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.