What Are Complete Markets?
Complete markets are a theoretical construct in financial economics where every possible future state of the world can be hedged against or invested in using available financial instruments. In such a market, participants can perfectly reallocate risk across different future economic outcomes. This means that for any imaginable future event, there exists a security or a combination of securities that precisely delivers a payoff in that specific state of the world and zero payoff in all other states. The concept of complete markets is central to advanced asset pricing theory and general equilibrium models.
History and Origin
The concept of complete markets is deeply rooted in the foundational work of economists Kenneth Arrow and Gérard Debreu. In their seminal 1954 papers, they introduced the idea of "Arrow-Debreu securities," which are hypothetical contingent claims that pay out one unit of a numeraire good if a specific state of the world occurs and nothing otherwise. Their work provided a rigorous mathematical framework for proving the existence of a general equilibrium in an economy where such securities exist for every possible future contingency. This theoretical breakthrough, which established the conditions under which markets could efficiently allocate resources and risk across time and states of nature, laid a significant cornerstone for modern financial economics.
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Key Takeaways
- Complete markets are an idealized economic scenario where all future risks can be perfectly hedged or speculated upon.
- The theoretical foundation for complete markets was established by Kenneth Arrow and Gérard Debreu, leading to the concept of Arrow-Debreu securities.
- In a complete market, there is no uninsurable risk, allowing for optimal risk sharing among market participants.
- The absence of arbitrage opportunities is a key characteristic, as any mispricing would be immediately exploited.
- Real-world markets are generally considered incomplete due to various frictions and complexities.
Interpreting the Complete Markets
In a complete market, every investor can construct a portfolio that perfectly matches their desired consumption pattern across all possible future states of the world, regardless of their initial endowments. This implies that individuals can fully separate their portfolio optimization decisions from their consumption-savings decisions. The price of any asset in a complete market can be determined by taking the present value of its state-contingent payoffs, discounted by the prices of the fundamental Arrow-Debreu securities. This theoretical framework provides a powerful benchmark for understanding how financial markets should function under ideal conditions, where prices reflect all available information and effectively allocate risk.
Hypothetical Example
Imagine a simplified economy where, a year from now, only two states of the world are possible: "Good Economy" (GE) or "Bad Economy" (BE). In a complete market, there would exist two fundamental securities:
- GE Security: Pays $1 if the economy is "Good" and $0 if it's "Bad."
- BE Security: Pays $1 if the economy is "Bad" and $0 if it's "Good."
Suppose an investor wants to ensure they have $100 regardless of the economic state next year. In a complete market, they could simply buy 100 units of the GE Security and 100 units of the BE Security. The cost today would be (100 \times \text{Price(GE Security)} + 100 \times \text{Price(BE Security)}). This ability to create a perfectly tailored payoff for any future contingency, even for complex outcomes, is the essence of a complete market. This setup allows for precise hedging against specific economic uncertainties.
Practical Applications
While perfectly complete markets do not exist in the real world, the theory of complete markets provides a valuable framework for understanding financial phenomena and the role of various financial instruments. The development of sophisticated derivatives markets, including options, futures contracts, and swaps, moves real-world financial systems closer to the ideal of completeness. These instruments allow market participants to unbundle and transfer specific types of risk. For instance, a farmer can use futures to lock in a price for a future harvest, effectively hedging against price volatility. Similarly, companies can use interest rate swaps to manage exposure to fluctuating interest rates. By facilitating risk transfer, t2hese markets enhance overall market efficiency and enable better capital allocation by allowing participants to manage their exposures more precisely.
Limitations and Criticisms
Despite its theoretical elegance and utility as a benchmark, the concept of complete markets faces significant limitations when applied to real-world economies. The most prominent criticism is that actual markets are, by nature, incomplete markets. This incompleteness arises from several factors:
- Transaction Costs: Real-world markets involve brokerage fees, bid-ask spreads, and other costs that prevent perfectly frictionless trading.
- Information Asymmetry: Not all market participants have access to the same information at the same time or with the same level of clarity. This can hinder the creation and pricing of all necessary contingent claims.
- Absence of Specific Securities: For many idiosyncratic risks (e.g., individual labor income risk, health shocks), perfectly tailored insurance or financial products simply do not exist due to moral hazard, adverse selection, or lack of liquidity.
- Bounded Rationality: Economic agents may not possess the perfect rationality or foresight assumed in complete market models, limiting their ability to identify or trade in all possible contingent claims.
- Regulatory Restrictions: Regulations can restrict the creation or trading of certain financial instruments, thereby contributing to market incompleteness.
Some academic research even suggests that financial markets, by their very nature, cannot be Pareto efficient except by chance, challenging the notion that competitive financial markets always efficiently allocate risk, particularly when considering realistic population demographics. The presence of incomplete markets can lead to suboptimal risk sharing and welfare losses.
1## Complete Markets vs. Incomplete Markets
The distinction between complete and incomplete markets is fundamental in financial economics.
| Feature | Complete Markets | Incomplete Markets |
|---|---|---|
| Risk Coverage | Every possible future state of the world can be hedged or insured. | Some risks cannot be perfectly hedged due to a lack of specific securities. |
| Risk Sharing | Allows for optimal risk sharing among all participants. | Suboptimal risk sharing often occurs, leading to uninsurable risks. |
| Existence of Assets | A sufficient number of linearly independent contingent claims exists. | The number of independent securities is less than the number of possible states. |
| Arbitrage | No arbitrage opportunities. | Arbitrage opportunities are theoretically rare but market inefficiencies may persist. |
| Realism | A theoretical ideal or benchmark. | Reflects the reality of most financial markets. |
| Implications | Supports efficient asset pricing and allocation. | Can lead to welfare losses and hinder efficient resource allocation. |
In essence, while complete markets represent a theoretical nirvana where all uncertainties can be managed financially, incomplete markets acknowledge the frictions, limitations, and missing instruments that characterize the real financial world.
FAQs
What are Arrow-Debreu securities?
Arrow-Debreu securities are hypothetical financial instruments that pay out one unit of value if a very specific future "state of the world" occurs and nothing in any other state. They are the building blocks of complete markets theory, allowing for the precise decomposition and pricing of all possible future contingencies.
Why are complete markets important in finance theory?
Complete markets are crucial because they provide a benchmark for market efficiency and optimal risk sharing. They help economists and financial professionals understand the ideal conditions under which markets can perfectly allocate resources and price assets, even if these conditions are rarely met in practice.
Do complete markets exist in the real world?
No, truly complete markets do not exist in the real world. Real markets face various "frictions" such as transaction costs, information asymmetry, and the absence of specific financial products to hedge every conceivable risk. Therefore, real markets are always, to some extent, incomplete markets.
How do derivatives relate to complete markets?
Derivatives are financial contracts whose value is derived from an underlying asset or index. They allow investors to manage specific types of risk (e.g., price changes, interest rate fluctuations) and can move real-world markets closer to completeness by enabling more sophisticated hedging and speculation against various future states.