Complete capital market

Under a complete capital market (engl. Complete market ) has a special, abstract shape of a capital market understood. The capital market in general describes an economic market for raising and investing medium and long-term capital (the short-term capital market is also referred to as the money market ).

A simplified description of the complete capital market reads: Any payment stream can be traded. The complete capital market is a strongly restrictive assumption which, for example in comparison to the arbitrage-free condition , has no clear economic justification.

The assumption of a complete market makes sense because it allows agents a Pareto-optimal allocation of resources. It also allows state-of-the-art analyzes of the capital market, capital structures and many other financial aspects.

The related term, the perfect capital market , on the other hand, describes the absence of transaction costs, taxes and barriers to market entry.

The concept of the complete market first appeared in the Arrow-Debreu equilibrium model .

introduction

The concept of the state of the environment is an important basis for the definition of the complete capital market . In the simplest case, these states only differ in terms of their return . However, if the definition of the states depends on private information, this leads to problems such as adverse selection and moral hazard .

A capital market is complete if there is a security for every future point in time that pays out exactly one monetary unit at precisely this point in time. Under uncertainty this means that for every possible future environmental condition there is a security that pays out exactly one monetary unit in precisely this environmental condition. An enormous number of different securities is required for the completeness of a capital market (therefore real securities markets are not complete). In reality, therefore, continuous trading is required (whereby the securities traded on the continuous capital market must also meet certain conditions, such as minimum maturity and minimum number).

For every possible state and point in time, it should be possible to conclude a state-dependent contract at a given price ( simple security ). Or there is the possibility for investors to implicitly create these simple securities through suitable combinations of other existing securities. A market would therefore be incomplete if all possible risk-return relationships could not be realized by combining the possible financial stocks.

All conceivable time and condition-dependent payment flows can be acquired on a complete capital market.

In other words, completeness here means that agents can insure any environmental condition. So you can trade assets in such a way that the payoff in one state changes without affecting payoffs in other states.

definition

A model capital market is considered complete if there are just as many financing instruments with linearly independent payment vectors as there are future environmental conditions . For each payment vector there is a portfolio of traded securities that have a cash flow of in the state . Then completeness means: ${\ displaystyle K}$ ${\ displaystyle (D_ {1}, \ dots, D_ {M})}$ ${\ displaystyle (n_ {1}, \ dots, n_ {N})}$ ${\ displaystyle D_ {j}}$ ${\ displaystyle j \ in [1, \ dots, M]}$

${\ displaystyle {\ boldsymbol {nD \ equiv D}} \ quad \ sum n_ {j} D_ {ij} = D_ {j},}$ ${\ displaystyle j \ in [1, \ dots, M]}$ has a solution for any . ${\ displaystyle {\ boldsymbol {n}} \ in \ mathbf {R} ^ {N}}$ ${\ displaystyle D \ in \ mathbf {R} ^ {M}}$

If one considers the set of all payment vectors as a vector space , the considered capital market is complete when the number of future environmental states is equal to the dimension of the vector space, i.e. the length of each base of this vector space. Or the rank of the matrices is equal to: . ${\ displaystyle {\ boldsymbol {D}} \ equiv M}$

properties

On a complete capital market , any future payment flow can be generated as a linear combination of existing payment flows (e.g. from the basis of the payment vector - vector space of this capital market). Such a linear combination of cash flows in the form of a linear combination of financing instruments is usually called a portfolio .

In particular, there is a portfolio that generates state-contingent cash flows in the form of Arrow-Debreau securities (cf. Arrow-Debreu equilibrium model ). An AD security has a fixed payout from one unit in a specific state and no payout in all other states. The AD collateral is also called state security , pure security or state contingent claim .

If a model capital market is complete, the equilibrium allocations are Pareto-optimal. In complete capital markets, the financial market equilibrium and the general equilibrium are identical and Pareto optimal. If a model capital market is complete, it also fulfills the spanning condition .

Individual evidence

↑ Mario C. Palli: Value-oriented corporate management: conception and empirical study of the company's orientation towards the capital market . German university publisher. 2004. ISBN 978-3824407378 . P. 47.
^ Lamberton, Damien, and Bernard Lapeyre. Introduction to stochastic calculus applied to finance. CRC press, 2007. p. 8.
^ Weber, Lars, Claudia Lubk, and Annette Mayer, eds. Changing society: current economic challenges. Springer-Verlag, 2008. p. 154.
↑ Fabozzi, Frank J., ed. Handbook of Finance, Financial Markets and Instruments. Vol. 1. John Wiley & Sons, 2008. p. 107.
↑ ^a ^b Ingersoll, Jonathan E. Theory of financial decision making. Vol. 3. Rowman & Littlefield, 1987. p. 136.
↑ ^a ^b ^c Lassak, Günter. Valuation of fixed-income securities on the German bond market. Vol. 41. Springer-Verlag, 2013. p. 18.
↑ Hastenpflug, Wolfgang. The securitization phenomenon. Springer-Verlag, 2013. p. 77.
^ Breuer, Wolfgang, Thilo Schweizer, and Claudia Breuer, eds. Gabler Lexicon Corporate Finance. Springer-Verlag, 2013. p. 291
↑ ^a ^b Lengwiler, Yvan. Microfoundations of financial economics: an introduction to general equilibrium asset pricing. Princeton University Press, 2009. p. 54.
↑ Zwirner, Thomas. Exchange rate risk, company and capital market. Deutscher Universitäts-Verlag, 1989. p. 108.
↑ Pham, Hoang, ed. Springer handbook of engineering statistics. Springer Science & Business Media, 2006. p. 856
↑ Barucci, Emilio. Financial markets theory: Equilibrium, efficiency and information. Springer Science & Business Media, 2012. p. 80.

literature

Lengwiler, Yvan. Microfoundations of financial economics: an introduction to general equilibrium asset pricing. Princeton University Press, 2009. Chapter 3.4 Complete Markets
Ingersoll, Jonathan E. Theory of financial decision making. Vol. 3. Rowman & Littlefield, 1987. Chapter 8 Equilibrium Models with Complete Markets
Fabozzi, Frank J., ed. Handbook of Finance, Financial Markets and Instruments. Vol. 1. John Wiley & Sons, 2008. Chapter 9 Complete Markets

[1] Mario C. Palli: Value-oriented corporate management: conception and empirical study of the company's orientation towards the capital market . German university publisher. 2004. ISBN 978-3824407378 . P. 47.

[2] Lamberton, Damien, and Bernard Lapeyre. Introduction to stochastic calculus applied to finance. CRC press, 2007. p. 8.

[3] Weber, Lars, Claudia Lubk, and Annette Mayer, eds. Changing society: current economic challenges. Springer-Verlag, 2008. p. 154.

[4] Fabozzi, Frank J., ed. Handbook of Finance, Financial Markets and Instruments. Vol. 1. John Wiley & Sons, 2008. p. 107.

[Ingersoll-5] Ingersoll, Jonathan E. Theory of financial decision making. Vol. 3. Rowman & Littlefield, 1987. p. 136.

[Lassak-6] Lassak, Günter. Valuation of fixed-income securities on the German bond market. Vol. 41. Springer-Verlag, 2013. p. 18.

[7] Hastenpflug, Wolfgang. The securitization phenomenon. Springer-Verlag, 2013. p. 77.

[8] Breuer, Wolfgang, Thilo Schweizer, and Claudia Breuer, eds. Gabler Lexicon Corporate Finance. Springer-Verlag, 2013. p. 291

[Lengwiler-9] Lengwiler, Yvan. Microfoundations of financial economics: an introduction to general equilibrium asset pricing. Princeton University Press, 2009. p. 54.

[10] Zwirner, Thomas. Exchange rate risk, company and capital market. Deutscher Universitäts-Verlag, 1989. p. 108.

[11] Pham, Hoang, ed. Springer handbook of engineering statistics. Springer Science & Business Media, 2006. p. 856

[12] Barucci, Emilio. Financial markets theory: Equilibrium, efficiency and information. Springer Science & Business Media, 2012. p. 80.