The Efficient Frontier with No Short Sales

Most institutional investors do not sell short. Indeed, many institutions are forbidden by law - in the UK and the US - from short sales, and others operate under self- imposed constraints forbidding short sales. However, the incorporation of short sales3

extends the efficient frontier. As figure 3.5 on the following page illustrates, the efficient set still begins with the minimum-variance portfolio. However, when short sales are allowed it has no finite upper bound.4

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3In this section we employ a simplified description of short sales. This reflects the general description of short sales in the literature, and assumes that there are no special transaction costs involved in the process. In the case of actual short sales, however, a broker will require a margin in addition to the retention of proceeds from the short sale. Since, in most cases, the amount of funds that must be put up is significant - upon which the broker pays no return - the above description of short sales overstates the return from them.

4Merton [1972] has shown that the efficient set is the upper half of a hyperbola.