Investment Model Uncertainty and Fair Pricing

Modern investment theory takes it for granted that a Security Market Line (SML) is as certain as its "corresponding" Capital Market Line. (CML). However, it can be easily demonstrated that this is not the case. Knightian non-probabilistic, information gap uncertainty exists in the security markets, as the bivariate "Galton's Error" and its concomitant information gap proves (Journal of Banking & Finance, 23, 1999, 1793-1829). In fact, an SML graph needs (at least) two parallel horizontal beta axes, implying that a particular mean security return corresponds with a limited Knightian uncertainty range of betas, although it does correspond with only one market portfolio risk volatility. This implies that a security' risk premium is uncertain and that a Knightian uncertainty range of SMLs and of fair pricing exists. This paper both updates the empirical evidence and graphically traces the financial market consequences of this model uncertainty for modern investment theory. First, any investment knowledge about the securities risk remains uncertain. Investment valuations carry with them epistemological ("modeling") risk in addition to the Markowitz-Sharpe market risk. Second, since idiosyncratic, or firm-specific, risk is limited-uncertain, the real option value of a firm is also limited-uncertain This explains the simultaneous coexistence of different analyst valuations of investment projects, particular firms or industries, included a category "undecided." Third, we can now distinguish between "buy", "sell" and "hold" trading orders based on an empirically determined collection of SMLs, based this Knightian modeling risk. The coexistence of such simultaneous value signals for the same security is necessary for the existence of a market for that security! Without epistemological investment uncertainty, no ongoing markets for securities could exist. In the absence of transaction costs and other inefficiencies, Knightian uncertainty is the necessary energy for market trading, since it creates potential or perceived arbitrage (= trading) opportunities, but it is also necessary for investors to hold securities. Knightian uncertainty provides a possible reason why the SEC can't obtain consensus on what constitutes "fair pricing." The paper also shows that Malkiel's recommended CML-based investments are extremely conservative and non-robust.capital market line, security market line, beta, investments, decision-making, Knightian uncertainty, robustness, information-gap, Galton's Error, real option value

On solving decision and risk management problems subject to uncertainty

Uncertainty is a pervasive challenge in decision and risk management and it is usually studied by quantification and modeling. Interestingly, engineers and other decision makers usually manage uncertainty with strategies such as incorporating robustness, or by employing decision heuristics. The focus of this paper is then to develop a systematic understanding of such strategies, determine their range of application, and develop a framework to better employ them. Based on a review of a dataset of 100 decision problems, this paper found that many decision problems have pivotal properties, i.e. properties that enable solution strategies, and finds 14 such properties. Therefore, an analyst can first find these properties in a given problem, and then utilize the strategies they enable. Multi-objective optimization methods could be used to make investment decisions quantitatively. The analytical complexity of decision problems can also be scored by evaluating how many of the pivotal properties are available. Overall, we find that in the light of pivotal properties, complex problems under uncertainty frequently appear surprisingly tractable.Comment: 12 page

Recursive Smooth Ambiguity Preferences

This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in Klibanoff, Marinacci, and Mukerji (2005). A key feature of the model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. In applications one may thus specify/vary these two characteristics independent of each other, thereby facilitating richer comparative statics and modeling flexibility than possible under other models which accomodate ambiguity sensitive preferences. Another key feature is that the preferences are dynamically consistent and have a recursive representation. Therefore techniques of dynamic programming can be applied when using this model.Ambiguity, Uncertainty, Knightian Uncertainty, Ambiguity Aversion, Uncertainty Aversion, Ellsberg Paradox, Dynamic Decision Making, Dynamic Programming under Ambiguity, Smooth Ambiguity.

Risk-reducing design and operations toolkit: 90 strategies for managing risk and uncertainty in decision problems

Uncertainty is a pervasive challenge in decision analysis, and decision theory recognizes two classes of solutions: probabilistic models and cognitive heuristics. However, engineers, public planners and other decision-makers instead use a third class of strategies that could be called RDOT (Risk-reducing Design and Operations Toolkit). These include incorporating robustness into designs, contingency planning, and others that do not fall into the categories of probabilistic models or cognitive heuristics. Moreover, identical strategies appear in several domains and disciplines, pointing to an important shared toolkit. The focus of this paper is to develop a catalog of such strategies and develop a framework for them. The paper finds more than 90 examples of such strategies falling into six broad categories and argues that they provide an efficient response to decision problems that are seemingly intractable due to high uncertainty. It then proposes a framework to incorporate them into decision theory using multi-objective optimization. Overall, RDOT represents an overlooked class of responses to uncertainty. Because RDOT strategies do not depend on accurate forecasting or estimation, they could be applied fruitfully to certain decision problems affected by high uncertainty and make them much more tractable

Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version

Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a “Grand State Space”, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing the formation of prior beliefs. On the other hand, this notion of rationality is too strong because there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs.Decision making, Bayesian, Behavioral Economics

Knightian Uncertainty and Capital Structure.

My dissertation aims to understand a firm's optimal capital structure decision when it confronts Knightian uncertainty. It contains three chapters. In Chapter One, I derive the optimal capital structure of a firm when its manager is ambiguity-averse. My model predicts substantially lower leverage for such firms, in comparison to traditional static trade-off models. I use the 1982 Voluntary Restraint Agreement (VRA) on steel import quotas between the U.S. government and the European Community as an exogenous reduction in Knightian uncertainty faced by firms in the U.S. steel industry. Using a difference-in-difference methodology, I find that when uncertainty is resolved, a median firm in the U.S. steel industry increases its market and book leverage by approximately 12 percent relative to a matched control firm from another industry. The results are not explained away by changes in traditional risk factors or by a change in expected future profitability. In Chapter Two, I develop a new measure of Knightian uncertainty using a mixture of normal distributions. Using this novel measure, I find that a median firm in the sample decreases its market leverage by approximately 3.6 percent, when the firm's measure of uncertainty increases by one standard deviation. I also find an increase in a firm's uncertainty measure from the minimum to the maximum is associated with a 6.3 percent increase in the firm's propensity to take almost zero leverage. In Chapter Three, I consider a firm's decision to exercise real options, when the firm faces Knightian uncertainty about the evolution of project value. I provide two continuous time applications extended from the discrete time applications in Miao and Wang (2011) that show the value of waiting (which increases with risk) decreases with uncertainty. I incorporate ambiguity-averse investors who are uncertain about the evolution of a firm's assets into the dynamic capital structure model of Leland (1994). I show that even in this dynamic setting, uncertainty provides a more plausible explanation for firms taking on low leverage than risk alone.PHDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99764/1/seokwoo_1.pd