FRM: Return measurement

Explanations, applications and practice for return measurement.

• Multiplying a periodic return without naming the method

  Distinguish simple scaling from compound annual equivalence.

  Common mistakes

• Build a total-return measurement boundary

  Separate asset income, endpoint values and external transfers before calculating a return.

  Lessons

• Break valuations at an external deposit

  Compute two subperiod rates without calling the contribution a gain.

  Worked examples

• Counting an owner deposit as investment gain

  Remove new capital from the performance interpretation without losing its timing.

  Common mistakes

• Using ending weights for an earlier period return

  Keep the weight date aligned with the return interval.

  Common mistakes

• Calculate an end-period fee from its stated base

  Reconcile a fictional fee to ending net wealth.

  Worked examples

• External transfers and investment income

  Classify cash movements by source before measuring performance.

  Concepts

• Linked-return frequency and covered horizon

  Set the equal-period frequency without changing the observed cumulative return.

  Tool guides

• Reconcile local asset growth and currency interaction

  Check domestic wealth through actual converted endpoint values.

  Worked examples

• Currency-return input boundary and costs

  Check total-income treatment and omitted conversions before using the output.

  Tool guides
• 

  Currency quote and converted-wealth log

  Retain quote units and endpoint conversion alongside the return.

  Templates
• 

  Domestic-currency return calculator

  Combine local asset growth with a clearly defined currency-quote change.

  Tools

• Geometric mean from linked return factors

  Recover a constant periodic rate matching terminal wealth.

  Formulas

• Holding-period return with an end distribution

  Use endpoint price and an income amount without double counting.

  Formulas

• Calculate price gain and an end-period distribution

  Reconcile price return, total return and endpoint wealth.

  Worked examples
• 

  Linked return and wealth calculator

  Compound equal-period returns, inspect the path and compare periodic and annual summaries.

  Tools

• Log returns and the positive-wealth domain

  Understand when logarithmic returns exist and how they combine.

  Concepts

• Using log return as a simple percentage

  Convert through a growth factor before relabeling the return.

  Common mistakes

• Arithmetic rate mean and geometric growth

  Choose a summary for rate observations or cumulative wealth.

  Comparisons

• Money-weighted return from a dated investor schedule

  Use investor cash-flow signs and dates to define the return equation.

  Lessons

• Reorder returns around an intermediate contribution

  Compare investor wealth when capital timing meets different return paths.

  Worked examples

• Same linked return, different wealth path

  Separate endpoint growth from the route taken between dates.

  Concepts

• Return bases, income and flow-timing practice

  Test the difference between investor transfers, income and return bases.

  Practice

• Linked-growth and currency-conversion practice

  Check compounded factors, quote direction and annual-rate descriptions.

  Practice

• Domestic-per-foreign currency quote direction

  Read the numerator and denominator before calculating currency movement.

  Concepts

• Reconcile nominal wealth and price-index growth

  Compare monetary gain with change in indexed purchasing power.

  Worked examples

• Exact real return from nominal growth and inflation

  Divide nominal wealth growth by growth in the chosen price index.

  Formulas

• Calculate movement in reciprocal currency quotes

  Show why reversing the quote does not merely reverse the percentage sign.

  Worked examples

• Using the loss percentage as the recovery gain

  Change the denominator when calculating recovery from a lower wealth base.

  Common mistakes

• Calculate a return spread and relative wealth

  Compare a percentage-point advantage with the wealth-ratio result.

  Worked examples

• Compare portfolio and benchmark wealth growth

  Distinguish a return difference from growth relative to the benchmark.

  Lessons

• Return-measurement reconciliation checklist

  Check boundaries, flow timing, rate labels and endpoint wealth together.

  Revision

• Solve a two-contribution money-weighted return

  Transform the original cash-flow equation into a checkable quadratic.

  Worked examples

• Link an equal gain and loss to terminal wealth

  Show why +20% and −20% do not cancel on changing wealth bases.

  Worked examples

• Return-measurement learning sequence

  Build from income classification to linked, investor and currency outcomes.

  Study plans

• Annualize a short observed return period

  Distinguish observed quarterly growth from its annual equivalent.

  Worked examples

• Link time-weighted subperiod returns

  Measure performance around external transfers and compound the resulting rates.

  Lessons
• 

  Return valuations and external-flow log

  Record values on both sides of a capital movement.

  Templates

• Time-weighted and money-weighted return questions

  Match the performance measure to portfolio linking or investor cash-flow experience.

  Comparisons

• Reconcile starting weights to portfolio gain

  Calculate contributions and resulting balances before updating weights.

  Worked examples