How does a Target Redemption Note (TARN) work, and why does the cumulative coupon cap create early termination risk?

A Target Redemption Note (TARN) is a structured product that automatically redeems once the cumulative coupons paid to the investor reach a predetermined lifetime cap (the 'target'). Each period's coupon is typically linked to a floating rate formula, meaning the speed at which the target is reached depends entirely on the path of interest rates.\n\nTARN Structure:\n\n`mermaid\ngraph TD\n A[\"Period Coupon Calculation
e.g., max(0, 8% - SOFR)\"] --> B{\"Cumulative coupons
reached target?\"}\n B -->|\"No\"| C[\"Pay full coupon
Continue to next period\"]\n B -->|\"Yes\"| D[\"Pay partial coupon
(only enough to hit target)\"]\n D --> E[\"Note redeems at par
Investor receives principal\"]\n C --> A\n`\n\nWorked Example -- Ridgeline Capital:\n\nRidgeline issues a 5-year TARN with:\n\n- Notional: $5,000,000\n- Coupon formula: max(0, 7.50% - 3M SOFR) per annum, paid semi-annually\n- Target cap: 18.00% cumulative lifetime coupon\n- If target reached mid-period, final coupon is truncated to exactly hit 18%\n\nRate Path Simulation:\n\n| Period | 3M SOFR | Period Coupon | Cumulative | Target (18%) Hit? |\n|---|---|---|---|---|\n| Year 1 H1 | 4.80% | 1.35% | 1.35% | No |\n| Year 1 H2 | 4.50% | 1.50% | 2.85% | No |\n| Year 2 H1 | 3.90% | 1.80% | 4.65% | No |\n| Year 2 H2 | 3.20% | 2.15% | 6.80% | No |\n| Year 3 H1 | 2.60% | 2.45% | 9.25% | No |\n| Year 3 H2 | 2.10% | 2.70% | 11.95% | No |\n| Year 4 H1 | 1.80% | 2.85% | 14.80% | No |\n| Year 4 H2 | 1.50% | 3.00% | 17.80% | No |\n| Year 5 H1 | 1.20% | 0.20% (truncated) | 18.00% | Yes -- redeems |\n\nIn this scenario, falling rates caused coupons to accelerate, but the TARN nearly ran to maturity. If SOFR had dropped to 1% by Year 2, the target would have been reached in approximately 3 years.\n\nReinvestment Risk:\n\nThe critical irony: the TARN pays highest coupons when rates are lowest (since coupon = fixed minus floating). But it also redeems earliest when rates are lowest. The investor receives principal back precisely when reinvestment opportunities are poorest. This negative convexity is the primary risk of TARN ownership.\n\nInvestor Profile:\n\nInverse floater TARNs (like the example above) appeal to investors who believe rates will decline moderately but want to cap their maximum return commitment. The target cap is the trade-off for receiving above-market coupons during the rate decline.\n\nVariations:\n- TARN with leverage: coupon = max(0, 2 x (8% - SOFR)), reaching target faster\n- FX-linked TARN: coupon depends on spot FX rate vs. a strike\n- Equity TARN: cumulative equity-linked coupons with target cap\n\nExplore path-dependent interest rate products in our FRM study materials.