TIPS vs Nominal Bond Calculator

What Break-Even Inflation Measures

Break-even inflation is the rate at which an inflation-linked bond and a conventional bond of the same maturity end at the same nominal value. It comes from the two yields alone: one plus the nominal yield, divided by one plus the real yield, minus one. At a 4.5% nominal yield against a 2% real yield that works out at 2.45098%. Realised inflation above that leaves the linker ahead; below it, the conventional bond ends ahead. Markets quote a simpler version, the plain difference between the two yields, which comes to 2.5% here and sits about 0.05 percentage points above the exact crossover. The gap between the two versions is the yield difference multiplied by the real yield and divided by one plus the real yield, so two signs govern the ordering. The simple quote sits above the exact crossover when the real yield and the yield difference share a sign, matches it when either is zero, and sits below when they differ. Both are positive at the sample figures, which is why the simple quote is the higher one there; at a 2% real yield against a 1% nominal yield the ordering reverses, with the exact crossover at -0.98% and the simple quote at -1.00%.

The break-even rate depends on nothing else. The amount and the holding period scale the gap between the two bonds, but neither can move the point where that gap changes sign.

How the Two Bonds Are Compared

The inflation-linked side grows at its real yield and then again at the inflation rate, so a 2% real yield with 3% inflation compounds at 5.06% a year rather than 5%. The two rates multiply rather than add, which is the Fisher relation. The conventional side compounds at its stated yield. Both are carried to the end of the period, and the difference between the two final values is the headline figure.

Inflation-linked government bonds are issued by a number of sovereign borrowers under different names. The arithmetic here applies to any of them, provided the yield entered on the linked side is a real yield rather than a nominal one.

Worked Example

The sample figures used on this page are 100,000 over ten years, a 2% real yield on the linker, 4.5% on the conventional bond, and 3% inflation. The linker compounds at 5.06% and reaches 163,822.66. The conventional bond compounds at 4.5% and reaches 155,296.94. The linker ends ahead by 8,525.71, which is 8.53% of the amount entered.

Realised inflation of 3% sits above the 2.45098% break-even, so the linker's inflation uplift more than covers the 2.5 percentage points of starting yield it gave up. Entering 2% inflation instead reverses the outcome and the conventional bond ends ahead by 6.70% of the amount.

Which Inputs Move the Result

The amount is a pure scaling factor: doubling it doubles the gap and changes nothing about which side ends ahead, so the comparison reads identically in every currency. The other three move the gap by different amounts. At the sample figures, a percentage point added to the real yield widens the linker's lead by 16.79% of the amount, and a point added to inflation widens it by 16.62%. A point on the conventional yield moves the gap the other way, by 15.52% of the amount. Lengthening the holding period amplifies all three at those figures, since each is compounded over the full term. The two linked-bond sensitivities depend on how that bond itself grows, so deep enough deflation changes their shape: at a -2% real yield with -5% inflation both peak around fifteen years and fall away across the rest of a thirty-year term. Whether a peak lands inside a given term depends on the exact pair entered, and at a -2% real yield with 0% inflation none appears within thirty years. The conventional-yield sensitivity depends on that yield alone, so it keeps rising with the term at any positive yield, including at those same deflationary settings.

Why the Real Yield and Inflation Are Interchangeable Here

The linker's growth is the product of one plus the real yield and one plus inflation, and multiplication does not care which is which. A 2% real yield with 3% inflation produces exactly the same final value as a 3% real yield with 2% inflation, 163,822.66 in both cases. The two are not quite equal as levers, though. A percentage point added to the real yield raises the annual product by that point multiplied by one plus inflation, while the same point added to inflation raises it by that point multiplied by one plus the real yield, so the two changes differ by that point multiplied by the gap between the rates. Compounding then carries that difference across the whole period, which means the levers separate with both the spread between the rates and the length of the term. At a 2% real yield against 20% inflation over the same ten years they finish about 71 times further apart than at the sample figures. The wider spread accounts for a factor of 18, and compounding across the ten years for the remaining factor of roughly 3.9.

This is a property of the arithmetic rather than of the instruments. The real yield is fixed at the point of purchase, while inflation is the outcome being guessed at, so the two carry very different degrees of certainty. The model cannot separate them: a result driven mostly by an optimistic inflation figure looks identical to one driven by a genuinely high real yield.

What the Model Does Not Capture

The comparison assumes both bonds are held to maturity, that coupons are reinvested at the same yield, and that inflation runs at the entered rate for the whole period. Real inflation varies year to year, and the path matters to the linker's principal even when the average does not change. Selling before maturity introduces price risk that this model does not represent at all.

Nothing here is net of tax or costs. Inflation-linked bonds are taxed differently from conventional ones in many jurisdictions, in some cases on principal adjustments that produce no cash until maturity, so an after-tax gap can differ substantially from the figure shown. Dealing costs, bid-ask spreads and fund charges are excluded.

One omission is worth naming specifically. Many inflation-linked government bonds repay at least their original face value at maturity even if the price index has fallen over the term. This model applies no such floor. The linked bond finishes below the amount originally put in whenever one plus the real yield multiplied by one plus inflation falls under one, which at a 2% real yield means inflation below -1.96%. That threshold moves with the real yield: at a real yield of -2% it rises to +2.04%, so a bond bought on a negative real yield can return less than capital even under mild positive inflation. Read that region as the arithmetic of the formula rather than the behaviour of an actual bond.