In this paper we find sufficient conditions for the robust design of assets that reduce asset price volatility. An intimately related question is whether and how the degree of market incompleteness affects asset price volatility.
We use the standard model of discrete-time dynamic trading of assets and multiple goods in a finite economy (see Duffie and Shafer (1986)). In our setup, asset design is not the result of optimizing behavior, and asset markets are exogenously incomplete. We concentrate on the equilibrium effects of having different financial structures. We impose time separability and use von Neumann Morgenstern expected utilities. Any weaker version of separability (such as time non separability, or habit formation) also gives rise to the same results as the ones presented in this paper. The model we use covers any finite time horizon trading economy, even though we focus on the three-period case. Although a new financial asset generally plays a role as a hedging device and as an information vehicle, the results in this paper do not address differential information economies. Rather, we concentrate on the spanning role of financial assets.
With these maintained general specifications, we first look at economies with no aggregate risk, i.e., invariant aggregate resources, and stationary conditional expected asset payoffs. Here asset prices show zero volatility with complete markets, so market-completing financial innovation never increases price volatility. In Proposition 3.2, we prove that within this class of economies any financial innovation is generically volatility reducing, if: i) we go from one asset to complete markets; ii) there is one commodity. We also give numerical examples, suggesting that the volatility reducing effects of innovation extend in this class of economies to a general comparison between incomplete and complete markets. Proposition 3.2 and the examples also suggest that no qualitative role is played by the convexity of marginal utility. The type of risk aversion, CRRA or CARA utility, determines in what dimension utility or endowment heterogeneity matters, and the level of risk aversion affects the volatility level.
Second, in Theorem 4.2 and its Corollary we establish that, generically, we can design a new asset which reduces price volatility for general incomplete market economies. This occurs when the dispersion in the cross-sectional distribution of traders’ characteristics is positive but less than the maximal degree of disagreement in individual pricing kernels. Moreover, if the new asset is retraded, Theorem 4.6 allows the comparison between incomplete and (dynamically) complete markets, with one initial asset and a binomial-tree structure for uncertainty.
The last result of the paper shows that it is easier to reduce volatility through financial innovation when traders cannot rebalance their holdings of the new asset. More precisely, in the case of impossibility of retrading (Theorem 4.2) the condition linking the number of states, traders and assets is weaker than in the case of retrading (Theorem 4.6).
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