MSc.MF Theses and Dissertations
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- ItemCalibration of vasicek model in a hidden markov context: the case of Kenya(Strathmore University, 2017) Chelimo, John KigenThis dissertation calibrates the Vasicek term-structure model to the evolution of interest rate dynamics in Kenya. This is done for both a single-state and a multi-state model using state estimated under a Hidden Markov Model (HMM). The findings of this paper provide a starting point for the management of the risk posed by interest rate-dependent instruments.The Vasicek model is calibrated using monthly observations of the 91-day treasury bill rate from September 1994 to July 2014 as a proxy for the short rate. Key results show an increase in the mean reversion parameter with an increase in the number of states, suggesting higher stability of states. The volatility is observed to move independently of the level of the interest rate,supporting the idea that risk is not necessarily a function of the level of the interest rate but rather related to the inherent variability of rates in a particular state. Findings from this parameter estimation provide support for interest rate models that incorporate regime switches.
- ItemPortfolio optimization in the Kenyan stock market: a comparison between mean-variance optimization and threshold accepting(Strathmore University, 2017) Masese, Josephine MokeiraThe Mean-Variance Optimization (MVO) model has been used in asset allocation problems since the inception of Modern Portfolio Theory in 1952. Several improvements and alternatives to MVO have been suggested and used since then. These include adding constraints to the traditional MVO model, using alternative risk measures and use of non risk-reward models. This study seeks to compare this risk-reward model against the Threshold Accepting model, which is a general optimization model, in portfolio selection in the Kenyan stock market to establish optimal stock portfolios to be held by investors in The Nairobi Securities Exchange (NSE). A comparison is done between the two models by measuring their performance using the following performance ratios: Sharpe Ratio, Sortino Ratio and Information Ratio using 29 stocks in the NSE from 1998 - 2016. Using portfolio performance ratios, it is concluded that the Threshold Accepting (TA) model outperforms the Mean-Variance Optimization model but the latter is observed as a more consistent model. The TA model has portfolios with generally more superior returns relative to the risk taken for the full period; however, this is not consistent over varying time estimates. This observation implies that attention should be given to the TA model rather than the classical MVO approach with the aim of improving optimal portfolio selection.
- ItemModeling SME credit ratings using non-homogenous backward semi-Markovian approach(Strathmore University, 2017) Magarita, Sara MuyaConsidering the growth in SME lending in Kenya and the obvious risks it posses to the banking sector, we establish a credit risk model that is responsive to the jumps in the economy. This is based on simulation of implied values of credit worthiness over a period of 12 months for 1000 SMEs, in which case we establish a case for the discrete time non-homogeneous semi-Markov approach as a proxy for internal rating model for a portfolio of SME loans. While viewing credit risk as a reliability issue, the model provides a credit indicator which gives a prospective measure of credit risk for an SME portfolio. Banks seeking to comply with the new IFRS9 guidelines can espouse this model to adequately measure impairment of financial instruments.
- ItemExotic derivatives pricing using copula-based martingale approach(Strathmore University, 2018) Muganda, Brian WesleyThis study examines the pricing of bivariate exotic derivatives, namely: capped spread option and bivariate digital options, using martingale approach and pair copulae formulations. Pair copulae is used to capture the joint distribution of asset price process and varying dependence structure rather than the univariate marginal distribution used in pricing univariate options. Unique payoff conditions for these exotic options are developed and the prices of these exotic options are obtained under the best fitting pair copulae. We then assess the sensitivity of the exotic option prices to the copula parameter, by formulating a `dependence delta' and `dependence gamma' formula obtained by application of chain rule de-composition to the copula derivative to have h-function and density function representation. Data from 2012 to 2018 from the NYSE of Equity ETFs and Bond ETFs of Frontier Markets, Emerging Market and Developed Markets to construct 10 pair combination of Equity and Bond ETFs as underlyings for the bivariate exotic options. The findings reveal that the t-copula captures best the dependence between the 10 pair combinations of underlyings. The prices of the bivariate exotic options are affected by the strength of the dependence of underlyings. Emerging and Developed market equity ETFs combination are more sensitive to changes in copula parameter. However, emerging market equity ETF and Developed market bond ETF exhibit lower downside dependence and have lower dependence delta. Dependence gamma is generally of similar strength and signage as the dependence delta.
- ItemEfficiency of the markov regime switching GARCH Model in modelling volatility for tea prices(Strathmore University, 2018) Maiyo, Mathew KiplimoThis study examines the ability of the Markov Regime Switching GARCH model, in comparison with the univariete GARCH models, in modelling and forecasting price volatility of the tea traded at the Mombasa Tea Auction within some time horizon. The study uses weekly data, from 2010 to 2017, to analysis regime switching in volatility and provides an in-sample and out-of-sample forecast. Volatility regime switching is first modelled with a Markov switching framework. In-sample and out-of-sample forecasts of volatility using competing MRS-GARCH models and the single regimes GARCH models are then provided. Comparison of in-sample forecast is done on the basis of goodness-of-fit and the comparison of the out-of-sample forecasts is done on the basis of forecast accuracy, using the statistical loss function. The results show that the MRS-GARCH models can remove the high persistence of GARCH models. This shows the priority of MRS-GARCH models and provides evidence of regime clustering. In out-of-sample forecast perfomance, the MRS-GARCH models were better than the single regime GARCH model. However, this superioirity fades for longer time horizon.
- ItemMeasuring and evaluating factors of dynamic term structure models for value-at-risk estimation in the Kenyan market(Strathmore University, 2018) Kanda, Felix KipkorirThe growth of the Kenyan fixed income market and the growing need for investors to diversify the risk in the portfolios has driven the need to quantify the risk associated with the fixed income assets. The measures that are commonly used to estimate bond risk are duration and convexity. However, these measures do not sufficiently assess the risk in fixed incomes. The risk associated with the yield curve illustrates how a portfolio will react to different exposures based on how the yield curve shifts. In this research, we will seek to model the yield curves for the Kenyan market using the dynamic factor models, namely, Nelson-Siegel and Svensson models. We will estimate the factors for both models and seek to establish the distributions of the estimated factors. We will then seek to use the estimated factors from both models to generate the vector of expected bond yields and the covariance matrix that will be used to measure the Value-at-Risk. The results of this research will be used to seek a parametric method of measuring risk in a fixed income in an illiquid market and check whether the estimated factors are good fits to be used in the parametric model.
- ItemDetermination of optimal public debt ceiling for Kenya using stochastic control(Strathmore University, 2018) Kithinji, MillicentPublic debt is a key economic variable. It is the totality of public and publicly guaranteed debt owed by any level of government to either citizens or foreigners or both. Due to recent debt crises in developed countries such as Portugal, Italy, Ireland, Greece and Spain, debt control has become a key important fiscal policy of every government. In this study, we applied a formula proposed by (Cadenillas and Aguilar, 2015) to find out the optimal public debt ceiling for Kenya. We made modification to subjective variables in the explicit formula and used the formula to find the optimal public debt ceiling for Kenya. We illustrate that it is prudent for that government to use a fiscal policy that maintains the debt ratio under an optimal debt ceiling.
- ItemThe Effect of the fluctuation of the Chinese Yuan on the returns of stocks traded in the Kenyan, Ugandan and Tanzanian markets(Strathmore University, 2018) Kibathi, Leonie NjeriThis paper investigated the relationship between Kenya, Tanzanian and Ugandan ex-change rates and the returns of three stocks traded in all three markets. The exchange rates analyzed were from the three countries versus the Chinese Yuan. The data was maintained at weekly intervals and the time period was from January 2012 to December 2017. In this study, both the exchange rate and the stock returns data were found to be non-normally distributed. A unit root test (Augmented Dickey-Fuller) found that both time series were stationary at level form. A test into the causal relationship between the two variables by the Granger Causality test showed that there was a unidirectional relationship between stock returns and the exchange rates that run from the stock returns to the exchange rates. Understanding the flow of influence between exchange rates and stock market returns is essential as the two variables have become important aspects in trading markets. The information about this relationship between stock market returns and exchange rates would help investors to invest prudently by reducing their exposure to risk.
- ItemA Quantitative analysis of the Kenyan students' loan default(Strathmore University, 2018) Kamau, Pauline NyathiraHigher education capacity, quality, and availability has driven more countries to turn to student loan schemes in order to assist students whose families are unable to meet their university costs. Ideally, all students seeking university education should be able to access these loans. It is also expected that student loan applicants pay back the entire loan in the stipulated time frame to allow other needy students joining university to utilize the repaid amounts. In this study, we seek to perform a quantitative analysis of loan applications by computing the probability of default of a given applicant using the qualitative information provided in the application forms. We apply multiple logistic regression with the binomial nominal variable defined either as defaulter or re-payer. Further, we treated different factors affecting default probability of the student as independent variables. The main objective was to find out the effect that the independent variables have on the dependent variable. We then validated the resulting model by comparing its results to observed data from the Kenyan Higher Education Loans Board. Results show the amount of loan reimbursed as the main factor affecting default. This can be an eye-opener for policy makers in their effort to mitigate non-repayment.
- ItemValuation of a locational spread option: the case of tomatoes in Nairobi and Mombasa Counties in Kenya(Strathmore University, 2018) Kimathi, Kenneth GitongaLocational Spread Options are financial instruments that can be used by traders wishing to purchase but not physically acquire produce; to hedge their risks, and / or to take speculative positions, based on their knowledge of market dynamics. In this study, we analyze historical tomato price data in Nairobi & Mombasa counties in Kenya; and observe that the Ornstein Uhlenbeck process best captures the price dynamics due to the mean reverting characteristics noted in the deseasonalized price data. We then derive pricing equations and estimate the model parameters via the use of Maximum Likelihood Estimation. Finally, we use these parameter estimations to perform Monte Carlo simulations, using the antithetic variate variance reduction technique to obtain the option price.
- ItemBad beta, good beta and stochastic volatility in an inter-temporal asset pricing model for the Kenyan stock market(Strathmore University, 2018) Kimundi, Gillian NdukuThe study seeks to investigate whether bad beta (sensitivity to cash-ow news), good beta (sensitivity to discount rate news) and volatility news are significantly priced in the Kenyan stock market. A comparison of the 3 models is done: 2-beta pricing model (with cash-ow news and discount rate news as risk factors), a 3- beta model (including volatility news) and a 4-beta model (including covariation risk in cash-ow and discount rate news). The findings from the study suggest that news terms related to cash flows, discount rates, volatility and the covariation of cash-ow news and discount rate news are all significantly priced in the Kenyan Market. There is evidence that Kenyan investors are highly risk averse, more so towards cash-ow news, than they are to discount rate news. Similarly, the premium charged for volatility news is just as high as that attached to cash flow news. Investors also attach a significant but relatively smaller premium to the risk due to covariation between cash-ow news and discount rate news.
- ItemFrontier stock market linkages: an African perspective(Strathmore University, 2018) Onyango, Christine AmandaVolatility modelling in the multivariate case is becoming an important area of study as the world becomes increasingly more integrated and as barriers to entry in frontier markets come down. Understanding how frontier markets in the African region behave in contrast to those in developed markets is vital in driving portfolio allocation decisions as well as regulatory interventions.In this study we investigate the co-movements of the stock indices of four African countries, Nigeria, Morocco, Mauritius and Kenya using various multi-variate volatility models in relation to those of South Africa and the United Kingdom. We also fit a Kalman filter to the data set and examine the goodness of fit of the two approaches. For the Multi-variate models we fit an Exponentially Weighted Moving Average (EWMA) model, two specifications of Dynamic Conditional Correlation (DCC) models as well as a multivariate volatility model based on Cholesky Decomposition. We use a dynamic linear specification of the Kalman filter to allow for time-varying variances, and generate forecasts. Empirical results show that the diagnostic tests with upper tail trimming reject the EWMA model while both specifications of the DCC model as well as a multivariate model based on Cholesky decomposition is found to be adequate. Kalman filters also provide adequate modelling for each return series on the basis of assessment of residuals.
- ItemComparison of survival analysis approaches to modelling credit risks(Strathmore University, 2019) Mungasi, Sammy MonyonchoCredit risk is a critical area in finance and has drawn considerable research attention. As such, survival analysis has widely been used in credit risk, in particular, to model debt's time to default mechanisms. In this study, we revisit different survival analysis approaches as applied in credit risk defaulters' data and assess their performance in light of the Kenyan context. In practice, inconsistency in the validity of credit risk models used by many companies when predicting and analysis of loan default is a common phenomenon that occurs unexpectedly. Loan defaults often cause major loses to creditors' and can be of great benefit if quantified correctly in advance by using correct models. Here, we address the unbiasedness, analysis, and comparison of survival analysis approaches, particularly, the models of credit risk. We carry out data analysis using the Cox proportional hazard model and its extensions as well as the mixture cure and non-cure model. We then compare the results systematically by investigating the most efficient awl preferable model that produces best estimates in the Kenyan real data, sets. Results show the Cox Proportional Hazard (Cox PH) model is more efficient in the analysis of Kenyan real data set compared to the frailty, the mixture cure, and non-cure model.
- ItemApplication of long-short term memory Deep Neural Network in financial forecasting(Strathmore University, 2019) Wanyonyi, Watua PeterThe goal of this research was to apply Long-Short Term Memory Deep Neural Networks in financial forecasting. In order to predict the financial data, we used long-short term model and we compared its performance to ARIMA-GARCH hybrid model. In the study we used the ARIMA-GARCH time series model and studied its limitations in time series forecasting. We then introduced Deep Neural Network model (DNN) so as to improve accuracy which was tested on different financial datasets. Lastly we compared the results of the models employed using the root mean square error (RMSE) and p-value; LSTM had RMSE of 0.09989178 while the ARIMA-GARCH had RMSE of 0.0178. It was then concluded that the long-short term memory (LSTM) model, which is one of the DNN models, had significantly better than the ARIMA-GARCH Hybrid model in prediction/forecasting financial returns on FTSEIOO and S&PSOO indices.
- ItemConsumer credit risk modelling using machine learning algorithms: a comparative approach(Strathmore University, 2019) Nyangena, Brian OkemwaConsumer credit risk scoring involves the assessment of the risk that is associated with a customer that applies for credit. The ability to confidently identify customers that will repay the credit and those that will not is therefore, an important aspect for any institution. The purpose of this study is to model consumer credit risk using machine learning models and compare the results to the traditional logistic model. The aim is to identify whether there is improved performance in the classification of default among customers when machine learning algorithms are used. Additionally, the study aims to identify how different customer characteristics affects their default experience. The data used was obtained from Kenya Metropol between 2014-2017 and had customer details such as age, loan amount, marital status and sex among others, during this period. 5 models are used to model the default experience namely: Logistic regression, Random Forest, Support Vector Machine, Gradient Boosting and Multi-layer Perceptron Neural Network. The efficiency of the models was assessed using the following metrics; Accuracy, Precision, Recall, F1-score and Precision-Recall curve. Due to the imbalanced nature of credit data set, the F1-score, which is a weighted average of the Precision and Recall, was eventually used as the metric to determine the best model for credit scoring. The findings showed that Random Forest performed the best, having an F1-score of 0.307. The machine learning algorithms outperformed the logistic model and showed an improved performance in the classification of default, especially in identifying false positives. It was also established that male customers had a higher default probability, younger customers were more likely to default and single customers defaulted more than married customers
- ItemAn Inclusive pension model for Kenya’s informal sector with late entries and early exit rates(Strathmore University, 2019) Lagat, Cherono AsumptaThe purpose of this study is three-fold: first, we develop 1'1 pension model that uses preretirement mobile phone airtime expenditures to accumulate the pension fund. Secondly, we · calculate the exit and entry rates into the comprehensive pension scheme. Finally, we determine the expenditure patterns experienced post-retirement and use these patterns to advise on the daily amount required to be charged per minute above the current rate in order to facilitate a comfortable post-retirement life. The data utilized in this study was retrieved from various secondary sources. Inflation and interest rates data -were retrieved from Kenya's Central Bank database. The entry and exit data into informal pension schemes was retrieved from Eagle Africa the administrators of Mbao Pension scheme the largest informal pension scheme in Kenya. The mortality rates were retrieved from the World Health Organization and the life expectancy from ·world Atlas, Lancet and World Life Expectancy. Pre-retirement data was retrieved from November 2013 from an integrated survey on land ownership and tenure, provision, access and control of basic services, asset ownership, financial resources, evictions and demolition of houses, as well as thirty-two key informant interviews with informal small-scale service provider’s facilitated by Strathmore University. The inflation and interest rates were forecasted using ARIMA (1,9,5)-GARCH (0,1) model while the backward entry and exit data points were simulated in R. Our results show that an unemployed Kenyan spends approximately KShs. 2, 000.37 a month considering inflation this amount will translate KShs. 4, 025.45 to maintain the same life style post-retirement assuming the person joins the scheme at 18 and exits at the age of 55. Given the expenditure pre-retirement of this group of people, it will require them to be charged KShs. 3.41 per minute above the current rate in order to raise an amount sufficient to sustain their lifestyle post-retirement.
- ItemModelling delayed correlation between interest rates and equity market returns(Strathmore University, 2020) Yalla, Brian OpiyoThis study models the interaction between interest rates and equity markets using wavelet analysis. This approach facilitates assessment of the lead-lag relationships in an intuitive way considering variation across frequencies and over time. Analysis is done progressively on varying scales where the lower scales encompasses high frequency components of the data over shorter time scales whereas higher scales encompass low frequency components over longer time scales. The study uses daily data obtained from Kenya for the period October 2003 to October 2019. The Nairobi Securities Exchange 20 share index returns are used as a proxy for equity returns whereas the interbank rates represent interest rates. Three key findings emerge: (1) There is at least two months delay in the correlation between interest rates and equity market returns, (2) The correlation is lower (correlation coefficients of 0.3 and below, including negative correlation coefficients) in the lower time scales of 4 to 8 days and higher (correlation coefficient of 0.3 and above) in higher time scales of 512 to 1,024 days, and (3) Equity returns lead interest rates in Kenya during the period of study. Unlike common practice of assuming joint stationarity of variables, the findings reiterate the need for modelling dynamic relationships considering delays, time variation and scaling over time horizons.Investors, portfolio managers and policy makers alike should therefore be cognisant of the dynamic nature of the relationship between interest rates and asset markets bearing in mind that changes in one variable may not have immediate impact on the other.
- ItemSavings and Credit Co-operative Societies as investment vehicles to enhancing affordable housing: a case of Kenyan SACCOs(Strathmore University, 2021) Wambui, David NyagaThe 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.
- ItemDynamic portfolio optimization using reinforcement learning(Strathmore University, 2021) Yegon, Donald KibetThis 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.
- ItemEmpirical performance of alternative risk measures in portfolio selection - the case of South African stock market(Strathmore University, 2021) Macharia, RichardPortfolio 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.