Continuously compounded return

The natural logarithm of one plus the holding-period return. Returns in this form add across periods, which makes multi-period arithmetic exact where simple returns mislead.

Where you will meet it

Continuously compounded return appears in 2 learning outcomes on the CFA syllabus. A few of them:

• Explain continuous compounding and the lognormal distribution
  CFA Level I · Quantitative Methods

  “Continuously compounded returns are the logs of price relatives, so if those log returns are normal the prices themselves are lognormal.”

• Name the assumptions behind the Black–Scholes–Merton model for valuing options
  CFA Level II · Derivatives and Risk Management

  “In Black–Scholes–Merton the underlying follows geometric Brownian motion, so prices are lognormally distributed and continuously compounded returns are normal.”

Practise it

• Today's practice question One question, with every wrong option explained.
• Free Level I diagnostic test Twelve questions that show which topics to start with.
• Free finance calculators Check your arithmetic on the exam's core formulas.

All terms beginning with C · Glossary