# Comparison of CAPM and APT Theories

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# Comparing Capital Asset Pricing And Arbitrage Pricing Theory

Investment and portfolio selection decisions are made on a regular basis in the daily routines of investment managers, financial managers of companies, mutual fund managers as well as by individual investors themselves. Selecting an investment or a portfolio of investments is a very important and tough decision because it not only involves estimating the expected value of the securities in the form of return but also requires the decision maker to make a reasonable assessment of risk entailed in the process. This gives rise to the great importance that is attributed to asset pricing theories in the literature of Finance, Financial Management, Investment and Portfolio Management and other related disciplines.

Asset pricing theories have long been a source of intrigue for academicians, researchers and practitioners alike. Although the history of these theories dates back to a few hundred years ago, the very first notable theory was proposed by Harry Markowitz. Markowitz theory is sometimes also called the “mean – variance model” because he represented return as mean while risk was represented as the variance. He proposed that investors acting rationally make a diversified portfolio of securities in order to minimize their risk and maximize their returns for a certain period. (Markowitz, 1952)

This theory by Markowitz marked the beginning of a long string of asset pricing theories proposed by a number of researchers. Most of these theories discussed the mechanics of risk and return and examined various ways in which risk could be minimized for a certain level of return or return could be maximized for a certain level of risk. In simplest words, we can say that these theories deal with the concept of risk-return trade-off in investment decisions.

First such theory based on Markowitz portfolio theory was Capital Asset Pricing Model (CAPM), which was proposed almost simultaneously by three researchers, Sharpe, Lintner and Mossin (Sharpe, 1964) (Lintner, 1965) (Mossin, 1966). This is a relatively simple model which suggests that there is a linear relationship between return and risk of an asset or a portfolio of assets. It is a one factor model which posits that return of an asset or a portfolio of assets can be assessed or measured by one factor, i.e. the beta (β) of that asset which is a measure of non diversifiable risk of the asset. Immediately after it was proposed CAPM became a target of intensive scrutiny and debate among researchers. Since almost three decades, this model has been subjected to rigorous testing and retesting where it has been approved and validated by some while rejected by others. Some researchers have even used its altered and more improved forms to try to decrease the problems encountered due to its oversimplifying assumptions.

A major alternative to the capital asset pricing model (CAPM) is arbitrage pricing theory (APT) proposed by Ross in 1976. Arbitrage pricing theory as opposed to CAPM is a multifactor model suggesting that expected return of an asset cannot be measured accurately by taking into account only one factor, i.e. the asset beta. Instead APT suggests that there are a number of factors at work that can help explain variance in return of assets thus giving us a measure of the assets' risk. These factors include various macroeconomic variables like inflation, growth in GDP (gross domestic product), political stability or instability etc (Ross, 1976).

## Reasons or objectives for choice of industry and topic of research

The industry that I have chosen to work in is the stock market because:

## Personal:

Firstly, investment is an important field of study in my area of specialization i.e., Finance and to study investment one must have sound knowledge of the workings of stock markets. Working in this area will help me apply the theoretical knowledge, that I gain in classroom as well as through reading, in a practical manner and also enrich my knowledge of the field.

## Professional:

Secondly, stock market can be rightly called the index of economic activity in a country. It is the place where companies can get listed to trade their stocks and raise money to finance and expand their business operations. At the same time it gives a platform to institutional as well as individual investors to invest their excess money and gain from their investment. Karachi stock exchange being the largest of the three stock markets in Pakistan is the hub of its investment activities, and therefore proves very good choice to study the behavior of stock returns in Pakistan as has already been done by many researchers.

Through this study I intend not just to enrich my knowledge but also to help future investors and decision makers make better informed decisions while making investment choices.

## Research Objectives

Can capital asset pricing model (CAPM) be applied to Pakistani stock market (i.e. Karachi Stock Exchange, KSE)?

Does CAPM succeed in explaining the behavior of stock returns in KSE? Does CAPM hold true in KSE

Can arbitrage pricing theory (APT) be applied to Pakistani stock market (i.e. Karachi Stock Exchange, KSE)?

Does APT succeed in explaining the behavior of stock returns in KSE? Does APT hold true in KSE?

Are the results of the two theories comparable, if yes what does this comparison reveal?

Is one theory proved to be better than the other in explaining stock return behavior?

## Literature Review

While making investment decisions, financial managers, mutual fund managers as well as individual investors tend to go for the asset or a portfolio of assets that gives high return for a certain level of risk, or poses low risk for a certain level of expected return. Therefore, a constant trade-off between risk and return has to be made during the selection process of any investment or investment portfolio.

Asset pricing theories help us determine risks of assets and provide us a framework to associate risks of assets with their expected returns. A multitude of theories and models have been presented to relate the risk and return of various assets to help practitioners in selecting investment portfolios. Since all of these models exhibit some limitations therefore these are still under constant scrutiny of researchers so that the existing shortcomings can be identified and overcome.

Although the history of study of risk-return trade-off in investments and asset pricing theories goes back a long time, the first notable theory was proposed by Harry Markowitz (Markowitz, 1952). Markowitz model was based on a number of assumptions and it gave a formula for calculating the variance of an investment portfolio assuming that variance in the return of a portfolio is a measure of its risk. Among other assumptions, this theory of asset pricing considered the investor's behavior for only one investment period. Markowitz model is often also known as “mean – variance model” because it assumes that risk averse investors try to select a portfolio of investments in such a manner that will minimize their portfolio's risk and maximize its return for a certain period of time. (Fama & French, 2004) This theory not only highlighted the importance of diversification to reduce risk but also suggested how to effectively diversify.

Markowitz theory is important in this discussion because it is the forerunner of those asset pricing models that we intend to study in this research. Another theory namely capital market theory was developed based on Markowitz portfolio theory which led to the development of Capital Asset Pricing Model (CAPM). This is one of the most widely used and extensively studied models of modern portfolio theory to date.

CAPM was proposed almost simultaneously by William Sharpe (Sharpe, 1964), John Lintner (Lintner, 1965) and Jan Mossin (Mossin, 1966). The capital asset pricing model proposed by Sharpe and Lintner is called Sharpe-Lintner CAPM and is depicted as follows:

“(Sharpe – Lintner CAPM)

E (Ri) = Rf + [E (Rm) – (Rf)] βim ................. (A)

In this model

E(Ri) – is the expected return on an asset or a portfolio ‘i'.

Rf – is the rate of return on a risk free asset, like government issued investment securities.

Rm – is the market return, and

βim – is a representation of the market risk premium, often referred to as the non diversifiable risk of the asset.” (Fama & French, 2004)

Since its proposition CAPM has been one of the most widely taught, used and researched of all asset pricing theories because it offers a simple and easy to understand method of assessing risk return relationship and calculating the risk of assets. In simplest words, CAPM proposes that an asset's expected return is a linear function of the asset's non-diversifiable risk as represented by the asset β (beta). It is also called a one factor model because it relates the return of an asset with only one factor i.e. its non-diversifiable risk. Ever since it was proposed, CAPM has been under constant scrutiny by academicians and researchers, and is still the target of an ongoing debate about whether it is capable of describing the risk return relationships in various markets accurately or not.

Immediately after its proposition, CAPM became a target of rigorous testing and scrutiny by various researchers who performed various tests of the model to prove or reject its validity when applied to different markets in different conditions. Until now numerous researchers have applied this model in different stock markets over different time periods and found contradictory results.

Some authors' findings validated the model like Fama and Macbeth who conducted a study on all common stocks traded on New York Stock Exchange (NYSE) for a period of January 1926 – June 1968. The results of their study supported the CAPM and they recommended that while making an investment portfolio decision the investors should take into account the fact that portfolio risk of a security is linearly related to its return. They also concluded that no other factor than risk of an asset can influence the return of that asset (Fama & MacBeth, 1973). Other researchers showed that this linear relationship did not hold true in later years (Lakonishok & Shapiro, 1986).

Some found that it is applicable to their sample and succeeds in showing accurate results like Fama and Macbeth (1973) found it to be accurate for a certain set of data but using the same set of data two other researchers Tinic and West (1984) found opposite results. In a very early study of CAPM, using monthly stock return data for portfolios of securities rather than individual securities the theory was validated (Black, Jensen, & Scholes, 1972). The model was also put to test when it was suggested that firm size might also influence and explain the changes in return of assets portfolio. Banz in his study showed that securities of firms with low market value of stock showed higher returns than those of the high stock value firm, thereby incorporating another dimension in the linear relationship as described in the CAPM (Banz, 1981).

In 1990, Greene proved in his study that CAPM does not hold true when applied to UK private sector while its validity was proved in German market in 1992 by Sauer and Murphy. Numerous studies focused on proving that risk or beta is not the only measure to predict the risk of an asset or a portfolio of assets but there are a number of other factors that must be taken into account. Fama and French in 1992 conducted tests finding no support for the simple positive relationship between average return and risk of the assets and they found out “that for the period of 1963-1990 size and book to market equity capture the cross sectional variation in average stock return associated with size, E/P, book to market and leverage.” (Fama & French, 1992)

Many other studies have also been conducted at various times to analyze the validity of CAPM in different markets. A study conducted in Tunisia tested nine different asset pricing models and among other findings they reached the conclusion that CAPM did not hold true in Tunisian stock exchange (Bennaceur & Chaibi, 2007). A study conducted in the Athens Stock Exchange (Greece) also examined the validity of CAPM using weekly stock return data for 100 companies for a period of 4 years. It was found that the results do not support the basic hypothesis that higher beta explains higher returns but it does explain excess returns. The same tests were conducted for yearly data in the same research with similar results showing no support for CAPM theory (Michailidis & Tsopoglou, 2006). Several authors showed that many other factors can influence return of assets in addition to the non diversifiable risk as represented by the asset beta. A study conducted in Indian National stock exchange (NSE) using data for stock returns of portfolio totally rejected the CAPM (Basu & Chawla, 2010). Another research conducted on Karachi stock exchange using monthly stock return data demonstrated that CAPM fails to explain the behavior of stock returns (Hanif & Bhatti, 2010). These contradictory findings of CAPM by various researchers led to many new models being proposed like inter temporal CAPM, three factor capital asset pricing model (TFPM) and four factor pricing model (FFPM), etc.

One of the main alternatives of CAPM is the arbitrage pricing theory (APT) or arbitrage pricing model which is the second asset pricing theory that will be tested in this research. APT was proposed by Ross in 1976 who suggested that return of an asset cannot be described as a linear function of only one factor that is its beta; instead many other variables might influence the returns (Ross, 1976)

Unlike CAPM, arbitrage pricing theory is a multifactor model of asset pricing which suggests that an asset's risk is not merely measurable by its beta. Instead APT suggests that the return and risk of an asset depends on the assets sensitivity to a number of factors like, inflation, risk premium, industrial production and term structure of interest rates. (Ross & Roll, 1984). The basic premise is that even those assets which have the same beta might have different returns depending on their different sensitivity to the above mentioned economic variables. According to APT the expected returns of an asset can be written in the form of the following model:

“Ri = E (Ri) + bi1 δ1 + bi2 δ2 + …+ bik δk + εi for i = 1 to n ……… (B)

Where:

Ri = the actual return on asset i during a specified time period, i = 1, 2, 3, …, n

E (Ri) = the expected return for asset i if all the risk factors have zero changes

bi1 = the reaction in asset i's returns to movements in a common risk factor j

δk = a set of common factors or indexes with a zero mean that influences the returns on all assets

εi = a unique effect on asset i's return (i.e., a random error tern that, by assumption is completely diversifiable in large portfolios and has a mean of zero)

n = number of assets” (Rielly & Brown, 2005)

Although CAPM has already been extensively studied in Pakistani stock market but this article will add to the literature in the sense that it does not only consider CAPM validity in Pakistani environment but it also intends to check the validity of APT. In addition the study also proposes to compare the results obtained from the application of the two theories and find out which of the two, if any, is better at explaining the behavior of stock returns.

## Research Methodology

The proposed methodology for the present research is described below.

## Variables

Following variables will be used in the study.

Weekly average closing prices of sample stocks – this is the dependent variable.

Weekly average inflation rates.

Weekly average closing KSE index.

Weekly average oil prices.

Weekly average KIBOR rates.

Weekly average PKR/USD exchange rate.

## Justification of variable choice

Since the objective of our study is to test the applicability and validity of two asset pricing theories namely, capital asset pricing model and arbitrage pricing theory, in Pakistan with particular emphasis on Karachi Stock Exchange which is the largest and busiest stock exchange in Pakistan, it is justifiable that the above mentioned variables be selected. These variables provide us enough relevant data to be studied so that we can conduct our research in a meaningful manner.

## Study type

The proposed study will be exploratory in nature with causal as well as correlational elements in it.

## Exploratory study

Exploratory study is the one in which we gather initial data about the variables and try to study their behavior and try to find out whether a relationship exists among them and later we decide if the relationships we observed can be explained by our research or not.

The element of exploration in this study comes from the fact that we are planning to test two theories namely CAPM and APT, for which we will gather appropriate data. On the collected data the test will be conducted to find out whether the two theories hold true in KSE or not. If both theories are found to be true with respect to our data, further analysis will be performed to find out which theory is more accurate in explaining the observed relationships.

## Correlational study

Correlation is when two variable change at the same time, either in the same direction or in opposite directions. In correlational study we do not make any attempt to manipulate the variables and study them as they naturally occur. The present study is proposed to be correlational because I intend to study the behavior of the selected variables as they are occurring in their natural environment rather than manipulating them in an experimental setting.

## Causal study

Causation is when one variable influences the other and causes it to change. Causation can be unidirectional where only one variable influences the other variable and not the other way round, or bidirectional where both variables influence each other.

The proposed study also has causal element in it because in this we will see if certain macroeconomic variables are causing the return of the asset to change or not.

## Theoretical Framework

A schematic diagram showing the relationship of independent variables with the dependent variable while testing the applicability and validity of APT in KSE is shown below. Only stock returns are dependent variable while others are independent variables whose influence we will be testing in our study.

KIBOR

Exchange Rate

Inflation Rate

Stock Returns

Inflation Rate

Oil prices

## Hypotheses

H1: CAPM is applicable in KSE.

H1a: CAPM is valid when tested in KSE.

H2: APT is applicable in KSE.

H2a: APT is valid when applied to KSE.

H3: CAPM and APT give comparable and similar results when applied to KSE stock returns data.

## Data Collection

The data in this study will be secondary data, which is the type of data not collected directly from the source. Instead this data is collected from already available sources which have collected the data initially from the original source. The data for this study will be collected from various online data sources like:

International Monetary Fund website, www.imf.org

Karachi stock exchange website, www.kse.com.pk

State bank of Pakistan website, www.sbp.org.pk

## Period of study

The period of study will be of three years including the time from July 1, 2007 to June 30, 2010.

## Sample

The sample in this study will be the companies listed in the KSE-30 index as on the first date of data collection period. The reason for this choice was first of all to try to limit the number of observations due to time constraints and secondly the reason for this choice is the importance of KSE-30 index.

KSE-30 index is calculated using the “free-float market capitalization” methodology, which is considered an industry best practice throughout the world. Almost all leading stock index providers have adopted this method of calculating stock index, for example S & P, SENSEX, and even MSCI which switched to this methodology for all its indices in 2002 (Brochure KSE-30 index).

## Statistical tools

The basic statistical methodology that will be used in the proposed study will be regression analysis which is the chosen technique to apply CAPM as well as APT on the collected data. The reason for this choice is that both the theories when depicted in the form of models are represented as regression equations as shown in the equations (A) and (B) in the literature review section. Therefore regression seems to be the logical choice when we are trying to test the applicability and validity of any of these models in a certain stock market.

The software package to be used in this study will be Microsoft Excel and if the need arises while trying to compare the results of the two theories, E-VIEWS software might also be used.

## Limitations of the study and future directions

The main limitation of this study is that it intends to test only two asset pricing theories in one emerging economy, i.e. Pakistan and even that for a relatively short period of time due to time and other constraints. The same framework can be expanded to a longer period of time, including other markets as well. In addition other variations of CAPM, APT and other asset pricing theories should also be applied to Pakistani stock exchange to test their usefulness in this market.

## Beneficiaries

Like it was mentioned in the beginning of this proposal this research can prove beneficial to a wide variety of individuals in their official responsibilities as well as in their personal decision making, for example, financial managers of companies, investment managers, mutual fund managers, institutional investors as well as individual investors etc.

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