Event History Analysis of the Stock Return:Taiwan Stock Market

Abstract— Although CAPM has been comprehensively applied in practice for a long time, it is established under the perfect-basis assumption which does not always exist in reality because there are several factors affecting the capital return. Hence, the actual performance of the CAPM model has been questioned. There have been numerous proposals in improving the performance of the model. And, our study aims at finding the actual correlation between price/book ratios effect and stock return so that investors may anticipate whether a certain stock will be transformed between growth stocks and value stocks, and buy/sell such stock to make profits in the future. Based on monthly data from listed companies on Taiwan stock market from 1991-2010, it is found that higher price/ earnings ratio generates high possibility in transformation as well as increase in the expected return. Therefore, investors should take these determinants as the key variables in their investing models in order to implement their proper stock-selection strategy. The investment methods from this research could be a new stock-selection strategy for investors' excess return and better investment performance.

Keywords— CAPM Model, Capital Return, Growth Stock, Value Stock, Stock Selection

I. INTRODUCTION

N principle, because stock value usually varies with information available and abnormal situations, which cannot be explained by efficient market hypothesis (EMH), investors can therefore earn price differences during their holding period, namely capital gain or capital return.

Capital asset pricing model (CAPM) developed by [1]-[3], is a sound theory for return change and is used to measure the correlation between individual asset risk and its expected return rate in the portfolios. Because portfolio is efficient under CAPM and non-systematic risk is totally dispersed by diversified portfolio, only systematic risk is usually considered in the model. The expected return of securities shows positive linear relationship with its market risk, meaning that higher

P.S. KO is an associate professor of Department of Wealth and Taxation Management, National Kaohsiung University of Applied Sciences, 415 Chien Kung, San-min, Kaohsiung 80778, Taiwan (e-mail: psko@cc.kuas.edu.tw).

J.C. Huang is with Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, 415, Chien Kung Road, Kaohsiung 80778 (corresponding author e-mail: y7891225@yahoo.com.tw).

M.H. Shu is a Professor of Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, 415, Chien Kung Road, Kaohsiung 80778 (email: workman@cc.kuas.edu.tw).

L.C.LI had gotten his master from National Kaohsiung University of Applied Sciences, 415, Chien Kung Road, Kaohsiung 80778 (email:

e3094@kcg.gov.tw)

return usually generates higher market risk β value which has been considered as the only factor to explain expected return. Although CAPM has been comprehensively applied in practice for a long time, it is established under the perfect-basis assumption which does not always exist in reality. Also, beside systematic risk β of CAPM, there are several other factors affecting the return including size effect [4], price/earnings ratios effect (PER) [5] and price/book ratios effect (PBR) [6]. Hence, the actual performance of the CAPM model has been questioned.

With the focus on U.S stock market, Fama and French [7] studied the difference factors of different stock return. They found market risk β value cannot explain the difference of the return of different stocks. Later, Fama and French [8] proposed three-factors model to explain variability of asset return via three complete models: market factor, size factor and price/book factor. In comparison with β value of CAPM, they considered market and price/book factors as two main variables which can better explain average return. When the size was under control, stocks with low price/book ratio had higher excess return than stocks with high price/book ratio. Bauman and Miller [9] also discovered value stocks had higher future expected return, and growth stocks had lower expected return.

Due to the existence of premium value and size effect, Fama and French [10] provided investors references for stock selection and excess return per company characteristics. Black and McMillan [11] believed the high risk of value stocks led the existence of excess premium. Therefore, investors usually ask for high return as compensation or the overreaction of market on news all makes long-term value stocks have higher return.

If premium value exists in Taiwan stock market, stocks classified as growth stocks in the beginning might become value stocks at the end of an observation period and vice versa. If this study could confirm the positive or negative correlation between PBR and stock return, investors may anticipate whether a certain stock will be transformed between growth stocks and value stocks, and buy/sell such stock to make profits in the future. After applying Event History Analysis (EHA) and econometric model, this research generalize what kind of characteristics (financial data and company characteristics are used as explanatory variables) and stocks might have transformation potential in the future, and thereby, act as references for investors’ stock-market prearrangement.

Event History Analysis of the Stock Return:

Taiwan Stock Market

PO-SHENG KO

, JUI-CHAN HUANG

, MING-HUNG SHU, LUO-CHIH LI

II. LITERATURE REVIEW

Since proposed PBR had better explanatory ability in return than β coefficient of CAPM [6], numerous scholars have devoted to find better variables to explain the change of stock return. Consequently, PBR becomes an important indicator in regarding to abnormal return effect. Several affecting factors of the PBR have been proposed, such as premium value, company size, price/earnings ratio, dividend yield rate, price/sales ratio, liquidity, and momentum.

A. The Effect of Premium value

It is found that investors can earn excess return by buying low-PBR stocks and selling high-PBR stocks, which also make low-PBR companies have excess return [6], [7], [12]. After portfolios were formed per PBR, Rosenberg et al. [6] examined the significance of the buying/selling behavior towards excess return and found that investors can earn excess return by buying low-PBR stocks and selling high-PBR stocks, which also signified low-PBR companies to have excess return. Similarly, Fama and French [7] also found PBR and company size best explained average return of stocks. However, Grinold and Kahn [13] used Britain stock market as sample, and concluded that high-PBR companies had higher return while low-PBR companies have lower return, which was contrary to the findings of [6]. After reviewing the return of value stocks and growth stocks, Bauman and Miller [9] pointed that value stocks had higher return, proving the existence of premium value. However, excess return gap between low-PBR stocks and high-PBR stocks was not huge; particularly, PBR has better predictive ability for the period before 1960, but it has no significant correlation in the period after 1960 [13], [14]. Chow and Hulburt [12] studied large-scale and low-PBR portfolios in Japan stock market, then discovered their returns were significantly higher than those of small-scale and high-PBR ones. Besides, the investment performances of low-PBR portfolios were significantly better than the return of any random portfolios. Nevertheless, if only size effect is considered, results could not reveal any significant improvement on portfolio efficiency. In order to improve portfolio efficiency, PBR should be the key factor to be first taken into consideration. As for future profitability, low-PBR stocks were found relatively sensitive to the change of economic environment, thus their reaction on stock price impact was more rapid than that of high-PBR ones [5]. When the size was under control, low-PBR stocks can keep ahead of high-PBR ones in term of the return because PBR and company size was negative related.

Based on PBR index, the stocks on Taiwan stock market are classified into high, middle and low portfolios. Several researchers found that the return rates of low-PBR portfolios were higher than those of the high-PBR ones, proving that the PBR effect indeed existed in Taiwan stock market. The effect of company size was also found existing in Taiwan stock market despite the insignificance of the risk coefficient β. From integrated viewpoints of cross section and vertical section, PBR effect shows the biggest influence on annual return rate. There

has been a huge attempt to find the relationship between the risk compensation, investors’ behavioral bias and the premium value. It was found that if value firms had better fundamental analyses, investors could have higher excess return in the following one or two years. Therefore, investors’ behavioral bias can better explain the phenomenon of premium value.

Numerous empirical researches have proven that significant effect of premium value actually exists in stock market. However, it has been also found that different research period and different samples may have different premium value effects. Most scholars claim that low-PBR stocks have higher return, namely value stocks have higher return than growth stocks. Assuming that premium value exists in Taiwan stock market as the aforementioned, this paper aims to study the transformation factor between growth stocks and value stocks.

B. The Effect of Company Size

Company size is often referred as the market value of listed companies, specifically their number of outstanding shares (NSO). Company size effect refers to certain correlation between listed-stock return rate and its company size. For instance, operational risk of small companies is higher than large-scale ones. Therefore, investors expect to obtain higher expected return. Such phenomenon implies that the return rate of small stocks is higher than large-scale ones after their risk adjustment. When size-effect was added as a variable into CAPM, Banz [16] found that small stock portfolios had higher risk premium than large-scale ones. The reason was that small-stock companies were often equipped with high growth rate, significant rise on stock value and unstable size effect during research. Hence, except for company size effect, other anomalies were possibly undiscovered.

Reinganum [17] ranked 10 portfolios per stock value at the end of every year, and compared their daily excess return. When PER and company size are separately tested, they are found to have significant relationship with the stock return: the annual average return rate of small-scale stocks was 20％ higher than that of the large-scale ones; meanwhile, the return rate of small companies was steadily stable at least 2 years and thereby proved the existence of size effect. Taking seasonal factors into consideration, Fant and Peterson [18] found negative correlation existing between company size and return, namely size effect. However, they found that company size and return only show strong negative correlation in January after analyses were divided into 2 parts (i.e. January vs. February to December). This could be explained that size effect only existed in January, none in other months. According to Kim and Burnie [19], size effect significantly appeared during economic expansion and disappeared during economic recession. Compared to large-scale companies, small ones had lower return on assets (ROA) and higher leverage ratio (LR); therefore, their performances were easily affected by negative economic change. Meanwhile, their size effect mainly occurred in January regardless of the economy situation. As for researches on advanced countries, Maroney and Protopapadakis

[20] discovered significant negative size effect existing between company size and stock return in U.S.A., Canada, France, Germany, Japan and Australia.

In Taiwan stock market, the correlation between stock price behavior, size effect and the stock return rate was studied in several researches which already proved the existence of negative size effect because the stock return rate of large-scale companies was usually higher than that of small ones. Similarly, size effect also existed in stock return even though risk variable was substituted by company size, thus size effect seemed better explained the difference of stock return than risk. It was also found that both weekly and monthly data had a significant positive correlation. In term of the determinants of cross-sectional returns, there was a linear relationship existing between the expected return rate and system risk β value. Furthermore, β value was the only factor could explain cross-section expected return, meaning that there was no size effect in Taiwan stock market.

Therefore, it is often believed that there is a negative correlation between company size and stock return because most small companies have high growth rate and risk, as well as the possibility of stock price rise.

C. The Effect of Price/Earnings Ratio (PER)

Stock price is the cost investors pay for stocks; and earning per share (EPS) is the profit companies earn for their stockholders, therefore, PER is the market price of that stock divided by the annual EPS. The PER effect indicates that low-PER stocks have higher return on investment (ROI) because their stock values might be underrated.

Basu [5] classified 5 portfolios by PER, then measured their monthly return rates (1956-1969) by Sharpe, Jensen and Treynor indexes. It was found that greater PER stocks generated smaller return rate, confirming the existence of PER effect. Nevertheless, Reinganum [17] examined the influence of PER and market value on return rate, then conducted study per quarterly and yearly data (1963-1977). Based on the quarterly data of PER, high-PER portfolio return was found statistically better than that of the low-PER ones. Reinganum believed that Basu’s findings in [5] might be caused by size effect, instead of PER. To response Reinganum's research [17], Basu re-studied NYSE listed stocks (1963-1983), and found that the return rate of low-PER stocks was still higher than that of high-PER stocks. Even after the size difference was adjusted, PER effect was still significant. However, the research results of Johnson et al. [21] were also contrary to [5]. Based on the Basu’s research methods in [5], Johnson et al. [21] selected NYSE listed companies (1979-1984) as their samples, and their findings showed that PER effect indeed existed in early US stock market. Fama and French [7] proved that PER was equipped with explanatory ability basically. Besides, they further described the instability of PER effect: PER could not explain stock return rate before company size and PBR were added.

In Taiwan stock market, it was found that after PER portfolios were under control, every January from 1980 to 1986 had a significant impact on the return. This implies that research

period profoundly affects research results when market structure changes. PER of Taiwan stock market was found negatively related to the excess return. Moreover, PER effect only existed when PER was positive, and stocks with negative PER had significant excess return.

Though being mentioned in numerous researches, the existence of PER effect has been still a controversial issue [17], [18].

D. The Effect of Dividend Yield Rate

As a stock selection indicator among value investing strategies, dividend yield rate (DYR) is dividend per share (DPS) divided by market value per share (MVPS). Because most US listed companies prefer divided payment, investors accordingly use DYR as their selection index. Litzenberger and Ramaswamy [22], [23] assumed that high-DYR stocks should have higher return rate because investors' higher income tax can thus be compensated. Nevertheless, Miller and Scholes [24] pointed that the relation between DYR and return rate was not significant based on empirical analyses designed by Litzenberger and Ramaswamy [22], [23].

Fama and French [25] held portfolios for one month to four years in order to explore the predictive ability of DYR on stock return rate. The findings indicated longer holding period generated more predictive ability. In the long term, most high DYR in particular had high return rate, which was the same as findings of Campbell and Shiller [26] as well as Bekaert and Hodrick [27], namely DYR could act as one of factors to predict stock return.

According to above mentioned literatures about DYR, high-DYR portfolios are mostly associated with higher return rate. It can be inferred that investors have heavier income tax, so they request higher nominal return rate. However, it does not guarantee the equally high real return rate. Besides, companies with more cash dividends signify high DYR, good company operation, stable earnings, and further leading high return rate. While US companies which usually paid dividends quarterly, Taiwan companies paid dividends yearly. For this reason, the DYR of Taiwan companies did not change much in the short term. Among the small changes identified, the change in stock price was prominent. As a result, DYR was usually used to provide references for long-term manipulation and seldom used to explain stock return rate.

E. The Effect of Price/Sales Ratio

Price/sales ratio (PSR) is the ratio of market value per share (MVPS) and revenue per share (RPS). PSR effect means low-PSR stock return is higher than high-PSR stocks. In the late 1950, Philip [28] mentioned PSR could act as an important research tool if investors considered investment target such as growth companies. Twenty years later, PSR was also selected as one of the stock-selection variables in [29].

O’Shaughnessy [30] found the ROI of 50 low-PSR stocks in US stock from 1954 to 1994 was higher than others; meanwhile, the ROI of the highest PSR was only 4.15％. The logic of utilizing price/sales ratio (PSR) was to consider a company with

industries are orderly ranked after the electric and cable sector. The constant in the regression model is a negative number, indicating that the probability of transformation from growth stocks to value stocks is lower than transformation from value stocks to growth stocks; hence, the growth stocks do not easily transform to value stocks.

IV. CONCLUSION

Based on monthly data from listed companies on Taiwan stock market from 1991-2010, this research found that only DYR doesn’t financially affect transformation between growth stocks and value stocks; whereas, other factors are all correlated. In this study, it is found that higher PER generates high possibility in transformation as well as the increase in the expected return. The findings indicate PER effect does not exist in Taiwan stock market, which is contrary to Basu [5].

With the above technical analyses, the optimism upon market of stock investors leads to increases in stock demand, volume, and stock price. On the contrary, stock price will decrease. The research also found that higher volume generates high possibility in transformation and the increase in expected return; meaning that there is a positive correlation existing between volume and return rate. These findings refute the existence of liquidity effect, which is contrary to Demsetz [27]. Return rate affects transformation. According to the empirical results, higher return rate generates high possibility in transformation and return rate has momentum effect, which fully agrees with the premium value [7] and momentum effect [32] as well.

Under the company characteristics, higher RPS generates lower possibility in transformation and the increase in the expected return. This matches the finding of Beaver et al. [44].

BVP shows influence on transformation. Early-period growth stocks with higher BVP generate higher possibility in transformation and the increase in the expected return. This signifies that the lower net value generates higher PBR and lower expected return under the circumstance of premium value.

In general, NSO might raise stock price and expected return because of companies’ capital-reduction policy. The early-period growth stocks with higher NSO generate lower possibility in transformation and the increase in the expected return. This result also presents negative relation between NSO and return.

The results of MV analyses indicate that early-period growth stocks with higher MV generate low possibility in transformation and the increase in the expected return. This shows that the return rates of small companies are usually higher than those of large-scale ones, which is found the same as the size effect proposed by Banz [16]. Our results also show that early-period growth stocks with higher PSR generate low possibility in stock transformation (growth stocks transformed to value stocks) and the increase in the expected return. This indicates that a negative correlation actually exists between PSR and return rate, which matches the conclusion in [30].

Based on the analyses of industrial stocks, the probability of

transformation from growth stocks to value stocks is lower than transformation from value stocks to growth stocks. This signifies that transformation of growth stocks to value stocks is difficult. Specifically, technical analysis shows that Plastic industry sector, Electronic industry sector, Tourism sector and Trade & Department store sector are the sectors with longer growth stocks state; therefore, their transformation might be disadvantageous.

Though DYR does not significantly affect transformation between growth stocks value stocks and growth stocks, changes of other variables all affect the transformation between these two stocks. For these reasons, the influence factor on transformation might be varied because of research model, sampling period and sample difference. During the measurement of stock return, investors should apply several determinants to regression models in order to explore stock-selection strategy. The investment methods from this research could be a new stock-selection strategy for investors’ excess return and better investment performance.

REFERENCES

[1] J. Treynor, “Toward a theory of the market value of risky assets”, unpublished.

[2] W.F. Sharpe, “Capital of asset prices: A theory of market equilibrium under conditions of risk,” J. Financ., vol. 19, no. 3, pp.425-442, 1964. [3] J. Mossin, “Equilibrium in a capital asset market,” Econometrica, vol. 34,

pp.768-873, 1966.

[4] R. Banz, “The relationship between return and market value of common stocks,” J. Financ. Econ., vol. 9, no. 1, pp.3-18, 1981.

[5] S. Basu, “Investment performance of common stocks in relation to their price earnings ratios: A test of market efficiency,” J. Financ., vol. 32, no. 3, pp. 663-682, 1977.

[6] B. Rosenberg, K. Reid and R. Lanstein, “Persuasive evidence of market inefficiency,” J. Portfolio Manage., vol. 11, no. 3, pp.9-17, 1985. [7] E.F. Fama and K.R. French, “The cross-section of expected stock

returns,” J. Financ., vol. 47, no. 2, pp.427-465, 1992.

[8] E.F. Fama and K.R. French, “Common risk factors in the returns on stocks and bonds,” J. Financ., vol. 33, no. 1, pp.3-56, 1993.

[9] W.S. Bauman and R.E. Miller, “Investor expectations and the performance of value stocks versus growth stocks,” J. Portfolio Manage., vol. 23, no. 3, pp.57-68, 1997.

[10] E.F. Fama and K.R. French, “The premium value and the CAPM, J. Financ., vol. 61, no. 5, pp.2163-2185, 2006.

[11] A.J. Black and D.G. McMillan, “Value and growth stocks and cyclical asymmetries,” J. Asset Manage., vol. 6, no. 2, pp.104-116, 2005. [12] V. Chow and H.M. Hulburt, “Value, Size and Portfolio Efficiency,” J.

Portfolio Manage., vol. 26, no. 3, pp.78-89, 2000.

[13] R.C. Grinold and R.N. Kahn, “Information Analysis: A two-step approach to information ratios, information coefficients and the value of investment information,” J. Portfolio Manage., vol. 183, pp.14-21, 1992. [14] J. Pontiff and L.D. Shall, “Book-to-market ratios as predictors of market

returns,” J. Financ. Econ., vol. 49, no. 2, pp.141-160, 1998.

[15] K. Hou, “Industry Information Diffusion and the Lead - Lag Effect in Stock Returns,” Rev. Financ. Stud., vol. 20, no. 4, pp.1113-1138, 2007. [16] R. Banz, “The relationship between return and market value of common

stocks,” J. Financ. Econ., vol. 9, no. 1, pp.3-18, 1981.

[17] M.R. Reinganum, “A new empirical perspective on the CAPM,” J. Financ. Quant. Anal., vol. 16, no. 4, pp.439-462, 1981.

[18] L.F. Fant and D.R. Peterson, “The effect of size, book-to-market equity, prior returns and beta on stock returns: January versus the remainder of the year,” J. Financ. Res., vol. 18, no. 2, pp. 129-142, 1995.

[19] M.K. Kim and D.A. Burnie, “The firm size effect and the economic cycle,” J. Financ. Res., vol. 25, no. 1, pp.111-124, 2002.

[20] N. Maroney and A. Protopapadakis, “The book-to-market and size effects in a general asset pricing model: Evidence from seven national markets,” Eur. Financ. Rev., vol. 6, no. 2, pp.189-221, 2002.

[21] R.S. Johnson, L.C. Fiore and R. Zuber, “The investment performance of common stocks on relation to their pricing- earnings ratio: An update of the Basu study,” Financ. Rev., vol. 24, no. 3, pp.499-505, 1989. [22] R.H. Litzenberger and K. Ramaswamy, “The effect of personal taxes and

dividends on capital asset price: Theory and empirical evidence,” J. Financ. Econ., vol. 7, no. 2, pp.163-195, 1979.

[23] R.H. Litzenberger and K. Ramaswamy, “The effects of dividends on common stock prices tax effects or information effects,” J. Financ., vol. 37, no. 2, pp.429-443, 1982.

[24] M.H. Miller and M.S. Scholes, “Executive compensation, taxes and incentives,” Financ. Econ., Essays in Honor of Pual Cootner, pp.179-201, 1982.

[25] E.F. Fama and K.R. French, “Dividend yields and expected stock returns,” J. Financ. Econ., vol. 22, no. 1, pp.3-25, 1988.

[26] J.Y. Campbell and R.J. Shiller, “Stock price, earnings, and expected dividends,” J. Financ., vol. 43, no. 3, pp.661-676, 1988.

[27] G. Bekaert and R.J. Hodrick, “Characterising predictable components in excess returns on equity and foreign exchange markets,” J. Financ., vol. 47, no. 2, pp.467-509, 1992.

[28] A.F. Philip, Common stock and uncommon profits, Harper & Brothers, 1958.

[29] L.F. Kenneth, Super Stocks, McGraw-Hill, 1984.

[30] J.P. O’Shaughnessy, What works on wall street- A guide to the best-performing investment strategies of all time, McGraw-Hill, New York, 1996.

[31] H. Demesetz, “The costs of transacting,” Q. J. Econ., vol. 82, no. 1, pp.33-53, 1968.

[32] B. Branch and W. Freed, “Bid -Asked spreads on the AMEX and the Big Board,” J. Financ., vol. 32, no. 1, pp.159-163, 1977.

[33] G.J. Benston and R.L. Hagerman, “Risk, volume and spread,” Financ. Analysts J., vol. 34, no. 1, pp.46-49, 1978.

[34] Y. Amihud and H. Mendelson, “Asset pricing and the Bid - Ask spread,” J. Financ. Econ., vol. 17, no. 2, pp.223-249, 1986.

[35] M. Charles, C. Lee and S. Bhaskaran, “Price, momentum and trading volume,” J. Financ., vol. 55, no. 5, pp.2017-2069, 2000.

[36] D. Vinay, N. Narayan and R. Robert, “Liquidity and asset returns: An alternative test,” J. Financ. Markets, vol. 1, no. 2, pp.203-219, 1998. [37] A.C.W. Chui and K.C. Wei, “Book-to-market, firm size, and the year

effect: Evidence from Pacific-basin emerging markets,” Pac.-Basin Financ. J., vol. 6, pp.275-293, 1998.

[38] V. Datar, N. Naik and R. Radcliffe, “Liquidity and assets returns: An alternative test,” J. Financ. Markets, vol. 1, no. 2, pp. 203-220, 1998. [39] N. Jegadeesh and S. Titman, “Returns to buying winners and selling

losers: Implications for Stock market efficiency,” J. Financ., vol. 48, no. 1, pp.65-91, 1993.

[40] E.F. Fama and K.R. French, “Multifactor Explanations of Asset Pricing Anomalies,” J. Financ., vol. 51, no. 1, pp.55-84, 1996.

[41] A. Hameed and K. Yuanto, “Momentum strategies: Evidence from the Pacific Basin stock markets,” J. Financ. Res., vol. 25, no. 3, pp.383-397, 2002.

[42] A.C.W. Chui, S. Titman and K. C. Wei, “Momentum, legal systems and ownership structure: An analysis of Asian stock markets” Working paper, Hong Kong Polytechnic University, 2002.

[43] D. Hong, C.M.C. Lee and B. Swaminathan, “Earnings Momentum in International Markets.” Working Paper, Cornell University, 2003. [44] W.H. Beaver, R.A. Lambert and D. Morse, “The information content of