Explanation

Insurance on a portfolio of risky assets is most likely negatively correlated with the portfolio's assets. Here's why:

Key Concept: Insurance as a Hedge

Insurance acts as a hedge against losses in the underlying portfolio. When the portfolio's assets decline in value, the insurance pays out, providing compensation for those losses. This creates an inverse relationship:

• When portfolio assets perform poorly (decrease in value) → Insurance pays out (increases in value)
• When portfolio assets perform well (increase in value) → No insurance payout needed (insurance has no or minimal value)

Mathematical Relationship

If we consider:

• Portfolio return = Rₚ
• Insurance return = Rᵢ

The correlation coefficient ρ(Rₚ, Rᵢ) would be negative because:

• Rₚ ↑ → Rᵢ ↓ (or remains low)
• Rₚ ↓ → Rᵢ ↑

Real-World Example

Consider portfolio insurance strategies like put options:

• Buying put options on a stock portfolio provides downside protection
• When stocks fall, put options increase in value
• When stocks rise, put options expire worthless or lose value

Why Not the Other Options?

• Option B (uncorrelated): Incorrect because insurance is specifically designed to respond to portfolio performance
• Option C (positively correlated): Incorrect - this would mean insurance pays out when the portfolio does well, which defeats the purpose of insurance

CFA Curriculum Context

This concept relates to:

1. Risk management strategies
2. Portfolio hedging techniques
3. Understanding correlation in portfolio construction
4. Insurance products as risk mitigation tools

Correct Answer: A - Insurance on a portfolio of risky assets is most likely negatively correlated with the portfolio's assets.