CORPORATE SIZE, STOCK RETURN, AND COST EFFICIENCY

CORPORATE SIZE, STOCK RETURN, AND COST EFFICIENCY Ruey-Shii Chen Tatung University Taipei, Taiwan rschen@ttu.edu.tw

OUTLINE • INTRODUCTION • LITERATURE REVIEW • HYPOTHESIS • RESEARCH METHOD • ESTIMATED RESULTS • CONCLUSION

INTRODUCTION • The Capital Asset-Pricing Model (CAPM) of Sharpe (1964)、Lintner (1965) and Black (1972) depicted that there existed a positive relation between risk and expected returns and the systematic risk (beta) is the only risk factor to predict expected returns. • Fama and French (1992, 1993) examined a number of securities markets and show that the stocks of small firms generally provide higher mean returns than do the stocks of large firms. The empirical observation are known as the size effect.

INTRODUCTION • The validity of size effect as well as other empirical anomalies is a controversial issue in empirical finance. • Size effect are found in many countries including U.S (Banz (1981), Reinganum (1983), Keim (1983), Fama and French (1992)), Japan (Kato and Schallheim (1985)), and Australia (Brown, Klein, Kleidon and Marsh (1983)).

EXISTENCE OF SIZE EFFECT • Scholars also found that size effect is related to seasonality (Keim (1983)) , business cycle and market condition (Bhardwaj and Brooks (1993), Ibbotson and Sinquefeld (1995) and Kim and Burnie (2002) ). • Empirical studies on U.S. found that size effect disappeared after 1980 (Bhardwaj and Brooks (1992), Jagannathan and McGrattan (1995), Hawawini and Keim (1995), Dichev (1998) and Horowitz, Loughran and Savin (2000)).

CAUSE OF SIZE EFFECT • infrequent trading of small firms (Banz (1981), Lustig and Leinbach (1983)) • the difference of price-earnings ratio (Cook and Rozeff, 1984) • transaction costs (Stoll and Whaley, 1983) • tax-loss selling (Reinganum, 1983) • information effect (Barry and Brown, 1984)

RISK FACTOR BEHIND SIZE EFFECT • Size effect could be explained by default risk (Chan, Chen and Hsieh (1985), Chen, Roll and Ross (1986), and Fama and French (1993) ) • Size effect is generated by inefficient firm’s high leverage and cash flow problems. (Chan and Chen (1991))

ARTICLES AT ODDS RISK ASPECT • Daniel and Titman (1997) and Daniel, Titman and Wei (1999) use factor loadings of three factors model proposed by Fama and French (1993) to form portfolios, they argued that it’s characteristics other than factor loadings influencing expected returns. • Dichev (1998) demonstrated that bankruptcy risk is not rewarded by higher returns but at the same time there still existed size effect.

DELISTING BIAS • Shumway and Warther (1999) argued that most of the survived small firms in the stock market are good ones. • Firms are delisted from stock market due to their poor performance are small firms often. • That is why there exists size effect if studies use listed firms as their sample.

LONG-TERM AVERAGE COST LMC AC LAC Q MES

LMC and LAC • When a firm is producing at an output at which the long term average cost is falling, the long term marginal cost is less than long term average cost. • Conversely, when long term average cost is increasing, long term marginal cost is greater than long term average cost. • The two curves intersect at a point where long term average cost achieves its minimum.

HYPOTHESIS • Under the U-shaped average cost curve • If firm size is less than the corresponding size of the minimum long term average cost, the firm expanding its scale, and they tend to, would decrease average cost and improve efficiency. (higher stock return) • On the other hand, if firm size is larger than the corresponding size of the minimum long term average cost, the firm expanding its scale would increase average cost.

DATA SOURCES • two databases in Taiwan. • Manufacturing census data from Directorate-General of Budget, Accounting and Statistics, Executive Yuan, R.O.C. during the period of 1981 to 1996. • Census data is used to estimate minimum efficient scale for each industry. • Taiwan’s listed companies data from the Taiwan Economics Journal (TEJ) database during the period of 1976 to 2004. • The second database is used to calculate listed corporate related variables.

DATA PROCESS • The census data classify industries according to the CIC code, and the listed companies in Taiwan are classified into industries by Taiwan Exchange Stock Corporation. • Only after adjusting the two different industry classification codes to be consistent, we can apply the minimum efficient scale estimated from census data to listed companies. • The data in this study exclude financial firms and observations within one year of IPO. We also delete some observations due to missing book value or other related variables.

DESCRIPTIVE STATISTICS • Ret is the log monthly return, in percent. Beta is computed following Fama and French (1992). Size is the market price multiple number of common stock outstanding denominated in ten billions of dollars. BtMis book to market ratio.

CORRELATION COEFFICIENTS • In the first stage, we calculate correlation coefficients during period of 1981 to 1996 each month. In the second stage, we calculate the monthly average correlation coefficients. • Economies of scale dummy variable (ESDM) is equal to one if firm’s net sales revenue more than the MES of the industry, and zero otherwise.

PEARSON CORRELATIONS

Trans-log Cost Function • We assume firms only employ two factors—labor and capital. The two factors trans-log cost function is : • Cost elasticity

Trans-log Cost Function • We use iterating SUR (seemingly unrelated regression) to estimate trans-log cost functions for industries each year . The results are presented in Appendix 1 to 4. We then use the estimated coefficients to calculate cost elasticity. • The MC and AC curves intersect at a point where long term average cost achieves its minimum.

ESTIMATION-1 • We run cross-sectional regressions each month using various specifications of the following model: • At the end of December of each year t, portfolios are formed on the basis of ranked values of size or pre-ranking beta. The pre-ranking betas use 5 years of monthly returns ending in December of t. Stocks are assigned the post-ranking beta of the size-beta portfolio they are in at the end of December of year t.

ESTIMATION-1 The slope is the time-series average of the monthly regression slopes for January 1981 to December 1996, and the t-statistics is the average slope divided by its time-series standard error. The values in parentheses are t-statistics.

Table 4-1 ***, **, * significant at 0.01, 0.05, 0.1 level respectively

FINDINGS • Size is negatively significant in second model. • Size still remains significant when BtM is added in third model . • Size becomes not significant when dummy variable ESDM substitute for BtM in the fourth model. • Size is not significant in the fifth model when ESDM and BtM are added together. • The significance of size largely depends on whether ESDM is included in the model.

Data Envelopment Analysis • Charnes et al. (1978) developed the CCR model which assumes constant returns to scale (CRS) and can measure overall technical efficiency (OTE). • Banker et al. (1984) allowed for variable returns to scale (VRS) in their model, which is known as the BCC model. The overall technical efficiency in the CRS model can be decomposed into pure technical efficiency (PTE) and scale efficiency (SE): OTE = PTE  SE in VRS model.

EFFICIENCY ESTIMATION (DEA) • We choose net sales revenues as the single output and the value of the assets, staff number, and R&D expenditures are the three inputs. • Using the results from DEA estimation we calculate the extent of scale, pure technical, and total technical efficient improvement (symbolized by DSE, DPTE, and DTTE respectively) for each firm-year observations.

ESTIMATION-2 • This regression covers all listed electronic industry firms in Taiwan from 1986-2004. • There are 1980 firm-year observations in our pooled dataset. • Dummy variable DMS equals one if the firm’s scale is allocated in increasing returns to scale, and zero otherwise. • We regress firm’s yearly return on DSE (DTTE or DPTE) and the interaction term DSE*DMS (DTTE*DMS or DPTE*DMS).

ESTIMATION-2 • The dependent variables in all regressions are all the same -- stock return. • The influence of total technical efficiency change on stock return is decomposed into pure technical efficiency and scale efficiency change. • The whole period 1996-2004 is divided into two sub-periods 1996-2000 and 2001-2004. The values in parentheses are p-values.

Table 4-2

Table 4-2 (cont.) ***, **, * significant at 0.01, 0.05, 0.1 level respectively

FINDINGS • Panel A of table 4-2 shows that the interaction term DSE*DMS is positively significant in all period regressions. • The positive relationship between extent of scale efficient improvement and stock return is pronounced for firms with increasing returns to scale.

FINDINGS • Panel B of table 4-2 shows similar results as panel A, which indicate firms with increasing returns to scale enhancing the positive influence on total technical efficiency except period 2001-2004. • Panel C of table 4-2 show the extent of pure technical efficient improvement is not significant at all. • Overall, it is scale efficiency plays an important role in influencing stock return.

CONCLUSIONS • For firms with scale less than the minimum efficient scale tend to increase their production scale and gain benefits from cost saving. We therefore hypothesize it is the cause of size effect. • In the first regression we find that whether size effect is significant or not largely depends on if economies of scale dummy ESDM is included in the model.

CONCLUSIONS • In the second regression we find the positive relationship between extent of scale efficient improvement and firm’s return is pronounced for firms with increasing returns to scale. • The results of this study thus support our hypothesis that size effect may result from firms with scale less than the MES of the industry gain benefits if they increase their scale.

THE END Thank you very much for your attention!

CORPORATE SIZE, STOCK RETURN, AND COST EFFICIENCY