FRM: Investment performance

Explanations, applications and practice for investment performance.

• Uncorrelated does not always mean independent

  Use a finite non-linear model to show zero covariance alongside dependence.

  Concepts

• Correlation from covariance and standard deviations

  Use matching units and positive standard deviations in the Pearson-correlation formula.

  Formulas

• Discrete probability-model mean and variance

  Apply probability weights to outcomes and squared deviations without a sample-size divisor.

  Formulas

• Sample tracking error: deviations of active returns

  Distinguish sample tracking error from mean active return and root mean square deviation.

  Formulas

• Preparing paired returns for a tracking error calculation

  Check date alignment, return conventions and missing observations before entering two series.

  Tool guides

• Variance in percentage units and decimal-return units

  Account for the squared scale factor when converting variance.

  Common mistakes
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  Scenario expected return and risk calculator

  Calculate expected return, variance and standard deviation from explicit scenario probabilities.

  Tools
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  Tracking error calculator

  Calculate sample tracking error from paired portfolio and benchmark returns.

  Tools

• Converting covariance into correlation with consistent units

  Normalize a covariance of −18 using standard deviations of 6% and 5%.

  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

• Annualizing monthly tracking error: why the square root appears

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

  Worked examples