Page 23 - FINAL CFA II SLIDES JUNE 2019 DAY 3

READING 8: MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS
Detecting Heteroskedasticity – 2 Methods

MODULE 8.6: ASSUMPTIONS: HETEROSKEDASTICITY
1. Examining scatter plots of the residuals; and
2. Using the Breusch-Pagan (BP) chi-square (χ ) test.
2

1. Examining scatter plots of the residuals..

EXAMPLE: Detecting heteroskedasticity with a residual plot: You have been studying the monthly returns of a mutual fund over the past
five years, hoping to draw conclusions about the fund’s average performance. You calculate the mean return, the standard deviation, and the
portfolio’s beta by regressing the fund’s returns on S&P 500 index returns (the independent variable). The standard deviation of returns and
the fund’s beta don’t seem to fit the firm’s stated risk profile. For your analysis, you have prepared a scatter plot of the error terms (actual
return – predicted return) for the regression using five years of returns, as shown in the following figure. Determine whether the residual
plot indicates that there may be a problem with the data.

The variance of the fund’s returns about the mean is related
to the level of the independent variable; So?

A problem is present in the data: What kind?

Conditional heteroskedasticity!

Answer:
Variation in regression residuals increases as the
independent variable increases: Meaning?