CFAI Book 3 pg. 299

In the paragraph about accrued benefits, it states that People has no inflation indexing for their benefits but the benchmark will consist of nominal bonds. Wouldn’t it only need the real interest rate to hedge the benefits since inflation adjustments are not included in the liabilities?

After reading further, my actual question is…what is the difference between a “real bond” and a “nominal bond”? Assuming: nominal interest rate=real interest rate + inflation; this entire section seems to be worded backwards to me. Wouldn’t a “real bond” be needed to hedge the pension liability of a company who does not inflation adjust payments to retirees? What am I missing here?