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FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"

A desk is short 1,000 European calls on a stock. Each call has a rho of +0.30 per one percentage point rise in rates. The desk wants to neutralise rho using European puts on the same stock, each with a rho of -0.20 per one percentage point rise. Which trade makes the position rho-neutral?

Sell 1,500 puts. The short call position has a rho of -300 per one percentage point rise in rates. Short puts contribute +0.20 each because put rho is negative, so 300 divided by 0.20 gives 1,500 puts to sell. Buying puts would add more negative rho.

  1. ABuy 1,500 puts
  2. BSell 667 puts
  3. CBuy 667 puts
  4. DSell 1,500 putsCorrect

Explanation

The short calls have rho of -1,000 × 0.30 = -300 per 1%. The hedge must add +300. Each long put contributes -0.20, so each short put contributes +0.20. The required number of short puts is 300 / 0.20 = 1,500. Buying puts would deepen the negative rho.

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