Page 34 - FINAL CFA II SLIDES JUNE 2019 DAY 3

LOS 8.n: Describe models with qualitative READING 8: MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS
dependent variables –Dummy variables!
MODULE 8.9: MODEL MISSPECIFICATION, & QUALITATIVE DEPENDENT VARIABLES
Example: a model to predict when a bond issuer will default (‘’1’’ for default and ‘’0’’ for no default. Several types exist:

• Probit and logit models: Probit is based on the normal distribution, while a logit is based on the logistic distribution
• Applied to estimate say probability of dichotomous dependent variable: default/no default, yes/no, agree/disagree, like/dislike..
• Uses maximum likelihood methodology to estimate coefficients for probit and logit models.
• Coefficients relate the independent variables to the likelihood of an event occurring (e.g. merger, bankruptcy, or default).

• Discriminant models: Similar to probit and logit models but make different assumptions regarding the independent
variables. Results in a linear function similar to an ordinary regression, which generates an overall score, or ranking, for an
observation (e.g. z-score). The scores can then be used to rank or classify observations.
• Applied to financial ratios as the independent variables to predict the qualitative dependent variable bankruptcy.
• A linear relationship among the independent variables produces a value for the dependent variable that places a company in a
bankrupt or not bankrupt class.

The analysis of regression models with qualitative dependent variables is the same as previously discussed:
• Examine the individual coefficients using t-tests,
2
• Determine the validity of the model with the F-test and the R , and
• Look out for heteroskedasticity, serial correlation, and multicollinearity.

LOS 8.o: Evaluate and interpret a multiple regression model and its results.

Model interpretation focuses on coefficient/s in the ‘’economic’’ sense: In economic terms: On average, a one unit increase in
Suppose say Return = 5.0 + 4.2 Beta − 0.05 Mkt.Cap. + ε beta risk is associated with a 4.2% increase in return,
while a $1 billion increase in market capitalization
Say coefficients are statistically-speaking, significantly different from zero! implies a 0.05% decrease in return.

For instance, a study of dividend announcements may identify a statistically significant abnormal return following the announcement, but
these returns may not be sufficient to cover transactions costs.
Investment decisions are based not only on statistical but economic significance as well!