1. Is size a priced factor in Germany? Presented by : Wen Huang Savang Kittikhoun Kim-Tuan Nguyen Yong Yao Tianxue Zhang

2. Introduction CAPM : –Excess return = ß * market premium Empirical studies show that stock price not fully explained by CAPM –Returns of small firms turn out higher –Returns of big firms turn out lower

3. Introduction Does the size of a firm affect its return ?

4. Methodology Excess return = ß * market premium + ?? Period of analysis : Jan 1991 to Dec 2000 Randomly pick 200 out of 800 firms Sort by size (market capitalization) –Group in 10 portfolios of 20 firms each –Re-balance portfolio every year

5. Attribute portfolio Quintiles

6. Attribute Portfolio - Graph

7. Regression Construction of a factor-mimicking spread portfolio Small minus Big (SMB) –Returns of smallest 30% - returns of biggest 30% –Spread portfolio has no market risk

8. Regression - cont’d r nt =  n +  nm r mt +  nA SMB t + u nt Where: –r nt : average excess return –  n : intercept; –r mt : excess return of German market index –  nm : market beta of portfolio n –SMB t : return of spread portfolio –  nA : sensitivity beta of the return of portfolio n to this size attribute –u nt : the error term

9. Regression results

10. Regression results - Graph

11. Another test r nt =  0t +  mt  nm +  1t  nA +  2t A n + v nt –  nm,  nA taken from previous regression –A n is the log (base 10) of the size of the firm If  1t significant, but  2t not significant : –>  nA fully captures the attribute induced risk

12. We cannot conclude that  nA fully captures the risk induced attribute Regression results...

13. Sensitivity analysis - SMB Variation of returns of SMB could change  nA substantially Independance International Associates (IIA) –Set of 5 portfolios for each country –Covers 75% of market capitalisation –Big cap portfolio : 70% of total market cap –Small cap portfolio : 30% of total market cap Repeat time series analysis

14. Results

15. Sensitivity analysis - SMB

16. Sensitivity Analysis - Time Divide our samples into two sub-periods : –January 1991 to December 1995 –January 1996 to December 2000 Purpose of check : –Does the correlation between portfolio returns and the two risk factors time dependent ?

17. Regression Results

18. Conclusion Our work provides evidence that : –Larger firms have lower returns –Smaller firms have higher returns We encountered a few inconclusive results –May require larger sample –Return could depend on other attributes Our model : –concurs with empirical observations –Still incomplete