Worked examples

• Reconciling assets, liabilities and retained earnings

  Use the accounting equation and explicit equity-component assumptions.

  Worked examples

• The same ROE from different factors

  Separate an equal headline ratio from its different arithmetic components.

  Worked examples

• Scenario variance and squared deviation from a target

  Calculate the implied mean before distinguishing variance from a target-based squared deviation.

  Worked examples

• Calculating a score-linked management fee under a stated contract

  Apply a fictional score-improvement condition before converting basis points to an annual fee.

  Worked examples

• Why two ESG scoring methods can produce different results

  Recalculate a fictional issuer score using two explicit sets of weights.

  Worked examples

• Reallocating weights after a sector exclusion

  Calculate pro-rata weights and distinguish them from an optimized portfolio.

  Worked examples

• Combining conditional probabilities with scenario weights

  Calculate an unconditional probability from a complete weighted scenario table.

  Worked examples

• Annualizing monthly tracking error: why the square root appears

  Derive the square-root-of-12 calculation and identify its covariance assumption.

  Worked examples