A three-rung ladder: payments, present value and scenario loss

Define the three rungs

Each rung has $10,000 face value and uses semiannual coupon payments. The two-year rung has a 3% coupon and a 4% yield. The five-year rung has a 4% coupon and a 4.5% yield. The ten-year rung has a 5% coupon and a 5% yield. All three are valued on a regular coupon date, with no accrued interest or issuer-specific features.

These yields are chosen assumptions, not points downloaded from a market curve. Each rung discounts all its payments at its own flat yield. The worksheet does not bootstrap zero rates from the three inputs or interpolate rates between their maturity dates. Calling the inputs a curve would overstate the calculation that has actually been performed.

Reconcile principal and coupons

The annual coupon amounts are $300, $400 and $500. Over their respective remaining terms, they produce $600, $2,000 and $5,000 in coupons, or $7,600 altogether. Principal repayments sum to $30,000. Adding them gives $37,600 of scheduled receipts across the entire ten-year horizon, assuming all payments occur.

Year one receives $1,200 in coupons and no principal. Year two receives the same coupons plus $10,000 principal, totaling $11,200. Years three and four receive $900 each. Year five receives $900 plus the next $10,000 redemption, totaling $10,900. Years six through nine receive $500 annually, and year ten receives $10,500.

Do not confuse receipts with accumulated wealth

The schedule stops counting a rung's coupon after that rung matures. It does not automatically buy another security with the returned principal. Nor does it compound a coupon receipt until year ten. This makes the payment schedule an explicit account of contractual timing rather than an implicit reinvestment strategy.

A report that wanted ending wealth would need a policy for every intervening receipt: whether it is spent, held as cash or reinvested, at what rate, with which fees and under what risk. Without those choices, subtracting the initial price from $37,600 and annualizing the difference would not be a valid single portfolio return calculation.

Value each rung before aggregating

The two-year rung is worth $9,809.6135650663, the five-year rung $9,778.3445912783 and the ten-year rung $10,000 under its par-bond assumptions. Their sum is $29,587.9581563446. The face-value total is a different quantity, reflecting promised principal rather than the present value of every future payment.

The rung DV01 magnitudes are approximately $1.880764, $4.375482 and $7.794581 per basis point. Together they are $14.050827 per basis point for a small common upward yield move. Dividing aggregate DV01 by aggregate price and 0.0001 gives a value-weighted modified duration of 4.748833 years. Equal face amounts do not imply equal sensitivity weights.

Apply maturity-specific shocks exactly

The reference scenario increases the two-year rung's yield by 100 bp, the five-year rung's yield by 75 bp and the ten-year rung's yield by 50 bp. Repriced values are $9,623.8025791990, $9,456.5123352609 and $9,619.3186966556. Their sum is $28,699.6336111155, a change of -$888.3245452290 or -3.0023178367%.

Because those shocks differ, multiplying aggregate duration by a single arbitrarily selected yield change would not reproduce the scenario. Repricing each rung and adding the resulting dollar changes preserves the intended assumptions. It also exposes which rung contributes to the modeled loss, instead of hiding that information behind a portfolio average.

Separate a ladder from a liability match

Suppose a future obligation occurs during year three. This schedule provides $900 that year, but the worksheet has no liability input and does not know the required amount or exact date. The year-two principal might be available if retained, or it might have been spent. A genuine funding comparison must record that cash-management policy explicitly.

Annual totals also hide within-year timing. Semiannual payments do not arrive all at the start of the year. A liability due before the first coupon cannot necessarily be funded by that year's displayed coupon total. Currency, tax treatment, default exposure and liquidity constraints would add further questions that this educational ladder intentionally leaves separate.

Preserve the inputs and inspect the export

Download the default input CSV and select semiannual frequency to reproduce the example. The input file deliberately excludes frequency; the selected convention remains visible and does not change on import. The scenario JSON includes that frequency, the calculation version, all rung results and the annual schedule. Retain both when comparing a modified ladder with this reference.

Primary references

1. TreasuryDirect: Treasury notes
2. Financial library: net present value convention
3. FINRA: Bonds, interest-rate changes and duration