Comparative Statics and Asset Substitutability/Complementarity in a Portfolio Model: A Dual Approach

Asset Demands and Slutsky Equations When All Assets Are Risky

“…The basic model is a cross between that used by Royama and Hamada (1967), and by Sandmo (1977) and Dalal (1983). In common with these papers, the units in which assets are denominated are ((one dollar's (l) While Fischer (1972) obtains an otherwise complete set of Slutsky equations, the Slutsky equation for a change in risk is obtained only in the presence of a riskless asset.…”

“…Yet, two of the more complete analyses of Slutsky equations for assets (Sandmo (1977), Dalal (1983) )base their results on models which include a riskless asset (l). Others lack generality in that the analyses are based explicitly on a quadratic utility function (Royama and Hamada (1967)), or on the assumption that utility depends only on the mean and variance of net worth (Bierwag and Grove (1968)) (2).…”

“…The methodology used throughout is that of duality theory. The usefulness and economy of this approach has been well documented for problems under certainty (see, for example, Diewert (1982)), and has been demonstrated for problems involving uncertainty by Pope (1980) and Dalal (1983). Attention is focused on the indirect expected utility function, and a property of this function (not hitherto found in the literature) is established, which is extremely useful for determining the signs of the substitution terms.…”

Portfolio selection and duality under mean variance preferences

“…Sandmo (1977) and Dalal (1983) formulated primal and dual problems, applied duality and used Roy's identity and Shephard's lemma when deriving the Slutsky equation. The dual problem in Sandmo (1977) and Dalal (1983) consists of minimizing initial wealth 2 that is disposable for investments in different assets subject to the constraint that the investor attains a certain level of expected utility. While the primal and dual problems are analogous * Tel.…”

“…the variance. While under certainty changes of income parallely shift the budget line, in a mean variance diagram increases in the initial income shift the portfolio frontier to the top and to the right which makes it difficult to give the income effect of Sandmo (1977) and Dalal (1983) an economic interpretation.…”