How does CPPI work, and how does the multiplier affect the strategy's risk-return profile compared to a static allocation?

Constant Proportion Portfolio Insurance (CPPI) dynamically allocates between a risky asset and a safe asset based on the cushion (the distance between portfolio value and a predefined floor). The multiplier amplifies the cushion into a risky asset exposure.\n\nCPPI Mechanics:\n\nRisky Asset Allocation = m x (Portfolio Value - Floor) = m x Cushion\nSafe Asset Allocation = Portfolio Value - Risky Allocation\n\nwhere m is the multiplier (typically 2-5) and the Floor grows at the risk-free rate.\n\n`mermaid\ngraph TD\n A[\"Portfolio Value: $10M
Floor: $8.5M
Cushion: $1.5M
Multiplier: 3\"] --> B[\"Risky Allocation
3 x $1.5M = $4.5M
(45%)\"]\n A --> C[\"Safe Allocation
$10M - $4.5M = $5.5M
(55%)\"]\n B --> D{\"Market Moves?\"}\n D -->|\"Risky +5%\"| E[\"New Portfolio: $10.225M
New Cushion: $1.725M
New Risky: $5.175M (50.6%)\"]\n D -->|\"Risky -5%\"| F[\"New Portfolio: $9.775M
New Cushion: $1.275M
New Risky: $3.825M (39.1%)\"]\n`\n\nMultiplier Selection:\n\n| Multiplier | Behavior | Max Tolerable Drop |\n|---|---|---|\n| m = 2 | Conservative, slow participation | 1/m = 50% before breach |\n| m = 3 | Balanced | 33% |\n| m = 4 | Aggressive, faster participation | 25% |\n| m = 5 | Very aggressive | 20% |\n\nThe maximum single-period drop before breaching the floor = 1/m. With m = 3, a risky asset decline exceeding 33% between rebalancing points would push the portfolio below the floor.\n\nWorked Example:\n\nLarkspur Wealth implements CPPI with:\n- Initial portfolio: $10M\n- Floor: $8.5M (85% capital protection)\n- Multiplier: 3\n- Rebalancing: weekly\n\n| Week | Portfolio | Cushion | Risky (m x C) | Safe | Risky Return | New Portfolio |\n|---|---|---|---|---|---|---|\n| 0 | $10.00M | $1.50M | $4.50M | $5.50M | | $10.00M |\n| 1 | $10.00M | $1.50M | $4.50M | $5.50M | +3% | $10.135M |\n| 2 | $10.135M | $1.635M | $4.905M | $5.230M | -2% | $10.037M |\n| 3 | $10.037M | $1.537M | $4.611M | $5.426M | +4% | $10.221M |\n| 4 | $10.221M | $1.721M | $5.163M | $5.058M | -6% | $9.911M |\n\nCPPI vs Static Allocation:\n- CPPI increases equity exposure after gains (buy high) and decreases after losses (sell low) --- this is a momentum-like behavior\n- In trending markets, CPPI outperforms static because it rides the trend\n- In choppy, mean-reverting markets, CPPI underperforms because it whipsaws\n\nDoes CPPI Guarantee the Floor?\nNo. If the risky asset drops more than 1/m between rebalancing dates (a gap), the floor is breached. This is called gap risk. CPPI with m = 3 cannot protect against a 35% overnight crash.\n\nMitigation: combine CPPI with actual put options for gap protection, or use lower multipliers with more frequent rebalancing.\n\nExplore structured protection strategies in our CFA Derivatives course.