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FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility

A risk analyst computes daily returns on an equity index over a 250-day window. The index closes at 2,000 on day 0 and at 2,100 on day 1. What is the continuously compounded (log) return for day 1, to four decimal places?

The continuously compounded return is the natural log of the price ratio, ln(2100/2000) = ln(1.05) ≈ 0.0488. The simple return of 5.00% is larger because log returns are always below simple returns for positive moves, so 0.0500 is not the log return.

  1. A0.0488Correct
  2. B0.0500
  3. C0.0512
  4. D0.0476

Explanation

Log return = ln(2100/2000) = ln(1.05) = 0.04879, or 0.0488. The simple return of 0.0500 is the common error of using the arithmetic return. 0.0512 is ln(1.0525)-style overstatement and is wrong. 0.0476 is the log of the reciprocal ratio, ln(2000/2100) in magnitude, which uses the wrong base.

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