| dc.description.abstract | There have been various innovation of the capital asset pricing model (CAPM). These innovation are meant to redress the assumption of the CAPM in view of capturing the variability of the asset returns. Many attempts have been made to capture this variability by extending the factors affecting the individual assets. These factors include the economical, fundamental and statistical factors. The time varying aspect of returns has also been addressed by using time series models like the ARCH models. These attempts have however not been satisfactory. This emerges from the fact that returns have been assumed to be normally distributed. High frequency (daily or weekly) financial data exhibit non-normal characteristics. The returns are usually skewed, more peaked and experience fat tails than the normal distribution. The class of generalized hyperbolic distribution is a class of normal variance-mean mixtures with generalized inverse Gaussian distribution as the mixing distribution. The distribution captures skewness, peakedness of data and fat tailed empirical data depicted by high frequency financial data. The class nest other distributions as special or limiting cases.
In this dissertation, the distribution has been used to model weekly returns of the NSE20 index, Safaricom company and Mumias Sugar company. The marginal distributions results are satisfactory and realible compared to the normal distribution. Correspondingly, the marginal distribution have been used to construct copula functions and bivariate distribution to capture the dependence between returns. The estimation difficulty is overcome using the EM algorithm which is easily programmable and surely converges to give precision result with few iteration compared to other optimization technique. The suggested model does not underestimate the risk measured by the beta of the company. The beta of the company measures in part the covariance of the returns between company and the market. This bivariate data is modeled using the bivatiate normal inverse Gaussian distribution. Unlike the bivariate normal distribution, the bivariate NIG does not underestimate the risk of the company. For the NSE20 index, Safaricom company and Mumias Sugar company weekly follow the normal inverse Gaussian distribution which is a special case of generalized hyperbolic distributions. The distribution fits well to the empirical weekly returns than the normal distribution.
The exploratory data analysis using the QQ-plots show that the NIG distribution is better compared to the normal distribution. The bivariate NIG model fits well to the bivariate weekly returns of NSE20 index and safaricom weekly returns and NSE20 index and Mumias Sugar weekly returns. The bivariate returns is underestimated in using bivariate normal distribution. In particular, the beta of Safaricom company is estimated by the bivariate distribution to be
1.512042 and normal distribution to be 1.10226. The beta of Mumias Sugar company is
estimated by the bivariate distribution to be 1.012042 and normal distribution to be 0.9226. Clearly, the normal distribution underestimate the systematic risk of the company. The required returns computed using the beta of the bivariate NIG distribution are 21.87% for the Safaricom company and 18.42% for the Mumias Sugar company. These returns better describe the trade-off between risk and returns in non-normal settings.This study ensure that the assumption of normal distribution of high frequency returns as depicted in theory of CAPM is replaced by the generalized hyperbolic distribution which are more competent. The practical value of study is the fact that the systematic risk of the company as measured by the beta is not underestimated or overestimated. This ensures policy making, especially in risk management, is accurately done and observed. | en |
