How do I optimize the width of a collar, and what trade-offs am I making between protection and participation?

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AcadiFi · Accepted Answer

Collar optimization is an advanced risk management topic that requires balancing downside protection against upside participation. Here's the analytical framework. **Collar Construction:** - Own the underlying stock (or long position) - **Buy** a protective put at K_1 (below current price) - **Sell** a covered call at K_2 (above current price) The call premium received partially or fully offsets the put premium paid. **Zero-Cost Collar:** When the call premium exactly equals the put premium, the collar is 'costless.' But this constrains your strike choices. **Collar Width Optimization Framework:** | Collar Width | Put Strike (Floor) | Call Strike (Cap) | Trade-off | |-------------|-------------------|-----------------|-----------| | Narrow | Close to current price | Close to current price | Maximum protection, minimum participation | | Medium | 5-10% below | 10-15% above | Balanced | | Wide | 15-20% below | 20-30% above | Minimal protection, maximum participation | | Asymmetric | Tight floor | Wide cap | Expensive (put costs more than call generates) | **Factors Driving Optimal Width:** **1. Risk Tolerance / Maximum Acceptable Loss** If your investment policy limits losses to 10%, the put strike must be no more than 10% below current price. **2. Return Target** If you need at least 15% upside to meet your target, the call strike must be at least 15% above. **3. Volatility Skew** Put skew makes OTM puts relatively expensive. A zero-cost collar with a 10% OTM put might require selling a call only 7% OTM (asymmetric, favoring the issuer side). **4. Time Horizon** Longer collars have wider zero-cost ranges because more time value is available to sell. **5. Dividend Yield** High dividends reduce call value (calls don't capture dividends) and increase put value. This narrows the zero-cost collar range. **Worked Example:** Ridgeview Wealth manages a $10M position in Helios Energy at $50/share (200,000 shares). They need protection against >12% declines but want at least 8% upside. Constraints: - Put strike >= $44 (12% below $50) - Call strike >= $54 (8% above $50) Option prices (6-month expiry): - $44 put: $1.85 - $54 call: $2.10 - Net credit: $2.10 - $1.85 = **$0.25 per share** This collar is actually a slight net credit, so it meets the zero-cost requirement. Total credit: 200,000 x $0.25 = $50,000. **Result:** - Max loss: ($50 - $44) x 200,000 = $1.2M (12%) minus $50K credit = **$1.15M** - Max gain: ($54 - $50) x 200,000 = $800K + $50K credit = **$850K (8.5%)** - Dividends: Retained (you still own the stock) ```mermaid graph LR A[Collar Optimization] --> B[Tighter Put
More protection
Higher cost or lower cap] A --> C[Higher Call
More upside
Less premium to offset put] A --> D[Zero-Cost Constraint
Forces put/call balance] B --> E[Conservative investors
Loss budgets] C --> F[Growth-oriented
Bull market view] D --> G[Most common institutional
structure] style D fill:#c9a84c,color:#000 ``` **Advanced Considerations:** - **Rolling collars**: As the stock appreciates, roll the collar up to lock in gains - **Tax implications**: The collar may trigger constructive sale rules if too tight (< 15% width in the US) - **Dynamic collars**: Adjust strikes as volatility changes **Exam Tip:** Be able to calculate collar payoffs, understand the protection/participation trade-off, and know that zero-cost collars are the most common institutional structure. The skew effect (puts more expensive) means zero-cost collars typically have asymmetric widths. Study protective strategies in our CFA Level II derivatives course.

How do I optimize the width of a collar, and what trade-offs am I making between protection and participation?

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