0.77)

0.462

(1.08)

[108]

-0.098

(-0.54)

[111]

-0.186

(-0.52)

[107]

0.0851

26

8/13/2019 3-3-2Beta9

28/30

Table 5Average slopes of monthly cross-sectional regressions of excess returns on market beta, firmsize, and book-to-market ratio: Chinese New Year versus the non-CNY monthsExcess returns are regressed month-by-month on the explanatory variables, unadjusted and adjusted market beta,firm size, and book-to-market ratio (B/M). Market beta is the estimated conditional beta as of the two months

previous to excess returns. Firm size (ME) is measured as of the end of the second to last month. BE/ME isequal to book value of equity divided by the market value of equity as of the end of December of year t-1 and isused to explain the excess returns from July of year t to June of year t+1. There are 20 observations for Chinese

New Year (CNY) months and 220 observations for non-CNY months. OLS and GLS denote that coefficients areestimated from OLS and GLS regression, respectively. Ln(.) denotes the natural log operator. and denotethe unadjusted and adjusted market beta, respectively. The t-statistics are in parentheses and is equal to theaverage regression coefficient divided by its time-series standard error. The numbers of positive regressioncoefficients are in bracket. Panel A shows the results for the CNY months only while Panel B shows the resultsfor non-CNY months. Significance indicators: 1 (***), 2.5 (**), and 5 (*).

k



Panel A: Chinese New Year only (20 observations)

3.357(1.73)

3.555(1.84)*

[14]

0.0224 3.280(1.71)

3.625(1.87)*

[14]

0.0223

3.359

1.86

3.503

(1.76)*

[12]

0.0339 3.242

(1.80)

3.570

(1.77)*

[12]

0.0337

9.516

(1.60)

-0.361

-0.63

[8]

0.0456 9.223

(1.52)

-0.332

(-0.57)

[8]

0.0454

7.780

(2.68)

1.649

(1.67)*

[12]

0.0302 7.737

(2.66)

1.679

(1.71)*

[11]

0.0302

5.467(1.03)

3.692(1.65)*

[13]

-0.189-0.31

[9]

1.379(1.76)*

[12]

0.0873 5.473(1.00)

3.655(1.61)

[13]

-0.263(-0.42)

[9]

0.819(1.60)

[12]

0.0870

5.779

1.05

3.429

1.48

[12]

-0.198

-0.32

[10]

1.416

(1.75)*

[15]

0.0954 4.822

(0.84)

3.388

(1.56)

[12]

-0.159

(-0.27)

[10]

1.013

(2.24)**

[5]

0.0949

Panel B: Except Chinese New Year (220 observations)1.233

1.50

-0.102

-0.24

[99]

0.0135 1.218

(1.47)

-0.115

(-0.27)

[95]

0.0133

0.690

1.03

0.482

1.09

[109]

0.0156 0.621

(0.93)

0.518

(1.17)

[109]

0.0155

3.025

1.37

-0.193

-0.98

[109]

0.0473 2.989

(1.35)

-0.190

(-0.97)

[109]

0.0471

0.648

-1.16

-0.229

-0.55

[106]

0.0402 0.631

(0.70)

-0.185

(-0.44)

[107]

0.0400

2.525

1.29

0.379

0.94

[102]

-0.231

-1.24

[107]

-0.378

-1.02

[102]

0.0848 2.347

(1.20)

0.386

(0.95)

[102]

-0.215

(-1.15)

[105]

-0.378

(-1.01)

[102]

0.0843

2.696

1.34

0.269

0.61

[110]

-0.241

-1.24

[107]

-0.483

-1.30

[100]

0.0884 2.121

(1.10)

0.628

(1.44)

[110]

-0.206

(-1.12)

[105]

-0.236

(-0.64)

[113]

0.0877

27

8/13/2019 3-3-2Beta9

29/30

Table 6Average slopes of monthly cross-sectional regressions of excess returns on market beta, firmsize, and book-to-market ratio: Pure Chinese New Year and JanuaryExcess returns are regressed month-by-month on the explanatory variables, unadjusted and adjusted market beta,firm size, and book-to-market (B/M). Market beta is the estimated conditional beta as of the two months

previous to excess returns. Firm size (ME) is measured as of the end of the second to last month. B/M is equalto book value of equity divided by the market value of equity as of the end of December of year t-1 and used toexplain the excess returns from July of year t to June of year t+1. There are 20 observations for CNY monthsand January months. However, there are 6 January months are just CNY month simultaneously. These monthsare excluded from either regression analysis. OLS and GLS denote that coefficients are estimated from OLS andGLS regression, respectively. Ln(.) denotes the natural log operator. and denote the unadjusted andadjusted market beta, respectively. The t-statistics are in parentheses and the numbers of positive regressioncoefficients are in bracket. Panel A shows the results for the pure CNY months only while Panel B shows the

pure January months only. Significance indicators: 1 (***), 2.5 (**), and 5 (*).

k



Panel A: January only but exclude Chinese New Year (14 observations)

3.8411.31

3.866(1.95)*

[8]

0.0147 3.775(1.28)

3.902(1.98)**

[7]

0.0146

2.621

1.13

5.304

(2.96)***

[12]

0.0137 2.681

(1.16)

5.260

(2.94)***

[12]

0.0136

28.663

3.66

-2.464

(-4.14)***

[1]

0.0632 28.393

(3.62)

-2.423

(-4.08)***

[1]

0.0630

7.449

2.13

2.589

1.33

[9]

0.0475 7.413

(2.12)

2.611

(1.34)

[9]

0.0473

23.2103.26

5.088(2.24)**

[9]

-0.468(-4.06)***

[1]

0.8280.46

[9]

0.1158 23.324(3.28)

4.920(2.09)**

[9]

-2.477(-4.08)***

[1]

0.781(0.42)

[9]

0.1152

23.936

3.29

5.565

(2.18)**

[12]

-2.622

(-4.02)***

[2]

0.312

0.17

[7]

0.1170 22.631

(3.48)

5.641

(2.93)***

[11]

-2.447

(-4.17)***

[2]

1.119

(0.62)

[7]

0.1161

Panel B: Chinese New Year but exclude January (14 observations)

4.085

1.65

3.070

1.61

[10]

0.0053 4.015

(1.64)

3.140

(1.63)

[10]

0.0052

4.515

2.05

2.680

1.59

[8]

0.0090 4.423

(2.00)

2.757

(1.60)

[8]

0.0086

14.924

2.44

-0.919

(-1.75)*

[5]

0.440 14.792

(2.42)

-0.904

(-1.72)*

[5]

0.0439

8.606

2.45

2.597

(2.27)**

[9]

0.0325 8.525

(2.42)

2.598

(2.32)**

[8]

0.0324

11.349

2.09

4.502

(1.97)**

[10]

-0.817

-1.42

[5]

1.641

1.58

[9]

0.0753 11.563

(2.08)

4.408

(1.96)*

[10]

-0.839

(-1.41)

[4]

1.665

(1.65)*

[10]

0.0749

5.779

1.05

3.429

1.48

[9]

-0.198

-0.32

[6]

1.416

(1.75)*

[11]

0.0954 12.126

(2.17)

3.029

(1.60)

[9]

-0.744

(-1.46)

[6]

1.900

(1.92)*

[11]

0.0747

28

8/13/2019 3-3-2Beta9

30/30

3-3-2Beta9

Documents

Transcript of 3-3-2Beta9