A Garch Approach to Measuring Efficiency: A Case Study of Nairobi Securities Exchange

Abstract

The efficiency of capital markets is important if savers funds are to be channeled to the highest valued stocks. A recent review of markets in Africa categorized the Nairobi Securities Exchange as one which has no tendency towards weak form efficiency. Recent efforts to establish its efficiency have used mainly Ordinary Least Squares regression and have yielded inconclusive results. Ordinary Least Squares method assumes that the variance of the error term obtained is constant over time. However due to economic cycles some time periods are known to be generally riskier than others and the latter assumption fails to hold. There is therefore need to use other models which relax this assumption. The Autoregressive Conditionally Heteroscedastic models have been popular and widely used. They recognize that the value of the variance of errors depends upon previous lagged variances and lagged innovation terms. Kenya has also increasingly embraced ICT which may be attributed to the comparative lower cost of access to internet via computers and mobile phone technology. This is expected to increase the rational buyers in the market none of whom can influence prices in the market which may make the market more efficient. This study first used non parametric methods to check for randomness and independence of stock market returns at the Nairobi Securities Exchange. Results show that daily returns are non-random and the GARCH analysis shows that the current returns are dependent on the returns of the previous 3 days. The GARCH (3,1) model shows that returns on a particular day would be determined by the mean returns plus a white noise error term which would vary by 25.3% of return on day t-1, 9.5% of return on day t-2 and 12.05% of returns on day t-3 at 0.05 level of significance.  This signifies market inefficiency of the weak form.

Keywords: Market Efficiency, Weak-Form Hypothesis, OLS, GARCH