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FRM Part I · FRM Exam Part I · Options Markets

A portfolio manager holds a stock at $100 and buys a 1-year European put with strike $95 for $4, financing it by selling a 1-year European call with strike $110 for $4, forming a zero-cost collar. Ignoring interest and dividends, which statement about the portfolio value at expiration (stock plus options, excluding the initial stock price) is correct?

The collar caps the gain at $10 and limits the loss to $5 per share. The call's $110 strike caps value at $110 versus a $100 start, the put's $95 strike floors it at $95, and the premiums offset exactly, so no adjustment is needed.

  1. AThe gain is capped at $10 per share and the loss is limited to $5 per shareCorrect
  2. BThe gain is capped at $14 per share and the loss is limited to $5 per share
  3. CThe gain is capped at $10 per share and the loss is limited to $9 per share
  4. DThe gain is unlimited and the loss is limited to $5 per share

Explanation

Net premium is zero. Above $110, the short call caps the value at $110, a gain of $10 from $100. Below $95, the put locks the value at $95, a loss of $5. Option two adds the premium to the cap even though net premium is zero. Option three adds the put premium to the loss. Option four ignores the short call.

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