Date of Award

2020

Degree Type

Restricted to Claremont Colleges Dissertation

Degree Name

Economics, PhD

Program

School of Social Science, Politics, and Evaluation

Advisor/Supervisor/Committee Chair

Pual Zak

Dissertation or Thesis Committee Member

Joshua Tasoff

Dissertation or Thesis Committee Member

Pierangelo De Pace

Dissertation or Thesis Committee Member

Andrew Nguyen

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2020 Jungjun Park

Keywords

Bayesian asset allocation, Black-litterman model, Non-normal distribution, Skew normal distribution

Subject Categories

Economics | Finance and Financial Management

Abstract

This dissertation explores a Bayesian asset allocation problem based on the skew-normal distribution assumption and extends the Bayesian asset allocation model obtained by assuming hidden truncation skew-normal returns. Hidden truncation model provides a flexible family of skewed alternatives to the classical k dimensional normal distribution. In their groundbreaking framework in Bayesian asset allocation, Black and Litterman (BL) were able to construct stable mean-variance efficient portfolios. They had successfully combined subjective investors’ views through a prior distribution with market historical data to derive a posterior distribution of portfolio returns and optimal asset allocations under the assumption of normal returns. Many studies show that normality assumption is not empirically supported and turns out to be inappropriate in many cases because of the asymmetry in asset returns. By adopting the skew normal distribution, the new model not only captures the skewness of the asset returns but also provides a more flexible model in a Bayesian asset allocation problem. This paper, among other results, provides a closed form for the posterior predictive distribution of returns given the investors’ views. I investigate a parametric class of probability distributions, the skew normal distribution. Azzalini (see Azzalini and Dalla Valle (1996)) introduced the univariate skew normal (SN) distribution and studied the properties of its density functions and later extended it to the multivariate skew normal (MSN) distribution. And I explore the last multivariate skew-normal distribution developed by Gupta (See Gupta (2004)). For the empirical study in my dissertation, I construct two different portfolios: Large-cap and mid-cap portfolios. I extend the Black-Litterman (BL) asset allocation model by assuming hidden truncation skew-normal returns. Most of the well-known skew-normal models can be viewed as being products of such a hidden truncation construction. I present a new theoretical construction of the multivariate skew-normal distribution for mean-variance-skewness portfolio optimization. The empirical results suggest that, using the skew-normal returns, the skew-normal BL model provides optimal portfolios with the same expected return but less risk compared to an optimal portfolio of the classical BL model. For example, the skew-normal BL allocation provides a less monthly volatility of 0.36%. The portfolios become more negatively skewed as the expected returns of portfolios increase for given N, which suggest that the investors trade a negative skewness for a higher expected return. I also find that the negative relation between portfolio volatility and portfolio skewness. In other words, the investors trade a lower volatility for a higher skewness or vice versa reflecting that stocks with big drops in price are more volatile.

ISBN

9798664771459

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