# Relationship Risk and Return Capital Asset Pricing

The background of the study is about the relationship between risk and return with Capital Asset Pricing Model (CAPM) or in other words, the study is about how to measure risk and return using CAPM. Risk can be defined as a probability that an actual return on an investment will be lower than the expected return. This includes the possibility of losing some or all of the original investment while return can be defined as the gain or loss of a security in a particular period. The return consists of the income and the capital gains relative on an investment. It is usually quoted as a percentage. On the other hand, CAPM can be defined as a model for estimating equilibrium rates of return and values of assets in financial markets which uses beta as a measure of asset risk relative to market risk. The purpose of this research is to prove that the best way to measure risk and return is by using CAPM either than variance, standard deviation and others. The dependant variables are risk and return while the independent variable is the CAPM. The method of analysis for this study is monthly cross sectional regression. The paper uses monthly revised portfolio as it relies only on return and market capitalization data that are available on monthly basis. Data that will be use in this study is using random sampling methods which are about 100 sampling. The sources of data that these study use are from scholar journals. The nature of the data is secondary data. The period of the data is from 2007 until 2010. The sectors of companies that involve in this study are finance sector, investment sector, manufacturing sector and stock exchange sector. The scope of this study will be about measuring risk and return using CAPM in this all sectors. Finally, the expected result from this study is the relationship between risk and return with CAPM is positive correlated.

## 1.0 INTRODUCTION

## Introduction to Risk and Return

In general risk can be defined as an anything that unexpected result of damage, injury, or loses. In the term of finance, risk can be defined as the differences of what the investor expected and the return of the investment. The investor will have possibility of having loses of some or all of the original investment. The greater amount of risk that the investor willing to take, the higher return the investor will get from their investment.

There are several types of the financial risk which is basic risk, capital risk, default risk, exchange rate risk and interest rate risk, liquidity risk and also operation risk.

Return in general can be defined as what the person will get from the things that they do. In the term of finance, we can define return as the profit or loss that the investor or the company will get from the investment in a particular period. It is usually describe as an income or a capital gain relative on an investment. The investors will gain higher return when they are willing to take higher risk (higher risk, higher return).

## Theories of Capital Asset Pricing Model

Capital Asset Pricing Model (CAPM) can be defined as a model for estimating equilibrium rates of return and values of assets in financial markets which uses beta as a measure of asset risk relative to market risk. The CAPM formula represents the linear relationship between the return required on an investment (whether in stock market securities or in business operations) and its systematic risk. The formula is as below:

## E(ri) = Rf + βi(E(rm) - Rf)

E(ri) = return required on financial asset i

Rf = risk-free rate of return

βi = beta value for financial asset i

E(rm) = average return on the capital market

There are some components in the CAPM such as beta (β), Capital Market Line (CML) and Security Market Line (SML). Beta uses to measure the volatility of the security, relative to the asset class. It also can be use to predict security’s behaviour which meant investors require higher levels of expected returns to compensate them for higher expected risk and by knowing a security's beta then you know the value of r that investors expect it to have. Capital Market Line is one of the model that build blocks for deriving the CAPM. The CML specifies the return an individual investor expects to receive on a portfolio. Security Market Line is also one of the model that build blocks for deriving the CAPM. The SML expresses the return an individual investor can expect in terms of a risk-free rate and the relative risk of a security or portfolio.

There are some advantages of CAPM over other methods of calculating required return which also explain why CAPM has remained popular for more than 40 years. Firstly, it reflects a reality in which most investors have diversified portfolios from which unsystematic risk has been essentially eliminated because it considers only systematic risk. Secondly, it generates a theoretically-derived relationship between required return and systematic risk. Lastly, it is clearly superior to the WACC in providing discount rates for use in investment appraisal.

There are also some disadvantages of CAPM. Firstly, in order to use the CAPM, values need to be assigned to the risk-free rate of return, the return on the market, or the equity risk premium (ERP), and the equity beta. Secondly, problems also can arise when using CAPM to calculate a project specific-discount rate because one of the common difficulties is when finding suitable proxy betas.

## 1.2.1 Risk in the CAPM

The tools that included in CAPM are both of Unsystematic and Systematic risk. These two kinds of risk represent different scope of risk that maybe associates with the return. For Unsystematic risk, this kind of risk can be managed by diversification, and the source of unsystematic risk come from the firm’s itself. It can be the business area or sector which the firm is operating and also the management issues which can contribute to unsystematic risk. While for systematic risk, it can’t be control by the firm, and it is something that the management should accept. The used of diversification is not work when dealing with systematic risk which can influence the firm’s operations and earnings. Systematic risk included recession and war. In CAPM, the Systematic risk is expressed by the stock’s Beta.

## 1.2.2 Return in the CAPM

In determining the assets return, CAPM provide three guidelines to be follow. The first guidelines, CAPM states that any risky assets should have an expected return of at least the risk free rate bond’s return. The fact on this, there must be compensation to the risky assets holder at least the same as the return from the bond which doesn’t have any risk at all. Second guidelines, CAPM support that there is no expected return involve when unsystematic risk is incurred. The reason behind this, unsystematic risk is manageable by diversification and in fact, it should be easy to be avoided. Therefore, CAPM suggest that no incentive need to be given to the assets holder. The last guidelines stated by this model, by any systematic risk bear by the holder of the assets, there must be higher expected return compared to the risk free rate return. Since systematic risk can’t be prevented by diversification, investor need the incremental amount of the returns from the assets, above the amount of the risk free rate assets can give on its return, in order to accept the risk.

## Scope of Study

The scope of the study will be around several industries such as finance sector, investment sector, manufacturing sector and stock exchange sector. The CAPM will be use to measure expected return that investors should get relative to its risk and the market return in these industries. The CAPM also can be used as a tool to evaluate fund managers. An active fund manager will try to impress or challenge the market by selecting stock in the portfolio based on research and information receive or other opinions. The CAPM model will give us an estimation of what the return should be, given the risk of the market. So, by this it’ll be figure out whether the fund managers make the right decision or not.

2.0 Review of Past Studies

2.1 Studies in Capital Asset Pricing Model

Searching for the equivalent between expected return and risk for single assets and portfolio can be described for definition of CAPM. It means every level of risk will give the same outcome for the return. CAPM explaining that, in decreasing an unfavorable risk, investor will diversify his investment. Portfolio theory explained that investor will choose the most efficient portfolio, which selected based on the degree level of risk associates with that portfolio (Treynor 1961; Sharp 1964; Lintner 1965). Study on risk and return for CAPM in Tehran Stock Market give a result which there was a positive correlation between common stock’s return and systematic risk Bakhshande (1990), Hamedani et al., (1993) and Shafizadeh (1995).

Other studies, conducted by (Ng 2003), stated that CAPM is useful to forecasting the risk and return of stock market and currency market in United State, Japan, Germany and England. Research by Mohammad Reza Tavakoli Baghdadabad on application of CAPM in measuring risk and return for selected markets of Iran’s economy make a conclusion that, higher return will not exist even systematic risk is been taken. This situation occurred in Iran’s financial market including Currency and Stock Market. While for Iran’s physical assets market there was adverse result in what financial market had on CAPM. Taking high risk in Iran’s Real estate market will guarantee higher return. Based on this study, CAPM is only useful in certain market in Iran, in terms of analyzing the risk and return.

High profile projects and securities usually relates with a risky characteristics which mean higher expected return by the investors. CAPM was widely used by investors and fund or finance manager in estimating the risk that will emerge along with every investment/stock and also the return that can be produced by the same investment/stock (Jagannathan & Wang, 1993). As unsystematic risk can be prevented by diversifying the portfolio, investor will earn higher expected return for every high level of systematic risk that been taken which cannot be avoided with portfolio diversification.

Study from Michael E. Drew, Tony Naughton, and Madhu Veeraragavan emphasize on seeking the multi factor setting, in terms of idiosyncratic volatility. The results produced from this study reveal that the less size and small idiosyncratic volatility firms have greater risk from firm that have a high idiosyncratic volatility. This is the view of Chinese investors. Compare to others countries like Philippines, India, Hong Kong and Malaysia , investors in these countries see that is more riskier for the firm that have a high idiosyncratic volatility compared the low firm (Drew and Veeraragha van 2002). The study conducted also found instead of single factor CAPM, multi factor model far more appropriate as a model for estimating the risk. This is because study correctly show how idiosyncratic volatility, size of firm and book to market equity is being priced.

Previous studies by Fama and French (1992), they found that in estimating the average return of such securities associates with the firm size, earning to price and book to market. Hence it show that this study unable to seek the positive relation between beta and return of the stocks. Empirical evidence of Fama and French is against the CAPM, since the variable of the firm including all the facets mention previously, fails to explain about average cross-sectional returns. Kim (1995, 1997) states that, despite the significant explanatory power by beta, variables like book-to-market and size of firm also have the same behavior. But some others study, for instance by Kothari (1995), views the uses of annual return give a linear relationship for beta and cross-sectional returns. Subsequently, Down and Ingram (2000) found that there is no significant relation between total risk, firm size and average returns, but adversely, it show positive relation for beta and average returns.

Between year 1931 and 1965, Black (1972), through his study in estimating the expected return associates with the systematic risk, he found that high beta of firms stock in United States doesn’t perform well as compared to low beta stocks. Banz (1981), found during period of 1936 until 1975, large firm’s return doesn’t deliver the performance as expected, while for the return on small firm stocks, it show a better performance exceed the expectations. Later on, the firm size became the specific research for other people. Fama and French (1992), suggest that size of firm significantly can determine the cross-sectional variation in average stock return, since beta unable to explain it.

For Wiggins (1992), found behavioral of both for low and high beta. For large and low historical beta, it have a characteristics which has high systematic risk in downturn market compare than rising market, while for high historical beta, small and past losers stocks tend to have high systematic risk in up market. These authors namely as Martin Feinberg and Damir Tokic make a study on systematic risk which causes falls in stock price. From the observation, high beta stocks decline hugely with the drops in stock market in a single day compared to the lower beta stocks. In rising market conditions, high betas stocks relatively increase higher than the lower beta stocks in a single-day stock.

The study by Nurjannah analyze about the risk return relationship conditional on market condition and market volatility-evidence from Indonesian data. She found that the relationship between the CAPM beta and portfolio returns is consistent. The dependent variable is CAPM and the independent variable is risk-return. In this paper, she research based on the stocks in the Indonesian stock market. She uses a sample from the stocks as the portfolios. The researcher analyzes the conditional and unconditional risk-return models.

Liming Guan, Don R. Hansen and Shannon L. Leikam did a study regarding stable betas, size, earnings-to-price, book-to-market and the validity of the capital asset pricing model and conclude that CAPM is still useful and valid. From the paper, it specifies that even if the CAPM generates expected returns, the aforementioned variables may have correlation with the expected returns. It also states that if an error occurs with the beta, it is likely for the variables to be recorded as explanatory variables. In depth of the study, it also provides a hypothesis that as measurement error in beta decrease, the significance of the variables will decrease. This proposition is supported by a study conducted by Fischer Black, Michael C. Jensen and Myron Scholes.

The study that was done by Li-Hua Lai is about the underwriting systematic risk and profit margin in fuzzy CAPM and ICAPM models (the case of aviation coverage). The dependent variable is systematic risk and the independent variable is skew factors. In Li-Hua Lai study, he found that the return of underwriting systematic risk have positive relationship with the CAPM. Data from the insurance company was used to measure the profit margin. The data compares the result from it with the profit margins in the crisp environment and found the skew factors. From the skew factors, the researcher found the value of underwriting systematic risk.

## 2.2 Studies in Measurement of Risk and Return.

From the Yufeng Han’s research, he studied about the relation between the market risk premium and market volatility. The dependent variable in this research is market risk premium and the independent variable is market systematic risk. Capital Asset Pricing Model (CAPM) suggests that the risk premium and market systematic risk should be positive correlation. It is measured by the market volatility that is variance. The researcher used a single factor model that is market risk premium. He use market risk premium as a linear function of the conditional market variance. The slope of the market systematic risk shows the positive relationship with the expected return in the market. To know the relationship between market risk premium and market systematic risk, the researcher divide the risk premium from the market volatility risk.

In a study conducted by Robert A. Olsen, he brought a discussion on the origin of variance and beta as risk measure. The studies conducted were also to identify variance and beta shortcomings as perceived risk metrics. From the studies, empirical evidence was demonstrated which claim that investors are loss-averse and affectively influenced. It also state that variance and beta as conventionally calculated are inconsistent because they do not take account the inherent indeterminacy of the investor’s world or even include the limitations and decision processes that define the human mind. The result also states that the affective or qualia nature of risk needs to be examined as a potential determinant of asset risk premiums. According to Benartzi and Thaler, (2001) Fisher and Statman (1997), Shefrin, 2000 ;

“investors’ simplistic and non-optimal portfolio diversification may arise

because of investors’ inability to understand and identify covariance and the complex

problem associated with reconciling multiple portfolio goals that may not be reducible to a common risk denominator”

Based on Hein Ploegmakers and Mark Schweitzer, Standard deviation was used to measure mutual fund risk which in relation to this study is the measuring of risk and return. According this study, standard deviation is measured to be inconsistent. It state the problem of using standard deviation as a measure of risk is the time period which it is based. According to the study, the calculations are normally based on monthly returns. Most investors do not invest within a period of one month. Therefore, the volatility associated with the monthly figures is not significant.

## 2.3 The Determinants of Capital Asset Pricing Model

## 2.3.1 Capital Asset Pricing Model and Risk & Return

CAPM developed by Lintner (1965), Sharpe (1964) and Mossin (1966), stated that the increase in level of risk will lead to the high level of expected return. The idea of CAPM describes that asset’s beta represents the systematic risk that surrounds to the expected return that can be generated by that asset. CAPM had been used for past several years by the investors in forecasting the risk, but recently there were studies that against the CAPM theory.

In the general studies states CAPM’s expectations of the intercept should be zero and slope equal to market portfolio excess return. Grigoris, Stavros, Demetrios and Eleni (2006) generated a hypothesis that the expected return-beta relationship is linear. There were several studies in the late 1980s that propose the existence of deviation from the linear CAPM risk return trade-off due to other variables that affect this tradeoff. In addition, according to Lau and Quay (1974), linear relationship between systematic risk and its return is represented by Beta.

In modern economics, CAPM shows the main source in interpreting the risk of such portfolio. Generally, CAPM is used to determine the expected return for securities that have positive relationship with the systematic risk of that security. Fama and French (1992) had revealed that from the study conducted by them refuse to support the CAPM theory, because the equity’s average return in United States never confirm of positive relationship with traditional CAPM’s betas. They also suggest that when a stock is price correctly, then the risk associates will be vary. Miller (1999), observed that, in expecting the return of stock, there is no sufficiency if a single aspect of risk is taken.

In a studies carried out by Stephan C. Fan, an evidence is conceived which states higher or lower asset ex post returns does not necessarily being generated through higher-beta risk assets. The study by George Diacogiannis and David Feldman on the other hand, found that the CAPM have relation between expected return and betas. This study had found that CAPM implies non-zero relationship between expected return and the betas. This is supported by studies conducted by Hans O. Mikkelsen on July 1999 which he found that the relation between risk and return that measured by CAPM is positively correlated

Test conducted by Banz (1981) showed that the size effect explain on the cross sectional-variation in average returns on particular collection of assets better than beta. In a different comprehensive studies, it has establish that yield (Basu, 1977), leverage and the ratio of a firm’s book value of equity to its market value Stattman(1980), Rosenberg, Reid and Lanstein (1983) and Chan Hamao, Lakonishok (1991) were exploited to test the validity of CAPM.The studies provide supportive positive linear relationship between beta and expected returns. These results are consistent with the findings of Miller and Scholes (1972). It was stated in practice and empirical test that CAPM is not well accepted. CAPM theory was tested again by investing in higher-beta-risk assets. Malkiel (1990) and Bernstein (1992) found that higher expected returns would deliver higher ex post investment return were not aligned.

However on the other side of the CAPM opinion, given by Fama, Fisher, Jensen and Roll (1969), and Blume (1968), CAPM security market line were indeed supported (Fama, 1970). Later in the early 1970’s, another formal studies were implemented to analyze CAPM’s validity and it was specified positive results (Black, Jensen and Scholes, 1972; Blume and friend, 1973; Fama and Macbeth, 1973). Nonetheless, the empirical studies conducted by Rolls, 1977; Basu,1977 and 1983; Banz, 1981; Bhandari, 1988; Chan, Hamao, Lakonishok, 1991; Fama and French, 1992 opposed to the existence of CAPM’s security market line (Fama, 1991).

Another judgement conferred by Fama and French (1992) which provide insignificant statistical relationship with beta and cross-sectional average stock returns. Instead, it hit upon the empirical evidence that firm size, book-to-market, earnings-to-price have significant explanatory power for average returns. This finding has brought CAPM’s descriptive validity retrieved by Sharpe (1964), Lintner (1965) and Black (1972) in a doubt stage.

This emerging question on the CAPM’s validity was due to the positive linear relation between the ex ante expected returns and betas. The empirical evidence of Fama and French is therefore disagree with the theory of CAPM which position out that firm-specific variables such as firm size, book-to-market and earnings-to-price should not have any ability to explain average cross-sectional returns.

Bora Aktan, Anouar Ben Mabrouk, Mustafa Ozturk and Najet Rhaiem on the other hand, had done a study about Wavelet-Based Systematic Risk Estimation. From the studies they found that the CAPM model is more suitable to estimate the systematic risk. The dependent variable in this study is risk and the independent variable is CAPM beta. They conclude the beta have close positive relationship with the risk. In a study by Donna J.S Peterson and Dr. Ronald L. Straight, it uses CAPM to determine whether defence profits are excessive. From the study, they agree that CAPM provide insight into the problem. They conclude that CAPM has positive correlation with risk-return relationship.

## ii. Summary

This paper focuses on the implementation of CAPM in measuring risk and return. It consist several parts that highlight the relationship of CAPM with risk and return. From the studies conducted by William Sharpe, John Lintner and Jon Mossin between years 1964 until 1966, it was said that CAPM has significant and positive correlation with risk and return. It is proven and supported from studies namely Grigoris, Stavros, Demetrios and Eleni (2006), Lau and Quay (1974), George Diacogiannis and David Feldman, Hans O. Mikkelsen (1999), Fama, Fisher, Jensen and Roll (1969), and Blume (1968), Bora Aktan, Anouar Ben Mabrouk, Mustafa Ozturk and Najet Rhaiem that CAPM is the best model to be used in measuring risk and return. Other model or method that constructs the significant relationship in measuring risk and return is mean-variance and standard deviation. There are other several methods or model that can be used to measure risk and return. However, in this paper, standard deviation and mean-variance framework is highlighted. The paper firstly began with the definition of CAPM and its relevant significant. Basically CAPM can be defined as a tool that consists of both Unsystematic risk and Systematic risk of such stocks and the latter is represented by Beta. For Unsystematic risk, it can be managed by diversification, and the source of unsystematic risk can be the business area or sector which the firm is operating and also the management issues which can contribute to unsystematic risk. While for systematic risk, it can’t be control by the firm. The used of diversification does not work when dealing with systematic risk. Systematic risk include recession and war. After CAPM understanding has been well defined, the element of risk and return that has relevant relationship with CAPM is outlined. CAPM states that any risky assets should have an expected return at least the risk free rate bond’s return. There must be compensation to the risky assets holder same as the return from the bond. Regarding the unsystematic risk, CAPM advocate that there is no expected return involve when this kind of risk is incurred. The reason behind this, unsystematic risk is manageable by diversification and in fact, it should be easy to be avoided. The last guidelines stated by this model, by any systematic risk bear by the holder of the assets, there must be higher expected return compared to the risk free rate return. Extension to CAPM, calculating Variance and Standard Deviation, risk and return also can be computed. Variance, estimate the risk of asset which measure the volatility from an average return generated by that asset. Volatility consist of risk, which mean investor can use this statistic to determine the risk he will bear when purchase such particular security. While for Standard Deviation, is been used by investor to estimate the risk from stock individually or stock portfolio by applying it to the annual rate of return of that stock or stock portfolio. Usually, investor will see the higher standard deviation of such stock, means it has high volatility, but alongside of high return. As stated above, it can be concluded that CAPM is still seen as the appropriate model to measure risk and return of any given area, such as equity, fixed securities, firm performance, etc. Even though some of the earlier researcher like Banz (1981), Fama and French (1992), Miller (1999), Malkiel (1990) and Bernstein (1992), Rolls (1977) Basu (1977 and 1983), Bhandari (1988), Chan, Hamao, Lakonishok (1991) Fama and French (1992) opposed to the CAPM theory, the prevailing studies and research conducted by Grigoris, Stavros, Demetrios and Eleni (2006), Lau and Quay (1974), George Diacogiannis and David Feldman, Hans O. Mikkelsen (1999), Fama, Fisher, Jensen and Roll (1969), and Blume (1968), Bora Aktan, Anouar Ben Mabrouk, Mustafa Ozturk and Najet Rhaiem and many other respected authors had found that CAPM has positive linear relationship with risk and return and is seen as the required method to measure risk and return.

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