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Little attention has been given to the behavior of option portfolio risk across different portfolio sizes, perhaps because many individuals view unhedged long option positions as too risky for rational investor consideration. It appears possible, however, to combine long option positions with less risky assets to produce portfolios with favorable risk-return characteristics [10].

Recently in this Review, John Pencavel and P. J. Lloyd have given insights into the measurement of real wages. Their work is an application of the concepts of true cost of living indices to a joint labor supply and commodity demand decision. Pencavel (1977) and Lloyd (1979) offer several forms of real wage indices which are derived from explicit functional forms for utility. This paper examines the theory of real wage indices in a more general setting and derives bounding indices which are independent of the functional form for utility.