Modelling probabilities of corporate default

This dissertation follows, scrupulously, the probability of default model used by the National University of Singapore Risk Management Institute (NUS-RMI). Any deviations or omissions are noted with reasons related to the scope of this study on modelling probabilities of corporate default of South African firms. Using our model, we simulate defaults and subsequently, infer parameters using classical statistical frequentist likelihood estimation and one-world-view pseudo-likelihood estimation. We improve the initial estimates from our pseudo-likelihood estimation by using Sequential Monte Carlo techniques and pseudo-Bayesian inference. With these techniques, we significantly improve upon our original parameter estimates. The increase in accuracy is most significant when using few samples which mimics real world data availabilit

Multi-frequency bandwidth Empirical Market Factors in regularised covariance regression

We survey and test non-constructive basis decomposition algorithms capable of analysing the structures present in financial security times series data. We name these implicit financial structures Empirical Market Factors (EMFs) as a homage to Huang et al. (1998) and Empirical Mode Decomposition (EMD) upon which part of this work is based. The EMF covariates are isolated via implicit factor extraction (IFE) which is a decomposition algorithm or feature engineering technique. `Implicit' is used to differentiate these covariates from explicit (easily observable or contructable) covariates such as the return of a market portfolio, ratios of market capitalisations, and book-to-market ratios such as in Fama and French (1993). The forthcoming investment period's covariance structure is forecast using these estimated EMFs in a regularised covariance regression (RCR) framework from Hoff and Niu (2012) to which we made very modest extensions. We present a real-world case study in which we test our method in forecasting the covariance of the potential investments before we weight the portfolio accordingly. The strategies assessed are also restricted to Long/Short Equity (LSE) and Risk Premia Parity (RPP) weighting strategies in which there are cumulative weight shorting restrictions (speci cally the 130/30 strategy) as opposed to restrictions on the individual weights - this mimics real-world shorting limitations. All these techniques and technologies (IFE, RCR, RPP, and LSE) are combined to construct risk-conscious leveraged RPP portfolios using EMFs in a lagged RCR framework

Tutorial on Empirical Mode Decomposition: Basis Decomposition and Frequency Adaptive Graduation in Non-Stationary Time Series

This tutorial explores the class of non-parametric time series basis decomposition methods particularly suited for nonstationary time series known as Empirical Mode Decomposition (EMD). In outlining a statistical perspective of the EMD method, it will be contrasted and combined (for the betterment of both methods) with other existing nonstationary basis decomposition methods. Some such techniques are functional Independent Component Analysis (ICA), Empirical Fourier Decomposition (EFD) (nonstationary extension of the Short-Time Fourier Transform (STFT), Empirical Wavelet Transform (EWT) (nonstationary extension of Morlet Wavelet Transform (MWT)), and Singular Spectrum Decomposition (SSD) (nonstationary extension and refinement of Singular Spectrum Analysis (SSA)). A detailed review of this time series basis decomposition approach is presented that explores 3 core aspects for a statistical audience: 1) the basis functions (Intrinsic Mode Functions (IMFs)) representation and estimation methods including robustness and optimal spline representations including smoothing and knot placements; 2) the computational and numerical robustness of various aspects of the iterative algorithmic design for EMD basis extraction, including treating carefully boundary effects; and 3) the first attempt at a population-based characterisation of EMD that provides a novel stochastic embedding of the EMD method within a stochastic model framework. Furthermore, the basis representations considered will be connected to local frequency graduation smoothing methods, demonstrating that these can be adapted to a local frequency adaptive framework within the EMD context. This will provide new practical insights into the interface between time series basis decomposition and graduation-smoothed representations

Tutorial on Empirical Mode Decomposition: Basis Decomposition and Frequency Adaptive Graduation in Non-Stationary Time Series

This tutorial explores the class of non-parametric time series basis decomposition methods particularly suited for nonstationary time series known as Empirical Mode Decomposition (EMD). In outlining a statistical perspective of the EMD method, it will be contrasted and combined (for the betterment of both methods) with other existing nonstationary basis decomposition methods. Some such techniques are functional Independent Component Analysis (ICA), Empirical Fourier Decomposition (EFD) (nonstationary extension of the Short-Time Fourier Transform (STFT), Empirical Wavelet Transform (EWT) (nonstationary extension of Morlet Wavelet Transform (MWT)), and Singular Spectrum Decomposition (SSD) (nonstationary extension and refinement of Singular Spectrum Analysis (SSA)). A detailed review of this time series basis decomposition approach is presented that explores 3 core aspects for a statistical audience: 1) the basis functions (Intrinsic Mode Functions (IMFs)) representation and estimation methods including robustness and optimal spline representations including smoothing and knot placements; 2) the computational and numerical robustness of various aspects of the iterative algorithmic design for EMD basis extraction, including treating carefully boundary effects; and 3) the first attempt at a population-based characterisation of EMD that provides a novel stochastic embedding of the EMD method within a stochastic model framework. Furthermore, the basis representations considered will be connected to local frequency graduation smoothing methods, demonstrating that these can be adapted to a local frequency adaptive framework within the EMD context. This will provide new practical insights into the interface between time series basis decomposition and graduation-smoothed representations

Package CovRegpy: Regularized covariance regression and forecasting in Python

This paper will outline the functionality available in the CovRegpy package which was written for actuarial practitioners, wealth managers, fund managers, and portfolio analysts in the language of Python 3.11. The objective is to develop a new class of covariance regression factor models for covariance forecasting, along with a library of portfolio allocation tools that integrate with this new covariance forecasting framework. The novelty is in two stages: the type of covariance regression model and factor extractions used to construct the covariates used in the covariance regression, along with a powerful portfolio allocation framework for dynamic multi-period asset investment management. The major contributions of package CovRegpy can be found on the GitHub repository for this library in the scripts: CovRegpy.py, CovRegpy_DCC.py, CovRegpy_RPP.py, CovRegpy_SSA.py, CovRegpy_SSD.py, and CovRegpy_X11.py. These six scripts contain implementations of software features including multivariate covariance time series models based on the regularized covariance regression (RCR) framework, dynamic conditional correlation (DCC) framework, risk premia parity (RPP) weighting functions, singular spectrum analysis (SSA), singular spectrum decomposition (SSD), and X11 decomposition framework, respectively.These techniques can be used sequentially or independently with other techniques to extract implicit factors to use them as covariates in the RCR framework to forecast covariance and correlation structures and finally apply portfolio weighting strategies based on the portfolio risk measures based on forecasted covariance assumptions. Explicit financial factors can be used in the covariance regression framework, implicit factors can be used in the traditional explicit market factor setting, and RPP techniques with long/short equity weighting strategies can be used in traditional covariance assumption frameworks.We examine, herein, two real-world case studies for actuarial practitioners. The first of these is a modification (demonstrating the regularization of covariance regression) of the original example from Hoff & Niu ((2012). Statistica Sinica, 22(2), 729–753) which modeled the covariance and correlative relationship that exists between forced expiratory volume (FEV) and age and FEV and height. We examine this within the context of making probabilistic predictions about mortality rates in patients with chronic obstructive pulmonary disease.The second case study is a more complete example using this package wherein we present a funded and unfunded UK pension example. The decomposition algorithm isolates high-, mid-, and low-frequency structures from FTSE 100 constituents over 20 years. These are used to forecast the forthcoming quarter’s covariance structure to weight the portfolio based on the RPP strategy. These fully funded pensions are compared against the performance of a fully unfunded pension using the FTSE 100 index performance as a proxy

Long/Short Equity Risk Premia Parity Portfolios via Implicit Factors in Regularised Covariance Regression

A robust time series basis decomposition and non-stationary trend extraction technique, known as Empirical Mode Decomposition (EMD), will be combined with Regularised Covariance Regression (RCR) to produce a novel covariance forecasting technique. EMD is designed for multiscale and adaptive time-frequency decomposition in nonstationary time series. EMD-RCR generates multi-time-frequency resolution adaptive forecasting models of predictive covariance forecasts for a universe of selected asset returns. This provides a unique method to obtain predictive covariance regression structures for the short-, mid-, and long-time-scale portfolio dynamics. EMD isolates structures in a frequency-hierarchical fashion (with automated sorting of structures through EMD-MDLP available) which allows this multi-time-frequency covariance forecasting framework that uses the structures isolated using EMD (referred to as IMFs: Intrinsic Mode Functions) as the explanatory variables in the RCR framework. Having developed these techniques, a case study is used for exposition for active portfolio asset management. The case study is based on a dynamic long/short equity and risk premia parity (or risk parity) portfolio-of-portfolios investment strategy using the 11 sectors dividing the 505 stocks of the S&P 500. Each of the 11 sector indices is constructed using a market capitalisation ratio of the companies within the respective sector. The portfolio will be reweighted monthly based on the covariance structure forecast using covariance regression, in which covariance regression factors will be obtained at multiple time-frequency scales endogenously from the ETF asset price returns from each sector. At the end of each month, the covariance is forecast for the next month or investment horizon. This is done using low-, mid-, and high-frequency IMFs isolated using EMD from the 11 sector indices over the previous year. The IMFs isolated from the 11 sector indices over the previous year are fitted against the daily logarithmic returns in the RCR model to make multi-frequency covariance forecasts. We construct long/short equity and risk premia parity portfolios using each different covariance forecast and review the results. The performance of the portfolios will be measured using multiple performance measures (the most relevant being risk-related measures with risk premia parity in focus) and contrasted against multiple benchmark portfolios using several well-known portfolio optimisation techniques such as PCA and multivariate GARCH extensions. This paper promotes what we term “implicit factor" extraction, empirical market factors, and RCR in portfolio optimisation, horizon-specific active portfolio optimisation, long/short equity portfolios, and risk parity portfolios