THIS CHAPTER FOCUSES on prices—the prices of both securities and the state claims introduced in Chapter 3. Of particular interest are the relationships among expected returns, various measures of risk, and measures of responsiveness to changes in market-wide variables. We introduce alternative versions of the Market Risk/Reward Theorem (MRRT) and investigate the conditions under which one or more version may hold. As in previous chapters, we assume that investors agree on the probabilities of future states, have no outside positions, and discount the utilities from all states at a given time in the same way, leaving for future chapters the investigation of the characteristics of equilibrium when some or all of these assumptions are violated.
We have defined a state claim as a security that pays 1 unit if and only if a specific state occurs. We have also argued that such state claims can be considered the atoms of which actual securities are made. While some such claims may be traded explicitly, this is rare. Nonetheless it is extremely useful to consider the characteristics of a world in which all possible state claims can be traded. Such a world is defined as a complete market.
If financial institutions and markets operated without cost, everyone could trade their standard securities for state claims in the manner described in Chapter 3. However, it might be more efficient if a market maker simply opened a market for trades in one or more state claims, with sellers able to create them and buyers able to purchase them. In such a case, each state claim, like the bond in our previous cases, would be in zero net supply. And, as with other such instruments, buyers would have to make certain that issuers (sellers) could deliver on their promises.
To simulate a complete market we adopt a sequential approach. We let investors reach an equilibrium using available standard securities; we then open a market for trading state claims. The possible trading procedures used by the market maker for state claims are the same as those used for standard securities. In all the cases in this book, we use the simple type of price discovery in which trades are made in each market using a price halfway between the average of the reservation prices of investors who are able to buy and the average of the reservation prices of those who are able to sell.