Measuring Investors Preferences
In a simple two-date setting an investor allocates of his or her wealth to obtain current consumption and state-contingent amounts to be consumed in future states. Absent outside positions or state-dependent preferences, the future prospects for any allocation can be summarized in a probability distribution of future consumption. In a complete market setting such an investor's decision process can be summarized as follows Budget Prices Preferences Distribution Given a budget, a set of state...
Figure 67 Cases 114 and 15 Security Prices
In Case 1 security prices fully reflect the available information concerning the future states of the world, since every investor utilizes that information when making trades and choosing a portfolio. In Case 14 the prices do not fully reflect the information since there are only two partially informed investors. As a result the security prices are affected and, in a sense, wrong. In Case 15, however, the results are considerably closer to those in Case 1. With more investors more information...
Other Aspects of Equilibrium
This book has focused heavily on the properties of equilibrium in financial markets. While we have explored many aspects of such equilibria, many more remain to be considered but in other places and at other times. Our most glaring omission is the lack of more time periods. While we can interpret our framework as applying to a long, medium or short period, our analyses cannot fully take into account interactions among periods. We addressed this set of issues crudely by suggesting that state...
Figure 54 Case 9 Equilibrium Portfolios
Mario has adjusted his portfolio to reflect that fact that his salary is equivalent to 5 shares of MFC and Hue has adjusted her portfolio to reflect the fact that her salary is equivalent to 5 shares of HFC. Their total consumption in each of the future states of the world is thus precisely the same in both Case 1 and Case 9. Since Mario and Hue have the same consumption patterns across states as they did in Case 1, their marginal utilities of consumption will also be the same in both cases, as...
Figure 65 Case 14 Portfolios
There is more. Although Mario and Hue are able to act on their differing opinions by holding idiosyncratic portfolios of the existing securities, they would like to have more alternatives. This can be seen in Figure 6-6. After equilibrium is attained for each future state their reservation prices differ. This is not surprising. Investors who disagree wish to make bets with one another. To accommodate them the financial services industry provides a rich menu of vehicles, including such...
Dynamic Strategies
Absent extensive disagreement about likely market outcomes, the demand for preference-based downside protection may be too idiosyncratic to warrant large numbers of costly new financial products. But there are other ways to affect the way in which returns relate to market returns. In long-run settings it is possible to create a non-linear return function with a dynamic strateg that follows decision rules for changing asset mixes based on previous returns. The final results will be less than...