Term Structure Multiplicity and Clientele in Markets with Transactions Costs and Taxes

Abstract

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.

Cash Stream Valuation In the Face of Transaction Costs and Taxes

“…It is more restrictive also than the following. Strong no-arbitrage conditions have been developed and explained in many places (e.g., Garman (1978) and Dermody and Prisman (1988)). The version stated here is slightly different in that it incorporates holdovers h as well as taxes.…”

“…Utility models likewise fail to provide a unique term structured when transaction costs are present, so the difficulty cannot be thought of as arising because arbitrage models are rougher than utility models. Transaction costs in a no-arbitrage model imply the existence of not just one equilibrium term structure d but an infinite set of them for each tax class of investors, as shown by Dermody and Prisman (1988). This indeterminacy has nothing to do with error; it is inherent in the market.…”

“…We take the multiplicity of term structure as the starting point and, going farther than Dermody and Prisman (1988), use it to develop a consistent and rigorous approach t o the valuation of general cash streams in the context of readily available financial data. We introduce, for each cash stream w and tax class in class k can acquire w from a combination of transactions in the present market (i.e., take a "long position" in w).…”

“…The empirical results presented byRonn (1987) presumably refer to equilibrium cases. Although mathematically the term structure estimate d could therefore be any element of his set 3, his computer program comes up with a particular one.This framework for clientele has been sketched in part byDermody and Prisman (1988), who cited it from our working papersDermody and Rockafellar (1987a,b).…”