Problems in Portfolio Theory and the Fundamentals of Financial Decision Making

The following sections are included:

• Dedication
• Preface
• Contents

The following sections are included:

• The Handbook of the Fundamentals of Financial Decision Making, Leonard C. MacLean and William T. Ziemba (eds.), (2013)
• Stochastic Optimization Models in Finance, William T. Ziemba and Raymond G. Vickson (eds.), Editions 1 & 2 (1975, 2006)
• References

The theme of this book is financial decision making. The decisions are the amount of investment capital to allocate to various opportunities in a financial market. The opportunity set can be very complex, with sets of equities, bonds, commodities, derivatives, futures, and currencies changing stochastically and dynamically over time. To consider decisions in a complex market it is necessary to impose structure. In the abstract, the assets and, the participants buying and selling them, are parts of a system with underlying economic states. The system’s dynamics and the factors defining the states in the system have been studied extensively in finance and economics. The dynamics of the market and the behavior of participants determine the trading prices of the various assets in the opportunity set…

Decision makers in financial markets are faced with a variety of opportunities and must decide how much capital to allocate to the various assets in the opportunity set at points in time. Investing in assets produces returns (gains/losses), resulting from the price changes. The returns on a unit of capital invested in assets are uncertain, that is, the return vector is a random variable. The basic information input to the decision on how much to invest in each asset is the distribution for the return vector. In Section A, some models for the dynamics of the stochastic return vector were considered. Assuming that the return distributions are known, the investment decisions are based on preferences for changes in wealth or accumulated wealth. To structure the decision process, a theory of preferences is required. The theory of preferences concerns the ability to represent a preference structure with a real-valued function. This has been achieved by mapping it to the mathematical index called utility. To put the preference relation for an individual into a theory of utility the following axioms were proposed by Von Neumann and Morgenstern (1944) and Savage (1954)…

The ordering of individual preferences with a utility or value functional is dependent on the chosen utility. There are important almost canonical utilities. Bernoulli (1738) provided a rationale for log utility, which together with the broader class of power utilities, has been useful in analyzing problems in decision making under uncertainty. Log utility is the basis of the golden rule of investing or Fortunes Formula, the Kelly (1956) strategy, which maximizes the asymptotic rate of capital growth. However, as indicated in Section B, there is some indeterminacy over individual utilities in practice and even over classes of utilities which reflect consistent preference attitudes…

The components of the financial decision problems are assets, prices, utilities and efficiency. However, there are other important considerations in the decision models and the data inputs, which affect the quality of investment decisions in constructing a portfolio…

The concepts of utility and risk attitude such as decreasing risk aversion are general and qualitative. But risk is a basic to decision making models and requires a precise definition. The essential characteristics of risk are the chance of a potential loss and the size of the potential loss. If financial decisions are to be considered in the framework risk management, it is clear that a quantitative measure of risk is needed…

The components of financial decision making are financial assets, trading prices, wealth preferences, decision sets, dominance and efficiency. There is a rich literature on financial decision models, where variations on the components are proposed. Some of the models are considered in this final section. Most of the discussion concerns negative power/log utility functions and the associated capital growth. Within the framework of expected utility theory significant qualitative properties of decision behavior can be developed analytically for negative power utility, with log being the most risky power utility function…

The following sections are included:

• ABOUT THE AUTHORS
• INDEX