Answer: Both the upside and downside is limited.

## Explanation A butterfly spread using calls has the following structure: - Buy 1 call @ X1 (low strike) - Sell 2 calls @ X2 (middle strike) - Buy 1 call @ X3 (high strike) **Risk Profile Analysis:** **Maximum Profit:** - Occurs when the underlying price equals X2 at expiration - Limited to: (X2 - X1) - Net premium paid **Maximum Loss:** - Occurs when the underlying price is below X1 or above X3 - Limited to the net premium paid for establishing the position **Why both upside and downside are limited:** 1. **Downside Risk (Price < X1):** - All calls expire worthless - Loss = Net premium paid (limited) 2. **Upside Risk (Price > X3):** - The long call @ X1 and short calls @ X2 create offsetting positions - The long call @ X3 provides protection - The positions cancel out, resulting in limited loss equal to the net premium **Mathematical Proof:** - When S > X3: - Long call @ X1: S - X1 - Short calls @ X2: -2(S - X2) - Long call @ X3: S - X3 - Total payoff = (S - X1) - 2(S - X2) + (S - X3) = 0 - Profit = Payoff - Net premium = -Net premium (limited loss) **Key Characteristics:** - Butterfly spreads are **range-bound strategies** - They profit when the underlying stays within a specific range - Both maximum profit and maximum loss are predetermined and limited - This makes them suitable for low-volatility environments Therefore, option B is correct: **Both the upside and downside is limited.**

Author: LeetQuiz Editorial Team