Subspace portfolios: design and performance comparison

Data processing and engineering techniques enable people to observe and better understand the natural and human-made systems and processes that generate huge amounts of various data types. Data engineers collect data created in almost all fields and formats, such as images, audio, and text streams, biological and financial signals, sensing and many others. They develop and implement state-of-the art machine learning (ML) and artificial intelligence (AI) algorithms using big data to infer valuable information with social and economic value. Furthermore, ML/AI methodologies lead to automate many decision making processes with real-time applications serving people and businesses. As an example, mathematical tools are engineered for analysis of financial data such as prices, trade volumes, and other economic indicators of instruments including stocks, options and futures in order to automate the generation, implementation and maintenance of investment portfolios. Among the techniques, subspace framework and methods are fundamental, and they have been successfully employed in widely used technologies and real-time applications spanning from Internet multimedia to electronic trading of financial products. In this dissertation, the eigendecomposition of empirical correlation matrix created from market data (normalized returns) for a basket of US equities plays a central role. Then, the merit of approximating such an empirical matrix by a Toeplitz matrix, where closed form solutions for its eigenvalues and eigenvectors exist, is investigated. More specifically, the exponential correlation model that populates such a Toeplitz matrix is used to approximate pairwise empirical correlations of asset returns in a portfolio. Hence, the analytically derived eigenvectors of such a random vector process are utilized to design its eigenportfolios. The performances of the model based and the traditional eigenportfolios are studied and compared to validate the proposed portfolio design method. It is shown that the model based designs yield eigenportfolios that track the variations of the market statistics closely and deliver comparable or better performance. The theoretical foundations of information theory and the rate-distortion theory that provide the basis for source coding methods, including transform coding, are revisited in the dissertation. This theoretical inquiry helps to construct the basic question of trade-offs between dimension of the eigensubspace versus the correlation structure of the random vector process it represents. The signal processing literature facilitates developing an efficient subspace partitioning algorithm to design novel portfolios by combining eigenportfolios of partitions for US equities that outperform the existing eigenportfolios (EP), market portfolios (MP), minimum variance portfolios (MVP), and hierarchical risk parity (HRP) portfolios for US equities. Additionally, the pdf-optimized quantizer framework is employed to sparse eigenportfolios in order to reduce the (trading) cost of their maintenance. Then, the concluding remarks are presented in the last section of the Dissertation

Random Matrix Theory and Fund of Funds Portfolio Optimisation

The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a Fund of Hedge Funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The Inverse Participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.Comment: 17 Page

Applications of Eigensystem Analysis to Derivatives and Portfolio Management

Eigensystem structure plays the key role in principal component analysis (PCA). However, the application of it in high-frequency datasets is noticeably thin, especially for derivatives pricing. In my thesis, I will present the predictive power of eigenvalue/eigenvector analysis in several nancial markets. Performance of prediction based on eigenvalue/eigenvector structure shows the result that this methodology is reliable compared with traditional methodology. To verify the performance of eigensystem analysis in derivatives pricing, I select one of the most important nancial markets: the foreign exchange(FX) option market as datasets. The traditional pricing models for FX options are highly reliant on historical data, which leads to the dilemma that for those contracts with less liquidity investors nd it dicult to provide reliable guidance on price. I will present a brand-new model based on eigensystem analysis to provide accurate guidance for option pricing, especially in cases where the underlying asset is considered to be an illiquid currency pair. The importance of eigenvalues and eigenvectors structure in asset pricing will be explored in this thesis. The empirical study covers FX option contracts across deltas and maturities. The performance of eigensystem model are compared with other widely used models, results indicate that traditional models are outperformed in all selected underlying assets, maturities and deltas. In addition, I perform analysis of machine learning performance based on theFX market's empirical asset pricing problem. I demonstrate the advantage of machine learning in promoting the predictive power of eigensystem based on multiple predictors from the OTC market. Black-Scholes implied volatility is used as predictors for the eigenvalue error between market and our innovative eigensystem. I identify the regression tree algorithm's predictive gain with empirical study across contracts. The eect of currency pairs is numerical and sorted to generate an overview for global FX market structure. I also implement eigenstructure analysis based on the S&P500 market. I discover the convergence of rst principal component explanatory power. In order to generate the statistical summary for trend of principal components, I raise a set of measurements and thresholds to describe eigenvalue and eigenvector structure in market portfolios

What Determines Expected International Asset Returns?

This paper characterizes the forces that determine time-variation in expected international asset returns. We offer a number of innovations. By using the latent factor technique, we do not have to prespecify the sources of risk. We solve for the latent premiums and characterize their time-variation. We find evidence that the first factor premium resembles the expected return on the world market porfolio. However, the inclusion of this premium alone is not sufficient to explain the conditional variation in the returns. We find evidence of a second factor premium which is related to foreign exchange risk. Our sample includes new data on both international industry portfolios and international fixed income portfolios. We find that the two latent factor model performs better in explaining the conditional variation in asset returns than a prespecified two factor model. Finally, we show that differences in the risk loadings are important in accounting for the cross-sectional variation in the international returns.International investment, Asset pricing, Latent variables, Exchange rate risk, Factor models

Nonparametric sign prediction of high-dimensional correlation matrix coefficients

We introduce a method to predict which correlation matrix coefficients are likely to change their signs in the future in the high-dimensional regime, i.e. when the number of features is larger than the number of samples per feature. The stability of correlation signs, two-by-two relationships, is found to depend on three-by-three relationships inspired by Heider social cohesion theory in this regime. We apply our method to US and Hong Kong equities historical data to illustrate how the structure of correlation matrices influences the stability of the sign of its coefficients

Portfolio diversification utilising rolling economic drawdown constraints and risk factor analysis

This study investigates a new asset allocation technique termed Factor Adjusted Rolling Economic Drawdown (FAREDD), whereby resources are allocated to different assets by way of integrating Principle Component Analysis (PCA) with existing Rolling Economic Drawdown Methods (REDD). The primary purpose of this model is to create a portfolio with low drawdown levels, that can withstand turbulent market periods thus protecting portfolio value through providing stronger diversification benefits while still seeking to maximise risk adjusted and overall return. This will have strong implications for investors as it could provide an additional method and tool to be considered during the asset allocation decision stage if they have a strong drawdown aversion. The concept of FAREDD is developed in this study within a South African context and compares this method with several traditional allocation methods including mean-variance optimised models, risk parity as well as traditional rolling economic drawdown models. So far, at the point of writing this study, the author has been unable to find any previous studies documenting this type of application of PCA to REDD. In addition to this, all previous studies that has investigated rolling economic drawdown has been conducted exclusively on the United States of America. The literature finds that REDD provides a viable and superior alternative to traditional asset allocation in the long run. Thus, as part of this study, a second objective is to investigate whether REDD models provide sufficient protection and superior returns in a developing economy with a significantly lower number of available liquid assets and higher volatility due to increased political, economic and business risk, when compared to alternative more traditional allocation techniques. The key findings of this study are that the FAREDD model does outperform the traditional REDD model that it is compared to for the period and it also meets the objective of providing low drawdowns and volatility while achieving strong risk-adjusted returns. However, the model does not provide the strongest drawdown protection of all portfolios tested. The FAREDD model is surpassed by the minimum-variance portfolio in this regard but from a risk adjusted basis and an overall return perspective it far outperforms the minimum-variance portfolio. Therefore, the performance of the FAREDD model is mixed and its optimality would need to be assessed relative to an investor’s risk appetite and risk-return trade-off. In addition to this, the paper finds that the performance of traditional REDD models in the South African context are mixed when compared to traditional asset allocation techniques thereby indicating that REDD models may not be superior in the South African market place at all times. However, they can provide relevant and potential asset allocation alternatives for mangers to consider