Selected Projects
Robust Portfolio Optimization: An Empirical Analysis of the Risk-Adjusted Performance of Equity Strategies Constructed with Classical, Bayesian and Machine-Learning Techniques.
This study reviews the empirical evidence over the last decade of the risk-adjusted outperformance of US equity portfolios constructed with robust optimization techniques. The performance of such portfolios is compared to a market-weighted index, a naively diversified (equal-weighted) strategy, Maximal Sharpe Ratio and Global Minimum Variance portfolios constructed within the classical Markowitz optimization framework, a Risk Parity Portfolio and a portfolio optimized with Random Forest techniques. The results confirm that the utilization of robust covariance and return estimators in the portfolio design process yielded significant relative outperformance on a risk-adjusted basis. The paper provides detailed code in Python to facilitate investors’ practical implementation of the strategies and to enable academics to easily replicate and interrogate the results.
IFRS Technical Note: Design and Implementation of a Segmented Lattice-Based Model for the Valuation of Employee Stock Option Plans (ESOP) under IFRS 2: ‘Share-Based Payment’.
The Standard requires that the ESOP model framework should be sufficiently flexible to account for option exercise prior to expiration, a vesting period during which exercise is prohibited, potential option rights forfeiture due to employee exit and time-varying volatility. The restrictiveness of the assumptions inherent in the Black-Scholes-Merton option pricing model render it generally unsuitable for valuing Employee Stock Option Plans. This note describes and implements an IFRS-compliant model which involves constructing a binomial tree which is segmented into 4 domains to integrate: (1) The option’s intrinsic value at terminal nodes; (2) The option values at the nodes in the vesting period; (3) The option values at the nodes in the post-vesting period where the underlying share price is less than some supposed exercise criterion; (4) The option values at the nodes in the post-vesting period where the underlying share price is greater than the supposed exercise criterion.
Volatility Forecasting: Estimating market risk with statistical and implied volatility models under conditions of time-varying volatility, leptokurtotic and skewed distributions and leverage effects.
The assumptions of constant volatility and normally distributed stock returns (lognormally distributed prices) are violated by the empirical observations of price behaviour in both the equity cash and options markets. Notable violations include negatively skewed and fat-tailed distributions, volatility clustering and persistence, asymmetric volatility impacts (the Leverage Effect), the term structure of implied volatility and implied vol’s dependence on moneyness (the volatility smile and skew). This note provides both the detailed theoretical context and code for implementation of several methods of risk estimation which capture systematically observed phenomena in asset return time series and option-implied distributions. These methods include the Generalised Autoregressive Conditional Heteroskedasticity (GARCH) and GJR-GARCH models, instantaneous VaR estimation with implied volatility, the extraction of indicators of non-normality from the implied volatility surface, the determination of implied risk-neutral distributions from the volatility smile via the Breeden-Litzenburger approach and the generation of correlated stochastic processes for the volatility level and stock price with the Heston Model.
IFRS Technical Note: Design and Implementation of Credit Valuation Adjustment (CVA) Model for a Portfolio of OTC Derivatives under IFRS 9: ‘Financial Instruments’.
This note begins with a summary and interpretation of the guidance on valuation principles in the Standard before demonstrating a technique to calculate a Credit Valuation Adjustment (CVA) for a portfolio of Interest Rate Swaps (IRS). The CVA is computed to reflect the present value of the credit risk related to the instruments until expiry. The expected (positive) exposure (EE) is obtained by simulating the price process of the underlying reference interest rate and the marked-to-market valuation (MTM) valuation of the swap. A Hull-White One Factor Model calibrated to the swaptions market is employed in the Monte Carlo simulation for this purpose. The probability of default (PD) is derived from the Credit Default Swap (CDS) Market.
IFRS Technical Note: Design and Implementation of an Expected Credit Loss (ECL) Model for a Portfolio of Credit Card Receivables under IFRS 9: ‘Financial Instruments’.
According to the Standard, the ECL calculation model should compute an unbiased and probability-weighted amount to be presented as an impairment to the book value of the financial assets in the balance sheet. The amount is the difference between the present value of contractual cashflows and the present value of cashflows that an entity expects to receive. The ECL is determined by the probability of default, the size of the exposure to defaulting customers, the expected recoverable amount in the event of default and the discount rate applied. The estimated size of the exposure is related to the expectations of the customers’ drawdown of the undrawn commitment over a defined time frame. The model should incorporate an expectation of the effect of correlation between the constituent assets. Following a detailed interpretation of the Standard and a description of the model design, I present the implementation of an IFRS-compliant model for the valuation of the ECL of a portfolio of credit card receivables.
Derivative Valuation: A Comparative Analysis of the Cox Ross Rubinstein (CRR) and Longstaff & Schwartz (LS) Methods for the Valuation of American-Style Options.
This project compares the prices obtained from the two most common methods employed for the valuation of American-Style options. We implement the binomial “tree-based” technique of Cox Ross Rubinstein (CRR) and the least-squares Monte Carlo method of Longstaff & Schwartz (LS). The design, implementation and output of both are validated by comparing our results to those produced in the academic literature.
Quantifying Tail Risk: An Implementation of Three Techniques to Model the Value-at-Risk of a Multi-Currency Portfolio Over a Specified Time Horizon.
This note begins by detailing the theoretical basis of the most common techniques to estimate the VaR of a portfolio composed of risky assets with correlated returns, namely the Delta-Normal (Variance-Covariance) Method, the Monte Carlo Simulation Method and the Bootstrap Historical Simulation Method. I proceed to implement the models in Python and compare the results.
Quantifying Tail Risk: Modelling Operational Value-at-Risk with the Loss Distribution Approach.
Based on empirical loss event data, a loss distribution is estimated by modelling the probability of loss events and the magnitude of potential losses attributable to the materialization of specified operational risks . To estimate aggregate losses over a period of time, the Loss Distribution Approach (LDA), is employed, a technique which convolutes the loss frequency distribution and the loss severity distribution to model an objective loss distribution. Based on this simulated loss distribution, we can state with a determined confidence level that losses due to operational risk will not exceed a certain dollar amount. This note explains and demonstrates an implementation in Python of the LDA model.
Performance Analysis: Evaluation of the Ex-Post Performance of Securities and Rules-Based Strategies on an Absolute, Relative and Risk-Adjusted Basis.
In this project I implement a model which backtests the returns of common rules-based portfolio diversification strategies with monthly rebalancing. The model enables a comparative analysis of the performance of the active and passive strategies by computing their risk-adjusted performance metrics (RAPM). In this context, risk is variously defined as volatility, downside volatility, skewness, kurtosis, Gaussian VaR, Modified (Cornish-Fisher) VaR, Historic VaR, Conditional VaR and Maximum Drawdown.
Care, Custody, & Control (CCC): Identification, quantification, and mitigation of cryptocurrency custodial risk.
The combination of the blockchain technology and the cryptographic protocols upon which Bitcoin and many other cryptocurrencies are founded gives rise to complex challenges in the context of asset safekeeping. The Digital Signature Scheme means that whoever holds the private key owns the asset. The immutability of the Blockchain means that transactions recorded on the distributed ledger are permanent and irreversible. This study develops a comprehensive database documenting loss events since the birth of Bitcoin. Using the empirical data, we employ an actuarial technique to estimate losses in the cryptocurrency universe. We examine the risks associated with auto-custodial solutions and offer recommendations on security hygiene for different types of wallets. We recommend multi-signature technology with protections against so-called “paralysis” where a key shareholder is unavailable or uncooperative. Finally, recognizing that trusted third party custodians will dominate the crypto landscape in the medium term, we describe a best practice framework which asset holders should observe when seeking to delegate the function of key management.