PREDICTION OF STOCK PRICES USING CAPITAL ASSET PRICING MODEL IN NIGERIAN STOCK MARKET

The main intention of this study is to use the accounting data using CAPM to determine the stock prices/returns for the Nigerian capital market. In this study, the independent variable is the prediction of the stock prices and the dependent variable is stock prices in the market. The proxy that is used in this study to measure the dependent variable is CAPM in Nigerian Market. The most important and interesting phenomenon to investors is the analysis from financial market pertaining to stock returns. The research method employed is quantitative which is unlike qualitative as a way of assessing the stock price. The study mainly aims at assessing the correlation of beta factors and the predictability of stock returns from Nigerian firms listed on the stock exchange. In order to boost the beta estimates and mitigate statistical problems resulted from incorrect measurement, the securities were combined into portfolios. In conclusion the study employs ordinary least squares (OLS) regression technique and obtained beta value which is positive and found conclusive evidence for using CAPM and is thus consistent with Nigerian stock market prices. The CAPM has implications for asset pricing since it shows how to calculate the requisite rate of return to assess the value of the stock prices with any given amount of systematic risk (beta) and since the beta is positive hence the policy makers and investors in the Nigerian stock market would make better informed decisions.


Introduction
The capital market is important for a nation's economic development. The money and capital markets in any country's economy have an impact on its overall economic growth. The CAPM model, derived from modern portfolio theory, was developed to quantify systematic risk. However, in the context of Nigeria, valuation multiples and macroeconomic variables such the impact of economic variables, political stability, industry attractiveness, and business position in the industry are closely related variables that have an impact on stock returns. Today, from the perspective of the investor, the estimation of stock returns and prices is a very important issue. This particular study, named as Capital Asset Pricing Model, is a technique recognized as one of the stock return forecasters. The use of CAPM as a model for pricing offers the most advantageous and effective on stock return predictability in order to cover a wide range of forecasts that have been employed by almost all past works.
However the two primary models that are used in the calculation of this study are the theory of arbitrage pricing (APT) and the asset pricing model (CAPM). The term "Corporate Financiers" means the most respected corporate funders and financial experts. This study concentrates on how the CAPM is employed in practice as "investment practitioners". In order to appraise equity and evaluate investment prospects, the WAC of Capital is calculated using the CAPM, which is a key technique, according to academic research by the South African Institute of Chartered Accountants (SAICA) (Nel & Nel, 2011).
The research method employed is quantitative method, which is unlike qualitative, as a way of assessing the stock price .The most effective methods for determining the stock return have been the subject of extensive research (Paul & Asarebea, 2015). While the majority of research (Magni, 2005;Fama & French, 2004) agree that using CAPM is an essential application area of finance for stock valuations and investment decisions, they disagree on relative advantages of the CAPM and the APT model. The CAPM's rigid assumptions and incapacity to be empirically tested are cited by those who favor the APT model (Harrington & Korajczyk, 1993;Nel & Nel, 2011).
In this research, it has been observed that it has predicted stock returns based on the historical financial information on CAPM. Therefore, the answers obtained are based on the estimation that foretelling 100% accuracy is impossible. I have investigated the above Capital Asset Pricing Model in that it has predicted stock returns and on the grounds of their applicable regression models. Statistically, there is a significant relationship between stock return and the method employed where it gained 70% confidence level. Therefore, it's probable that the majority of the investors in the Nigerian capital market follow speculation and other macro-economic factors such as political stability, attractiveness of the industry, economic factors, etc. The major purpose of the study is to determine or predict the stock prices in the Nigerian capital market for the period of 1 year from (22/6/2021 -17/6/2022). Research and investment specialists may be impacted if there is a gap. The computation will be highlighted consistently throughout the entire study.
The most well-known model for determining the risk and return of a speculation is the CAPM. It is defined as an idealized portrayal of how financial market prices, securities are thereby determined by return on capital investment. Therefore, the model provides a methodology for quantifying risk and translating risk into estimates of expected return on equity. The CAPM was established by Sharpe (1964), Lintner (1965) and Mossin (1966) in the 1960s (Majumder, 2012). The foundation of CAPM is a theory that bases a security's relevance completely on a portfolio setting. The CAPM defines the frequency with which investors clutch or seize onto a portfolio in order to prevent unsystematic risk exposure through diversification. As a result, a security's equilibrium rate of return is solely based on systematic risk scaled using the security's beta. Fama & French (2004) examined the period from 2003 and 2004. In light of the companies listed on the Nigerian capital market, the aim of this study is to apply CAPM to estimate or forecast stock prices and returns.

Literature Review
A literature review is a survey review of the literature undertaken by other writers to assess the current state of a certain research area. In this chapter, we'll look at previous CAPM research studies undertaken by other academics. In the analysis of Capital Asset Pricing Model predicting stock prices /returns in the Nigerian capital market I use journals (secondary data) that are related to this research topic.

Theoretical Issues
A variety of research studies based on stock returns have used asset pricing models to determine the most likely drivers of stock market indices, specifically stock prices and returns. The financial products used by the models include shares, bonds, Treasury bills, and certificates. Compared to other asset classes, stocks are perceived as being riskier. We assess the most popular APM, such as CAPM and the Arbitrage Pricing Theory (APT), in light of this (Nurhan et al., 2016).

Capital Asset Pricing Model (APM)
Investors continue to compare different APM and use the CAPM as their benchmark when assessing the profitability of certain stocks (i.e., company-specific stock returns). According to Sharpe (1964), investors can select an asset mix that will maximize expected returns while lowering associated risks. Systematic and non-systematic hazards are the two categories into which the strategy classifies risks. When compared to the latter, which can be totally avoided by employing strategies like portfolio diversification and hedging, the former can only be controlled. According to the CAPM, market returns, the risk-free rate, and a beta factor all affect expected investment returns. The beta-factor measures the riskiness of an asset. In other words, the beta component shows how much changes in market returns overall influence changes in returns on particular stocks (Adekunle et al., 2020).

Theory of Arbitrage Pricing
Ross created the arbitrage pricing model (APT) in 1976 as an alternative method for valuing assets. An arbitrage portfolio is one that, according to Krause (2001), has a guaranteed positive return but no risk or net investment. The arbitrage pricing model makes the assumption that there is no chance of arbitrage at an equilibrium. In contrast, the arbitrage pricing model is a multifactor model with many beta factors. As a result, in addition to market risk, the APT also considers other types of risk, such as issues unique to a given industry. The arbitrage pricing theory, in contrast to the CAPM, embraces both efficient and inefficient assets as well as the whole systemic risk of the market. In other words, the beta factor is a measure of the market's volatility sensitivity of the returns on each stock.

Empirical Research
The CAPM was applied to the Nigerian stock market using weekly stock returns from 20 companies listed on the Nigerian Stock Exchange (NSE) between June 22, 2021 and June 22, 2022. The study supports the CAPM's hypotheses that increased risk (beta) is connected with higher levels of return and that the intercept should equal zero when estimating SML. This analysis also disproves the CAPM's claim that the excess return on the market portfolio should be equal to the slope of the security market line (SML). This effectively invalidates the CAPM's projection for Nigeria. Adedokun & Olakojo (2012) compare using the monthly stock prices of the top 20 most profitable. Between June 22, 2021 and June 17, 2022, researchers looked at capitalized companies in Nigeria to assess the empirical validity of CAPM on the Nigerian Stock Exchange (NSE). The empirical findings show that CAPM falls short in its ability to effectively explain how asset risk affects the anticipated return on investment in Nigeria's equity market. They discovered data that contradicted the CAPM's assertion that more risk is connected with higher asset returns and prices (Man & Wong, 2013;Rossi, 2017).
Over the past few decades, many studies have looked at the variables that affect stock returns in both single-country and multi-country settings. Here, a quick review of the empirical literature is provided. Narayan & Sharma (2011) examined the relationship between the price of oil and business returns for 560 US companies listed on the New York Stock Exchange, looking beyond financial indicators as potential drivers of stock returns. The aforementioned makes it evident that there is controversy regarding the empirical validity of CAPM. Academics have used CAPM to tie a number of variables other than the risk component (beta) to returns in various ways. The variables not previously discussed include debt, earnings yield from 1977, conditional due to non-normality in stock prices, and the proportion of a company's book value of equity to its market value (Chan et al., 1991).
Testing the Capital Asset Pricing Model in the Nigerian Stock Market by Shobayo and Ibrahim was published in 2018 and looked at the CAPM's application to the Nigerian stock market. The study used data from 2000 to 2015 as its source and concluded that the CAPM is a valid model for predicting stock returns in the Nigerian market. The Nigerian stock market was empirically examined by Afolabi et. al. (2017) using the Capital Asset Pricing Model (CAPM). The beta coefficients and expected returns for the Nigerian stock market were compared in this study (Harrington & Korajczyk, 1993). The CAPM is supported by the analyses' finding of a positive association between expected returns and beta coefficients. The Validity of the Capital Asset Pricing Model in the Nigerian Stock Market by (Okoli, 2012) the hypothesis can also be used to describe the size of an asset's risk premium, which is the disparity between the asset's expected return and the risk-free interest rate. The CAPM is a reliable model, according to the study, for forecasting stock returns in the Nigerian market. These studies, along with numerous others of a similar nature, demonstrate that the CAPM can be a helpful technique for forecasting stock returns on the Nigerian stock market. The CAPM may not be the only factor influencing stock prices in the Nigerian market, and it is crucial to remember that no model can accurately forecast stock returns.
Previous studies using the Capital Asset Pricing Model CAPM in the Nigerian capital market have focused on a range of model-related issues, such as examining the model's verifiability of assumptions and determining how well the model can explain stock returns in the Nigerian market. Other studies have also looked at the relationship between macroeconomic conditions and stock returns using the CAPM. Here are a few illustrations of potential hypotheses that might be developed for this kind of research: 1. The CAPM is a trustworthy model for predicting stock returns in the Nigerian capital market.
2. Expected returns and a stock's beta coefficient are correlated on the Nigerian stock market.
3. The market risk premium in Nigeria's capital market is considerably different from that of industrialized economies.
4. On the Nigerian stock market, forecasting stock returns can be done using the book value of equity as well as other accounting factors like earnings per share.

Data and Research Method
This research intend to use quantitative method by which obtained the information from Nigerian stock exchange which consist of returns of monthly stocks from share index effective from the period of 22 nd June 2021 to 17 th June 2022. In this study will use secondary data obtained from journal articles, text books, Nigerian Stock Exchange and so on. This particular index is structured in a way to provide real time measures of the Nigerian Stock Exchange. All stocks in this area here are traded in NSE on a continuous basis throughout the NSE trading day. The time period was selected because it intends to use return volatility with historically high and low returns for the NSE. When conducting research analysis, it is critical that the practicality meets the applicant's perception rather than simply addressing what the study entails or comprises. The data were selected from the NSE data base and all stocks returns were adjusted and I used regression model to do the analysis. In order to arrive at a beta estimated value of the study I adopted returns from each month representing the sample. The return was based on a long time period of several months which might be the results of the beta examined period, thereby introducing high frequency data such as observation consisting relatively short and stable can result from using unusual data. The predicted price was determined through the use of regression spread sheet analysis and the trend reflects stock market price. The proxy that is used to measure the dependent variable in this study is CAPM. Since this is a quantitative study, the data analysis techniques will be regression analysis, which will be based on information from the Nigerian Stock Exchange. There are numerous methods for quantitative data analysis, and the method used here is specially tailored to the research topic being addressed. This study specifically uses regression analysis, which is the process of using a mathematical model to forecast the value of one variable based on the values of one or more other variables. The independent variable in this study is stock price prediction, and the dependent variable is market stock prices. The proxy that is used in this study to measure the dependent variable is CAPM in the Nigerian market. The study follows the procedure of OKE and Mihailidis, Tsopoglou, Papanastasiou, and Mariola (2006) (Man & Wong, 2013). At the beginning stage is the estimation of beta coefficient for each stock using weekly returns during the approximation period. Moreover, in this particular study I approximate beta by regressing each month's return against the market index as highlighted in following equation:

Findings and Discussions
The beta value estimated for the individual stocks are obtained from the observation of rate of return for the sequence of dates in the table presented below and which range from monthly records from stock A to stock B in the year 22/6/2021 -17/6/2022. Subsequently, it is in line with the principles of CAPM assumption and it examines the law as it assumes that high risk beta is associated with high level of return. This law is in line with the Nigerian Stock Exchange which is consistent with the period reviewed or examined; stock with high risk portfolio is B because it has highest alpha whiles portfolio A is the one with low risk according to their alpha, as shown in the table below.       The table under footnote (appendix) indicates the assumption tested the following values as indicated in Table above and the table for output 1 and output 4 contain the following subheadings-coefficient, standard error, t-stat, P-values, lower and Upper and these answers were obtained from regression analysis and are summarized in Table 7 which shows the subheadings average, variance, standard deviation, covariance, correlation, beta and alpha. As indicated in the summary in Table 7, in terms of average both of the stock A (-0.005) and B (-0.00072) have negative value whiles the variance and standard deviation in both cases are equal, which is (0.035) and (0.19), respectively, and the covariance and correlation of stock B has shown positive values (0.002145, 0.237449) as the highest value. Table 5 indicated that stock A has high beta value (0.003022) while stock B shows highest alpha (0.031004), showing that stock B is high risk. These particular results have invalidated zero beta assumption of CAPM. Meanwhile the assumption that the slope of regression analysis (SML) should equal to excess return on market portfolio was found to be valid. While the slope of approximated SML for output 1 in the regression analysis the value for significant F (0.589240338) is greater than market MS (0.000642767) and for that of output 2 the value for significant F (0.017370691) is higher than that of the market (MS 0.006584535). Therefore, it can be concluded the results obtained from the beta are positive which is consistent with Nigerian Stock Exchange for the period examined (22 nd June 2021 -17 th Jun 2022), hence t the average excess return on portfolio (RP) and the approximated beta of Portfolio (β) are important statistically.

Conclusion
This particular research was aimed to establish the validity of the law of CAPM in the Nigerian Stock Exchange (NSE) using monthly stock returns from 20 companies for the period of one year (22/6/2021 -17/6/2022). The results obtained concluded that the value that is obtained is beta and it is positive and thus consistent with CAPM in the Nigerian stock exchange since the final results are consistent with NSE for the period examined and, thus, it shows evidence of correlation between NSE and CAPM. In summary, both the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) describe the link between risk and return. The CAPM is a popular model that only analyzes one element (beta) and assumes a linear relationship between risk and return, whereas the APT considers numerous factors and generalizes the risk-return relationship. The main limitation of this study is that it is difficult to estimate beta, which is the fundamental problem with CAPM. The sample size and the period for analysis may have an impact on the CAPM's efficiency. Results may not be generalizable to the broader Nigerian capital market if the sample size is too small or the time period is not representative. Determining an exact beta value can be difficult and time-consuming. Usually, a proxy value for beta is used.

Declarations
From today i the author of this paper with above mentioned title declared that there is no conflict of interest that warrant me to write this paper but is a requirement for the partial fulfillment of Master of Accounting in university of Airlannga

Conflict of Interests
I the authors declared that there is no significant competing financial, professional, or personal interests that might have affected the performance.

Availability of Data and Materials
The data that is used in this is obtained strictly from Nigerian stock market and the references that are provided in the references column.

Author's Contribution
This article intends to contribute by offering empirical evidence of the chosen model's applicability and reliability (like CAPM) in the setting of the Nigerian stock market.

Funding Sources
This program, where I am studying in Airlangga University it's a scholarship program under ADS.

Acknowledgments
I would first and foremost like to express my sincere gratitude to Novrys Suhardianto, SE., MSA., Ph.D., Ak., CA, my principal supervisor, for his selfless dedication, priceless time, ongoing guidance, astute advice, closed supervision, and enthusiastic encouragement while I was writing this paper. His feedback and meticulous review of several revisions had a considerable impact on this paper style and content. He supplied advice and suggestions that will significantly enhance my school life in addition to advice for this paper. I want to publicly thank Prof. Dr. Moh Nasih, S.E., M.T., Ak., CMA, the rector of Airlangga University, as well as the academic staff of Universitas Airlangga in Surabaya for providing me with the opportunity and support I needed to complete the Master's degree in Accounting. I also want to thank The Gambia's government for allowing me to pursue my studies abroad.