Stochastic Dominance Efficiency Tests under Diversification

This paper focuses on Stochastic Dominance (SD) efficiency in a finite empirical panel data. We analytically characterize the sets of unsorted time series that dominate a given evaluated distribution by the First, Second, and Third order SD. Using these insights, we develop simple Linear Programming and 0-1 Mixed Integer Linear Programming tests of SD efficiency. The advantage to the earlier efficiency tests is that the proposed approach explicitly accounts for diversification. Allowing for diversification can both improve the power of the empirical SD tests, and enable SD based portfolio optimization. A simple numerical example illustrates the SD efficiency tests. Discussion on the application potential and the future research directions concludes.Stochastic Dominance, Protfolio Choice, Efficiency, Diversification, Mathematical Programming

State-dependent Asset Allocation Using Neural Networks

Changes in market conditions present challenges for investors as they cause performance to deviate from the ranges predicted by long-term averages of means and covariances. The aim of conditional asset allocation strategies is to overcome this issue by adjusting portfolio allocations to hedge changes in the investment opportunity set. This paper proposes a new approach to conditional asset allocation that is based on machine learning; it analyzes historical market states and asset returns and identifies the optimal portfolio choice in a new period when new observations become available. In this approach, we directly relate state variables to portfolio weights, rather than firstly modeling the return distribution and subsequently estimating the portfolio choice. The method captures nonlinearity among the state (predicting) variables and portfolio weights without assuming any particular distribution of returns and other data, without fitting a model with a fixed number of predicting variables to data and without estimating any parameters. The empirical results for a portfolio of stock and bond indices show the proposed approach generates a more efficient outcome compared to traditional methods and is robust in using different objective functions across different sample periods

Value-at-Risk time scaling for long-term risk estimation

In this paper we discuss a general methodology to compute the market risk measure over long time horizons and at extreme percentiles, which are the typical conditions needed for estimating Economic Capital. The proposed approach extends the usual market-risk measure, ie, Value-at-Risk (VaR) at a short-term horizon and 99% confidence level, by properly applying a scaling on the short-term Profit-and-Loss (P&L) distribution. Besides the standard square-root-of-time scaling, based on normality assumptions, we consider two leptokurtic probability density function classes for fitting empirical P&L datasets and derive accurately their scaling behaviour in light of the Central Limit Theorem, interpreting time scaling as a convolution problem. Our analyses result in a range of possible VaR-scaling approaches depending on the distribution providing the best fit to empirical data, the desired percentile level and the time horizon of the Economic Capital calculation. After assessing the different approaches on a test equity trading portfolio, it emerges that the choice of the VaR-scaling approach can affect substantially the Economic Capital calculation. In particular, the use of a convolution-based approach could lead to significantly larger risk measures (by up to a factor of four) than those calculated using Normal assumptions on the P&L distribution.Comment: Pre-Print version, submitted to The Journal of Risk. 18 pages, 17 figure

Dynamic Asset Allocation in a Conditional Value-at-risk Framework

The thesis first extends the original Black-Litterman model to dynamic asset allocation area by using the expected conditional equilibrium return and conditional covariances based on three volatility models (the DCC model, the EWMA model and the RW model) into the reverse optimisation of the utility function (the implied BL portfolio) and the maximised Sharpe ratio optimisation model (the SR-BL portfolio). The momentum portfolios are inputted as the view portfolios in the Black-Litterman model. The thesis compares performance of the dynamic implied BL portfolio and the dynamic SR-BL portfolio in the single period and multiple periods with in-sample analysis and out-of-sample analysis. The research finds that dynamic BL portfolios can beat benchmark in in-sample and out-of-sample analysis, the dynamic implied BL portfolio always show better performance than the dynamic SR-BL portfolio. The empirical VaR and CVaR of the dynamic SR-BL portfolios are much higher than that of the dynamic implied BL portfolio. The dynamic BL portfolios based on the DCC volatility model perform best in contrast to other two volatility models. In the aim of improving performance of SR-BL portfolios, the thesis further constructs dynamic BL portfolios based on two new optimisation models including maximised reward to VaR ratio optimisation model (MVaR-BL portfolios) and maximised reward to CVaR ratio optimisation model (MCVaR-BL portfolios) with assumption of the normal distribution and the t-distribution at confidence levels of 99%, 95% and 90%. The thesis compares performance of the dynamic MVaR-BL portfolio and the dynamic MCVaR-BL portfolio in the single period and multiple periods with in-sample analysis and out-of-sample analysis. There are three main findings. Firstly, both the MVaR-BL portfolio and the MCVaR-BL portfolio could improve the dynamic SR-BL portfolio performance at moderate confidence levels. Secondly, the MVaR-BL portfolio and the MCVaR-BL portfolio show similar performance with normal distribution assumption, the MCVaR-BL portfolio performs better than the MVaR-BL with t-distribution assumption at certain confidence levels in single period and multiple periods. Thirdly, the performance of the DCC-BL portfolio with t-distribution assumption is superior to the performance of the DCC-BL portfolio with normal distribution assumption. As the result of higher empirical VaR and CVaR of dynamic SR-BL portfolios, the thesis develops to constrain VaR and CVaR in construction of dynamic BL portfolios with assumption of the normal distribution and the t-distribution at confidence levels of 99%, 95% and 90%. The research studies the effect of assumptions of two distributions, three confidence levels and levels of the VaR constraint and the CVaR constraint on dynamic BL portfolios. Both in-sample performance and out-of-sample performance could be improved by imposing constraints, and they suggest adding moderate CVaR constraints to maximal Sharpe ratio optimisation model with t-distribution at certain confidence level could obtain the best dynamic DCC-BL portfolio performance in the single period and multiple periods. The performance evaluation criterion (higher Sharpe ratio, reward to VaR ratio, and reward to CVaR ratio) would affect the choice of optimisation models in dynamic asset allocation

Sharp style analysis in the MSCI sector portfolios: a Monte Carlo integration approach

We examine a decision-theoretic Bayesian framework for the estimation of Sharpe Style portfolio weights of the MSCI sector returns. Following van Dijk and Kloek (1980) an appropriately defined prior density of style weights can incorporate non-negativity and other constraints. We use factor-mimicking portfolios as proxies to global style factors such as Value, Growth, Debt and Size. Our computational approach is based on Monte Carlo Integration (MCI) of Kloek and van Dijk (1978) for the estimation of the posterior moments and distribution of portfolio weights. MCI provides a number of advantages, such as a flexible choice of prior distributions, improved numerical accuracy of the estimated parameters, the use of inequality restrictions in prior distributions and exact inference procedures. Our empirical findings suggest that, contrary to existing evidence, style factors do explain the MSCI sector portfolio returns for the particular sample period. Further, non-negativity constraints on portfolio weights were found to be binding in all cases

State-dependent asset allocation using neural networks

Changes in market conditions present challenges for investors as they cause performance to deviate from the ranges predicted by long-term averages of means and covariances. The aim of conditional asset allocation strategies is to overcome this issue by adjusting portfolio allocations to hedge changes in the investment opportunity set. This paper proposes a new approach to conditional asset allocation that is based on machine learning; it analyzes historical market states and asset returns and identifies the optimal portfolio choice in a new period when new observations become available. In this approach, we directly relate state variables to portfolio weights, rather than firstly modeling the return distribution and subsequently estimating the portfolio choice. The method captures nonlinearity among the state (predicting) variables and portfolio weights without assuming any particular distribution of returns and other data, without fitting a model with a fixed number of predicting variables to data and without estimating any parameters. The empirical results for a portfolio of stock and bond indices show the proposed approach generates a more efficient outcome compared to traditional methods and is robust in using different objective functions across different sample periods

A behavioural approach to financial portfolio selection problem: an empirical study using heuristics

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel UniversityThe behaviourally based portfolio selection problem with investor's loss aversion and risk aversion biases in portfolio choice under uncertainty are studied. The main results of this work are developed heuristic approaches for the prospect theory and cumulative prospect theory models proposed by Kahneman and Tversky in 1979 and 1992 as well as an empirical comparative analysis of these models and the traditional mean variance and index tracking models. The crucial assumption is that behavioural features of the (cumulative) prospect theory model provide better downside protection than traditional approaches to the portfolio selection problem. In this research the large scale computational results for the (cumulative) prospect theory model have been obtained. Previously, as far as we aware, only small laboratory (2-3 arti cial assets) tests has been presented in the literature. In order to investigate empirically the performance of the behaviourally based models, a differential evolution algorithm and a genetic algorithm which are capable to deal with large universe of assets have been developed. The speci c breeding and mutation as well as normalisation have been implemented in the algorithms. A tabulated comparative analysis of the algorithms' parameter choice is presented. The performance of the studied models have been tested out-of-sample in different conditions using the bootstrap method as well as simulation of the distribution of a growing market and simulation of the t-distribution with fat tails which characterises the dynamics of a decreasing or crisis market. A cardinality and CVaR constraints have been implemented to the basic mean variance and prospect theory models. The comparative analysis of the empirical results has been made using several criteria such as CPU time, ratio between mean portfolio return and standart deviation, mean portfolio return, standard deviation , VaR and CVaR as alternative measures of risk. The strong in uence of the reference point, loss aversion and risk aversion on the prospect theory model's results have been found. The prospect theory model with the reference point being the index is compared to the index tracking model. The portfolio diversi cation bene t has been found. However, the aggressive behaviour in terms of returns of the prospect theory model with the reference point being the index leads to worse performance of this model in a bearish market compared to the index tracking model. The tabulated comparative analysis of the performance of all studied models is provided in this research for in-sample and out-of-sample tests