Answer: zero.

## Explanation **Correct Answer: B (zero)** ### Key Concepts: 1. **Risk-Free Asset**: A risk-free asset has a guaranteed return with zero variance (no uncertainty). Examples include short-term government Treasury bills. 2. **Correlation**: Measures the degree to which two variables move together. Correlation ranges from -1 to +1. 3. **Portfolio of Risky Assets**: Contains assets with uncertain returns that have some variance. ### Why the Correlation is Zero: - The returns of a risk-free asset are **constant and certain** - they don't vary regardless of market conditions. - The returns of risky assets **do vary** based on market conditions. - Since the risk-free asset's returns don't change, they cannot co-vary with anything else. - Mathematically: Correlation = Covariance(X,Y) / (σ_X × σ_Y) - For risk-free asset: σ_risk-free = 0 - Therefore, correlation is undefined mathematically, but conceptually it's zero because there's no co-movement. ### Important Implications: - This zero correlation property is fundamental to Modern Portfolio Theory. - It allows for the creation of the Capital Market Line (CML). - When combined with risky assets, risk-free assets help create efficient portfolios along the CML. ### Common Misconceptions: - Some might think correlation is positive if both assets provide positive returns, but correlation measures **co-movement**, not direction of returns. - Others might think it's negative if risk-free assets are seen as safe havens, but this is incorrect - risk-free returns are fixed, not inversely related to risky assets. **Conclusion**: The correlation between a risk-free asset and any risky portfolio is zero because the risk-free asset's returns are constant and do not vary with market conditions.

Author: LeetQuiz .