A five-year bond after a 100-basis-point yield rise

Freeze the instrument before the scenario

The example starts with $1,000 face value, a 4% annual coupon, five whole years remaining and semiannual payments. The nominal annual yield is 5%, compounded twice each year. Valuation occurs on a coupon date after any payment due that day, so the next payment is a full half-year away. There is no accrued interest in this constructed setup. Neither the starting yield nor the shock is an observed market quote.

The issuer is assumed to pay every scheduled amount, and there is no call provision, principal amortization, indexation or embedded option. These choices are material. They make the cash flows invariant when yield changes, allowing the example to isolate discounting. Changing the instrument assumptions would require a different cash-flow model, not merely a new label on this result.

Rebuild the price from ten payments

Each coupon is $1,000 multiplied by 4%, divided by two, or $20. Nine periods contain only that coupon. Period ten contains $20 plus the $1,000 principal. Discount each amount using a 2.5% half-year rate. The sum is $956.2396803451, displayed as $956.24. The undiscounted payments total $1,200, which is not the price because those payments occur at different future times.

An independent reconstruction should retain full precision until the final display. Rounding each present value to cents and then adding can produce a small difference from rounding the final sum. The downloadable reference preserves the unrounded schedule so that a reviewer can distinguish display rounding from a disagreement about discount factors.

Apply the shock without advancing the clock

A rise of 100 basis points means adding one percentage point to the annual yield: 5% becomes 6%. The period yield becomes 3%. No coupon is earned during the scenario and no maturity date moves closer. Discounting the original ten payments at the new rate produces $914.6979716322. Subtracting the initial value gives a change of -$41.5417087129.

Divide that dollar change by the original $956.2396803451 value, not by face value, to obtain -4.3442778591%. Dividing by $1,000 would instead express the change as a fraction of par. Both ratios can be computed, but they answer different questions and should not share an unlabeled percentage column.

Compare the local approximations

The baseline modified duration is 4.4580563244 years. Multiplying its negative by a 0.01 annual yield change gives -4.4580563244%. Convexity is 23.1944099076 years squared; the second-order term adds roughly 0.1160 percentage points. Together they estimate -4.3420842748%, slightly less negative than exact repricing.

The reported approximation error is approximation minus exact, here +0.0021935843 percentage points. It is not a relative error percentage and not an extra return. A small error in this particular example does not establish accuracy for much larger shocks or for cash flows that respond to rates. Retaining both estimates makes their different boundaries visible.

Interpret DV01 at the actual position size

The initial DV01 magnitude is about $0.426297 per basis point. It is obtained from price multiplied by modified duration and 0.0001. For a small upward move, the first-order price effect is negative. The worksheet displays the magnitude as positive so that the user must apply the direction of the scenario explicitly rather than confuse a risk measure with a profit.

Multiplying face value by ten multiplies price, scheduled payments, DV01 and dollar scenario change by ten. It leaves normalized duration, convexity and the percentage price change unchanged. This scaling check is useful when reconciling a quote per 100 with a position measured in actual currency units.

Retain the boundary of the conclusion

The case demonstrates a regular bond calculation, not a forecast that yields will rise and not a proposal to buy or hedge a bond. A transaction would introduce an executable price, settlement convention, fees and potentially different accrued interest. A longer holding period would introduce coupon receipts and reinvestment choices. Those inputs are outside the immediate-shock calculation.

To reproduce the result, use the default bond inputs, retain the scenario JSON and compare the payment schedule against the independent reference. Record the compounding frequency together with the nominal yield. A later analyst should be able to recreate the number without guessing whether 5% meant an annual effective rate or a nominal semiannual quotation.

Primary references

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