Capital Asset Pricing Model, Arbitrage Pricing Theory - Example

Introduction The financial experts have come up with two approaches that are used to measure the expected returns of any given stock and investment in assets. These approaches help the investors and the financial and investment analyst to come up with a portfolio of stock that would give good returns with relatively lower risk. These approaches are CAPM and APT model. Using CAPM model the return of a given stock is the summation of the risk free assets the market premium. However, CAPM does not factor in other factors like GDP, inflation and other factors, hence the evolvement of APT model. APT is used to predict the expected returns of stock taking into consideration factors like inflation and the Gross Domestic Product (GDP). The APT model therefore, is better than the CAPM since it factors in more factors which affect the value of the stock like the interest rate, GDP and the rate of inflation in a country. Theoretical Review This part seeks to address the major theories that are used to measure the expected returns of stock in the market. These theories include the portfolio theory, the APT theory and the CAPM theory. Portfolio Theory A portfolio is a combination of more than one stock. Since most investment has different risk profile and varying rate of return, it is prudent for an investor to invest in more than one stock. This would help in diversification of risk and reduces the uncertainty of income. Most of the stock available for investment has is risky as they have uncertain returns, and therefore, an investor needs to come up with the portfolio to invest in. The challenge of coming up with the correct portfolio is known as the portfolio selection problem. In order to find solution to this problem, Markowitz (1991) conducted a research study which is the origin of the present theory of portfolio of making investment. Investors should make choose portfolio to invest in based only the expected returns and the risk involved measured using standard deviation, (Markowitz, 1991). The investors should find out the estimated expected risk involved and the expected return of various stock of each portfolio and choose the best based on these parameters. The expected return measures the potential reward which an investor may obtain from investing in a given stock over a given period while the standard deviation measures the risk involved in investing in that given portfolio. According to Markowitz, 1991, investors are assumed to also prefer portfolio with higher returns to the one with lower returns, as a higher return generate more wealth hence more income will be available to an investor for consumption. Therefore, given two stock with equal standard deviation, the investor will always choose one with higher expected returns. The investor is also assumed to be risk averse, hence given two investment with equal returns and different standard deviation, the investor will always choose investment with lower standard deviation as it has lower risk. The Markowitz portfolio selection is seen from the perspective of profit maximization and wealth creation. The investors prefer more wealth to less wealth; this is the assumption of non-satiation. An investor derives more wealth from every extra increment in dollar of wealth (marginal utility). Markowitz also proposed the use of indifference curve to make good selection of portfolio. The indifferent curve will indicate the expected risks and the expected return combinations which will give the investor same amount of utility. The expected return can be plotted on the vertical axis, while the standard deviation which is a measure of risk is plotted on the horizontal axis, (Heston, S. A. 2012). The investor will be indifferent on any investment along the indifferent curve. The risk-averse investors will invest on the portfolio lying on the indifferent curve. To obtain the return of a particular portfolio, the weighted average of the expected returns is calculated, with the given proportion of the components acting as weight. The standard deviation of each particular portfolio is also measured based on the proportion of the standard deviation of each component of stock and the covariance with each stock. The main purpose of calculating the weighted average is to determine the desirable proportion of portfolio to invest in which generate more wealth to the investor. Another theorem, the efficient theorem, provides for an investor to select the portfolio that’s optimizes his or her returns. This means that an investor will select the option with the maximum rates of expected returns although with the variations in risk degrees, the offer should also offer a minimum risk with the variation in the returns expected. These set of portfolio where the two conditions meet is referred to as the efficient frontier or the efficient set. It includes the investor to identify a set which is the most feasible represented by the portfolios deriving from the available securities. An optimal solution will then be selected from the indifference curve plotted on the same figure as the indifference curve which will be selected as the one that is farthest to the north east. Capital Asset Pricing Model CAPM describes relations between the expected returns and the risk (Grinblatt, M. A. 2014). It is used to price the riskier securities. Emphasis on this model is on the calculation of the expected returns of the security where it the risk premium of the portfolio and the market beta should be noted and consequently aggregated. The risk premium of the security is the part of the yields which has a direct correlation to the market meaning that portion to which a security will serve as a substitute for an investment in a market (Grinblatt, M. A. 2014). Generally, the security return component is that part of a security which is not correlated to the market and its diversification would not add a demand risk premium. This model provides the return for the investors should be similar to: risk free rate (rf), added to the stock premium then multiplied to the probability of the risk of a firm. The expected return of a security may be further explained using the security market line (SML). This equation uses the linear and the coefficient beta. Βi =σi m/σ2m This equation, also known as the asset pricing model equation, states that for a portfolio M to satisfy the relationship in the return of a security, the return and the security beta must also be satisfied. The CAPM model provides that the managers and the investors need to evaluate and compare between the return expected and the returns required. If the expected return is less than the required returns, then the portfolio is dismissed but if the expected returns are more than the required, then the project is viable (Fama, E. A.2013). The assumptions of the model are dependent on the empirical accuracy in predicting the outcomes while the reality is assumed. The basic assumption of the model is that all investors are rational in their decisions and that they will be risk averse. It also assumes that they will diversify their investments over a wide range, and they have no way of influencing the prices, they can obtain unlimited amounts under the risk free rates and that there are no taxes and lastly, the information is readily available to all the investors. Arbitrage Pricing Theory The Arbitrage Pricing Theory commonly referred to as the APT is a stochastic model which ensures consistency of the returns in the capital assets return with the structures of the factor, (Fama, E. A.2014). The equilibrium prices do not provide any opportunities over the portfolio of an asset and that the returns expected have a linear relationship with the loading factor. The loading factor will then be proportional to the covariance of the returns. This model maybe used as a substitute for the CAPM model because both models have a similar assertion: there’s a linear correlation between covariance of other random variables and the assets expected rate of return. The interpretation of the covariance is a risk measure which the investors will strive to avoid through diversification, (Cooper, M.2015). In the linear relation, the slope represents the risk premium which is the relationship between the returns expected and the covariance. This should be reliant on the efficiency of the mean and the variance. APT, cannot be however used as a definitive model it only shows the list of portfolios with their expected returns and their covariance with its portfolios and thus cannot be used to be make decisions. Method In order to find out the market premium and the expected return of the stock, the CAPM model is used. The formula is: E (R) = Rf + βi (Rm – Rf) Where; E (R) = the expected return of the stock Rf = the risk free rate of return βi = the beta factor of the security, which represents sensitivity of the stock. Rm = the market expected return (Rm – Rf) = the market premium The linear equation above shows how the expected return of a security can be calculated using the market premium and the risk free rate. However, the CAPM does not factor in the influence of interest rate, inflation and the GDP, hence the need to use APT model to measure the expected returns by factoring in these factors. Using APT model: E (Rt) = a0 + b1GDP + INTt + eO Where: E (Rt) = the expected return of the given stock at a given time period t A0 = the constant bi = the sensity of each factor represented INTt = the interest rate at a given time period eO = the random error. Data collection and analysis The data is based on the firms listed in the NewYork stock exchange. The data is obtained from firms which report and publish yearly report and are available to the public. All the variable which are used are based on ratios of the firms of listed in New York stock exchange. From the ratios, we obtain the expected returns, the market premium and the risk free rate. The risk free rate is obtained by taking the rate offered by the government treasury notes, which stands at 7% as at 2016. The results of CAPM In order to determine how, the excess return affects the return of stock, we will use the regression equation: R = -0482 + 0278 ER + e Where: R = the return ER = excess return E = the error From the results calculated, this regression indicates that the variable excess return has a significant positive effect on the stock returns. The APT results This research also uses the multiple regression models in order to find out the effect of independent variable, that is, the GDP and the interest rate on the dependent variable that is the returns on the companies listed in the New York stock exchange. In order to find out how the interest rate and the GDP affects the return of stock, a regression equation formulated is use; R = 0.099 + 0.0588 GDP – 0.139 I + e Where: R = the expected returns GDP = Gross Domestic Product I = interest rate E = random error Based on the results of this regression equation, it shows the effect of independent variable (interest rate and GDP) on the dependent variable (expected return). It can be seen that the interest rate has negative effect on the stock while the GDP has positive effect on the stock. The results of this regression model indicate the direction of the effect of each independent variable consisting of GDP and Interest rate on the dependent variable (stock returns). GDP has a positive influence on stock returns, while Interest rate has a negative effect on stock returns. When the GDP, interest rate and the error term is zero, then the expected return is 0.099 = 9.9% Discussion From the results of CAPM, the regression model shows that the excess return of variable gives a positive significant effect on returns. This indicates that when there is higher excess market return, the stock return will be higher and the investors gain more confidence on the company, hence the firm becomes attractive to the potential investors. This will in turn lead to the appreciation of the shares which in turn leads to the increase in the stock prices. Based on the results of this study, it is found out that the excess market returns can be used by the investor to predict the expected movement of the stock prices. From the APT regression analysis, it was found out that the interest rate has negative influence on the stock price movement. This is true because when the interest rate increases, the investors will rush to invest their money on the fixed deposit which generates fixed income with a very minimal risk, hence reducing the investment in shares, this would lead to a decrease in the stock prices. Therefore, lower interest rate will lead to more investment in shares, hence higher returns. Previous Studies From the previous studies done on the relationship between the APT and CAPM, with the stock returns, they produce different results and therefore, investor would arrive at different conclusions. Some of the previous studies that discuss CAPM and APT are: a. H. Jamal Zubairi and Shazia Farooq. This is a study which was done between 2004 and 2009. The study revealed that APT and CAPM, both does not give a good conclusion to be used in determining the prices of the fertilizer, gas and oil. b. Delly (2001 – 2006), according to this study, based on the standard deviation it was found out that the CAPM is more accurate model in predicting the return and risk on stock than the APT model.. c. Gancar Premananto Candra and Muhammad Madyan. They did a research in 1991 – 2001. According to their study, there is a wide difference in the accuracy between the APT model and CAPM model when predicting the expected returns of stocks in manufacturing firms more so during economic crisis. The CAPM model gives more accurate results than APT model. Reference Cooper, M. G. (2015). Asset Growth and Crossection of Stock Returns. Journal of Finance,Vol.63, 1609-51. Delly.” Perbandingan Keakuratan Capital Asset Pricing Model CAPM) dan Arbitrage Pricing Theory (APT) dalam Memprediksi Return Saham yang Aktif di PT. Bursa Efek Indonesia (BEI) dan di Singapore Stock Exchange, 2001-2006”. Surabaya. Universitas Kristen Petra. Fama, E. A. (2014). The Cross Section of Expected Stock Returns. Journal of Finance Vol. 47, 427-466. Fama, E. A. (2013). Common Risk Factors in the Returns on Stocks and Bonds . Journal of Financial Economics Vol.33, 3-56. Gujarati,Damodar N and Dawn Porter.2008.Basic Econometrics. McGraw- Hill/Irwin; 5 edition Grinblatt, M. A. (2014). Predicting Stock Price Movements from Past Returns:The Role of Consistency and Tax-Loss Selling. Journal of Financial Economics, Vol.71, 541-79. Heston, S. A. (2012). Seasonality in the Cross-Section of Stock Returns. Journal of Financial Economics Vol. 87, 418-45. Markowitz, Harry M. "Foundations of portfolio theory." The journal of finance46.2 (1991): 469-477. Read More