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Omitted variable bias occurs when a missing factor both affects the outcome and moves with a variable kept in the regression. The included variable’s estimated slope then absorbs part of the missing factor’s effect. To find the direction, combine the sign of the missing factor’s effect with the sign of its relationship to the included variable.
Why the coefficient moves
Suppose a model explains a portfolio’s return using a broad market return, but leaves out a sector return. If sector and market returns tend to move together, the market coefficient can reflect both market exposure and some sector exposure. This is a specification problem, not a matter of reporting extra decimal places. The World Bank’s instrumental variables notes describe the same mechanism: an included coefficient can pick up an omitted factor’s effect.
Both conditions matter. If the missing factor has no effect on the outcome, it cannot contaminate the slope. If it matters but is unrelated to the included variable, it may make the model noisier without systematically shifting that variable’s coefficient. More observations alone do not remove bias caused by a missing, correlated driver.
Work out the sign and size
Take a purely illustrative return model. Let the true market coefficient be 0.80 and the true sector coefficient be 0.50. Suppose a separate regression of sector return on market return has a slope of 0.60. These are invented numbers for the calculation, not measured market estimates.
The bias is 0.50 times 0.60, or +0.30. A regression that omits the sector return would therefore tend towards a market coefficient of 1.10, rather than the true direct market coefficient of 0.80, under the stated model. The positive sign is predictable: the omitted sector contributes positively to portfolio return and tends to rise with the market.
Reverse either sign and the bias turns downward. Reverse both and it turns upward again. The slope of sector on market is the covariance divided by market variance; a correlation coefficient alone is not enough to calculate the bias’s size. Keep that distinction clear when a question supplies both correlation and standard deviations.
What to check in an exam answer
GARP lists Quantitative Analysis among the subjects in its 2026 FRM Part I study materials. CFA Institute’s model misspecification overview likewise identifies omitted variables as a possible source of regression failure. When reading a model description, name the plausible missing driver, ask whether it affects the dependent variable, and then ask whether it is associated with the regressor whose coefficient you are interpreting.
The common mistake is to infer bias merely because an important variable is absent. Its relationship with the included regressor determines whether that regressor’s slope is systematically distorted. The FRM programme page gives the wider syllabus context, while the study methodology offers a way to organise revision around these diagnostic checks.
Sources
- FRM® Study Material, Guide, Books, Practice Exams | GARP · garp.org · Retrieved
- Model Misspecification | CFA Institute · cfainstitute.org · Retrieved
- Instrumental variables | The World Bank · thedocs.worldbank.org · Retrieved
