Inflation Risk Factor Exposure: Asset Allocation

Reading 5: Asset Allocation pg. 254

In reference to isolating the inflation risk factor, the reading says “Going long nominal Treasuries and short inflation-linked bonds isolates the inflation component”

This is counterintuitive to me given that you would go long TIPS as a long-term hedge against inflation.

If you were long TSY’s and Short TIPS, and for example nominal rates go up 5%, and 1% of that is inflation. Isn’t your return 4%? Isn’t that just isolating real rates, and not inflation?

What am I missing?

Inflation linked bonds offer the real interest rate. If nominal rate is 5%, the TIPS rate is 4%, then the breakeven inflation rate is 1%. The real interest rate is isolated and the risk factor—inflation is achieved.