  The paper investigates quadratic hedging in a semimartingale market that does
not necessarily contain a risk-free asset. An equivalence result for hedging
with and without numeraire change is established (Proposition 3.16). This
permits direct computation of the optimal strategy without choosing a reference
asset and/or performing a numeraire change (Theorem 4.1). New explicit
expressions for optimal strategies are obtained, featuring the use of oblique
projections that provide unified treatment of the case with and without a
risk-free asset (Theorem 4.3). The analysis yields a streamlined computation of
the efficient frontier for the pure investment problem in terms of three easily
interpreted processes (Equation~1.1). The main result advances our
understanding of the efficient frontier formation in the most general case
where a risk-free asset may not be present. Several illustrations of the
numeraire-invariant approach are given.
