Risk-premium relief

A positive control for the adverse scenarios

The purpose of this preset is directional comparison. Positive-beta equity should rise with the assumed equity market; positive-duration bonds should benefit from lower yields; positive spread duration should benefit from tighter spreads. The resulting gain checks how the chosen exposures behave when several assumed pressures ease together.

These are hypothetical conditions, not observations of a recovery or a forecast of policy easing. The preset has no assigned probability and is not the exact sign reversal of another scenario. Its favorable result cannot be averaged with adverse results to claim an expected return without a separately justified probability model.

Convexity makes equal rate shocks asymmetric

For the reference Treasury sleeve, a 75 basis point rate decline gives 5.25% through duration plus 0.16875 percentage points through convexity, totaling 5.41875%. A separate, rate-only 75 basis point rise would instead produce a 5.08125% loss. Both calculations keep duration seven and convexity 60 unchanged.

The squared rate term explains that asymmetry: it remains positive when the shock changes sign. FINRA's duration discussion notes that bond responses need not be symmetric and that redemption features matter [1]. This engine's fixed, nonnegative convexity is an approximation, not full repricing of those features.

A favorable bond mark can overstate an option-bearing gain

The SEC identifies call risk when an issuer retires debt early, potentially following a rate decline [2]. The calculator does not exercise calls, accelerate mortgage repayments or shorten duration during a rally. A callable or prepayable holding should not inherit the example's upside merely because it is labelled a bond.

Spread tightening adds a separate linear benefit, with no spread convexity or interaction with rates. Starting yield and spread levels are absent, so the engine cannot check whether the assumed decreases imply sensible ending levels. Those checks require instrument data beyond the change inputs, even when every input passes validation.

Currency appreciation compounds the upside

For an illustrative EUR equity holding at beta one, a 15% local gain and 5% currency appreciation combine into a 20.75% USD gain. Multiplying 1.15 by 1.05 preserves the interaction. The default USD holdings do not receive that additional benefit, regardless of the foreign-currency assumptions shown above.

This arithmetic tests translation direction, not the success of a currency hedge. The engine has no hedge contracts, foreign revenue model or changing equity beta. Likewise, USD cash remains unchanged because income is excluded; its zero contribution is not evidence that an actual cash account would earn nothing over time.

Do not confuse a comparison with a recovery path

A 15% gain does not undo a preceding 30% loss: 0.70 times 1.15 leaves 80.5% of the original value. More importantly, the preset comparison starts each scenario from the same holdings. It does not apply relief to the ending positions of an adverse scenario or simulate rebalancing between them.

Use the favorable case to question signs, units and unusually large sensitivity-driven gains, then compare nonlinear holdings with independent repricing. Keep capital gains separate from coupon income, refinancing effects and realizable sale proceeds. A reassuring positive total cannot validate the adverse scenarios, establish liquidity or measure the likelihood of recovery.

Review checkpoints

• Use relief as a directional comparison, not an expected-return estimate or exact inverse scenario.
• Positive convexity creates unequal results for equal upward and downward rate changes.
• Check calls, starting yield levels and sequential-return arithmetic outside the fixed-sensitivity result.

Source notes

1. FINRA: Duration - What an Interest Rate Hike Could Do to Your Bond Portfolio (official syndication)
2. SEC Investor.gov: Bonds - FAQs, call risk

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