Page 24 - FINAL CFA II SLIDES JUNE 2019 DAY 3

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2. Using the Breusch-Pagan (BP) chi-square (χ ) test. READING 8: MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS
MODULE 8.6: ASSUMPTIONS: HETEROSKEDASTICITY

Regress squared residuals against independent variables: If these significantly explain the squared residuals, then CH is present!

1TT: Why? X is always +

CH is only a problem if the R2 and the
BP test statistic are too large!

EXAMPLE: The Breusch-Pagan test: The residual plot of mutual fund returns over time shows evidence of heteroskedasticity. To confirm your
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suspicions, you regress the squared residuals from the original regression on the independent variable, S&P 500 index returns. The R from that
regression is 8%. Use the Breusch-Pagan test to determine whether heteroskedasticity is present at the 5% significance level.

Answer: With 5 years of monthly observations, n is equal to 60.

1TT critical value for a chi-square distribution with one df and α equal to 5% = 3.841.

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The test statistic is: n × R = 60 × 0.08 = 4.8
Reject Ho and conclude that you have a
Decision? problem with conditional heteroskedasticity.