Page 32 - FINAL CFA II SLIDES JUNE 2019 DAY 3

EXAMPLES OF MISSPECIFICATION OF READING 8: MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS
FUNCTIONAL FORM
MODULE 8.9: MODEL MISSPECIFICATION, & QUALITATIVE DEPENDENT VARIABLES

Given 4 independent variables for predicting monthly returns on portfolios of Chinese stocks (R):
• B = portfolio beta;
• lnM = natural log of market capitalization;
• ln(PB) = natural log of the price-to-book ratio; and
• FF = free float = ratio of available shares to total company shares

With 72 monthly observations (July 1996 to June 2002), model specification is: R = b + b B + b lnM + b lnPB + b FF + ε
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Say lnM and FF are statistically significant at the 1% level.
What will constitute misspecification?
Misspecification #1: Omitting a Variable

Say we omit lnM, the model becomes: R = a + a B + a lnPB + a FF + ε
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If lnM is correlated with the others, then ε too is; a , a , and a become biased and inconsistent: hypothesis tests and
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predictions will be unreliable.
Misspecification #2: Variable Should Be Transformed
Regression assumes linearity but the natural log of M (rather than M) is linearly related to P/E. We must transform the model from:

R = c + c B + c M + c lnPB + c FF + ε Other examples include squaring or taking the square root of the variable.
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to
For common-size financial statements, we do same when we standardize
variables by dividing by sales (for income statement or cash flow items) or total
R = f + g B + g LnM + g lnPB + g FF + ε assets (for balance sheet items).
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