In principle, the set of attainable payoff vectors is reduced if assets cannot be sold short. However, the authors show that the original space of payoff vectors is spanned despite short sale restrictions if there is one additional asset whose payoff is a positively weighted sum of the payoffs of the original assets. For example, this condition is automatically fulfilled if the original assets are stocks and the additional asset is an index future consisting of these stocks.

ABSTRACT In principle, the set of attainable payoff vectors is reduced if assets cannot be sold short. However, we show that the original space of payoff vectors is spanned despite short sale restrictions if there is one additional asset whose payoff is a positively weighted sum of the payoffs of the original assets. For example, this condition is automatically fulfilled if the original assets are stocks and the additional asset is an index future consisting of these stocks.