Hedge Ratio and Basis Risk

The two legs won't move in perfect sync

The physical and the futures often differ in product, delivery location and term, so they move broadly together but there's always a gap. The higher the correlation, the smaller the gap; what's left after hedging is basis risk.

How much hedging is steadiest?

As the hedge ratio rises from 0, portfolio volatility first falls, then rises. The lowest point is the minimum-variance hedge ratio: correlation × spot volatility ÷ futures volatility.

Correlation decides how much can be hedged away

hedge effectiveness = the correlation squared. With a correlation of 0.8, the best hedge removes at most 64% of the variance, cutting volatility by only 40% (60% remains). With a poorly correlated instrument, no ratio will help much.

Key takeaways

• Minimum-variance hedge ratio = correlation × spot volatility ÷ futures volatility.
• The optimal hedge can remove at most correlation² of the variance (hedge effectiveness): a correlation of 0.8 removes only 64%.
• The part you can't hedge away is basis risk. The lower the correlation, the bigger the basis risk.
• A higher hedge ratio isn't always better: beyond the optimum, portfolio risk starts climbing again.

Try it yourself

You can do these exercises in this lesson's interactive simulation:

1. Click "Example: 0.8 · 3% · 2%," then "Set to the optimal ratio": what's the optimal ratio? Where's the bottom of the curve in the right-hand chart?
2. Drag the hedge ratio past the optimal value all the way to 2.0: how does portfolio volatility change? What are the short futures doing now?
3. Drag the correlation to 1.0: how low does the minimum go? Then drag it to 0.5: how much risk can you still remove at most?
4. Keep the correlation at 0.8 and change spot volatility from 3% to 1.5%: what does the optimal ratio become?

Quiz and explanations

1. Spot volatility is 3%, futures volatility 2% and the correlation 0.8. Roughly what's the minimum-variance hedge ratio?

Answer: 1.2.0.8 × 3% ÷ 2% = 1.2.

2. If the correlation drops from 0.95 to 0.6, the risk an optimal hedge can remove will…

Answer: Decrease.The lower the correlation, the less the two legs move together, and the more basis risk is left.

3. With a correlation of 0.8, hedging at the optimal ratio can cut portfolio volatility (standard deviation) by at most how much?

Answer: 40%.It removes 0.8² = 64% of the variance, leaving 36%. Volatility = √0.36 = 60% of the original, so it falls by 40%.

Terms in this lesson

• basis risk (Basis Risk): The risk left after hedging because the asset and the hedging instrument don't move perfectly together.
• correlation (Correlation): How much two prices move together, from −1 to 1; the closer to 1, the more in sync.
• hedge effectiveness (Hedge Effectiveness): The most risk (by variance) an optimal hedge can remove = correlation squared; at a correlation of 0.8 it removes at most 64% of the variance.
• hedge ratio (Hedge Ratio): The size of the hedge relative to the original exposure; 1 means a full hedge, 0.5 means hedging half.
• minimum-variance hedge ratio (Minimum-Variance Hedge Ratio): The ratio that makes the hedged portfolio swing the least = correlation × spot volatility ÷ futures volatility.
• over-hedging (Over-Hedging): Hedging more than your actual exposure, which creates a new risk in the opposite direction.