Australian equity portfolio sets in a pre- and post-global financial crisis contexts

• Author: Suganya Eliot - Jean-Pierre Fenech
• Position: Department of Accounting and Finance Monash University, Caulfield East, 3145, Australia - Department of Accounting and Finance Monash University, Caulfield East, 3145, Australia

Introduction

Exogenous shocks to financial markets make the correlation estimates of portfolio assets returns unreliable [Malgorzata and Krzych, 2006]. From a practical perspective, the impact of the Global Financial Crisis (GFC) on a finite length T of any empirical time series inevitably leads to noise within the data. This phenomenon is commonly known as measurement error, and is generally present in the covariance matrix estimates of portfolios. Evidence of noise becomes stronger as the risk of contagion spreads across financial markets on a worldwide scale [Nowak, Andritzky, Jobst and Tamirisa, 2011]. During the GFC, many financial institutions faced significant liquidity problems, with funds being pulled out of stocks and positioned into gold, bonds and currencies, viewed as safer alternatives to the stock market. In comparison to other economies, Australia was seen as the least affected [Battellino, 2011]. However, a consistently bearish stock market clearly signalled the inherent volatility and related risks associated within the Australian Securities Exchange [Davis, 2011]. It is evident that no market has been left unaffected by the GFC.

The main objective of this study is to empirically determine the association between minimising risk and maximising return on optimal portfolios within the Australian context in the period 2001 to 2012. The years 2007/08 in particular were turbulent times for global economies and financial markets alike. High volatility in the stock markets triggered instability and unpredictability, ultimately affecting the performance of risk and return associations in portfolios. With a view to better estimating the covariance matrices of returns in a portfolio context, a wavelet shrinkage denoising technique is adopted in order to mitigate the measurement errors caused principally by noise. There has been little empirical study of the performance of risk and return within pre- and post-GFC contexts, which provides the main motivation for this paper.

A large sample of historical returns is generally needed to obtain good quality statistical estimates for covariance matrices and related expected returns. However, only a limited series of recent historical data was considered for estimation purposes, due to market changes over time. Furthermore, the highly unpredictable nature of markets and decline in stock prices would have induced measurement errors in the risk estimations. [Galluccio, Bouchaud, and Potters, 1998; Laloux, Cizeau, Bouchaud, and Potters, 1999; Plerou, Gopikrishnan, Rosenow, Amaral and Stanley, 1999] have structured strategies to mitigate the high degree of noise within the covariance matrix. As portfolio risk and return is calculated based on these estimates, such measures must be free from error to result in reliable optimal portfolio sets. [Pafka and Kondor, 2002, 2003] analysed the impact of noise on the portfolio optimisation problem, and found that the risk of the optimal portfolio in the presence of noise is about 5 to 15%, depending on the portfolio size. However, upon inclusion of non-linear constraints, the presence of noise leads to significant instability in the portfolio sets, negatively affecting the performance of optimal portfolios. Hence, in order to obtain reliable portfolio sets, better estimators are required by mitigating the noise from the covariance matrices. One of the most recent and widely used filter estimators, as advocated by Papp, Pafka, Nowak and Kondor [2005] and Laloux, Cizeau, Bouchaud and Potters [1999], is the Random Matrix Theory (RMT). There is also the cluster-based filter, supported by Tola, Fabrizio, Gallegati and Mantegna [2008] and Vijayalakshmi Pai, and Michel [2009].

Suganya and Pai [2009] demonstrated that the wavelet shrinkage denoising technique outperforms both the RMT and the cluster-based filters. Both were tested on data sets covering the pre-GFC period. It is as yet unknown how the wavelet shrinkage denoising technique performs within a post-GFC period. Another motivation for this study, therefore, is to analyse the association between portfolio risk and return in pre- and post-GFC periods within the context of more reliable Australian portfolio sets.

In order to effectively incorporate modern portfolio theory (MPT) into the investment portfolio decision-making process, investors need to initially estimate and evaluate the expected risk and return for individual assets and investment portfolios. In reality, it is unlikely to accurately forecast future scenarios in line with related expected returns. Although various historical means do not represent future performances, many researchers and practitioners estimate the expected mean return based on this assumption. In MPT literature, the risk for the entire portfolio is more important than the individual asset’s risk. Therefore, portfolio risk does not depend on the average risk of the individual assets, but on the covariance measures between the assets.

In this study, we investigate the performance of the portfolio risk and its return based on the Australian Securities Exchange's 100 stocks (ASX100 index) over the period January 2001 to September 2012. We divided the data into pre- and post-GFC time intervals and measured the association between risk and return over these periods. Due to volatility in the data resulting in measurement errors, we adopted a wavelet shrinkage denoising technique, and as a result, could demonstrate more optimal efficient frontiers in both periods. The difference between the empirical covariance and the wavelet filtered matrix in the post-GFC period is less pronounced due to the instability within the data range. Portfolio reliability values were also calculated with the wavelet matrix portfolios, resulting in more reliable values. This is consistent in both periods. Finally, we found significant differences in the efficient frontiers calculated over both periods, revealing the extent of the effect of the GFC on optimal portfolio sets in Australia. In the pre-GFC period, the extent of the expected portfolio annual returns spreads from 12% to 138%, depending on the annualised risk attached to the portfolio. This scenario is in line with a bullish equity market. However, when the same methodology is applied to a post-GFC period, it is clear that high risk investment strategies do not generate strong and high yield returns. In an optimal portfolio set, the maximum expected annualised portfolio annual return is 40% when risk is at its highest, i.e., at 33%. Exposing the portfolio to more risk does not automatically suggest that higher returns are derived. This pattern is synonymous with a bearish market accompanied by high volatility. This finding represents a paradigm shift for investors seeking to balance out a risk/return perspective. Therefore, this study empirically demonstrates that the GFC has changed the risk/return association, forcing investors to rethink their investment strategies and objectives.

The global financial crisis and the wavelet shrinkage denoising technique

Although the financial crisis may have originated in the U.S. and Europe, it spread to other countries and markets, as all are interconnected and interrelated [Debelle, 2011]. The initial crash stemmed from direct exposure to sub-prime related securities. Initially, the impact was comparatively small, but it was only a matter of time before the extent of the loss was revealed on a global scale. Market players reacted by primarily deleveraging their balance sheets, reversing capital flows, which resulted in a faltering stock market. This trend caused uncertainty in the interest rate and foreign exchange rate markets alike.

The global liquidity problem affected many countries due to financial contamination, with the downturn in house prices not exclusive to the U.S., as several other countries experienced significant declines in asset markets [Pagan and Robinson, 2011]. In addition, the quick decline in expected economic growth for the global economy also affected countries like Australia, heavily dependent on commodity exports.

The economic decline caused anxiety amongst investors due to sudden changes in financial market expectations [Park, 2011]. The impact of this was that investors started selling their stocks, subsequently withdrawing money from banks. In order to provide additional liquidity and improve solvency, banks raised further cash by injection capital. However, even though central banks may introduce liquidity, they can do little to influence investors' behaviour...