Simple and enlarged separation portfolios: On their use when arbitraging and synthesizing securities

This paper seeks to provide a framework for separation portfolios when they are used not only as synthetics of a matching security but also as building blocks of arbitrage portfolios, in a background provided by the CAPM world. Firstly, synthetics are defined by means of a vectorial framework that maps portfolios onto their risk-return profiles. Separation portfolios are extensively analyzed afterwards, establishing three propositions that lay the groundwork for using them as synthetics. Next, a distinction is brought about between plain separation portfolios (which are located on the Capital Market Line) and enlarged separation portfolios (which lie outside the CML). Furthermore, it is shown that simple separation portfolios become synthetics in few cases only, whereas enlarged portfolios allow for synthetics in much wider contexts. Later, arbitrage portfolios are designed by means of simple separation portfolios in the context of the Security Market Line, and also by resorting to the enlarged ones without requiring the SML as a benchmark. Finally, the discussion extends over bond portfolios, to embody their risky features into the viewpoint set forth in the paper.