Answer-first summary for fast verification
Answer: The payoff must be at least $\$3.00$; i.e., minimum of $\$3.00$
Let the future asset price be $S_T$. - Long forward payoff = $S_T - K$ - Long put payoff = $\max(K+3 - S_T, 0)$ Total payoff: - If $S_T \le K+3$: \[ (S_T-K) + (K+3-S_T) = 3 \] - If $S_T > K+3$: \[ (S_T-K) + 0 = S_T-K > 3 \] So the portfolio payoff is never less than $3$ and is exactly $3$ when $S_T \le K+3$. Therefore, the payoff must be at least $\$3.00$.
Author: Manit Arora
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Q-21.9.2. Peter creates a portfolio with the following two positions with identical maturities: a long forward contract with delivery price equal to dollars; and a long European put option with a strike price equal to K + \`3.00`$. Recall that the payoff excludes the premium. Which statement is TRUE about this portfolio's payoff?
A
The payoff must be less than \`3.00$; i.e., maximum of $\
B
The payoff must be at least \`3.00$; i.e., minimum of $\
C
The payoff is equal to \`3.00`$ regardless of the future asset price
D
We need the current asset price to answer the question
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