Farah, Reid Anton;
(2023)
Risk Models, Portfolio Risk Analytics and Smart Beta Strategies.
Doctoral thesis (Ph.D), UCL (University College London).
Abstract
This thesis investigates original research in modelling risk-driven smart beta strategies. This is motivated by: 1. Investigating the impact of short history on risk models and to offer a more automated risk driven imputations approach for the backfilling of the short history. 2. Investigating three popular types of Risk driven smart beta strategies and introducing the crowding as a strategy: i) Equal Risk Parity (ERC) with formulation of the math problem and offering a solution using an improved form of the sequential quadratic procedure (SQP) which is faster and always converges, then comparing performance against the classical market cap weighted strategies . ii) Naïve Risk Parity with a simplified math and straight solution and then comparing performance against the ERC procedure. iii) Minimum Variance (Volatility) strategy and comparing performance against the ERC procedure. iv) Crowding, we introduce as an investment strategy that holds stocks popular with investors. Smart Beta is a term covering strategies that, although being benchmarked, do not replicate the market cap benchmark by applying some different weighting scheme and claim to yield better performance. This thesis starts by looking into issues that could impact the structure of the risk model and offers a solution, then defines and formulates the strategies mentioned above, then suggests and uses algorithms for finding the portfolio weights for each strategy. The study then investigates the performance against the market cap weighted benchmark and compares the procedures against each other. 4 The thesis comprises 4 investigations, believed by the author to offer original contributions to risk modelling and to the sequential quadratic procedure. The thesis consists of the following studies: Experiment 1: Risk Parity (ERC) in this trial we define the math for the portfolio having the underlying assets equally contributing to the total volatility of the portfolio and then, establish the null hypothesis for testing the performance against the market cap weighted benchmark. Experiment 2: Naïve Risk Parity in this trial we define the math for deriving portfolio with underlying assets equally contributing to the total volatility however with ignoring the covariances between the assets, then establish the null hypothesis for testing the performance against the ERC strategy. Experiment 3: Minimum Variance (Volatility) in this trial we define the math for deriving the portfolio with the minimum possible volatility, then establish the null hypothesis for testing the performance against the ERC procedure. Experiment 4: Crowding in this trial crowding is tested as an investment strategy, the math for determining whether a stock is crowded is explained and then we establish the null hypothesis for testing the performance of an equally weighted and market cap weighted portfolio of the most crowded stocks against the performance of an equally weighted and market cap weighted portfolio of the least crowded stocks. The thesis presents the following original contributions to science: 1. Automated imputation procedure based on the returns of the principal components. Short history leads to badly structured risk models, in the literature review we survey some available imputation procedures however we suggest (joint work with Dr. Michael Benjamin at Bernstein Portfolio Trading Strategy team) a procedure based on the returns of the principal components as an automated procedure that also has control on level and type of the variability explained. 2. Improvement to the Rebonato procedure. The Rebonato procedure can be used to recondition a correlation matrix with the aim to produce a well-defined correlation matrix after introducing own views on pairs of 5 correlations or due to data issues. The current procedure doesn’t converge to the most optimal solution. In our work we propose an iterative adjustment to the Rebonato procedure that will lead to a more optimal solution. 3. Improvements to the sequential quadratic optimisation procedure. There are views that the sequential quadratic optimisation does not always converge. We find this is due to a negative hessian in the first iteration and propose to start the optimisation with a warm start and also to adjust the diagonal of the hessian. These adjustments will insure that the procedure converges and with a lower number of iterations.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Risk Models, Portfolio Risk Analytics and Smart Beta Strategies |
| Language: | English |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10176103 |
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