#### Semester

Spring

#### Date of Graduation

2018

#### Document Type

Dissertation

#### Degree Type

PhD

#### College

College of Business and Economics

#### Department

Finance

#### Committee Chair

Victor Chow

#### Committee Member

Alexander Kurov

#### Committee Member

Bingxin Li

#### Committee Member

Ann Marie Hibbert

#### Committee Member

Eric Olson

#### Abstract

The primary focus of this dissertation is a new risk measure, Swap Variance (SwV), and its applications to expected utility maximization, portfolio theory, and capital asset pricing models (CAPM) with loss aversion and gain preference. Superior to the classical mean-variance (MV) model, the mean-swap variance (MSwV) efficiency is consistent with expected utility maximization for all concave utility without any restriction on the form of either utility function or return distributions. Specifically, the MSwV efficiency is necessary and sufficient to the second-degree stochastic dominance (SSD). Thus, the SSD optimization can be consistently replicated by the SwV minimization for given means. The consistency between MSwV and SSD implies that the capital market line, Sharp ratio and other portfolio performance measures can now be modified in a generalized framework of expected concave utility maximization without utility or distributional assumptions of the MV model. Since the MSwV analysis retains the same simplicity as the MV approach, I apply the MSwV approach to the conventional procedure of portfolio optimization in determining capital market equilibrium. As a result, similar in form to the classical CAPM, the beta coefficient derived from the MSwV model is a ratio of the co-swap variance between returns on an asset and those on the market portfolio over the market SwV. Although the MSwV beta captures all high order co-moments of return and is thus more general than the traditional MV beta, it is insufficient to explain the generalized relationship between expected return and risk under a single factor model. This research explicitly proves the necessity of additional factors in equilibrium for determining the asset return generating process, if the beta of MSwV is different from that of MV. Empirically, from an out-of-sample analysis, the larger the distinction (both positive and negative) of the MSwV-beta from the MV-beta, then the average return will be significantly higher. This empirical evidence strongly indicates that, in addition to the market factor, additional factors captured by the asymmetric systematic risk help explain the equilibrium risk-return relationship.

The MV model is valid under the assumption of a rational decision maker. The distinction of MSwV from MV thus captures the behavioral biases of human decision makers. The viewpoint of behavior finance (Benartzi & Thaler, 1995) demonstrates that loss-aversion appears when investors are unwilling to recognize loss and tend to afford more risk. On the other side, Kumar (2009) posited that individual investors prefer stocks with lottery features, which means a human decision maker may tolerate more risk to pursue potential gain. So, utility on a human decision maker shifts by three primary risk attitudes: loss-aversion for downside asymmetry (significant losses), rational risk-version for symmetry (normal returns), and overly risk-averse for upside asymmetry (substantial gains). Mathematically, the expected utility can be quantified by the MSwV approach without any restriction on the form of utility and return distribution functions. The major contribution of this dissertation is the development of a portfolio theory that can capture the loss aversion and gain preference of human decision makers. Based on the portfolio theory, a multi-factor linear model is theoretically formulated. Precisely, the loss aversion (gain preference) factor is captured by the negative (positive) asymmetric beta, and the MV-beta captures the symmetric factor. Therefore, the factor portfolios can be replicated by the zero-cost (long-short) portfolios constructed from the sorted securities concerning the past asymmetric betas. The mimicking portfolio of the symmetric factor is the optimal portfolio without asymmetry. Empirical examinations show that the Fama-Macbeth cross-sectional regression results in asymmetric factor loadings and have significant explanatory power for security returns.

#### Recommended Citation

Wang, Jhan, "Mean-swap Variance, Portfolio Theory and Asset Pricing" (2018). *Graduate Theses, Dissertations, and Problem Reports*. 7993.

https://researchrepository.wvu.edu/etd/7993