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| Type | Bachelor's Thesis |
| Scope | Discipline-based scholarship |
| Title | Empirical Estimation of Risk Aversion |
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| Institution | University of Zurich |
| Faculty | Faculty of Business, Economics and Informatics |
| Number of Pages | 43 |
| Date | 2021 |
| Zusammenfassung | Von Neumann and Morgenstern (1944) laid the foundation for explaining risk-averse behavior. Their finding of a concave utility function is considered a linchpin for classical economic theory. The pricing kernel, as sum over different states of the world, is a measure that allows us to gain an understanding of investors’ attitude towards market risk. By means of the asset pricing kernel, backward-looking probabilities are transformed into forward-looking risk-neutral probabilities (Cuesdeanu and Jackwerth (2018)). As further explained by Cochrane (2005) and many others, based on von Neumann and Morgenstern’s (1944) models, economic theory would imply a pricing kernel with a monotonously decreasing slope pattern accounting for investors’ risk-averse behavior. The pricing kernel would therefore be a monotonously decreasing function, assigning higher returns to riskier states. Controversially, seminal empirical studies, including those by Jackwerth (2000) and Rosenberg and Engle (2002), have demonstrated that the pricing kernel can increase at a certain level. A local increase in the range of small positive returns can be observed. With this finding, the pricing kernel puzzle was born. Jackwerth (2000) and Rosenberg and Engle (2002) were among the first ones to discover this irregularity. The methods applied by these authors are still widely used. Therefore, it is helpful to understand in depth how they work. The aim of this paper is to replicate and critically discuss the methods of Jackwerth (2000) and Rosenberg and Engle (2002). The paper provides a detailed understanding of their methodologies and assumptions and compares their approaches with each other. Following the course of action of the underlying papers, the empirical pricing kernel as measure of risk aversion is inferred from option prices and realized returns on the S&P500 index between 1987 and 1995. Jackwerth (2000), on the one hand, draws a connection between risk-neutral and subjective probabilities and chose an indirect approach to estimate the empirical pricing kernel. Based on options on the S&P500, he computes the pricing kernel as well as the relative risk aversion. The subjective probabilities are computed from backward-looking four-year time frames of returns on the S&P500. As for the risk-neutral probabilities, Jackwerth (2000) chose to get a set of options by matching and smoothing implied volatilities instead of strike prices. The risk-neutral probability is then derived directly as the second derivative regarding the strike. Rosenberg and Engle (2002), on the other hand, opted for a direct approach to retrieve the pricing kernel. Introducing a stochastic volatility model, they project the pricing kernel on payoffs x_(t+1). In doing so, through the pricing kernel, the authors approximate synthetic forward-looking option prices, composed of the aforementioned payoffs and a payoff function to a set of actual observed option prices. |
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