What market condition is most necessary for an effective (risk reducing) and most predictable hedging outcome?

Question

BlackTom AI · Accepted Answer

Hedging effectiveness depends on the correlation between cash and futures prices; a strong positive correlation between the cash and futures markets is necessary for predictable risk reduction.

1. Relevant knowledge points and concepts
- Basis = cash price − futures price. Hedging works by offsetting changes in the cash position with opposite changes in the futures position.
- Covariance and correlation determine how well futures movements offset cash movements.
- The minimum-variance hedge ratio h* = Cov(cash, futures) / Var(futures) = ρ · (σ_cash / σ_futures). Hedging effectiveness depends primarily on ρ (the correlation).

2. Step-by-step reasoning
- Write the variance of the hedged position: Var(cash − h·futures) = σ_cash^2 + h^2σ_futures^2 − 2h·Cov(cash,futures).
- Differentiate with respect to h and set to zero to obtain h* = Cov / σ_futures^2 = ρ·(σ_cash/σ_futures).
- Substituting h* back reduces variance by a factor dependent on ρ^2. The closer ρ is to +1, the larger the reduction.

3. Intermediate steps (algebra)
- Cov = ρ·σ_cash·σ_futures.
- h* = (ρ·σ_cash·σ_futures) / σ_futures^2 = ρ·(σ_cash/σ_futures).
- Variance reduction proportional to ρ^2: residual variance = σ_cash^2·(1 − ρ^2).

4. Why the correct answer is correct
- If ρ ≈ +1, residual variance → 0 (perfect hedge possible with appropriate h). Thus a strong positive correlation produces the most effective and predictable hedging outcome because futures reliably move with the cash market.

5. Why other options are incorrect
- Low volatility in both markets: may reduce absolute risk but does not guarantee an effective hedge if correlation is low.
- Weak positive correlation: gives only limited risk reduction (ρ small → little variance reduction).
- Weak/strong negative correlation: futures move opposite to cash; typical hedging positions will amplify rather than offset risk unless reversed and carefully managed.
- High volatility in both markets: large price swings increase potential loss; without high positive correlation, hedging remains unpredictable.

6. Conclusion
A strong positive price correlation between the cash and futures market is required for the most effective and predictable hedging outcome. This matches the provided answer.

What market condition is most necessary for an effective (risk reducing) and most predictable hedging outcome?单项选择题

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