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FRM Part I · FRM Exam Part I · Properties of Options

A portfolio manager holds a stock at $100 and buys a 1-year European put with strike $95 for $4, financed by selling a 1-year European call with strike $115 for $4 (a zero-cost collar). Ignoring discounting and dividends, at which stock price at expiration does the combined position (stock plus options) show a profit of exactly $0 relative to the initial $100 stock price?

The break-even is $100. Because the collar costs nothing, within the $95 to $115 range neither option pays off and profit equals the stock price minus $100. The floor of -$5 and cap of +$15 only apply outside that range.

  1. A$95
  2. B$100Correct
  3. C$105
  4. D$115

Explanation

Premiums net to zero, so the position profit equals the stock price change, bounded by the options. Between $95 and $115 neither option is exercised, so profit is S - 100, which is zero at S = $100. Below $95 the put floors the loss at -$5 and above $115 the call caps the gain at +$15. Break-even is therefore $100.

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