### THE EFFECT OF TIME-VARYING BETA ON THE VALIDITY OF THE CAPM IN NAIROBI SECURITIES EXCHANGE

#### Abstract

**Purpose-**The Capital Asset Pricing Model (CAPM) is widely used to price assets in the Nairobi Securities Exchange (NSE). This paper examines whether it is more adequate for capital asset pricing in the NSE if the beta estimate is assumed to be a random variable rather than a point estimate. ** **

**Methodology-**The study follows a descriptive approach and it is based on secondary data. Precisely, it is based on the monthly returns of the 20 companies that formed the NSE 20-share index from 1^{st} January 2013 to 31^{st} December 2016. First, the CAPM is tested on this data using the Classical Linear Regression Model (CLRM), where the beta estimate is assumed to be a constant. Then, a multivariate General Autoregressive Conditional Heteroscedastic (GARCH) model of the Diagonal BEKK (Baba, Engle, Kraft and Kroner) type is fitted on the data to compute time-varying betas and the test of the CAPM is repeated using these betas. Analysis is done using the E-views software, 9^{th} edition. ** **

**Findings- **From the regression analysis in the first test, beta is statistically significant. Ranking the securities from the one with the highest beta to the one with the lowest beta shows that the security with the highest beta is not the one with the highest expected return. Neither does the security with the lowest beta have the lowest return. ICDC has the highest beta (1.649329) estimate but it actually has negative expected returns (-2.18494). From these results, it is clear that the CAPM does not hold in the NSE. When time-varying betas are calculated, it is possible to construct various combinations of returns and beta where the stocks with the highest returns have the highest betas and those with the lowest returns have the lowest betas. This clearly shows that using time-varying betas improve the validity of the CAPM on the NSE.

**Implications- **Beta, which is a measure of the systematic risk, is the most important parameter of the CAPM model. Assumptions about it should therefore be made carefully. Precisely, it should not always be assumed to be constant. Other assumptions of the CAPM should also be put to test before it is applied in pricing assets in the NSE.

**Value- **The CAPM is used to compare securities such as stocks, investment funds, equities, and bonds. It is also used to price portfolios and to choose the mean variance portfolio. Investors also use this model to compare the intrinsic value of an asset to its book value. In project appraisals, the CAPM gives a better view of the feasibility of a project than the Net Present Value (NPV). When using the CAPM in all these ways, investors, financial officers and managers will find using time-varying betas more useful than using constant ones. Indeed, using time-varying betas will give a more realistic picture of the economic reality underlying the trading of securities.

**Key words: CAPM, Dynamic CAPM, beta, time-varying beta **

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