Answer: the risk-free rate of return.

## Explanation In the context of derivatives and hedge portfolios, the fundamental principle of no-arbitrage states that a perfectly hedged portfolio should earn the risk-free rate of return. Here's why: ### Key Concepts: 1. **Hedge Portfolio**: A portfolio constructed by combining underlying assets with derivatives (like options) to eliminate risk. 2. **No-Arbitrage Principle**: In efficient markets, there should be no opportunity to earn risk-free profits without any initial investment. 3. **Risk-Free Rate**: The theoretical return on an investment with zero risk, typically represented by government bonds. ### Why Option B is Correct: - When a portfolio is perfectly hedged, all market risk is eliminated through the derivative positions. - Since there is no risk remaining, the portfolio should earn the risk-free rate of return. - If it earned more than the risk-free rate, arbitrageurs would exploit this by borrowing at the risk-free rate and investing in the hedge portfolio, earning risk-free profits. - If it earned less than the risk-free rate, arbitrageurs would short the hedge portfolio and invest at the risk-free rate. ### Why Other Options are Incorrect: - **Option A (zero return)**: Incorrect because even risk-free investments earn some return. Zero return would create arbitrage opportunities. - **Option C (weighted average return)**: Incorrect because a hedge portfolio eliminates systematic risk, so it shouldn't earn the average return of the underlying assets, which includes risk premiums. ### Mathematical Foundation: This principle is fundamental to derivative pricing models like the Black-Scholes model, where the risk-neutral valuation approach assumes that all assets earn the risk-free rate in a risk-neutral world. ### Real-World Application: This concept is crucial for understanding how options and other derivatives are priced and for constructing arbitrage-free trading strategies.

Author: LeetQuiz .