Complete and incomplete markets with short-sale constraints

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract This paper argues that the introduction of a short-sale constraint in the ArrowRadner framework invalidates standard definitions of complete and incomplete markets. In this constrained set-up, two threshold values with familiar properties arise. The case of a zero short-sale bound set on some security fulfills the standard definition of "incomplete" financial markets. Beyond a particular level of the short-sale bound financial markets are "complete", since the short-sale constraint is not active. For intermediate bounds the distinction between complete and incomplete financial markets is blurred. Although some technical definitions hold, agents can not fully transfer wealth among states. These intermediate cases, called "technically incomplete markets", exhibit interesting welfare properties. For instance, the resulting equilibrium allocations may not be Pareto dominated by those of the non-restricted complete markets equilibrium. Terms of use: Documents in

On the positive fundamental value of money with short-sale constraints

“…At each period, the state price system above defined is unique (up to an arbitrary normalization a(s 0 )) if, and only if, for every node s t the number of independent securities with no limits on short-sales is equal to the number of immediate successors of s t . We can then say that financial markets are complete at node s t ; otherwise, financial markets are (technically) incomplete (see Giménez 2003). In the example studied here markets are (technically) incomplete because agents cannot smooth consumption further by transferring all the wealth they want from "bad" nodes to future "good" ones.…”

On borrowing limits and welfare

“…The endowments of the consumption good in each period can be either "high" or "low", with 0 < e l t < e h t for t = 1, 2, and we let π t ∈ (0, 1) be the probability of receiving the high endowment in period characterized by a larger amount of capital than in the first best (Huggett 1993, Aiyagari 1994). Nevertheless, Hart (1975), Grossman (1977), and more recently Gimenez (2003), can be seen as examples of the fact that alleviating a constraint in incomplete market economies does not necessarily result in larger welfare.…”

Discount Rates in Emerging Capital Markets

“…An incomplete market arises once one relaxes one of the conditions needed to have a complete market. The following conditions must be met in order to have a complete market (Giménez 2001, Duffie 1996, and Mas-Collel et al 1995:…”

“…As Giménez (2001) has pointed out, whenever investors cannot trade freely with financial assets, the capital market will be technically incomplete. Assuming that this situation affects all investors in the market, there will be shadow prices for the financial assets, so they will not longer have a unique price.…”