Beyond risk and return modeling - How humans perceive risk

Abstract

The intention of this paper is to show that the statistical approach to risk is not enough to explain the behavior of investors. It furthermore proposes ideas and alternative approaches on how to deal with risk. Psychological findings are of particular interest as they might enhance our understanding of risk perception and assessment. The chapter “From the normal distribution to fat tails” starts with the rejection of the normal distribution as a simplifying basis for risk and return. This rejection is supported by several empirical observations like clustering of volatility and fat tails. This leads to a two-step approach for modeling risk and return based on the distinction of conditional and un-conditional changes. Conditional time series models (ARMA, ARCH, GARCH) and alternative distributions are presented (Stable Paretian, Student’s T, EVT) as a way to improve the art of risk and return modeling beyond the normal distribution assumption. The chapter ends with the conclusion that each model is only a statistical approximation and never encompasses the unpredictability of black swans and the nature of human behavior in the financial markets. After having discussed the limitations of the purely statistical approach to risk and return this paper goes beyond the standard theory of finance for two purposes. Firstly, behavioral finance provides some arguments for the limitation of statistics in assessing risk. Secondly, an alternative approach to risk perception is presented. This alternative is called Prospect Theory, a rather psychology-based approach using preferences to explain investors’ actions by human behavior in decision making processes. Starting point is the utility function and the value function followed by a description of the two phases: framing and evaluation. The value function is then clearly distinguished from the utility function by elaborating certain effects like reference points, loss aversion or the weighting function. In this section the paper enters the arena of human risk perception which is far from being monetarily rational in the sense of the homo oeconomicus. With Cumulative Prospect Theory there exists an extension to multiple outcome scenarios where risk does not necessarily have to be known. In such a situation, besides risk, there also exists immeasurable uncertainty. Current research confirms and rejects parts of (Cumulative) Prospect Theory which is not necessarily a bad sign as human behavior is rarely exactly replicable and the complexity does not really allow generalizations. Therefore, even if the theory is not completely correct it still enhances our understanding of risk perception and human decision making which can be a very valuable input for agent-based models. The next chapter analyses in more detail possible distortions from psychological biases in the assessment of risk. In this context the law of small numbers, overconfidence and feelings/experience are discussed. Knowing these biases complicates the idea of developing a risk model even further. However, this is again another step to better understand the underlying processes and motives of decision making in the context of financial markets. The last chapter is an attempt to link the different aspects to get a holistic view on risk behavior. Two possibilities are discussed: Hedonic psychology, with the distinction between blow up and bleeding strategy, and heuristic-based explanations for real observations like clustering of expectations and trust in experts. This leaves space for further research as we do not have a tool that is based on current findings and can actually help us in explaining and predicting behavior in financial markets. One possibility would be to link all these aspects in the approach of computational finance to develop agent-based models in which market observations, psychological findings and the situational context can be integrated.