  We consider a reference security, understood to be an attractive investment,
with the caveat that an investor is not willing to directly invest in the
security, for presence of constraints, either investor specific or pertaining
to the security itself. The investor, however, is open to a portfolio
constructed with an accepted set of securities, where returns could be
considered similar to the reference security. We demonstrate, under a measure
of similarity, such a portfolio could be selected with a mean-variance
characterization, as defined by Markowitz. Furthermore, we consider the
performance relative to the reference security, with the Sharpe Ratio. The
objective of the paper is to derive an optimal portfolio to address an investor
preference for the accepted set of securities.
