Asymmetric Dependence Structures

Anthony Hatherley (2009). Asymmetric Dependence Structures PhD Thesis, School of Business, The University of Queensland.

       
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Author Anthony Hatherley
Thesis Title Asymmetric Dependence Structures
School, Centre or Institute School of Business
Institution The University of Queensland
Publication date 2009-04
Thesis type PhD Thesis
Supervisor Jamie Alcock
Stephen Gray
Total pages 277
Total black and white pages 277
Subjects 350000 Commerce, Management, Tourism and Services
Abstract/Summary Asymmetric dependence (AD) is defined as dependence that differs across opposing regions of the joint return distribution. Recent evidence of AD between equity returns suggests that dependence can be decomposed into a linear component, captured by the correlation matrix, and a higher order component. When these higher order terms are characterised by increased correlation in bear or bull markets, the effectiveness of diversification strategies is reduced. To the extent that an investor is unable to completely diversify these higher order terms of dependence, it follows that they should be reflected in asset prices and managed explicitly during the portfolio construction process. The aim of this thesis is to determine the extent of AD amongst asset returns, to investigate whether AD is priced and to develop a means of managing AD in the portfolio. I justify the existence of AD and the separation of AD from linear dependence via the bivariate Edgeworth expansion, finding that the joint return distribution may be described by an infinite number of higher order co-moments. Correlation (and hence β) describes one dimension of an infinite number of higher dimensions describing dependence. To determine the importance of AD in finance, I first develop measures that can detect AD independent of the level of linear dependence and idiosyncratic risk. These measures are used to determine the extent of AD amongst US stock returns and the market, to obtain an understanding of how AD changes through time and to re-examine the evidence of AD between equity portfolios. By measuring AD separate from linear dependence, I demonstrate several findings. First, I find evidence of non-stationary AD that can exists irrespective of the magnitude of linear dependence, measured by β. This time-varying AD consists of both significant upper tail dependence (UTD) and significant lower tail dependence (LTD), although LTD is found to occur more frequently than UTD, especially for small stocks and stocks displaying high idiosyncratic risk. Significant time-varying AD is also detected between domestic equity indices and international equity markets, implying that if a portfolio is weighted towards certain industries or countries, portfolio construction methods may need to be adjusted in order too meet risk and return targets, particularly if future AD cannot be adequately forecasted. Next, I investigate whether AD is priced in US equities using the Fama and MacBeth (1973) regression methodology in conjunction with my β invariant AD metrics. I find that AD is as important as linear dependence in explaining the variation in returns. In particular, a positive relationship between LTD and return is found. I document an AD risk premium of 2.7% pa, compared to a β risk premium of 6.18% pa. The AD risk premium increases to 6.9% pa for stocks with significant LTD. This result holds after controlling for size, book-to-market ratio, downside β and coskewness. I also find past AD is a significant variable in predicting the future returns of small firms, whilst neither AD nor linear dependence predict the future returns of large firms. I subsequently demonstrate a means of incorporating AD structures during the portfolio construction process using copula functions. I then investigate how asymmetric return dependencies affect the efficient frontier and subsequent portfolio performance under a dynamic rebalancing framework. By considering the problem of tactically allocating a small set of domestic equity indices, I demonstrate several findings. First, I show that a Mean-Variance efficient frontier differs from the efficient frontier constructed under AD. Constructing paper portfolios based upon these differences, I find that real economic value lies in correctly accounting for AD structures. The primary source of this economic value stems from the ability to better protect portfolio value and reduce the size of any erosion in return relative to the normal portfolio. Finally, I document the benefits of actively managing AD during the portfolio construction process and determine a number of portfolio management principles required to successfully manage AD. I illustrate that managing asymmetry risk in a portfolio of international equity indices results in increased return, decreased risk and decreased transaction costs. I show that in order to yield these benefits, investors must actively and dynamically manage their portfolio. Furthermore, I illustrate that the ability to short-sell assets provides most of the benefits described.
Keyword asymmetric dependence
correlation
asset pricing
portfolio theory
copula theory

 
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Created: Fri, 28 Aug 2009, 17:19:20 EST by Mr Anthony Hatherley on behalf of Library - Information Access Service