Title: Rebalancing Portfolio to Minimize Squared Tracking Error (April - June 2021)
Supervisor: Dr. Steve Murray
This project focused on rebalancing a passively managed Real Estate Investment Trusts (REITS) portfolio over five distinct time points. The portfolio was rebalanced to ensure that the active risk of the portfolio remained low. The portfolio was rebalanced over five weeks despite knowledge of what the current and future benchmark entailed at week zero. This strategy ensured that the cost of rebalancing was low due to dampened market impact from rebalancing. It was also a simulation of real-world constraints wherein liquidity and transaction costs prevent a simple one-time rebalancing.
The first part of the project involved formulating a quadratic expression for the objective function - minimizing the weighted sum of squared tracking error relative to the current and future benchmark. The objective incorporated current as well as the future benchmark to ensure that the portfolio's active risk, which was measured relative to the current benchmark at all time points besides week five, did not increase extensively during any one week. This part also entailed determining a mathematical expression for the constraints (no shorting, full investment each week, and active return of two basis points each week).
In the next part, I cleaned and parsed the data and then implemented the mathematical expressions from the first part in Python using the Quadprog optimization package to determine the weights that the portfolio should hold in each security in each week. As the last step, I analyzed the solution to provide key insights on the rebalancing process, identifying extensions to the implementation approach that would lead to a more accurate solution. This project gave me exposure to the type of problems passive asset managers and the strategies they employ to reduce costs.
Title: Data Analysis and Machine Learning for Bankruptcy Prediction (April - June 2021)
Supervisor: Dr. Kevin Lu
The project explored bankruptcy prediction to develop a machine learning model that could accurately identify companies that would go bankrupt. Predicting bankruptcy is important since it allows lenders to decide whether or not they want to initiate or continue a credit line (loan) with companies.
In this project I used SQL to perform preliminary data analysis which included extracting relevant data, parsing it into a feature set (Industrial, Management, Financial Flexibility, Credibility, Competitiveness, and Operating Risks), and using cleaning the data using pre-processing pipelines. Data from 250 firms were divided into training and test sets. Then with the help of Sklearn and Tensorflow packages, supervised and unsupervised machine learning algorithms were implemented with bankruptcy as a categorical target variable. The accuracy of the different models was compared to evaluate the best model. These results were substantiated by plotting precision vs accuracy curves and looking at the ROC score. Finally, an algorithm using decision trees and neural networks was implemented on the test data to gain key insights into identifying feature combinations that lead to bankruptcy.
Title: Strong Future or Unnecessary Optimism - Financial Analysis of Apple Inc. and its competitors (January-March 2021)
Supervisor: Dr. Jhon Guerard
This project was a comprehensive analysis of the technology sector of the United States. The analysis was based on data from 1960-2020 which was taken from Compustat Wharton Research Data System (WRDS). I analyzed Apple and its competitors (Intel Corporation, IBM Corporation, Sony Corporation, and AT&T) in four modules.
The first module involved a comprehensive analysis of the health of the company. I used R and SAS to calculate profitability, efficiency, leverage, and liquidity ratios along with the companies' Altman Z score and Corporate Exports up until 2020. In the second module, I ran a regression of the returns against the S&P 500 to determine the company's beta. The figures were then used to determine the discount rate through the cost of equity and the Weighted Average Cost of Capital. Using the Free Cash Flow method, I determined the intrinsic value of the company and compared it with the market value to present a buy-sell decision (I decided to buy Intel and sell Apple). In the third module, I substantiated my buy-sell decision by further analysis. I calculated the price-to-earning ratio of Apple and its competitors and compared the result with the industry ratios. I ended up with the same decision to buy Intel and sell Apple. In the last module, I ran an ARIMA model to forecast the Sales and Net Income figures up until 2025. I ran tests to check for the normality of my model. I ran tests including a check for influential and outlier observations using tests such as studentized residual test, Cook's ratio, and Hat ratio.
The project allowed me to work with real-world data and it exposed me to problems related to data cleaning and management which are often not considered in theoretical settings. I worked with missing data and incorporated the effects of multicollinearity, trend, and seasonality in the data. I carried out hypothesis testing and used F tests and chi-square tests to establish the significance of my regression results. I was able to apply different statistical metrics which built on my understanding of how analysts value growth and value stocks differently.
Title: Customized Retirement Advice - Private Wealth Management (September-December 2020)
Supervisor: Dr. Steve Murray
This project focused on investing retirement savings, in an optimum manner, of six individual investors to increase the likelihood that they would meet their retirement goal. Each individual had unique financial circumstances and retirement goals. The project was divided into three parts. In part one, I wrote the mathematical formulation of the dynamic and stochastic optimization problem. In the second part, I implemented the problem in R. I incorporated appropriate probability distributions while running simulations to determine appropriate investment action at each year up till investors' retirement. Lastly, I reported and defended the investment decisions to the class. Through this project, I was able to apply my learnings in optimizing investment decisions in a real-world problem (a problem that is particularly common in the wealth management domain).
Title: Valuation of Oil and Marketing Companies (OMC) of Pakistan with a Buy-Sell decision (January-May 2018)
Supervisor: Dr. Salman Khan
I applied various valuation techniques including the Free Cash Flow model and Comparative Price model to determine the intrinsic value of Shell Pakistan and Petroleum State Oil (PSO). In the first phase, I cleaned historic data of OMCs of Pakistan and then used a mixed approach (top-down and bottom-up) to determine the growth rate for each company. The main macro-economic factors leading the top-down approach were: international oil prices, shipping costs, storage cost, distribution cost, government policies, and regulation. The micro-economic factors were both quantitative and qualitative. For quantitative factors, I analyzed the company's income statement and balance sheet. I calculated ratios that highlighted the company's working capital management, return on investment, quality of assets, and liabilities. Within qualitative factors, l analyzed the company's management, board stability, company reputation. Additional external factors linking the company to the economy were also considered. These included liquidity in the financial markets and the company's ability to finance projects. After calculating the growth rate, I constructed a projected cash flow statement.
In the second phase, I ran a regression (after cleaning the data) of weekly returns against the market index (KSE-100) and determined the beta (sensitivity of stock returns to market index) of each company. Using the beta, I calculated an investor's required rate of return for each company (discounting factor). I used the discounting factor, to calculate the intrinsic value of the projected cash flow statement from phase 1. I compared the intrinsic value with the existing price of the stock to determine that the stock was undervalued, signaling investors to make a buy decision. Comparative Price analysis substantiated the results of the Free Cash Flow model and also determined that Shell Pakistan and PSO were undervalued.
Title: Resource optimization for Engro Foundation (September-December 2016)
Supervisor: Dr. Zehra Waheed
I examined the effectiveness of the System Productivity Innovative Rice Trainings (SPIRIT) program, a Corporate Social Responsibility (CSR) initiative, on farmers' agricultural productivity in Punjab and Sindh. The first objective of the program was to educate farmers on methods through which they could increase their harvest per acre for rice. The second aim was to make efficient use of water and machinery to reduce costs, and to avoid crop losses during plantation and harvest. The last aim of the program was to educate and mobilize the women workforce in order to improve agricultural productivity. During the research, I assessed the scope, objectives, and implementation framework by working closely with Engro Foundation’s business units in Southern Punjab. I wrote a detailed report comparing planning and scheduling activities of SPIRIT with best practices outlined by project management theory. I revamped the scheduling activities using Microsoft Project to identify improvement opportunities throughout the project. The research allowed Engro Foundation to complete the project two weeks prior to the deadline
Title: Impact of government expenditure on health on deaths per 100,000 due to Tuberculosis (September-December 2015)
Supervisor: Dr. Mohsin Nasir
In this study, I made using of statistical tools such as R to establish the impact of 10 additional independent variables on the Tuberculosis death rate i.e. number of deaths per 100,000 people. The data was taken from the World Bank and World Health Organization (WHO) on deaths due to Tuberculosis, the number of cigarettes per adult per year, etc (these were a few of the independent variables). I cleaned and compiled data from these secondary sources, and developed multiple linear regression models using a step-up approach. A variable was added to the regression analysis only if it led to an increase in adjusted R square. As a result of hypothesis testing, I determined a statistical relationship between government expenditure on health and the Tuberculosis death rate. To build on my results and to improve the strength of my results, I determined correlations between variables using R software and then adjusted my regression model accounting for the correlations.
Course: Simulation Modelling and Analysis (DISC 324)
Instructor: Dr. Mohsin Nasir
In the first half of the course, I studied the theoretical concepts for modeling business operations through case studies. I then applied these concepts to multiple businesses to gain a practical viewpoint. Additionally, I learned the application of Simio software in this course. The final project involved determining process flows that optimized business profits in the given constraints.
Course: Economics of Investment and Finance (ECON 363)
Instructor: Usman Khan
In this course, I studied financial instruments and the processes and analysis of investments in financial markets. I was exposed to the theory and practice of investment decisions with the different financial instruments used as investment tools to implement those decisions. In the second half of the course, I studied modern tools of investment such as options and futures along with real applications in risk management and hedging techniques.