FRM: Return decomposition

Explanations, applications and practice for return decomposition.

• Equity multiplier in a consistent DuPont chain

  Use the equity multiplier in a consistent dupont chain relationship with explicit definitions.

  Formulas

• Five-factor DuPont identity and denominator conditions

  Use the five-factor dupont identity and denominator conditions relationship with explicit definitions.

  Formulas

• Net profit margin

  Use the net profit margin relationship with explicit definitions.

  Formulas

• Return on equity with a stated average

  Use the return on equity with a stated average relationship with explicit definitions.

  Formulas

• Three-factor DuPont identity

  Use the three-factor dupont identity relationship with explicit definitions.

  Formulas

• Total asset turnover with an average base

  Use the total asset turnover with an average base relationship with explicit definitions.

  Formulas

• Reconciling DuPont analysis to return on equity

  Use consistent period and average-balance inputs to reconstruct the direct return ratio.

  Lessons

• Mixing average and ending assets in DuPont analysis

  Check that the asset amount cancels between turnover and the equity multiplier.

  Common mistakes
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  DuPont analysis calculator

  Reconcile three and five factors with direct return on equity.

  Tools

• Reconciling all five DuPont factors

  Use the full precision of each factor and check the product against direct ROE.

  Worked examples

• The same ROE from different factors

  Separate an equal headline ratio from its different arithmetic components.

  Worked examples