Irr and equivalence of cash-flow streams, loans, and portfolios of bonds

We show, through a Linear Algebra approach, that a general deterministic cash-flow stream admits a given Internal Rate of Return ( irr , either constant or time-varying) if, and only if, it can be replicated by a suitable portfolio of bonds, each with yield to maturity equal to that same irr . Five particular replicating portfolios are examined, including and generalizing other representations known from the the literature, which allow for a unified, irr -based, interpretation of apparently diverse objects. Considering the amortization of a loan as a particular case, further equivalences are found and lead to some original consideration.