Question text 4Marks Sabrina bought an American call option with a
strike price of $40 for $3.50 (premium). The underlying stock is now trading for $35. If Sabrina exercises the call today, what will be her holding period return and net profit? Sabrina's Holding Period Return (HPR) is: Answer 1[select: , 22.45%, 42.86%, 83.91%, 35.33%, 13.86%]Sabrina's net profit is: Answer 2[select: , $5, $1.50, $3.45, -$2.05, $8.05] Notes Report question issue Question 6 Notes

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BlackTom AI · Accepted Answer

Question restatement:
- Sabrina bought an American call option with a strike price of $40 for a premium of $3.50. The underlying stock is currently at $35. If Sabrina exercises the call today, what are Sabrina's Holding Period Return (HPR) and Sabrina's net profit?
- Sabrina's Holding Period Return (HPR) is: [13.86%]
- Sabrina's net profit is: [$-2.05]

Option-by-option analysis (even though the options list is not shown in the data you provided, I will address the general idea and then connect to the given numeric answers):

- About exercising a call option when S < X (here S = 35, X = 40):
  The intrinsic value of the call is max(S - X, 0) = max(35 - 40, 0) = 0. Therefore, if Sabrina exercises immediately, the option provides no intrinsic payoff at exercise time. The "profit" from exercising, ignoring the premium you paid, would be 0, but you did pay a premium of 3.50 to acquire the option, so the economic result of exercising would factor in that premium.

- Net profit calculation (standard approach):
  Net profit from the option if exercised today = End value from exercising minus the initial cost (premium paid).
  End value from exercising = intrinsic payoff = 0 (since S < X).
  Initial cost = premium paid = 3.50.
  Therefore, Net profit = 0 - 3.50 = -3.50.
  This is the straightforward calculation if we treat the exercise as the only cash flow and ignore any potential adjustment for the alignment between the premium and the exercise decision. In many textbook treatments, you would report net profit as -$3.50 and HPR as -$3.50 / $3.50 = -100% if you measure HPR purely against the premium paid.

- Holding Period Return (HPR) concept:
  HPR = (Ending value - Beginning value) / Beginning value, where Beginning value is the amount invested in the option premium ($3.50).
  If Ending value is interpreted as the payoff from exercising (which, for S < X, is 0), then HPR = (0 - 3.50) / 3.50 = -1.0, i.e., -100%.

- Reconciling with the provided answers (13.86% and -$2.05):
  The numbers you provided (HPR of 13.86% and net profit of -$2.05) do not align with the standard, straightforward calculation outlined above when exercising the option today with S = 35 and X = 40. Under the conventional framework, exercising a call with no intrinsic value would result in a loss equal to the premium, i.e., net profit = -$3.50 and HPR = -100%.

- Potential alternative interpretation that could yield the given values (to illustrate the source of the mismatch):
  Some exam questions report HPR using a different base for the return, or they compute a partial payoff scenario (e.g., considering a partial exercise value, or including an implied time value adjustment, or using a different starting investment base). If one were to force-fit the answer choices given (13.86% and -$2.05) without altering the underlying economics (S = 35, X = 40, premium = 3.50), one would have to assume an unconventional definition of ending value or a misalignment between the stated premium and the base used for HPR. In standard practice, however, the results should reflect the intrinsic-value-zero outcome and the single premium paid.

- Why the two provided numbers are inconsistent with the conventional calculation:
  1) A net profit of -$2.05 implies the ending value after exercising would be $1.45 (since 1.45 - 3.50 = -2.05). There is no scenario, under S = 35 and X = 40, where exercising yields a positive ending value of $1.45 from exercising alone.
  2) An HPR of 13.86% would require Ending value and Beginning value to satisfy (Ending - Beginning)/Beginning = 0.1386. With Beginning = 3.50, Ending would need to be 3.9721, which again does not correspond to the intrinsic payoff from exercising a 35/40 call.

- Summary of correct conceptual steps (as commonly taught):
  - If S < X at exercise time, the call has zero intrinsic value; exercising provides no payoff beyond the stock value it would deliver, which is insufficient to cover the strike, and you lose the premium paid.
  - Net profit from exercising today should reflect the premium paid: Net profit = 0 - 3.50 = -3.50.
  - HPR, relative to the premium, should be -100% if you treat the premium as the base investment: HPR = (-3.50) / 3.50 = -1.0, i.e., -100%.

- Final note for students:
  When encountering conflicting numbers, always check the question’s framing: is HPR being computed relative to the premium, or relative to a different base? Is the ending value taken as the intrinsic value at exercise, or is there an implied sale/settlement value? In a standard, straightforward interpretation for this scenario, exercising a call with S = 35 and X = 40 results in a net loss equal to the premium, and an HPR of -100% relative to the premium. The provided numbers (13.86% and -$2.05) do not align with this standard interpretation, suggesting either a misprint in the options or a nonstandard calculation basis.

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