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**CFA Practice Question**

An investor is considering whether to buy one of two American calls on the same stock (price S) with the same expiration date. The exercise prices of the calls are different, with X

_{L}< X_{H}. If C_{L}and C_{H}are the premiums on the respective calls, which of the following statements is FALSE?A. The minimum value of [C

_{L}- C_{H}] is 0.B. If X

_{L}< S < X_{H}, the payoff on the exercise of [C_{L}- C_{H}] is S- X_{L}.C. The maximum payoff on [C

_{H}- C_{L}] is X_{H}- X_{L}.**Explanation:**A call option with a lower exercise price is worth more, all other factors remaining constant. The difference between the values of such calls is capped by the difference between their exercise prices, i.e., X

_{H}- X

_{L}.

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**User Contributed Comments**
9

User |
Comment |
---|---|

MUSK |
Why not A? |

nike |
A is true. CL >= CH so the minimum value is 0. |

patsy |
I thought A also. If XL < XH then min value of CL - CH is > 0 . However, notice the question asks which one is FALSE! |

kellyyang |
I am still get confused for this question, can any explain a littl more details! thanks |

jpducros |
What does "the payoff of the exercise on (CH-Cl) means ? |

Kashi2010 |
XL is lower thatn XH, therefore CL is worth more than CH, therefore CL > CH, therefore CL - CH > 0. I still think A is false (so the right answer), CL-CH will always exceed 0? |

jpducros |
Kashi2010, you've just demonstrated that A is right. |

Mgtw |
C is false because it should be CL - CH. I don't think the bracket is meant to be for taking absolute value. |

adamrej |
Guys, it's simple. Max payoff for CH is S-XH. For CL it's S-XL. So... max(CH-CL) = S-XH- (S-XL) = XL-XH < 0 and not(!) XH-XL >0 |