MSc.MF Theses and Dissertations (2021)

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Savings and Credit Co-operative Societies as investment vehicles to enhancing affordable housing: a case of Kenyan SACCOs
(Strathmore University, 2021) Wambui, David Nyaga
The study seeks to explore whether SACCOs can profitably invest in affordable housing through special-purpose investment vehicles such as REITs. The ultimate goal is to increase the domestic funding of the affordable housing agenda. To carry out the study, we built a hypothetical portfolio for the SACCOs using three asset classes namely: Treasury Bonds, Treasury Bills, and seven stocks from the Nairobi Securities Exchange with the best Sharpe ratio and calculated the expected return and standard deviation of that portfolio. We then added real estate (REITs) as the fourth asset class and calculated the expected return and standard deviation of the portfolio and compared the results. From the research, we find that though SACCOs can reduce the housing finance deficit as evidenced by their huge asset base, it is not profitable for them to invest in housing through REITs as this declines their portfolio return. However, these results do not bar them from investing directly in housing since they can offer housing loans to their members in their bid to provide affordable housing and in return earn interests from those loans.
Dynamic portfolio optimization using reinforcement learning
(Strathmore University, 2021) Yegon, Donald Kibet
This study uses machine learning in the development of a dynamic investment strategy for portfolio optimization. We aim to explore the efficiency of this approach over a passively managed portfolio and assess the whether transaction costs erode the gains in the dynamically managed portfolio. To this end we explore the application of recurrent reinforcement learning for optimal asset allocation of a portfolio consisting of stock prices for six companies in different sectors. We develop an environment based on monthly historic prices of these stocks and a re-balancing agent that acts on the environment. The risk and return factors of the individual stock are taken as the state of the environment. Using a modified version of Sterling Ratio as the performance measure, we select model parameters through direct recurrent reinforcement learning from historical data and test the efficacy of the strategy on unseen data. From the analysis we find that the regularly re-balanced portfolio out performs the market portfolio based on buy and hold strategy based on both the terminal wealth and the risk adjusted return measure.
Empirical performance of alternative risk measures in portfolio selection - the case of South African stock market
(Strathmore University, 2021) Macharia, Richard
Portfolio selection is the process of apportioning capital to a finite number of assets given the wider set of all investment options. The decision of best combination of assets to invest in is the subject of debate among practitioners and researchers alike. Individuals face a multitude of constraints when making allocation decisions thus their patterns of investing are wildly different. However, economists have studied asset price patterns for long enough to be able to pick out aggregate patterns and develop a theory of decision making: Utility Theory.
Modelling and forecasting of crude oil price volatility: comparative analysis of volatility models
(Strathmore University, 2021) Ng’ang’a, Faith Wacuka
This study aims at providing an in-depth analysis of forecasting ability of different GARCH models and to find the best GARCH model for VaR estimation for crude oil. The VaR forecasting performance of GARCH-type models are analyzed and compared in a long horizon; based on the Kupiecs POF-test and Christoffersens interval forecast test as well as a Backtesting VaR Loss Function. Crude oil is one of the most important fuel sources and has contributed to over a third of the world’s energy consumption. Oil shocks have influence on macroeconomic activities through various ways. Sharp oil price changes delay business investment because they raise uncertainty thus reducing aggregate output for some time. Modelling and forecasting of crude oil prices plays a significant role in supporting policy and decision making in the economy. Successive developments of models used provide opportunities to analyse crude oil market in depth and improve the accuracy of oil price forecasting. The study uses Brent Crude Oil prices data over a period of ten years from the year 2011 to 2020. The study finds that the IGARCHT distribution model is the best model out of the five models for VaR estimation based on LR.uc Statistic (0.235) and LR.cc Statistic (0.317) which are the least among the values realized. ME and RMSE for the five models used for forecasting have negligible difference. However, the IGARCH model stands out with IGARCH- T-distribution being the best out of the five models in this study with ME of 0.0000963591 and RMSE of 0.05304335. We therefore conclude that the IGARCH- T distribution model is the best model out of the five models used in this study for forecasting Brent crude oil price volatility as well as for VaR estimations.
Analysis of risk measures in portfolio optimization for the Uganda Securities Exchange
(Strathmore University, 2021) Birungi, Criscent
For the most recent years, risk has become one of the essential parameters in portfolio optimization problems. Today most practitioners and researchers in portfolio optimization have used variance as a standard risk measure. This approach has been found subjective. The Markowitz (1952) mean-variance model considered variance as an adequate portfolio risk measure, and asset returns are multivariate normally distributed and that investors have a quadratic utility function which is subjective too. Other risk measures have been suggested to overcome the limitations of the mean-variance model. This paper analyzes which portfolio optimization models can better explain the optimal portfolio performance (high return, low risk) for the Uganda Security Exchange(USE). We compare Mean-Variance (MV), Mean Absolute Deviation (MAD), Robust Portfolios and Covariance Estimation Models( The Shrinked Mean-Variance (SMV) Models & Alternative Covariance Estimator (ACE) Models ) and Mean-Conditional Value-at-Risk (Mean-CVaR) models in terms of the risk and performance. Portfolios were developed by employing the MV, MAD, SMV, ACE and Mean-CVaR models. For the computed monthly returns and price data (February 2010 to January 2021) for USE selected stocks, we considered the results show that Mean-CVaR and ACE portfolios have the highest performance ratio compared to other models. We find that VaR is the best risk measure for portfolio optimization for the USE since it has lower values across all models than other risk measures. It is vital to consider all the available risk measures for a regulator or practitioner to make a good decision since using one can be subjective; as seen in our results, different risk measures yield different results.
An Empirical evaluation of alternative asset allocation policies for emerging and frontier market investors in Africa
(Strathmore University, 2021) Okwaro, Douglas Job
Despite forming an integral part of literature and practitioner knowledge, Markowitz based optimization has been shown to suffer severe drawback of estimation errors and sensitivity to input parameters when implemented in practice. The best diversification methods from the perspective of a private investor in real-life situations still remains largely unsolved. Most of the potential diversification benefits so far have primarily been analyzed for internationally diversified stock portfolios, with focus on the special viewpoint of U.S investors. Studies have suggested that the Mean-Variance optimization can be robustified by the use of robust covariance estimators other than the sample covariance that relies on the classical Maximum Likelihood Estimator. Using a portfolio formed from 2 Emerging Market and 5 Frontier Market indices in Africa, this study sought to compare the performance of the traditional Mean-Variance model against the performance of the Mean-Variance optimization model robustified with the Orthogonalized Gnanadesikan-Kettenring, Minimum Covariance Determinant, Minimum Volume Ellipsoid and shrink estimators, with an aim of recommending the best model applicable to the African emerging and frontier markets investors. The robustified models were found to indeed have better characteristics in terms of gross returns, annualized returns and net portfolio returns over time compared to the traditional Mean-Variance optimization model.
A Comparative modelling of price dynamics of Certified Emission Reductions using diffusion processes: a case study of the European Energy Exchange
(Strathmore University, 2021) Kariuki, Evalin Wanjiru
In this study, the price dynamics of Certified Emission Reductions were forecasted by comparing and acquiring the most consistent and accurate forecast model using the diffusion processes: Geometric Brownian Motion, Vasicek Model and Mean Square Root Process. The assumption of each model with drift and diffusion component were investigated focusing on the Certified Emission Reductions prices traded within European Energy Exchange (EEX) between the years of 2012-2020.The forecasted prices were compared to the actual to evaluate the validity of the models. Based on the research findings, Bayesian information criterion, which determined the goodness of fit to assess the performance of the model with respect to how well it explains the data, shows that vasicek model is the most preferred model among the three models since it has the lowest Bayesian information criterion (BIC). This study compared the accuracy of the models, Geometric Brownian Motion, Vasicek Model and Mean Square Root Process, in terms of forecasting the price dynamics of CERs, and concluded the vasicek most is the most accurate among the three models since the predictive power is high toward a specified time frame proven by the lower value of mean absolute error and Mean Absolute Percentage Error.
Modelling the relationship between spot and futures prices: an empirical analysis of the South African Power Pool
(Strathmore University, 2021) Mutembei, Kellyjoy Makena
This study investigates the relationship between electricity spot and future prices in the South African Power Pool (SAPP). The objectives of the study included investigating whether forward prices in the SAPP are a true and unbiased estimate of the observable spot prices by determining whether or not a forward premium exists in the market. Investigating whether the forward premium (if it exists) can be explained by the behaviour of spot prices in the market in the period preceding delivery and lastly whether current future prices in the SAPP can be used to predict future spot prices in the market. The study used daily electricity spot prices in the SAPP for the period between April 1, 2017 and January 31, 2021 and electricity futures price data for weekly and monthly contracts during the same period. Relying on methodologies highlighted in the expectation hypothesis to describe the relationship between spot and futures prices, results indicate the existence of positive significant premiums in the market for the sample period. The premiums decrease with increasing maturity with the value of relative forward premiums ranging between 1.23 USD/MWh for peak weekly contracts to 0.46 USD/MWh for peak monthly contracts. Power purchasers in the SAAP are on average incurring a cost that inflates their cost of power by 0.24% to 1.23% depending on the hedging strategy they adopt and type of contracts they select. To explain the risk premia, the study followed methodologies highlighted in the General Equilibrium Model. Ordinary Least Square (OLS) regression results for forward premia modelling suggests that for some of the contracts in the SAPP, forward premiums can be at least partially explained by the mean, variance, standard deviation and skewness of the spot prices in the period preceding delivery. Particularly, the premiums have a negative relationship with average spot prices and a positive relationship with skewness. This implies that the higher the average spot price level, the lower the likelihood of overestimating future prices thus the lower the premium. Additionally, the higher the probability of upward price spikes, the higher the futures price thus the higher the premium. Lastly, to investigate forecasting ability of electricity futures in the SAPP, the study relied on the fundamentals of futures pricing suggested in the expectation hypothesis. Results reveal that future’s prices at the SAPP do not contain significant forecasting power over future spot prices in the SAPP. They reveal that variations in the forward premiums in the market are attributable to time varying risk premiums. The SAPP to a large extent relies on coal and nuclear power for electricity generation thus this could explain the reason why results led to the conclusion of the existence of time varying risk premiums.
Stochastic modeling of electricity prices and option pricing
(Strathmore University, 2021) Omungoh, Philgonah Awuor
Volatility and abrupt price changes is a problem that has marred the electricity market for decades. This problem is especially observed in deregulated markets whose prices are influenced by supply and demand factors. Another consideration is the fact that electricity is non-storable which means that its prices are quite difficult to control. In an effort to address these problems, the current study was developed to price electricity and options used to hedge against volatility and unexpected price jumps. The mean reverting jump diffusion was applied by taking into account day ahead spot prices derived from the Nordic electricity market or the Nord Pool. To price spread options, I applied the Monte Carlo simulation model. The analysis of the data was undertaken through R programming undertaken within the Anaconda software. The need to price electricity options was to furnish market participants with instruments to manage the financial risks that come with price volatility due power failure and demand factors. The analysis shows the complex nature of electricity pricing, hence there is no closed form solution for pricing these derivatives. While the study findings were not directly applicable to the Kenyan and East African context, it provided a robust context for future research especially as the need for a deregulated market grows in the country.
Predictability of stock returns at Nairobi Securities Exchange
(Strathmore University, 2021) Mrabu, Omar Matano
Stock market is regarded as a leading indicator of all possible changes in the economy as it reflects investors' expectations of future economic conditions. In this regard, stock investors are always concerned about the direction of stock price movement because this directly determines their future wealth through capital gains and losses. They constantly study and review the market to understand the emerging trends which can affect firm performance. While extensive literature provides evidence that firm characteristics are essential in forecasting stock returns hence play pivotal role in determining the profitability of listed firms, this study sought to assess the role of key valuation ratios i.e., book to market ratio, price to earnings ratio and dividend per share in predicting stock returns of selected firms at the Nairobi Securities Exchange (NSE). Using seven listed firms and daily data spanning 1st January 2015 to 31st December 2019 and a static pooled panel data model, and controlling for firm size, leverage and beta, the study established that the selected valuation ratios do not depict significant effects on stock returns and recommends that these ratios can be ignored when predicting future stock returns of the selected firms.
Construction of a Financial Inclusion Index for Kenya
(Strathmore University, 2021) Wafula, Kelly Akuku
This study constructed a Financial Inclusion Index (FII) to measure access to, availability of and usage of financial services in Kenya using data collected from IMF reports for the period 2013 – 2019. A two-stage principal component analysis (PCA) method was applied in constructing the FII that was found to satisfy the Kaiser-Meyer-Olkin (KMO) measure to both the indicators and the dimensions. The research offers ideas for policy-making by highlighting the contributions of the variables to the dimensions, subsequently, the contributions of the dimensions to the index. Therefore, the FII can act as an analytical tool for surveillance of the variables for a more inclusive financial system.
Modelling stochastic volatility using hidden Markov models: a case study of the Kenyan securities Market
(Strathmore University, 2021) Bosire, Matilda Bosibori
The biased parameter estimates generated by the Black-Scholes model have been attributed to the failure of the normality and constant volatility assumption to hold. Results of the improvement of the Black-Scholes-Merton model include time-varying volatility models which capture certain stylized facts of stock returns, with their use expected to improve the ability to price assets beyond the benchmarks provided by Black-Scholes. This thesis models stochastic volatility using Hidden Markov Models in Kenya. The univariate Stochastic volatility Model is calibrated to the Nairobi Securities Exchange 20 share index daily data for the period January 2012 to February 2021. The hidden Markov model (HMM) is employed in establishing volatility regimes while the Expected Maximization (EM) algorithm is employed in parameter estimation. Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) techniques are employed in filtering out noisy observations in parameter estimation. The 4-state model, which divides the economy into periods of very high, high, low, and very low volatility, is established to be optimal. Under each regime and filtering technique, different parameter estimates for single and multiple state models suggest a more dynamic framework for modeling the volatility process. The research findings contribute to theoretical literature on volatility-backed financial valuation and risk management in the context of regime switches.
Swaption pricing under Libor market model using Monte-Carlo method with simulated annealing optimization
(Strathmore University, 2021) Ondieki, Kennedy Munene
The thesis seeks to use simulated annealing optimization to minimize the difference between the value of the libor model volatility and the ones quoted in the market for a congruent pricing of a Swaption contract. The simulated annealing optimization technique, being a global minimisation method, would provide accurate parameters that will simulate libor rates that are harmonious with the observed yield curve. This latter feature employed in a Monte- Carlo pricing method would price the Swaption contract fundamentally closer to its market value than other local optimization method. The SA method starts from an initial point, often random, then searches the neighbourhood of the current solution for the next point. The neighbourhood function search is in accordance with the set probabilistic distribution that will determine the distance between the two solution. Each solution has a cost value associated with it. The cost function determines the eligibility of the solution by measuring its discrepancy with the set limit. If the discrepancy is larger than the set limit, a new solution is sought. If the discrepancy is still large, the old and new cost value is compared, and the latter is accepted if its less than the former or otherwise rejected with a certain probability that is largely dependent on the control mechanism. The method terminates if the cost value attained is equal to the set tolerance level. Different from other heuristic methods that solely base their solution on iterative improvement of the solution’s cost value, simulated annealing accepts some inferior solutions so as to have a wider search in the design space. The main advantage of the method is the ability to escape local minimum entrapment through the aforementioned acceptance/rejection criteria. The results indicate that the advantageous aspects of the Simulated annealing enable it to outperform the least square non-linear optimization method commonly used in simulation.
Stock market volatility forecasting at the Nairobi Securities Exchange: a comparison between asymmetric GARCH models and neural networks
(Strathmore University, 2021) Rugut, Diana Chemutai
In this study, we conducted a comparative study on the volatility forecasting models focusing on the asymmetric GARCH models and the Artificial Neural Networks. The study focused on the Nairobi Securities Exchange and used the daily data from the NSE-20 Share Index for a period between January 2012 - February 2021. We took advantage of the year 2020 to investigate whether the models are still effective or they break during a period of turbulence. The parameters of the asymmetric GARCH models were estimated using Maximum Likelihood Estimation (MLE). The asymmetric GARCH models, namely the EGARCH and GJR-GARCH models were compared using AIC and BIC to determine the model with the best fit when it comes to modelling and based on the results of the AIC and BIC, the EGARCH was the better model. The study then compared the forecasting ability of the asymmetric GARCH models to that of the Artificial Neural Networks in terms of the standard deviations as a measure of the actual volatility to determine the better model. The RMSE and MAE measures were used to evaluate the forecasting abilities of the models and based on the results of the RMSE and MAE from the study, the Artificial Neural Networks outperformed the asymmetric GARCH models when it comes to forecasting.
A Comparative study on mathematical models for interest rate dynamics: a Kenyan case study
(Strathmore University, 2021) Maina, Hudson Mwangi
This dissertation calibrates equilibrium one-factor short-term interest rate models to the evolution of interest rate dynamics in Kenya. The aim of the study is to find out which one-factor short-rate model best captures the dynamics of the short-term interest rate in Kenya. Additionally, the study aims to evaluate the relationship between conditional volatility of interest rate changes and the level of interest rate. The findings of this study provide a basis for valuation of contingent claims and hedging of interest rate risk. The data used in the study was obtained from the Central Bank of Kenya (CBK) website 1 for the period between January 2005 to July 2016. Since the short-term interest rate is unobservable in the market the 91-day Treasury Bill (TB) rate was used as its proxy. The Generalized Method of Moments (GMM) estimation technique was used to obtain the parameters for all the models under study. Key results showed that there is weak evidence of mean reversion for all the models evaluated. Furthermore, it was established that there exists a positive relationship between interest rate volatility and the level of interest rate. The best performing model from the study is determined to be the Chan, Karolyi, Longstaff and Sanders (CKLS) model which allows the volatility of interest rate changes to be highly dependent on the level of the interest rate. This model also has the best volatility forecasting ability among the models under study. It is therefore recommended to interest rate policy makers for use in their work.
Day of the week effect on stock returns and volatility in emerging and frontier markets in Africa
(Strathmore University, 2021) Mbonoka, Faith Mbula
The study examines the day of the week effect on average stock returns and compares the daily price volatilities in emerging and frontier markets in Africa. The study focuses on eight key stock markets in Africa’s emerging and frontier markets of Nigeria, Botswana, Egypt, Tunisia, South Africa, Kenya, Mauritius and Morocco for the period May 11th, 2018 to May 12th, 2021. Average stock returns generated from daily closing price indices are regressed against a measure of volatility while controlling for trading day effect. From the findings based on a static panel data regression analysis, there is a Monday effect evident across both the emerging and frontier markets. In addition, there is also evident statistically significant differences in the volatility patterns across the days of the week in the emerging and frontier markets. In particular, Thursday records the highest average volatility and Monday the least in the emerging markets, while Friday and Tuesday show the highest and lowest volatilities in the frontier markets respectively. The research findings contribute to empirical literature on risk-return analyses generating useful insights for investment decision making. Based on these findings, investors will be able to make better investment selections based on return and risk; possibly prompting them to consider day of the week in their trading strategies.

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