Case 092Global macro tradesCore

Calderra's 10-year nominal bond yields 7.0% and its inflation-linked bond 2.5%. You expect inflation to average 5%. What is breakeven inflation, what trade expresses your view, and what do you make if inflation averages 5.5%?

The situation

The Republic of Calderra issues a 10-year nominal government bond yielding 7.0% and a 10-year inflation-linked bond, whose principal rises with the consumer price index, yielding 2.5% real. Both are liquid enough to trade in size, and the linker can be financed through repo.

Your macro team expects inflation to average 5% over the decade, because wage settlements are running hot and the central bank has been slow to react. Assume no default risk and ignore indexation lags for the first pass.

Your task

What inflation is the market pricing, what trade expresses your view, and what does it earn if inflation averages 5.5%?

Quick check

Roughly what average inflation makes the two bonds return the same?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Breakeven inflation is about 4.4%, so a 5% view says the market is under-pricing inflation, and the trade is long the linker, short the nominal bond. The trade earns roughly the gap between realised inflation and breakeven. If inflation averages 5.5%, it earns about 1.14% a year on the notional, around Rs 22 crore per Rs 100 crore over ten years if held to maturity.

Step 1What inflation is the market pricing?

Think of two rent agreements for the same flat. One fixes rent rising 7% a year; the other rises 2.5% plus whatever inflation turns out to be. A landlord indifferent between them is betting inflation will average about 4.5%. That indifference point is breakeven inflationThe average inflation rate at which a nominal bond and an inflation-linked bond of the same maturity give the same return.: 7.0% against 2.5%, about 4.5% by subtraction and 4.39% exactly, since 1.07 over 1.025 is 1.0439. Your 5% is above it, so your view is that inflation will beat what the market is paying for.

The relationship

1 + y_{nom} = (1 + y_{real})(1 + \pi^{BE}) \quad\Rightarrow\quad \pi^{BE} = \frac{1.070}{1.025} - 1 = 4.39\%

y nom	nominal 10-year yield, 7.0%
y real	real yield on the inflation-linked bond, 2.5%
pi BE	breakeven inflation priced by the market

What it says in wordsThe nominal yield equals the real yield compounded with the inflation the market expects; solve for that inflation.

Breakeven inflation of 4.39% divides the line: if inflation averages above it the linker beats the nominal bond, so a 5.0% forecast favours the linker and 5.5% earns about 1.14% a year.

Step 2What trade isolates the inflation view?

Buy the linker and short an equal duration of the nominal bond. Owning the linker alone is also a bet on real rates; shorting the nominal cancels most of the rate exposure and leaves only the inflation gap. The position then earns, each year, roughly realised inflation minus breakeven. At 5.5% that is 1.025 x 1.055 less 1.07, about 1.14% of the notional a year; at your 5.0% base case, about 0.62%. Held to maturity on Rs 100 crore a side, the 5.5% outcome is worth about Rs 21.9 crore.

Average inflation	Yearly gain on notional	Rs crore a year per Rs 100 crore
3.5%	-0.91%	-0.91
4.4%	+0.00%	+0.00
5.0%	+0.62%	+0.62
5.5%	+1.14%	+1.14
6.0%	+1.65%	+1.65

Held to maturity, the long linker, short nominal trade loses about 0.91% a year if inflation averages 3.5%, breaks even at 4.39% and earns about 1.14% a year at 5.5%.

Step 3Do you have to wait ten years to be paid?

No. If data confirm your view, breakeven itself rises, and the trade is marked up. With about 7.5 years of duration on each side, a rise in breakeven from 4.4% to 5.0% is worth roughly 4.5% of the notional at once. In the meantime the linker's principal accrues each month's inflation, so if prints run hot the position also carries positively. That is how a macro fund usually runs it: as a position on breakeven moving, with the ten-year arithmetic as the fallback.

Step 4What makes breakeven a biased forecast?

Two premia pull in opposite directions. Nominal bond holders demand extra yield for bearing inflation risk, which pushes breakeven above expected inflation. Linkers are usually less liquid, so their real yield is pushed up and breakeven down. A breakeven of 4.4% is therefore market-expected inflation plus one premium less another, and your 5% view has to beat that, not a clean forecast. Add the practical risks: indexation lags, the cost of financing the linker, and a recession that pulls inflation down fast just as you are sitting on the trade.

Where candidates lose it

The common miss is buying the linker outright to express an inflation view. That position loses if real yields rise, even when inflation comes in hot; the short nominal leg is what makes it an inflation trade.

The second is treating breakeven as the market's clean forecast of inflation. It is a price with premia inside it, and saying so is part of a good answer.

What the interviewer asks next

Inflation averages 5.5% but real yields rise 1 point in year one. What happens to the hedged and the unhedged versions?
How would you size the nominal short to match the linker's duration?
What would make you close the trade before maturity?

Company names and figures are illustrative.