The Evolution of Security Designs

We consider a competitive and perfect financial market in which agents have heterogeneous cash flow valuations. Instead of assuming that agents are endowed with rational expectations, we model their behavior as the product of adaptive learning. Our results demonstrate that adaptive learning affects security design profoundly, with securities mispriced even in the long run and optimal designs trading off underpricing against intrinsic value maximization. The evolutionary dominant security design calls for issuing securities that engender large losses with a small but positive probability, but that otherwise produce stable payoffs, almost the exact opposite of the pure state claims that are optimal in the rational expectations framework. The real operations of the economy produce random cash flows. If investors have varying attitudes toward risk, they will have different valuations of these risky cash flows. For this reason, the received wisdom is that investor welfare can be improved by sharing rules that allocate risky cash flows among investors. Financial markets can serve as a mechanism for implementing such welfare-improving risk sharing. These markets enable agents with different risk preferences to trade securities and, through their trades, establish equilibrium prices for risky assets. In equilibrium, state prices are determined by the marginal investor’s valuation; and the marginal investor may be different in different states of the world. Although the welfare-enhancing effects of dividing and marketing cash flows have long been recognized, Allen and Gale (1988) are the first researchers to consider the matrix of risksharing securities not as an exogenous datum but rather as an endogenous product of design. In particular, Allen and Gale develop a model of financial markets in which corporations profit by designing securities. They show that, in the absence of transactions costs, the optimal security design calls for the issuance of pure state securities, that is, firms should issue a bundle of many securities, with each security paying off only in a single state of the world and only one security paying off in any given state. Such a design captures the highest marginal valuation for each security across the heterogeneous pool of investors. However, in actuality, corporations tend to issue only a few securities that often provide positive payoffs simultaneously by splitting the cash flows associated with individual states across multiple securities. Indeed, Allen and Gale show further that given transaction costs that are proportional to the number of securities a firm issues, a firm will reduce the number of securities it issues by issuing bundles of pure securities and thereby bundling together cash flows from multiple states. Nevertheless, splitting a given state’s cash flow among multiple securities is still suboptimal. By relaxing the assumptions of no transactions costs, free information, and competitive financial markets, the extant literature attempts to rationalize the stylized fact of firms issuing a narrow range of securities in a world with a broad range of investor preferences. For instance, Madan and Soubra (1991) show that marketing costs can make both the bundling and splitting