Parallel and Nonparallel Yield Shocks

Name the object being shocked

A curve can contain spot rates, par yields or forward rates. Adding the same number of basis points to each curve is not generally the same valuation experiment. Before discussing parallelism, identify the curve representation and compounding convention. Also distinguish a benchmark-rate shock from changing each bond's own yield to maturity. Those rate inputs can summarize different information even when they share a maturity label.

The parent tool uses a single annual nominal yield for regular fixed-coupon bullet pricing. Changing that input produces a coherent own-yield experiment. It does not, by itself, show what happens when selected points on a spot curve move independently. The explicit two-date illustration below explains that wider concept outside the parent tool's calculation scope, without claiming an implemented curve-construction or scenario engine.

Define parallel moves in absolute units

A parallel spot-rate shock means adding the same absolute rate increment at every included maturity while retaining the selected compounding basis. It does not mean multiplying each starting rate by the same percentage. Relative changes depend on starting levels and become especially confusing around zero. Basis points provide an unambiguous absolute unit once the rate definition and direction have been specified.

The Basel Committee's archived interest-rate-risk framework distinguishes parallel increases and decreases from steepeners, flatteners and short-rate shocks. That taxonomy is useful educational context, not a claim that this site implements regulatory capital calculations or current prescribed shock sizes. The invented scenarios here use their own stated magnitudes solely to expose how the timing of receipts interacts with different rate movements.

Establish a two-date spot valuation

Take a hypothetical USD 100-face, two-year bullet with a 4% annual coupon and annual payments, valued immediately after a coupon date. Its receipts are USD 4 in one year and USD 104 in two years. Assume annual compounding and baseline spot rates of 5% at both dates. There are no calls, defaults, taxes, accrued interest or transaction costs.

The baseline price is 4/1.05 + 104/(1.05)^2 = USD 98.140590. Because the baseline spot curve is flat at the two payment dates, it happens to match a single-yield valuation at 5%. That equivalence is specific to the stipulated inputs. It should not be interpreted as proof that a coupon bond's YTM is always the correct discount rate for each payment on a nonflat curve.

Compare a parallel rise with a twist

First increase both spot rates from 5% to 6%, an absolute rise of 100 basis points at each date. Price becomes 4/1.06 + 104/(1.06)^2 = USD 96.333215. Next consider a separate twist: reduce the one-year spot rate to 4% and increase the two-year spot rate to 6%. Price then becomes 4/1.04 + 104/(1.06)^2 = USD 96.405784.

Both stressed cases use the same two-year rate, but the twist produces a slightly higher value because the first coupon is discounted less heavily. The final USD 104 receipt dominates this short example, so the difference is modest. The point is structural: a terminal-maturity rate alone does not determine a coupon bond's value when earlier receipts use different spot rates.

Connect curve shape to localized sensitivity

CFA Institute describes key rate duration as sensitivity to a benchmark yield at a specified maturity. The practical motivation is visible in the example: early and late receipts respond to different rate inputs. A collection of localized sensitivities can therefore reveal exposure hidden by a single aggregate number. The bump construction must still explain what happens between the selected maturities, not just at the labeled nodes.

Equal total duration does not guarantee equal responses to a twist. One cash-flow distribution may concentrate value near the middle of a curve while another spreads value between earlier and later dates. Those structures can share a similar parallel sensitivity while differing under shape changes. No portfolio holdings or strategy recommendations are needed to understand the limitation; it follows from applying different rate changes to different payment dates.

Separate instantaneous shocks from passage of time

Every scenario above occurs at the same valuation instant. Coupon dates, cash-flow amounts and remaining maturity are unchanged. A holding-period scenario is different because time passes, payments may occur and the remaining bond moves to shorter maturities. Calling both exercises a rate shock can conceal a carry or roll-down assumption inside what appears to be a pure change in discount rates.

Credit spreads and other valuation inputs also need a declared treatment. Holding them fixed is a scenario assumption, not a forecast that they will remain fixed when benchmark rates move. Conversely, changing a bond's entire yield without decomposition does not isolate benchmark exposure. A useful scenario description lists what changes and what remains constant before presenting any resulting price or sensitivity total.

Keep the scenario conclusion proportional to the model

A full curve exercise needs enough information to discount every payment date, including a rule for dates between nodes and beyond available inputs. It also needs consistent conventions across the base and shocked curves. A visually smooth curve is not sufficient evidence that these choices were made coherently. Sparse-node illustrations should remain illustrations until their interpolation and extrapolation rules are defined and checked.

The parent regular-bond calculator cannot certify arbitrary curve twists, key-rate hedges or regulatory stress results from one YTM input. Its supported frequency and whole-year limits remain in force. The educational lesson is to match the complexity of the claim to the complexity of the valuation: a scalar scenario answers a scalar question, while a curve-shape question requires a separately specified multi-rate framework.

Primary references

1. CFA Institute: Curve-Based and Empirical Fixed-Income Risk Measures
2. Basel Committee: Interest Rate Risk in the Banking Book, archived 2019 framework