The usual notion of every future cash stream having a net present value determined from a single term structure breaks down when transaction costs are taken into account, especially the sizable costs associated with short-borrowing. the difficulties are compounded by taxes, which can lead to paradoxes of disequilibrium if elementary NPV is assumed to be a rational basis for decision making. This paper systematically develops a theory of valuation which overcomes these shortcomings by accepting the multiplicity of no-arbitrage term structures that may be present for each tax class of investors, and uses the entire set of them to impute both a "long price" and a "short price" for every cash stream, regardless of the sign of the future payments. the valuation operators giving these prices are nonlinear but readily calculated from linear programming formulas. Copyright 1991 Blackwell Publishers.
The value of a future cash stream is often taken to be its net present value with respect to some term structure. This means that a linear formula is used in which each future payment is discounted by a factor deemed appropriate for the date on which the payment will be made. In a money market with taxes and shorting costs, however, there is no theoretical support for the existence of a universal term structure for this purpose. What is worse, reliance on linear formulas can be seriously inaccurate relative to true worth and can lead to paradoxes of disequilibrium. A consistent no-arbitrage theory of valuation in such a market requires instead that taxed and untaxed investors be grouped in separate classes with different valuation operators. Such operators are linear to scale but nonlinear with respect to addition. Here it is established that although these valuation operators provide general bounds applicable across an entire class, individual investors within a tax class can have more special operators because of the influence of existing holdings. These customized valuation operators have the feature of not even being linear to scale. In consequence of this nonlinearity, investors from the same or different tax classes can undertake advantageous trades even when the market is in a no-arbitrage state, but such trade opportunities are limited. Some degree of activity in financial markets can thereby be understood without appeal to differences in utility functions or temporary disequilibrium due to random disturbances. Copyright 1995 Blackwell Publishers.
The authors investigate term structure with realistic transactions costs and taxes. Its properties are derived from a certain no‐arbitrage condition via duality theory in convex programming. Transactions costs imply an infinite multiplicity of term structures. A simple example with realistic transactions costs shows that this multiplicity can induce a valuation range of over 277 basis points. Transactions costs also allow equilibrium without short sale restrictions. The authors find the minimum transactions costs that prevent arbitrage. In addition, the exact conditions for weak clientele, in which investors will not buy some bonds and may not sell any that they already hold, are established.
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