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Published byMelina Henderson Modified over 9 years ago
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Is size a priced factor in Germany? Presented by : Wen Huang Savang Kittikhoun Kim-Tuan Nguyen Yong Yao Tianxue Zhang
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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
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Introduction Does the size of a firm affect its return ?
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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
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Attribute portfolio Quintiles
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Attribute Portfolio - Graph
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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
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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
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Regression results
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Regression results - Graph
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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
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We cannot conclude that nA fully captures the risk induced attribute Regression results...
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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
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Results
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Sensitivity analysis - SMB
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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 ?
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Regression Results
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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
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