Capital Asset Pricing Model Theory Research Articles

Capital Asset Pricing Model (CAPM) 2.0: Account of Business and Financial Risk

The famous Capital Asset Pricing Model (CAPM), widely used in practice, takes into account only the business risk associated with investments in a specific company [not the entire market (or industry)]. In practice, most listing companies use debt financing and operate at a non-zero leverage level. This means that the financial risk associated with the use of debt financing, along with business risk, must be taken into account. The purpose of this paper is to simultaneously account for business and financial risk. We combined the CAPM theory and the Modigliani-Miller (MM) theory, which is the perpetual limit of the BFO (Brusov-Filatova-Orekhova) theory. The article shows that R. Hamada’s attempt to take into account both business and financial risks has proved unsustainable, and the formulas he obtained, widely used in practice, are incorrect. The paper outlines the correct formulae that made it possible to generalize CAPM for the first time, taking into account both business and financial risk. The application of the new CAPM 2.0 model to a number of companies is considered and the difference between the results obtained within the framework of CAPM 2.0 and CAPM is demonstrated. CAPM is one of the main models [along with APT (arbitrage pricing theory) and WACC] within the income approach to business valuation. This significantly increases the value of the developed CAPM 2.0 approach, which can significantly improve the accuracy of the assessment.

Quantitative trading portfolio optimization based on machine learning

The capital asset pricing model (CAPM) is to study the quantitative relationship between the expected return rate of assets and risky assets in the securities market. With the development of computer network technology and the trading market, quantitative trading has gradually become a new way of investment. Its essence lies in the decision of trading strategy. This paper obtains the relative price data of the subsequent short-term investment period through the time series method, then uses the PA algorithm in machine learning to update the portfolio and verify the effectiveness of the strategy in the data set. Based on the exchange rate change trend of the US dollar, gold, and bitcoin within five years given in the question, we constructed dynamic portfolio models for the three assets to ensure maximum profits. First, we use the time series model to predict the relative price data of the next period in a continuous trading period. Then, we implement the PA passive attack algorithm by calling the Sklearn package in Python to update the asset components in real-time every day and calculate the average annual return rate in 5 years. Based on the above analysis, we used the ADF unit root to test the stationarity of the time series. Meanwhile, we also carried out a white noise test of time series. The specific test indexes include: According to CAPM's theory, this product has a high yield, with an annual interest rate of 195.849%, which is entirely objective. However, the annual standard deviation reached 0.919164, and the maximum retractable rate exceeded 50%, indicating a sizeable overall risk. Despite this, the composite product's Calmar ratio is 3.556, Sharpe ratio is 2.104623, and its return per unit risk is still high. Compared with other quantitative trading models, this paper combines time series, machine learning, Monte Carlo, and other algorithms to effectively solve the portfolio investment optimization problem of nonlinear time-varying correlation structure among multiple assets. It enriches the results of portfolio investment structure decisions.

Hamada’s equation and the beta of debt under CAPM

AbstractThe Hamada equation based on Miller–Modigliani (MM) Proposition I shows the ‘no arbitrage’ relationship between the firm’s levered and unlevered beta. This relationship can be obtained from a capital asset pricing model (CAPM). MM is not required because asset prices under CAPM are inherently additive under any arbitrary slicing or securitisation of the firm’s cash flows (the size of the pie is unaffected by how it is cut). Our CAPM theory shows why the market rate of return on debt increases when the firm takes risks that increase its probability of default, even when the risk is idiosyncratic and unconnected to market conditions.

Measuring risk exposure in the banking sectors: evidence from Gulf Cooperation countries

PurposeUsing capital asset pricing model (CAPM) and the Z-risk index based on weekly data, this study aims to estimate yearly unsystematic, total, three systematic and insolvency risks in the Gulf Cooperation Council (GCC) countries for the period 2010–2018. The findings of CAPM show positive systematic market risk exposure in all GCC countries for all years, which support the contribution of stock markets to bank prices and returns. The mixed signs of systematic interest rate and exchange rate risks in GCC countries provide hedging opportunities, diversification strategies and regional cooperation, which help risk managers to hedge and stabilize their portfolios against interest rate and exchange rate fluctuations. Therefore, it is necessary that managers and policymakers develop a monitoring system on factors affecting bank insolvency risks to avoid bankruptcies and insolvencies.Design/methodology/approachThis study uses the three-factor CAPM and Z-risk index to measure six types of risks. The CAPM uses market information to estimate the sensitivity of banks to the fluctuations of equity markets, debt markets and foreign exchange markets. Sharpe (1964), Lintner (1965) and Treynor (1965) developed a single-factor CAPM and the coefficient of the model was called systematic market risk. The single-factor CAPM highlights stock markets as the only non-diversifiable source of systematic risks, whereas Stone (1974) and Jorion (1990) highlighted interest rate and exchange rate fluctuations as the other types of non-diversifiable systematic risks. The following functional form in equation (1) estimates five types of risks using CAPM.FindingsThe findings of CAPM show positive systematic market risk exposure in all GCC countries for all years, which support the contribution of stock markets to bank prices and returns based on CAPM theory. The mixed signs of systematic interest rate and exchange rate risks in GCC countries support hedging opportunities and diversification strategies which may help risk managers to hedge and stabilize their portfolios against the fluctuations of interest rate and exchange rate. Although, this policy may decrease the profits of banking sectors but at the same time it would stabilize the portfolios and prevent bankruptcies and big losses because of the fluctuations of interest rate. Moreover, a bank has a better chance to have more liquidity position during financial crises because of the diversifications into different regional markets.Research limitations/implicationsTherefore, this study contributes to the existing literature by using risk measurement by a three-factor CAPM and the Z-risk index as discussed further in methodology.Originality/valueIt is necessary that managers and policymakers develop a monitoring system on factors affecting bank insolvency risks to avoid bankruptcies and insolvencies.

Capital Asset Pricing Model (CAPM) and the Douala Stock Exchange

This study examines if the Capital Asset Pricing Model (CAPM) can be applied to the Douala Stock Exchange. The study utilized monthly stock returns from the three companies listed on the Douala Stock Exchange (DSX), for the period 30th April 2009 to 31st August 2017. Ordinary Least Square regression analysis was adopted for the study to examine if individual stocks can predict a better stock beta. The Black, Jensen, and Scholes (1972) CAPM version were also examined in this study to assess the validity of the zero beta estimate. The result of the individual estimates could not establish the validity of the CAPM theory. Further analysis showed that the Beta for the three assets combined portfolio was not statistically significant. However, when two securities were combined into a single asset portfolio, the portfolio bêta was statistically significant. The significant result of the two asset portfolio confirms that Beta was a linear function of security returns in the DSX market. The study concludes that there will be a need for the government of Cameroun to liberalize the DSX market and allow more firms to be quoted on the floor of the exchange. This decision will allow for the deepening of the DSX market, enhance the liquidity level of the market, and enable investors to reap adequate returns from their investment through holding a portfolio of assets.

Nature of Beta in the Nigerian Stock Market – Challenges and Prospects

The paper appraise the nature of beta in the Nigeria stock market and the impact of Beta on Investors’ wealth maximization strategy in the Nigerian Stock Market. Ex-pos facto was iused to design the research as secondary data from the Nigerian stock market was deemed fit for the study. The study also indicated that there is a strong relationship between the firms’ Stock Return and Beta Coefficient. Finally, the study established that Beta Coefficient has a significant effect on the Stock Return of Firms Listed on the Nigerian Stock Exchange. Three years data collected (from January 2017 to December 2019) from the database of the Nigeria Stock Exchange was used to estimate the coefficient of the stocks’ betas. The data collectected were monthly price rates of the stocks, the All Share Index monthly rates and the Nigeria Treasury Bills monthly rates. The All Share Index is used to calculate the market returns and the Treasury Bills used as the risk free rate. To carryout the data analysis, returns were calculated for stocks and the market. Regression Analysis wss then to regress the stocks’ returns against the market returns in order to estimate the beta coefficient using the CAPM (Capital Asset Pricing Model) theory: Ri=Rrf + Bi (Rm-Rrf). The result showed that Guanranty Trust Bank, Ashaka Cement, Dangote Cement, Flour Mills Nigeria plc and Northern Nigeria Flour Mills plc have higher risk (beta) of investment than the other stocks meaning they are more volatile than the market and the other stocks that have beta value les than one (1), thence higher expected retuns. It is, therefore, recommended that Investors should invest in these mentioned Companies with higher risk as higher risk is synanimous to higher returns in order to maximise their returns.

Analysis of the Capital Asset Pricing Model: Application to General Electric Performance

In the world of investment, the essential question is, to what degree does the risk of a security influence its expected return? The Capital Asset Pricing Model (CAPM) helps in answering this question. CAPM showed that the risk which can be spread away when seized together with other investments in a particular portfolio should not affect asset price. The adequacy of the CAPM theory as a measurement tool of the relationship between a security’s beta and the expected return of a security is now seriously challenged as it has a set of assumptions that are mostly criticized by their absence in reality. This research re-examines these assumptions (markets are ideal, all investors are averse to risk, markets are highly efficient, Beta coefficient is the only measure of risk and markets are in equilibrium) by applying them to measure the performance of General Electric between March 2017 and March 2020. The methodology adopted in this study is quantitative approach. The main finding of this research indicates that the risk-free rate decreased, the risk increased and the expected return moved up and down in each year. Therefore, the failure of the CAPM in empirical tests implies that most applications of the model are invalid.

Fundamental Error in Capital Asset Pricing Model Theory Beta Gearing and its Demystifying Solution

Fundamental Error in Capital Asset Pricing Model Theory Beta Gearing and its Demystifying Solution

PENGUJIAN CAPITAL ASSET PRICING MODEL (CAPM) DALAM MENILAI RISIKO DAN RETURN SAHAM JAKARTA ISLAMIC INDEX (JII) DENGAN TWO PASS REGRESSION

The aim of this research is to investigate the validity of Capital Asset Pricing Model (CAPM) in assessing risk and return of Sharia stock in JII during 2014-2016. The samples are 18 companies obtained by purposive sampling. This research uses quantitative approach with two pass regression method. The result of empirical testing explains that CAPM is not accurate because one of the CAPM assumption is unfulfilled that the beta value is negative and not significant to the expected return. This results fail to confirm linear and positive relation between beta and the expected return such in the CAPM theory. The overall results demonstrate that the CAPM is not accurate particularly on JII sharia stocks during the observation period

STOCK PORTFOLIO PERFORMANCE BASED ON STOCK VOLATILITY: A STUDY OF INDONESIA STOCK MARKET

The aim of the study was to investigate the relevancy of capital asset pricing model (CAPM) in Indonesia. CAPM states investor who has willingness to take higher risk should compensate with higher return as compensation. Hypothesis testing uses the one sample t-test to validate the return portfolio is not equal to zero. The result of the study revealed that portfolio with highest risk did not provide highest return. Supposition of the results is because limitation of CAPM theory (frictionless market and everyone has risk averse profile). This creates low risk anomaly phenomenon in Indonesia stock market which lower risk portfolio can provide higher return and contractive monetary policy magnify the portfolio performance differences.

SELEKSI SAMPEL SEBAGAI PROKSI INDEKS PASAR DALAM PENGUJIAN CAPITAL ASSETS PRICING MODEL DI PASAR INDONESIA

Some test about Capital Asset Pricing Model (CAPM) are in fact, most of them showed that there were in equilibrium between the CAPM theory with the empirical facts. This in equilibrium most can be see in the intercept which is not the same as zero. Some tests are resulting that linear relation between the return level which can be hoped by the risk which is measured with beta, but in the other fact shows that there is still factor or variable beside beta which influence the return of security, those variables are not explained by CAPMThe failure of empirical test for proving the CAPM hyphotesis are caused by the failure of the L""'APM specification itself then the use of market model which maybe is not relevant because of the return fluctuation and the free investment risk The investment process in security is doing evaluation to the investment performance, in security investment which is often done in portofolio form, so it is needed portofolio performance l!valuation. Some tests, empirical CAPM can be concluded that: (1) Security return is in fact in linear way can be related with beta as it is predicted in CAPM test; (2) There is positive relation between beta with historical return, that it means the bigger the beta the bigger the return; (3) The market line security test (SML) is in fact less steeply slope comparing to the theoretical SML, it means that shares with lower beta will have higher return as it is predicted by the Capital Asset Pricing Model, while the shares with higher beta have lower return as it is predicted, this is because of the mistake in the measurement; (4) The intercept criteria which is bigger can be predicted theoretically than the value offree risk return (RJ.Even the test result can not give support from the theory of Capital Asset Pricing Model, this test gives the consistent implication, beta is the linear systematic risk taht is related positively with the historical return.

The relationship between the risk of the asset and its expected rate of return: a case of stock exchange market of five European countries

The study proposes to verify the capital asset pricing model (CAPM) and its validity for stock markets in the selected European countries’ stock markets: Greece, Italy, Poland, Portugal, and Czech Republic. We examined the top 40 companies listed in the five European countries through a data-set collected on a weekly basis from January 2009 to December 2013. The CAPM model is tested by performing a two-stage regression methodology using Eviews. We performed a first-stage regression to estimate stocks of the beta through a linear regression. After that, we used a second-stage cross-sectional regression to estimate the relationship of the average return of the portfolio and its beta. It is concluded that there is no relationship between average return of the portfolio and its beta. However, we only found that there was a linear relationship between the expected returns and beta of the Italian stock market. The negative relationship does not support the CAPM theory. Therefore, it is concluded that the CAPM does not hold for the selected sample of the five European countries’ stock markets.

CAPM: A Covariance Adjustment Approach for Estimating Market Beta

Due to a lack of supporting evidence, market beta in the widely-acclaimed Capital Asset Pricing Model (CAPM) is considered dead nowadays. In this paper we propose a novel approach for estimating market beta using the traditional market model. Upon deriving a covariance adjustment term, we specify a so-called observed market beta for each asset. We show that observed market beta can be approximated from information contained in the market model, including the estimated market beta, variance of market index returns, and residual error variance. Based on historical U.S. stock returns, different test assets, and standard cross-sectional tests, we find that observed market beta is significantly priced in the cross section of average stock returns with no pricing error. Similar to the findings of other researchers, evidence does not support the traditional market beta. We conclude that observed market beta provides renewed empirical support for CAPM theory.

An Empirical Test of CAPM—The Case of Indian Stock Market

A deluge of tests have been conducted on asset pricing models in literature, more so on the Capital Asset Pricing Model (CAPM), to ascertain their validity, efficiency and efficacy in different markets in explaining asset prices. Such tests have been either individual in nature wherein any one model has been studied or comparative in nature where one model has been compared with another. Many studies have also resulted in the development of new models or extensions to the existing theory. However, majority of the aforementioned tests have been undertaken in developed markets, resulting in a dearth of such tests in emerging markets like India where the risk–return relationship gains more significance. A growing, emerging market is always less analyzed but more volatile and thus, more interesting. The article, thus, applies the fundamental CAPM theory to India. This study examines 10 portfolios, covering 50 stocks, over a 5-year period—from 1 January 2003 to 1 February 2008—to verify the efficiency and efficacy of the model and finds that CAPM fails completely in the Indian context. The intercept term, which is expected to be zero, is found to be significant for all 10 portfolios. The study also finds a negative relationship between beta and excess returns indicating an inefficient capital market. Moreover, residual variance, representing unsystematic risk, is also found significant in certain cases. Moreover, the regressions show poor explanatory power. Thus, it can be concluded that CAPM is not a suitable descriptor of asset prices in India over the chosen sample period.

Home Bias in Financial Markets: Robust Satisficing with Info Gaps

Abstract: The observed patterns of equity portfolio allocation around the world are at odds with predictions from a capital asset pricing model (CAPM). What has come to be called the phenomenon is that investors tend to hold a disproportionately large share of their equity portfolio in home country stocks as compared with predictions of the CAPM. This paper provides an explanation of the home-bias phenomenon based on information-gap decision theory. The decision concept that is used here is that profit is satisficed and robustness to uncertainty is maximized rather than expected profit being maximized. Furthermore, uncertainty is modeled nonprobabilistically with info-gap models of uncertainty, which can be viewed as a possible quantification of Knightian uncertainty. JEL classification: D81, F30, G11, G15 Key words: equity home bias, Knightian uncertainty 1 Introduction The observed patterns of equity portfolio allocation around the world are at odds with predictions from the Capital Asset Price Models (CAPM) of Sharpe [16] and Lintner [13]. What has come to be called the 'home bias' phenomenon is that investors tend to hold a disproportionately large share of their equity portfolio in home country stocks, as compared with predictions of the CAPM. This paper provides an explanation of the home bias phenomenon based on information-gap decision theory. The decision concept which is used here is that profit is satisficed and robustness-to-uncertainty is maximized, rather than expected profit being maximized. Furthermore, uncertainty is modelled non-probabilistically with info-gap models of uncertainty. French and Poterba [6, 7] quantify the magnitude of the home bias for a number of countries and conclude that the size of the home bias is substantial, which led to the terms Home Bias Puzzle or French and Poterba Puzzle. For more details see Jeske [10]. In their calculations, French and Poterba assume that the investor maximizes the expected return decremented with a variance-based risk term. Let w = ([w.sub.h];[w.sub.f])' represent the vector of home and foreign investments, let [??] be the expected returns for home and foreign investments, and let [SIGMA] be the covariance matrix of returns. In the French and Poterba model, w is chosen to maximize U(w) = w'[??] - [lambda]/2 w'[SIGMA]w where [lambda] is chosen to weight the risk term. An extremum of U(w) occurs when [??] = [lambda][SIGMA]w. Let [w.sup.o] denote the observed portfolio weights for a particular country, so that the expected returns consistent with CAPM profit maximization would be [[??].sup.o] = [lambda][SIGMA][w.sup.o]. For the same country, let [w.sup.mc] denote the portfolio weights based on world market capitalization, without any home bias effect. That is, [w.sup.mc.sub.h] is the fraction of the world market capitalization ascribable to the country in question. For example, [w.sup.mc.sub.h] = 0.475 for the US. Without any home bias, one would expect that 47.5% of US investments would be in US assets. The vector of expected returns consistent with the CAPM, based on world market capitalization without home bias, is [[??].sup.mc] = [lambda][SIGMA][w.sup.mc]. French and Poterba observed, for a wide range of countries, that: [[??].sup.o.sub.h] > [[??].sup.mc.sub.h] and [[??].sup.o.sub.f] The returns vectors [[??].sup.o] and [[??].sup.mc] are not observed market values, but rather calculated values which are consistent with the CAPM decision model and observed portfolio weights. If the investor's behavior is rightly modelled by the CAPM theory, then [[??].sup.o] and [[??].sup.mc] can be interpreted as returns vectors which are anticipated or perceived by the investor. Relations (1) imply that investors perceive the domestic assets to perform better, and the foreign assets to perform worse, than the bias-free portfolio would indicate. …

THE COVID-19 PANDEMIC & HERDING BEHAVIOR : EVIDENCE FROM BANGLADESH CAPITAL MARKET

This study aims to detect herding behavior during the COVID-19 pandemic, compare investor trading behavior pre (2015 to 2019) and post (2020 to 2022) pandemic, and examine how investors react in panic and uncertainty. Current asset pricing theory states that cross-sectional returns should reflect systematic risks like stock prices, where Capital Asset Pricing Model (CAPM) betas are often viewed as return volatility, but they do not account for price volatility. To reflect the uncertainty, CAPM and Asset pricing theory are not sufficient so the gap is filled by behavioral finance that examines investors’ personalities and trading behaviors to explain market swings. It examines which stock price data influences investors’ decisions that is depicted by herding behavior. People “herd” when they do not make individual decisions. Unpredictability, worry, and panic often cause such behavior and COVID-19 epidemic worsened such factors that hurt global economy and stock markets. Financial data cannot reveal herding behavior for which two models, Cross-sectional standard deviation (CSSD) and Cross-sectional absolute deviation (CSAD), acknowledged by Christie and Huang (1995), are used to identify herding behavior in Bangladesh’s capital market during the COVID-19 pandemic. CSSD uses standard deviation to understand investor herd behavior, while CSAD uses absolute deviation. As mentioned in the literature review from the journal of Christie and Huang (1995) that the CSSD model and CSAD model will provide a conflicting result, the above finding shows the same because in CSSD model, no herding behavior is found but in the CSAD model, the herding behavior is found in the bullish markets for the year 2020 and in the bearish markets from 2015 to 2022.