EMPIRICAL TEST OF CAPITAL ASSET PRICING MODEL ON SECURITIES RETURN OF LISTED FIRMS IN NIGERIA

This paper applied the capital-asset pricing model (CAPM) to determine stock returns of listed firms in the Nigeria Stock Exchange (NSE). For the purpose of investigation, annual data on stock price of twenty six (26) listed firms, Treasury bill a measure of riskfree rate and all share indexes a proxy for market returns were extracted while beta value was computed for the period 2010 to 2016 upon which the model was analyzed. Finding indicates that the CAPM generated a very high return among the firms given the influence of the beta coefficient. The study concludes that higher market risk measured by beta, is associated with higher expected returns. It is therefore recommended that managers of firms in other sectors in Nigeria need to constantly use this model to price security return with a view to guiding investors at investing in securities based on risk preference behavior and also to enable them maximize wealth from a basket of portfolio. .


Introduction
The capital asset pricing model (CAPM) of Sharpe (1964) grew from the mean-variance analysis of Harry Markowitz in 1952 and 1959 to assess securities risk and returns in the stock market. The mean-variance is used to assess the risk peculiar to individual securities against the expected returns. The mean-variance approach holds the view that expected return (gain) from securities is a reflection of the level of associated risk. Following this, the CAPM demonstrates the linear association between market risk and return of portfolios given risk-free rate (Lipiec, 2014). The risk free asset often measured with Treasury bills and government bond is used to minimize risk and maximize returns in the capital asset pricing model. Example of risk-free asset is Treasury bills. Treasury bills as money market instrument attract very minimal risk with a low return on it, unlike investment in risky assets such as shares in the stock market.
The CAPM shows the market risk associated with portfolio return for a time window (Oke, 2013). The risk common to the market portfolio is revealed through a beta co-efficient. Herbert, Nwude and Onyilo (2017), posit that the CAPM and its beta component are presumed to be good predictors of asset returns in finance literature. Usually the risk in the market portfolio determines its returns. What happens to the market affect every security in the market. The impact of beta in the stock market affecting security returns may be described in the U.S aphorism: 'when they raid the brothel, they took all the girls away', portraying that systematic factors occurring in the market, affect the securities return. Generally, the securities market as a whole has a beta coefficient of 1.0. The beta co-efficient of individual firms are calculated relative to the market beta. Beta can be calculated through dividing the co-variance between individual securities and market to the variance of market. A beta above 1.0 implies a higher risk and a beta below 1.0 implies less than the market average risk. Beta could be positive or negative. High and positive beta increase the risk of the investor's portfolio such that investors tend to demand higher expected return in compensation for the high risk. If the stock has negative a beta , it reduces the risk of the market portfolio and this ordinarily makes an investor to accept a lower expected return in exchange for the risk reduction. In this case, investors in the stock market are able to build a basket of portfolio around their risk preference behavior which consists of risk aversion, risk seeking and risk neutral.
Prediction of securities return in the light of market risks through CAPM holds under assumptions. These assumptions are segmented into classical and non-classical assumptions. The classical assumptions are often relaxed to give room for the non-classical assumptions. Some of the classical assumptions according to Olowe (1997) are that investors are risk averse, investors are price takers and have homogenous expectations about securities (or assets), there exists a risk free security (or asset) such that investors may borrow or lend unlimited amount at the risk-free, securities (or assets) are marketable and perfectly divisible, securities markets are frictionless. Information is costless and simultaneously available to all investors and there are no market imperfections such as taxes, regulations, or transaction costs. These classical assumptions partly do not hold in real life market situation. Hence they are relaxed to form the non-classical assumptions upon which investors are guided in taking investment decision on portfolio investments. Arguing in support of the non-classical assumption, Fama and French (2004) believe that the assumption that short selling is unrestricted is as unrealistic as unrestricted risk-free borrowing and lending. If there is no risk-free asset and short-sales of risky assets are not allowed, mean-variance investors will still choose efficient portfolios (Oke, 2013). But basically all attractive models involve impractical simplifications, which is why they must be tested against data. Against this backdrop, this study is undertaken with a view to contributing to accounting and finance literature using data from listed firms in the Nigeria Stock Market. Following the introductory part, section two is literature review, section three is methodology and section four is empirical analysis while section five dwells on conclusion and recommendations.

Theoretical framework
The portfolio theory developed by Markowitz (1952), has to do with a concept of using the variance of expected returns as a measure of risk an investor can form an efficient portfolio that minimizes the risk for a given level of return and maximizes the return for a given level of risk, had a greater influence over the development of CAPM by Sharpe (1964) andLinter (1965). The CAPM is an extension of portfolio theory, which implies that beta alone

INSIGHTS INTO REGIONAL DEVELOPMENT
ISSN 2669-0195 (online) http://jssidoi.org/jesi/ 2020 Volume 2 Number 4 (December) http://doi.org/10.9770/ IRD.2020.2.4(8) 827 is sufficient to explain the cross section return of any security at any given point of time. Thereafter, numerous researches on the CAPM have been made to test the validity of this model but empirical test results generated many unsolved questions regarding the applicability of this model in different markets throughout the world. The CAPM is built on the modern portfolio theory which was initially developed by Markowitz (1952). As developed by Sharpe (1964) and Lintner (1965), the CAPM models the equilibrium expected return on an asset as a positive linear function of its beta risk. In the CAPM world, the only relevant risk measure is systematic risk, as this cannot be diversified away. Investors should be proportionately rewarded for bearing this risk. Beta measures the volatility (risk) of a share or a share portfolio and hence estimates how the returns on the share or portfolio will move relative to the movements in the market portfolio (Jones, 1998). By definition, the market portfolio has a beta of one. The beta of a portfolio is the weighted average of the betas of all securities contained in the portfolio. Therefore, portfolios with betas greater than one have higher systematic risk than the market, while those with betas less than one have lower systematic risk. Hence, by adding securities with betas that are higher to a portfolio, we increase the systematic risk of the portfolio and hence shares, or share portfolios with high betas should exhibit high returns and viz. (Elton & Gruber, 1995).  (2014)  From the empirical result, the beta content of the entire sector ranges between 1.04% and -0.13 or between 6.78 and -2.31% providing an average beta content of 0.37 or 1.50% of the total risk for the sector. The results further indicate that the unsystematic risk content in chemicals/paints sector stocks constitutes the bulk of the sector's risk profile and that most of the stocks' betas had defensive attributes over the study period. The investment implication is that including an appropriate mix of chemical and paints stocks in the investors' portfolios would, all things being equal, help investors to achieve a combination of investments that are not highly correlated with larger economic cycle as well as higher-risk equity securities that can potentially yield higher returns than the market.

Methodology
The main objective of this research is to examine the validity of Capital Assets Pricing Model in pricing portfolio return of listed firms in Nigeria. To attain this objective, data on stock price of twenty six (26) listed firms were collected from the Nigeria Stock Exchange publications while Treasury bill rates and All Share Index data used as proxies for Risk-free rates and market Returns were sourced from the Central Bank of Nigeria Statistical Bulletin respectively. After calculating the beta for the security, expected return or required rate of return for the security was determine using the panel CAPM estimation method. The approach used is a follow up of the research procedure of Oke (2013).

Model Specification Capital Asset Pricing Model (CAPM)
The CAPM is usually expressed as: Where: is the expected excess return on the capital asset. Rf is the risk-free rate of interest. is the beta coefficient (The sensitivity of the asset returns to market returns).
is the expected return of the market. Rf is the risk premium (the difference between the expected market rate of return and the risk-free rate of return).

Empirical Analysis
The tables below represents the descriptive and correlation statistics analysis as well as the capital asset pricing model panel estimation results of the sampled manufacturing firms in Nigeria for the period 2010 to 2016. (As well see Appendix A and Appendix B).
stock_retu~s | 1.0000 market_ret~s | 0.1031 1.0000 free_risk_~e | -0.0989 0.3054 1.0000 beta | 0.1166 -0.0297 -0.1129 1.0000 Prob > F = 0.3807 Table 1 concerns the descriptive statistics result and it shows that the average stock returns of the sample firms is 72%, the maximum stock return is 572% while the average market return. The average beta is 20 and this may have compensated the investors by way of the mean portfolio return of 72%. The maximum beta value is 7.49. The risk free rate average value is 10.54% while the maximum return is 14.27%. Table 2 Table 4 relates to the capital asset pricing model panel estimation. It that shows that the overall R-squared result is 0.1330, which is 13%. The Fstatistic of 27.89 is statistically significant given the probability value 0.0000. The firm excess return (market premium) for the period was positive (1.1946) and significant at 95% and it means that the market risks contribute largely to the expected returns of the firms in the period observed. The empirical findings are consistent with Mobarek & Mollah (2005).

Conclusions and Recommendations
This study applied the capital asset pricing model to determine portfolio returns of listed firms in the Nigeria Stock Exchange. Three components of the model, namely, risk free rate, market return and beta were determine with the data from secondary sources. The empirical results of the study explicitly suggests that share price return of the sampled firms improved very well after the stock market melt-down in Nigeria. This intriguing results may have be an influencing factor to investors in optimal portfolio selection, diversification as well as guiding their risk preference behavior in the stock market after the global financial crisis. The model is thus validated in Nigeria and therefore remains a potent tool for investors to assess returns on investment in stocks, other than relying on the Markowitz mean-variance to determine efficient securities. It is therefore suggested that future researchers need to apply the model to determine portfolio return of firms on sector by sector basis in pre-andpost stock market melt -down in Nigeria as this reveal the magnitude of the loss encountered by investors during these periods.