Capm: Theory, Empirical Evidence and Interpretation

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Masaryk University Faculty of Economics and Administration Field of study: Finance

CAPM: THEORY, EMPIRICAL EVIDENCE AND INTERPRETATION

Diploma work

Thesis Supervisor: Author: Ing. Dagmar LINNERTOVÁ, Ph.D. Glory Ojone HARUNA

Brno, 2017

MASARYK UNIVERSITY Faculty of Economics and Administration

MASTER’S THESIS DESCRIPTION

Academic year: 2016/2017

Student: Glory Ojone Haruna

Field of Study: Finance (eng.)

Title of the thesis/dissertation: CAPM: Theoretical formulation, Empirical evidence and Interpre- tation

Title of the thesis in English: CAPM: Theoretical formulation, Empirical evidence and Interpre- tation

Thesis objective, procedure and methods used: The aim of the thesis is to analyze the logical theory of CAPM, review the empirical evidence on the shortcomings of CAPM and its interpretation and to determine whether the evidence is valid on current markets.

Process of Work: 1. Introduction and formulation of aims 2. Theoretical framework for CAPM 3. Analysis of the empirical evidence and its interpretation 4. Analysis of ﬁndings, formulation of recommendations 5. Conclusion and discussion

Methods: analysis, comparison, deduction

Extent of graphics-related work: According to thesis supervisor’s instructions

Extent of thesis without supplements: 60 – 80 pages

Literature: DA, Z, Ruiru GUO and R JAGANNATHAN. CAPM for Estimating the Cost of Equity Capital: Interpreting the Empirical Evidence. , 2009. FAMA, E and K FRENCH. The Capital Asset Pricing Model: Theory and Evidence.. , 2004, roč. 18, č. 3, s. 25–46. ZHANG, W. The Empirical CAPM: Estimation and Implications for the Regulatory Cost of Capital. , 2008, roč. 103, s. 204–220. PENNACCHI, George Gaetano. Theory of asset pricing. Boston: Pear- son/Addison Wesley, 2008. xvii, 457. ISBN 9780321127204.

Thesis supervisor: Ing. Dagmar Linnertová, Ph.D.

Thesis supervisor’s department: Department of Finance

Page 1 of 2 Thesis assignment date: 2016/05/09

The deadline for the submission of Master’s thesis and uploading it into IS can be found in the academic year calendar.

In Brno, date: 2017/05/12

Page 2 of 2

Name and surname of the author: Glory Ojone Haruna Title of the diploma thesis: CAPM: Theory, Empirical Evidence and Interpretation Department: Finance Head of the diploma thesis: Ing. Dagmar Linnertová, Ph.D. Year of defense: 2017

Annotation: This diploma thesis is devoted to the Capital Asset Pricing Model, its theory and the evidences against it. The first part introduction is an analysis of the theoretical framework of the CAPM. This is done by looking closely at the standard CAPM, how it is derived and its components. This is followed by an overview of other variations of and alternatives to the CAPM. The next section examines the empirical evidence against the CAPM, the basis for the evidence and their interpretations by critiques. The final section analyses the findings of the researcher and formulates recommendations based on these finding. And in conclusion, the writer discusses whether the evidence is sufficient to discard the CAPM.

Keywords: standard CAPM, empirical tests, beta coefficient, market premium, risk-free rate.

Statement

I hereby declare that I worked out the Diploma work CAPM: Theory, Empirical Evidence and Interpretation myself, under the supervision of Ing. Dagmar Linnertová, Ph.D, and that I stated in it all the literary resources and other specialist sources used according to legislation, internal regulations of Masaryk University and internal management acts of Masaryk University and the Faculty of Economics and Administration.

In Brno on 12. 5. 2017

Signature of the author

Acknowledgment I would like to thank Ing. Dagmar Linnertová, Ph.D, for her unwavering support, patience and collegiality, which contributed to the success of this diploma thesis.

Table of Contents Introduction ...... 13

1. The Standard capital asset pricing model ...... 16

1.1 The theory of portfolio choice ...... 16

1.2 The classic CAPM: theory and logic ...... 17

1.2.1 Assumptions of the model……………………………………….…………….. 17

1.2.1.1 Investors are risk averse……………………………………..…..…... 18

1.2.1.2 Homogeneity of expectations ………………………..……………… 18

1.2.1.3 Risk-free lending and borrowing…………………………………….. 19

1.2.2 Development of the Sharpe-Lintner model ……………..…………………….. 21

1.2.3 The security market line ……………………………………………….……… 28

2. Alternate asset pricing models ...... 30

2.1 Black “zero-beta” CAPM ……………………………………………..……………. 30

2.2 Consumption capital asset pricing model (C-CAPM) ………………….………….. 34

2.2.1 Key Assumptions……………………………………………………...………. 35

2.3 Arbitrage pricing theory (APT) …………………………………………..………… 37

2.3.1 Assumptions of the model ………………………………………………...……38

2.4 The three factor model ……………………………………………………………… 41

2.5 Intertemporal capital asset pricing model (I-CAPM) ……………………………….. 43

3. Criticisms, tests and the empirical evidence ……………………………………..……. 46

3.1 Roll’s (1977) critique of tests of asset pricing theory ………………………………. 46

3.2 Mayur Agrawal, Debabrata Mohapatra, and Ilya Pollak (2012) …………...………. 48

3.3 Philip Brown and Terry Walter (2013) …………………………………………….. 50

3.4 Ahmad Alqisie and Talal Alqurran (2016) ……………………………..…….……. 53

3.5 Others tests and criticisms ………………………………………………………..… 55

3.5.1 Black, Jensen and Scholes (1972) …………………………………………... 56

3.5.2 Fama and MacBeth (1973) ……………………………………….…………. 56

3.5.3 Banz (1981) …………………………………………….…………………… 57

3.5.4 Blume and Husic (1973) ………….……………………………..………...… 57

3.5.5 Basu (1977) ……………………………………………………..…………… 58

3.5.6 Fama and French (1992) ………………………………………..…...…….… 58

3.5.7 Kothari, S., Shanken, J., & Sloan G. (1995) ………………………………… 59

3.5.8 Jagannathan and Wang (1996) …………………………….……….……..…. 59

3.5.9 Choudhary and Choudhary (2010) ………………………………………….. 59

3.5.10 Bilgin and Basti (2011, 2014) …………………………………...... ……….. 60

4. CAPM and the current economy ………………………………………………..……. 63

4.1 CAPM and low/negative interest rates ……………...…………………………… 63

4.2 Current opinions on the CAPM ……………………………………….…………. 65

Conclusion ………………………………………………………….…………………….. 80

Bibliography ……………………………………………………….…………………….. 83

List of Figures ..…………………………………………………….…………………….. 87

INTRODUCTION

The capital asset pricing model (CAPM) is an important model in the field of finance. It is one of the simplest and highly revered models in finance. It explains variations in the rate of return on a security as a function of the rate of return on a portfolio consisting of all publicly traded stocks, which is called the market portfolio. The capital asset pricing model provides a formula that calculates the expected return on a security based on its level of risk. Generally, the rate of return on any investment is measured relative to its opportunity cost, which is the return on a risk-free asset. The resulting difference is called the risk premium, since it is the reward or punishment for making a risky investment.

The foundation of this model is seen in the portfolio choice model, especially as developed at the beginning of the 1950s by Harry Markowitz. Later, in the middle of the 60s, Sharpe, Lintner and Mossin adapted the basic idea of Markowitz by generalizing the individual decision problem of a single investor to all capital market participants. This step led to the CAPM and other asset pricing models (Wilhelm, 2001, p. 66-67). Accordingly, the CAPM builds upon the model of portfolio choice. The paper, "Portfolio Selection" by Harry Markowitz, established the idea of diversifying a portfolio of stocks in order to produce the maximum potential returns given the amount of risk an investor is prepared to undertake. And a few years later, William Sharpe, John Lintner, and Jan Mossin developed the CAPM in a series of articles.

As mentioned above, the Capital Asset Pricing Model (CAPM) laid the basis for modelling the risk-return relationship as it is considered “the basic theory that links risk and return for all assets.” (Gitman, 2006, p. 246)

The Capital Asset Pricing Model, which was developed in the mid 1960's, uses various assumptions about markets and investor behaviour to give a set of equilibrium conditions that allow us to predict the return of an asset for its level of systematic (or non-diversifiable) risk. The CAPM uses a measure of systematic risk that can be compared with other assets in the market. Using this measure of risk can, in theory, allow investors to improve their portfolios and managers to find their required rate of return.

The capital asset pricing model (CAPM) builds on the Markowitz mean–variance-efficiency model in which risk-averse investors with a one-period horizon care only about expected returns and risk. These investors choose only efficient portfolios with minimum variance, given expected return, and maximum expected return, given variance. Expected returns and variance

13 plot a parabola, and points above its global minimum identify a mean–variance-efficient frontier of risky assets.

Thus, the Sharpe–Lintner CAPM theory converts the mean–variance model into a market- clearing asset-pricing model. All investors agree on the distributions of returns and may borrow or lend without limit at a risk-free rate. The risk-free rate clears the market for borrowing and lending. Combining the risk-free asset and risky assets results in a linear mean–variance- efficient frontier that is tangent to the efficient frontier/risky asset frontier. All who hold risky assets hold this tangent portfolio, the value-weighted portfolio of all risky assets. The CAPM implies that the market portfolio is efficient.

The Sharpe–Lintner version assumes a risk-free rate, whereas the Black version of the CAPM allows unlimited short selling. Both imply that beta, the covariance of asset returns with the market relative to variance of the market, is sufficient to explain differences in asset or portfolio expected returns and that the relationship between beta and expected returns is positive. The risk-free rate is the intercept in the Sharpe–Lintner version, but the Black version requires only that the expected market return be greater than the expected return on assets that are uncorrelated with the market.

To understand the capital asset pricing model, there must be an understanding of the risk on an investment. Individual securities carry a risk of depreciation which is a loss of investment to the investor. Some securities have more risk than others and with additional risk, an investor expects to realize a higher return on their investment.

The CAPM is most often used to determine what the fair price of an investment should be. When you calculate the risky asset's rate of return using CAPM, that rate can then be used to discount the investment's future cash flows to their present value and thus arrive at the investment's fair value.

After the CAPM was developed, many empirical tests of the model were conducted using proxies for the different variables. Several of these showed that the CAPM didn't hold in many

14 situations and was often inaccurate or unsuitable in predicting asset values. In 1977, Richard Roll asserted that the CAPM holds theoretically but is hard to test empirically since stock indexes and other measures of the market are poor proxies for the CAPM variables. This came to be known as Roll's critique.

More recent tests, both cross-sectional and time series, find that variables such as size, earnings to price, debt to equity, and the book-to-market ratio (B/M) provide explanatory power not captured by beta. These studies confirm the now-recognized empirical flaws in both the Sharpe–Lintner and the Black versions of the CAPM. Behaviourists interpret the results as evidence of irrational pricing caused by investor overreaction. The rational pricing interpretation is that a more sophisticated asset-pricing model is needed.

Following this introduction is an analysis of the theoretical framework of the CAPM. This is done by looking closely at the standard CAPM, how it is derived and its components. This is followed by an overview of other variations of and alternatives to the CAPM. The next section examines the empirical evidence against the CAPM, the basis for the evidence and their interpretations by critiques. The final section analyses the findings of the researcher and formulates recommendations based on these finding. And in conclusion, the writer discusses whether the evidence is sufficient to discard the CAPM.

1. THE STANDARD CAPITAL ASSET PRICING MODEL 1.1 THE THEORY OF PORTFOLIO CHOICE

Harry Markowitz (1959)1 developed the model of portfolio choice which is commonly referred to as the mean-variance model. Markowitz derived the formula for computing the variance of portfolios while showing that the variance of the rate of return was a meaningful measure of portfolio risk. Markowitz’s model suggests that given expected return or variance, an investor would choose a portfolio that minimizes the variance or maximizes the expected return respectively. The model assumes that investors are risk averse and, when choosing among portfolios, they care only about the mean and variance of their one-period investment return. Hence, investors will select portfolios for only a single period of investment and concentrate on the mean and variance of their investment return, i.e. a portfolio at time t-1, which yields a stochastic return at t. 2The formula demonstrates the importance of diversifying investments to reduce the total risk of a portfolio and shows how to effectively diversify.

The Markowitz model is based on several assumptions regarding investor behaviour:

1. Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period. 2. Investors minimize one-period expected utility, and their utility curves demonstrate diminishing marginal utility of wealth. 3. Investors estimate the risk of the portfolio on the basis of variability of expected returns. 4. Investors base decisions solely on expected return and risk, so their utility curves are a function of expected return and the expected variance (or standard deviation) of returns only. 5. For a given risk level, investors prefer higher returns to lower returns.

Under these assumptions, a single asset or portfolio of assets is considered to be efficient if no other asset or portfolio of assets offers higher expected return with the same (or lower) risk or lower risk with the same (or higher) expected return.

1 Markowitz H M., “Portfolio selection: efficient diversification of investments.” New York: Wiley, 1959. [Rand Corporation, Santa Monica, CA] 2 REILLY, Frank K. and Keith C. BROWN. Analysis of investments & management of portfolios. 10th ed. Australia: South-Western Cengage Learning, 2012. ISBN 978-0-538-48248-6.

1.2 THE CLASSIC CAPM: THEORY AND LOGIC

The CAPM relies on several assumptions advanced by Markowitz (1959). Sharpe (1964)3 and Lintner (1965)4 build up on Markowitz's model and add two critical assumptions. The portfolio model provides an algebraic condition on asset weights in mean-variance-efficient portfolios. The CAPM turns this algebraic statement into a testable prediction about the relation between risk and expected return by identifying a portfolio that must be efficient if asset prices are to clear the market of all assets.

The CAPM extends the capital market theory in a way that allows investors to evaluate the risk-return trade-off for both diversified portfolios and individual securities. To do this the CAPM redefines the relevant measure of risk from total volatility to just the non-diversifiable portion of that total volatility (i.e., systematic risk). The new risk measure is called the beta coefficient, and it calculates the level of a security's systematic risk compared to that of the market portfolio. Using beta as the relevant measure of risk, the CAPM the redefines the expected risk premium per unit of risk in a commensurate fashion. This in turn leads to an expression of the expected return that can be decomposed into (1) the risk-free rate and (2) the expected risk premium (Reilly & Brown, 2012)5.

1.2.1 ASSUMPTIONS OF THE MODEL

Sharpe (1964) and Lintner (1965) added two principal assumptions to the Markowitz model: complete agreement, i.e. investors choose joint distribution of asset returns from period t-1 to period t, and all investors can borrow or lend at risk-free rate. Therefore, the Capital Market Pricing Model has the same assumptions as the Markowitz portfolio model as well as two assumptions Sharpe (1964) and Lintner (1965) added.

3 Sharpe, William F. 1964. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance. 19:3, pp. 425– 42. 4 Lintner, John. 1965. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics. Vol. 47, No. 1, pp. 13–37. 5 REILLY, Frank K. and Keith C. BROWN. Analysis of investments & management of portfolios. 10th ed. Australia: South-Western Cengage Learning, 2012. ISBN 978-0-538-48248-6

1.2.1.1 Investors are risk averse One practical assumption the CAPM is based on is that investors are naturally rational and are risk averse. They draw their own conclusions about the fundamentals of each prospective investment whether it be a single stock or a portfolio of risky assets by relying on the common law of distribution. The fundamentals include the investment’s normal return rate, the rate of return’s standard deviation, and the covariance between the rate of return of the asset and those of other assets.

Therefore, the risk averse investor will select the asset that has the highest expected rate of return, while the assets concerned have comparative measures of the standard deviations, and the asset with least measure of the standard deviation from all assets with comparable expected rates of return. Thus, the investor (guided by his judgments of probability) will allot his capital to assets that lie on the efficient frontier, and consequently attempting to limit the investment risk while maximizing the investment’s returns.

The measurement of an investor’s risk-aversion could be where the investor’s optimal point is located on the market opportunity line. The line shows linear function of the rate of return on standard deviation level. At any point on this line, the investor could be at his optimum point. When this point is reached, the indifference curve of the investor touches the market opportunity line, which means that the utility function of the investor is maximized.

1.2.1.2 Homogeneity of expectations All investors have homogeneous expectations which means that they estimate the same distributions for the future rates of return. Homogenous expectations mean that all investors share common beliefs about the joint probability distributions of future returns (i.e., means and covariances); thus, the market portfolio comprises the risky portion of their individual portfolios.

The fact that investors in the market have like-minded expectations about the return behavior of the asset is made apparent by this assumption as information any financial asset is equally assessible to all investors.

Therefore, it is assumed that to their period end values for equities available in the market, all investors allot identical sets of means, variances and covariances. This assumption can be understood to mean that the same portfolio of the risky assets are held by all investors (each investor has the same weight of every risky asset that is included in the said portfolio), but with varying proportion as combined with the risk- free asset. And it can be concluded from this fact that investors distribute their capital between the same portfolio of risky and risk-free assets, being led by only their personal level of aversion to risk.

Lintner finds that the connection between the defining essentials of the financial asset’s expected return remain unchanging despite the fact that the assumption of homogeneity of expectations does not hold.

Primarily, the investor’s homogeneity of expectations implies the selection of the same risky assets by any investor and then including them in their portfolio of investments in similar proportions, and thereby producing risky investment portfolios that are alike.

For each unit of the investment capital assigned to the risky portfolio, the CAPM states that the reward of investors come by way of differences between the return on the risky market portfolio and the risk-free asset’s return.

1.2.1.3 Risk-free lending and borrowing Although the standard Sharpe-Lintner CAPM allows for short selling, the assumptions of homogeneous expectations and borrowing and lending at a risk-free rate imply that no investor will hold a short position in equilibrium. The opportunity to borrow or lend at a risk-free

rate (rf) results in a unique mean-variance efficient portfolio of risky assets that is also the market portfolio (MP), by definition, given that all risky assets must be held in equilibrium. As a result of holding this assumption, individual investors are able to allot their capital to the risk-free asset and expect, from this allotment, certain previously determined return that is measured by the rate of interest. Say however, that the investor is willing to allot more funds than he has into the portfolio of risky assets, such an investor is allowed to borrow more funds at the same risk-free rate of interest.

Figure 1: CAPM with Risk-Free Borrowing and Lending

Source: slideplayer.com

Other assumptions are6:

1) All investors take a position on the efficient frontier, i.e., they follow the mean-variance rule and choose mean-variance efficient portfolios. The precise position on the efficient frontier which investors hold and the portfolio they opt for will depend on their utility function and the trade-off between risk and return.

2) All investors hold investments for the same one-period of time.

3) Investors can buy or sell portions from their shares of any security or a portfolio they hold.

4) There are no taxes or transaction costs on purchasing or selling assets.

5) There is no inflation or any change in interest rates.

6) Capital markets are in equilibrium, and all investments are fairly priced. Investors can not affect prices i.e. they are price takers.

1.2.2 DEVELOPMENT OF THE SHARPE-LINTNER MODEL Fama and French (2004)7 explain portfolio opportunities by way of Figure (2) above which also characterizes the CAPM. The risk of the portfolio shown on the horizontal axis is measured by the standard deviation of the portfolio return; while the vertical axis shows the expected return of the portfolio. The minimum variance frontier i.e. the abc curve shows the different combinations of expected risk and return for portfolios of risky assets that at different levels of expected return, minimize risk or at different levels of risk, maximize the expected return. The portfolios on this minimum variance frontier do not include risk-free borrowing and lending. There is a visible trade-off between risk and expected return for minimum variance portfolios. For example, at

6 Reilly, F., & Brown, K. (2003). “Investment analysis portfolio management” (7th Ed.). Thomson, Southwestern. 7 Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: theory and evidence. Journal of Economic Perspectives, 18(3), 25–46. Retrieved from http://dx.doi.org/10.1257/0895330042162430

Figure 2: Investment Opportunities

Source: Fama and French (2004)

point (a), an investor must put up with high levels of volatility to benefit from high levels of return. But the investor can have lower volatility coupled with moderate expected return at point (b). Only portfolios that lie above the point (b) along the abc curve qualify as efficient portfolios i.e. assuming there is no risk-free borrowing or lending, since at the same level of risk, they maximize expected return.

The efficient set becomes a straight line (Rf through to g) if the risk-free rate of return is added to the graph. A proportion of investors investment can be invested in risk-free securities while their remaining investment is invested in

risky portfolios of assets. If investors choose to invest all their funds in the

risk-free security then they will take a position at. The point (Rf), which represents portfolios with a risk-free rate of return and zero risk, is the position investors will take if they choose only risk-free securities to invest all their funds.

If investors, however, were to choose to invest only a portion of their investment in the risk-free return assets and the rest in a risky portfolio, they

will then take a position along line Rf – g where there is a possibility of risk- free lending and borrowing investment combinations along the line. In particular, lending and positive investment with a risk-free rate are shown by

all the points between Rf and g. On the other hand, the set of points lying on the line from the point g onwards on the straight line represent borrowing at the risk-free rate, with the earning from the borrowing being used as a means to boost investment in portfolio g. Basically, portfolios with a combination of risk-free borrowing or risk-free lending investments are shown in Figure (2)

on the straight line between Rf and g, where the investors borrow at the risk- free rate and then the borrowings are used to invest in the portfolio g.

According to Tobin's (1958)8 "separation theorem”, investors would invest in efficient portfolios with risk-free lending and borrowing that minimizes the risk for any given return and maximizes the return for any given risk, thus one draws a line from Rf and to the left as far as possible, to the tangency portfolio T in Figure (2). Hence, efficient portfolios all include a combination of a risky portfolio, T, and the risk-free asset.

Fama and French (2004) explain that since all investors hold the same portfolio T of risky assets, it must be the value-weight market portfolio of risky assets. Speciﬁcally, each risky asset’s weight in the tangency portfolio, which is called M (for the “market”), must be the total market value of all outstanding units of the asset divided by the total market value of all risky

8 Tobin, J. (1958). Liquidity preference as behaviour toward risk. Review of Economic Studies, 25(2), 65–86. Retrieved from http://dx.doi.org/10.2307/2296205

23 assets. In addition, the risk-free rate must be set (along with the prices of risky assets) to clear the market for risk-free borrowing and lending. So, the CAPM implies if the asset market is to clear, then the market portfolio M must be on the minimum variance frontier.

The expected return on assets not correlated with the market return must be equal to the risk-free rate when there is risk-free lending and borrowing. The CAPM equation following the Sharpe-Lintner assumptions of risk-free lending and borrowing are expressed below:

E(Ri) = Rf + [E(RM) – Rf]βiM

Where the market beta is as follows:

2 βiM = σiM/σ M

Where:

E (Ri) is expected return on an asset i.

β is the market beta of the asset i that determines the responsiveness of the asset’s return to changes in market return.

Beta is estimated by the covariance of the asset return with the market return divided by the variance of the market return.

Rf is the risk-free rate of return.

RM is the market return.

From the Sharpe and Lintner CAPM equation, an asset’s expected return is equal to the risk-free rate of return RF, and in addition, a risk premium consisting of a market risk premium - the risk-free rate of interest Rf subtracted from the expected market return E(RM) - times the market beta of the asset i. Therefore, the expected return on any asset i is the risk-free interest rate, Rf, plus a risk premium, which is the asset’s market beta, βiM, times the premium per unit of beta risk, E(RM) – Rf.

Components of CAPM explained:

First component of CAPM is RFR i.e. risk-free rate. It is, as the name suggests, the return that you can earn risk free. Though no asses is risk-free but U.S. Treasury bills and bonds are generally used as a proxy for the risk- free rate. RFR to be used depends on the duration of risky asset under consideration, using long term bonds for longer risky assets and so forth.

Second component is E(Rm) i.e. expected market return: It determines the expected return of the market as a whole and can be based on past returns or expected future returns. There are various ways to determine expected market return.

E(Rm) – RFR is also known as market risk premium i.e. how much did market as a whole return above the risk-free rate.

β i.e. Beta: This is the most crucial of all the components and measures the systematic risk of holding a risky asset. Basically, risk can be divided into two components: Unsystematic risk and systematic risk. Unsystematic risk also known as idiosyncratic risk refers to risk associated with individual assets. Ideally, we can reduce our unsystematic risk by holding a diversified portfolio. However, systematic risk refers to the risk that is common to all securities i.e. market risk. This cannot be reduced by holding a diversified portfolio and hence investor must be paid for exposing himself/herself to this risk. β measures this systematic risk and thus is considered while calculating the expected return on the risky asset.

If β > 1, it implies that asset is riskier than the market as a whole and thus E(Ra) > E(Rm)

If β < 1, it implies that asset is less risky than the market as a whole and thus E(Ra) < E(Rm)

β is defined by the formula:

where

Cov(i,mkt) = covariance between the asset’s return and return on the market

σ_mkt^2 = standard deviation of market

Thus, β is the standardized measure of systematic risk.

The biggest assault on the CAPM came from French and Fama. Using a large sample of cross-sectional stock data including many small-cap stocks and stocks with large book values, they analyzed the accuracy of the CAPM and looked for other factors that explained stock prices (besides systematic risk). They found that while the CAPM's measure of systematic risk was unreliable, firm size and book to market value ratios were more dependable. Even so, French and Fama's findings have encountered a great deal of criticism. For example, using better econometric techniques might lead to better results for the CAPM. Just as Roll stated, the CAPM also has many values for which proxies must be found, and the proxies are often inadequate. It is easiest to test the CAPM ex post, although it would be better if an ex ante trial could be realized. Similarly, data mining can lead to conclusions that have no theoretical base.

First, all investors will choose the market portfolio, M, as their optimal portfolio. M includes all assets in the economy, with each asset weighted in the portfolio in proportion to its weight in the economy. Since all investors have the same expectations and use the same input list, they will each choose an identical risky portfolio, which is the portfolio on the efficient frontier that lies on the tangency line drawn from the risk-free asset. If any asset were left out of that portfolio its demand would be zero and therefore its price would approach zero. Seeing this, all investors would adjust their portfolio to include this asset until it had a price that would reflect its amount of risk. Thus, we can see that all assets will be included in M.

Second, the market portfolio, M, lies on the efficient frontier and is the tangent asset to the risk-free asset. Since investors all have identical input lists and all hold M, all information about assets in the market is incorporated into M, resulting in an efficient portfolio. Each individual investor will then choose to allocate his wealth between M and the risk-free asset, or in other words the Capital Allocation Line runs between the risk-free asset and the portfolio M.

Third, the risk premium on the market portfolio will be proportional to its own risk and the degree of risk aversion of the average investor.

Markowitz created his analysis based on the axiom of expected utility and proposed a generally applicable solution for the problem of portfolio selection. Sharpe (1964) proposes a model of individual investor behaviour under risky conditions by illustrating the investor’s preferences with a group of indifference curves that indicate a higher level of utility moving up, and depicts equilibrium conditions for the capital market and arrives at the CML - capital market line.

Intuition for CAPM9

• Investors should not be compensated for diversifiable risk

E.g., Beta=0

• If expected return > risk-free, borrow at risk-free to buy zero-beta asset

• If expected return < risk-free, sell zero-beta asset short and buy more risk- free

• Both cases imply higher portfolio return without higher risk (at the margin)

Equilibrium for Beta=0

• Risk-free rate and price of zero-beta asset adjust to equate expected return and risk-free rate

9 Retrieved from http://research.economics.unsw.edu.au/jmorley/econ487/CAPM_lecture.pdf

• E.g., if expected return < risk-free rate, price falls today to make future expected returns higher

E.g., Beta=1

• If expected return > market, sell other assets to buy high-return asset

• If expected return < market, sell asset to buy more of market portfolio

• Both cases imply higher portfolio return without higher risk (at the margin)

• Prices adjust to bring about equilibrium

1.2.3 THE SECURITY MARKET LINE

The Security Market Line (SML) is the graphical representation of the capital asset pricing model (CAPM), with the x-axis representing the risk (beta), and the y-axis representing the expected return. It is applicable to any asset.

The risk premium on a stock or portfolio varies directly with the level of systematic risk, β and when the relative risk premium, represented by beta, is plotted in a graph against the required return, it yields a straight line known as the security market line (SML). Note that a beta of 0 is equal to the risk- free rate while a beta of 1 has a relative risk equal to the market. The SML shows the trade-off between risk and expected return as a straight line intersecting the vertical axis (i.e., zero-risk point) at the risk-free rate. It describes the equilibrium return on all portfolios as well as securities. The SML considers only the systematic component of risk can be applied to any individual asset or collection of assets. Individual assets that are correctly priced are plotted on the SML.10

10 Source: Boundless. “The SML Approach.” Boundless Finance Boundless, 26 May. 2016. Retrieved from https://www.boundless.com/finance/textbooks/boundless-finance-textbook/introduction-to-the-cost-of-capital- 10/approaches-to-calculating-the-cost-of-capital-89/the-sml-approach-381-3908/

Figure 3: The Security Market Line

Source: premium.working-money.com

The security market line is the predicted linear line of best fit when the expected returns are plotted against the beta values. An asset is said to be in CAPM disequilibrium if the observed return is different to the expected return. Therefore, in equilibrium, all stocks must lie on the SML since according to the CAPM the risk premium earned for bearing systematic risk should be proportional to the stock’s beta. Assets that lie above the SML are considered under-priced and offer greater return than predicted by the CAPM, investors will rush to buy these assets to the point where their prices are pushed up and their returns lowered enough for them to lie on the SML. On the other hand, assets that lie below the SML are considered overpriced since they offer lower return than predicted by the CAPM given their level of risk, investors will sell these assets to drive their prices down and increase their returns until they lie on the SML.

2. ALTERNATE ASSET PRICING MODELS The capital asset pricing model has a long history of theoretical and empirical investigation. Several authors have contributed to development of a model describing the pricing of capital assets under condition of market equilibrium. For the past three decades mean variance capital asset pricing models of Sharpe-Lintner and Black have served as the corner stone of financial theory. Alternate asset pricing models developed based on the standard CAPM and because of some of its shortcomings are discussed below.

2.1 BLACK “ZERO-BETA” CAPM11121314 Fischer Black (1972)15 created what is known as the Black CAPM which is assumed to have been a response to the allegedly unrealistic assumption of unlimited risk free borrowing and lending. Black (1972) developed a version of the CAPM without risk- free borrowing or lending, but nevertheless obtains the same result (market portfolio is Mean-Variance efficient) by allowing for unrestricted short sales of risky assets.

Black (1972) considers a model with risk-free lending but not borrowing, and this leads to a CAPM in which the Zero-Beta rate of the market portfolio exceeds the riskless lending rate, but is less than the borrowing rate. Black adds two assumptions to capital market equilibrium that are more restrictive than the usual assumptions used in deriving the CAPM. First, there is no riskless asset and no riskless borrowing or lending is allowed. Second, there is a riskless asset and long positions in the riskless asset are allowed but that short positions in the riskless asset are not allowed. In both cases Black (1972) assumes that an investor can take unlimited long or short positions in the risky asset, and concludes that the risky portion of every portfolio is a weighted combination of portfolios m, and z, where the portfolio m is the market portfolio, and portfolio z is the minimum variance zero-beta portfolio. The line relating the expected return on an efficient portfolio to its β is composed of two straight segments, where the segment for

11 Attiya Y. Javed, “Alternative Capital Asset Pricing Models: A Review of Theory and Evidence”, Pakistan Institute of Development Economics (2000), Issue 179 of Research report series 12 Rhys Frake, “Present a critique of the Capital Asset Pricing Model, and hence discuss the claim that ‘beta is dead’ in the context of empirical models of assets’ returns”, 0937708 13 Galina Mukhacheva, “CAPM and its Application in Practice”, Masaryk University Faculty of Economics and Administration, Diploma Thesis (April 2012). 14 Andros Gregoriou, “Asset Pricing”, BS2551 Money Banking and Finance 15 Fischer Black (1972), “Capital Market Equilibrium with Restricted Borrowing.” Journal of Business. 45:3, pp. 444-454

the lower risk portfolios have a greater slope than the segment for the higher risk portfolios. The beta of the portfolios that have returns uncorrelated with the market portfolio returns will be equal to zero. Investors will select from these portfolios with zero-beta, the portfolios with the minimum risk. These portfolios of zero-beta do not affect the Capital Market Line (CML) but a different line is created called the Security Market Line (SML). The intercept of this line with the y-axis is the expected return of a portfolio with zero-beta. The return of this portfolio with zero-beta will be higher than the risk-free asset. The slope of the line is flat as the difference between the market return and risk free return is small (Reilly & Brown, 2003)16.

Black (1972) showed that the major results of the CAPM do not require the existence of a risk-free asset that has constant returns in every state of nature. Without access to a risk-free asset, investors instead use a zero-beta portfolio, i.e. a portfolio of risky assets with zero covariance with the market portfolio. This Black model was formed as the result of the unrealistic assumption related to the unlimited and riskless borrowing and lending ability of investors. The creators of the model do not doubt that the risk-free asset is in existence. Rather, they doubt that the risk-free asset is available to all investors, since borrowing at the risk-free rate is available only to the government. So, in practice, though lending at the risk-free rate is possible, borrowing at the same rate is improbable.

According to the Black (1972) zero-beta CAPM the expected return on risky asset i is given by:

E[Ri] = E[Rz] + {E[Rm] – E[Rz]} βi

where E[Rz] is the expected return on the zero-beta portfolio Z: Portfolio Z is defined

as the portfolio that has the minimum variance of all portfolios uncorrelated with M.

16 F.K. Reilly and K.C. Brown (2003), “Investment Analysis and Portfolio Management”, 7th Edition, Thomson South-Western, Australia. ISBN 0324171730, 9780324171730

The zero-beta CAPM implies that beta is still the correct measure of systematic risk and the model still has a linear specification.

Black, in his article, also describes some of the attributes of the market and zero-beta portfolio. Being rationally risk averse, investors would select zero-beta portfolio such as which lie on the minimum-variance frontier. But the zero-beta portfolio at the same time cannot efficient. Therefore, investors would not hold only zero-beta portfolio. Furthermore, they will short-sell that portfolio and buy a market portfolio that is efficient.

The Black CAPM assumes that: (i) all investors act according to the µ−σ rule, (ii) face no short selling constraints, and (iii) exhibit perfect agreement with respect to the probability distribution of asset returns.

It is not assumed that they can lend and borrow at a common risk–free rate. Under these assumptions, the market portfolio is a mean–variance eﬃcient portfolio.

Thus, there is a portfolio Z, i.e., the zero–beta portfolio with respect to the market portfolio, such that for each risky asset or portfolio of risky assets i, we have

µi = µz + βi(µm −µz)

where µm is the expected return of the market portfolio. Black assumed that risk-free asset may not exist but there could be some number of the assets with returns equal to the riskless rate.

The market portfolio, M, should be efficient and must lie on the efficient frontier. This portfolio represents the weighted sum of all investors’ investment in the risky assets. If we assume that all investors are rational and invest their funds in minimum-variance portfolios, then the market portfolio which includes any of such portfolios will also be minimum-variance efficient. At equilibrium, investors choose efficient portfolios and since the market portfolio is the weighted sum of the investors’ investments in the risky assets, it follows that the market portfolio will be also efficient.

In the absence of riskless asset Black (1972) has suggested the use of zero-beta portfolio Rz, that is, cov(Rz,Rm) = 0, as a proxy for riskless asset. In this case CAPM depends upon two factors; zero-beta and non-zero-beta portfolios, and it is referred as two factor CAPM. The zero-beta model specifies the equilibrium expected return on asset to be a function of market factor defined by the return on market portfolio Rm and a beta factor defined by the return on zero-beta portfolio, that is, minimum variance portfolio which is uncorrelated with market portfolio. The zero-beta portfolio plays the role equivalent to the risk-free rate of return in the Sharpe-Lintner model. The intercept term zero implies that CAPM holds. Gibbons (1982)17, Stambaugh (1982)18 and Shanken (1985)19 have tested CAPM by first assuming that the market model is true, that is, the return as the ith asset is a linear function of a market portfolio proxy.

The straight capital market line within standard CAPM was described by two points: first point being an intercept with the vertical axis (the riskless asset’s rate of return) and the second is the efficient market portfolio with a beta that is equal to 1. In the zero- beta capital asset pricing model, the capital market line could have two variants of the shape. In either case, it represents the linear relation between the individual asset’s return and the asset’s beta, but also, in one case it is a solid straight line and in the other, the line consists of two sections that have different slopes.

The Black (1972) two-factor version requires the intercept term E(Rz) to be the same for all assets. Gibbons (1982) points out that the Black’s two factor CAPM requires the constraint on the intercept of the market model

αi = E(Rz) (1-βi)

for all the assets during the same time interval, stating that when the above restriction is violated the CAPM must be rejected. Stambaugh (1982) has estimated the market model and using the Langrange multiplier test has found evidence in support of Black’s

17 Gibbons, Michael R. (1982), “Multivariate Test of Financial Models: A New Approach”, Journal of Financial Economics 10: 3–27 18 Stambaugh, Robert F. (1982), “On the Exclusion of Assets from Tests of the Two Parameter Model”, Journal of Financial Economics 10: 235–268 19 Shanken, Jay (1985), “Multivariate Tests of the Zero-beta CAPM”, Journal of Financial Economics 14: 327– 348

version of CAPM. Gibbons (1982) used a similar method as that of by Stambaugh but employed likelihood ratio test (LRT). MacBeth (1975)20 used Hotelling T2 statistics to test the validity of CAPM. The classic capital asset pricing model assumes operations only with market portfolio of risky assets and risk-free assets and also presumes absolute liquidity in all economic sectors and that investors operate in the same investment horizon. Black’s zero-beta model takes into account not only capital assets but also any assets that make it possible to transform short-term speculative instruments into long-term assets.

2.2 CONSUMPTION CAPITAL ASSET PRICING MODEL (C- CAPM)21 The Consumption Capital Asset Pricing Model was developed by Robert Lucas22 in the late 1970s. The C-CAPM specializes the more general Arrow-Debreu model to focus on the pricing of long-lived assets, particularly stocks but also long-term bonds.

The C-CAPM is a model of the determination of expected asset returns, the foundations of which were laid by the research of Robert Lucas (1978)23 and Douglas Breeden (1979)24. According the model, the expected-return premium that an asset must offer relative to the risk-free rate is proportional to the covariance of its return with consumption. The coefficient from a regression of an asset’s return on consumption growth is known as its consumption beta. Thus, the central prediction of the C-CAPM is that the premiums that assets offer are proportional to their consumption betas.

In contrast to the standard CAPM, the C-CAPM is an intertemporal model within which investors maximize their expected lifetime utility. In this model, ﬁnancial assets are used to smooth the path of consumption over time, selling assets when times are bad

20 MacBeth, J. D. (1975), “Tests of Two Parameters Models of Capital Market Equilibrium”, PhD. Dissertation, Graduate School of Business, University of Chicago, Chicago IL 21 Douglas T. Breeden, Michael R. Gibbons and Robert H. Litzenberger, “Empirical Test of the Consumption- Oriented CAPM”, The Journal of Finance, Vol. 44, No. 2 (June 1989), pp. 231-262 22 Robert Lucas (US, b.1937, Nobel Prize 1995) 23 Robert Lucas, “Asset Prices in an Exchange Economy,” Econometrica Vol.46 (November 1978): pp.1429- 1445. 24 Douglas Breeden, 1979,”An intertemporal asset pricing model with stochastic consumption and investment opportunities”, Journal of Financial Economics 7, 265-296.

and investing in assets when times are good. Assets whose returns have a high negative covariance with consumption will be held with a low risk premium. Conversely, assets whose returns have a high positive covariance with consumption are not so useful when times are bad, and they will command a high-risk premium to convince investors to hold them. This model therefore associates an asset’s systematic risk with the state of the economy (consumption).25

2.2.1 Key Assumptions26 The CCAPM assumes that all investors are identical in terms of their preferences and endowments. This assumption allows for the characterization of outcomes in financial markets and the economy by studying the behavior of a single representative consumer/investor. Equilibrium asset prices will not depend on the distribution of wealth. They will behave as if they are generated in an economy with a single representative agent. The assumption that there is a single representative investor limits the model’s usefulness in helping us understand: 1. How investors use financial markets to diversify away idiosyncratic risks. 2. How differences in preferences – particularly differences in risk aversion – help determine asset prices. On the other hand, the assumption makes it possible to obtain a sharper view of how equilibrium asset prices reflect aggregate risk.

In the CCAPM, the economy is assumed to be populated by many households that are identical in all respects, including preferences and endowments. This assumption allows decision making to be analysed by examining the behavior of a single, representative household. Irrespective of the macroeconomic setting, one consequence of the CCAPM assumption that all households are identical is that households will never exchange assets with one another. For instance, it will never be the case that one household will borrow from another, because all households are identical; if one wishes to borrow, all will wish to borrow and there will be no household that wishes to lend. If there are any assets

25 Sebastien Walti, “Derivations of the consumption-CAPM”, October 2007: pp. 1 26 Peter Ireland, “Econ 337901: Financial Economics”, Boston College (Spring 2017): pp. 3-14.

that exist in positive net supply, these must come from outside the household sector (e.g. from governments, businesses, or the rest of world).

The CCAPM also assumes that investors have infinite horizons. The assumption of infinite horizons is unrealistic if taken literally. But it can be justified by assuming that mortal investors have a bequest motive27 as suggested by Barro (1974)28. To illustrate Barro’s idea, suppose that everyone from “generation t” cares not only about his or her own lifetime consumption Ct but also about the utility of his or her children, from generation t + 1.

Then,

Vt = U(Ct) + δVt+1

where Vt is total utility of generation t and δ measures the strength of the bequest motive. But if members of generation t + 1 also care about their children

Vt+1 = U(Ct+1) + δVt+2 Similarly,

Vt+2 = U(Ct+2) + δVt+3 and so on forever.

Another possible justification for infinite horizons is suggested by Blanchard (1985)29. He assumed that each consumer is mortal, and faces a small probability p of dying at the beginning of each period t. Blanchard’s model implies that each person has a very small probability of living 200 years or more. But what his model highlights is that the real reason for assuming infinite horizons is to avoid the “time T −1” problem: if everyone knows the world will end at T, no one is going to buy stocks at T −1. But, knowing this makes stocks less attractive at T −2 as well. The collapse in stock prices will start before the terminal date and the infinite horizon prevents this unravelling.

27 A bequest motive seeks to provide an economic justification for the phenomenon of intergenerational transfers of wealth. In other words, to explain why people leave money behind when they die. 28 Robert Barro, “Are Government Bonds Net Wealth?”, Journal of Political Economy Vol.82 (November- December 1974): pp.1095-1117. 29 Olivier Blanchard, “Debt, Deﬁcits, and Finite Horizons,”’ Journal of Political Economy Vol.93 (April 1985): pp.223-247.

However, the assumption that investors have inﬁnite horizons limit’s the model’s usefulness in helping us understand “life-cycle” behaviour such as:

1. Borrowing to pay for college or a house. 2. Saving for retirement.

On the other hand, it eliminates a mathematical curiosity that would otherwise inﬂuence the prices of long-lived assets in the model.

The original CAPM assumes that investors are concerned with the mean and variance of the return on their portfolio rather than the mean and variance of consumption. That version of the model therefore focuses on market betas— that is, coefficients from regressions of assets’ returns on the returns on the market portfolio—and predicts that expected-return premiums are proportional to market betas. The CCAPM is not in opposition to this concept, and has some further added degree of precision. From the viewpoint of smoothing consumption and risk diversification, an asset is desirable if it has a high return when consumption is low and vice versa.

Like the CAPM – and perhaps even more so – the CCAPM is an equilibrium theory of asset prices that very usefully links asset returns to measures of aggregate risk and, from there, to the economy but also suﬀers from important empirical shortcomings.

2.3 ARBITRAGE PRICING THEORY (APT)3031 The Arbitrage Pricing Theory (APT) which is an alternative to the standard CAPM was developed predominantly by Ross (1976)32. The APT is a single-period model in which all investors believe that the stochasticity of the capital assets returns are factor structure consistent. Ross asserts that if arbitrage opportunities are not offered by equilibrium

30 Mona A. Elbannan, “The Capital Asset Pricing Model: An Overview of the Theory”, International Journal of Economics and Finance; Vol. 7, No. 1; 2015 31 Gur Huberman and Zhenyu Wang, “Arbitrage pricing Theory”, Federal Reserve Bank of New York staff Reports, Staff Report no. 216 (August 2005) 32 Ross, Stephen A. (1976), “An Arbitrage Theory of Capital Asset Pricing”, Journal of Economic Theory 13: 341–360

prices over some fixed portfolio of assets, then the expected asset returns have a linear relationship with the factor loadings33. Ross’ formal proof shows that the linear pricing relation is a necessary condition for equilibrium in a market where agents maximize certain types of utility. A linear relation between the expected returns and the betas is tantamount to an identification of the stochastic discount factor (SDF). The APT is a substitute for the Capital Asset Pricing Model (CAPM) in that both assert a linear relation between assets’ expected returns and their covariance with other random variables34. The covariance is interpreted as a measure of risk that investors cannot avoid by diversification. The slope coefficient in the linear relation between the expected returns and the covariance is interpreted as a risk premium.

The intuition behind the model draws from the intuition behind Arrow-Debreu security pricing. A set of k fundamental securities spans all possible future states of nature in an Arrow-Debreu model. Each asset’s payoff can be described as the payoff on a portfolio of the fundamental k assets. In other words, an asset’s payoff is a weighted average of the fundamental assets’ payoffs. If market clearing prices allow no arbitrage opportunities, then the current price of each asset must equal the weighted average of the current prices of the fundamental assets. The Arrow-Debreu intuition can be couched in terms of returns and expected returns rather than payoffs and prices. If the unexpected part of each asset’s return is a linear combination of the unexpected parts of the returns on the k fundamental securities, then the expected return of each asset is the same linear combination of the expected returns on the k fundamental assets.

2.3.1 Assumptions of the model The APT assumes that returns on assets can be approximately determined by relying upon a random process seen in a number of factors of risk incorporated into the model and that will supposedly affect every asset’s generated returns. The theory maintains that many factors affect returns compared to the CAPM where the pertinent risk to estimate is the co-variance of the market portfolio with the asset, represented by beta. Beta is a measurement the sensitivity of the

33 The factor loadings, or betas, are proportional to the returns’ covariances with the factors. 34 In the CAPM, the covariance is with the market portfolio’s return

return on each asset to the returns of market portfolio, or how securities returns react to an individual common factor.

Three assumptions were addressed by Reinganum (1981)35. The first being that capital markets are perfectly competitive. Second, investors will always prefer to have more wealth than to have less wealth with certainty. And third, a K- factor model could represent the stochastic process that generates asset returns.

The major assumptions, which are used in the development of CAPM, and are not required in the APT:

1) Investors have utility functions. 2) Normally distributed security returns. 3) An efficient market portfolio that contains all risky assets.

The assumptions of the APT are as follows (John Wei, 1988)36:

1. All investors exhibit homogeneous expectations that the stochastic properties of capital assets return are consistent with a linear structure of K factors. 2. Either there are no arbitrage opportunities in the capital markets or the capital markets are in competitive equilibrium. 3. The number of securities in the economy is either infinite or so large that the theory of large numbers is applied. 4. The APT hold in both the multi-period and single period cases.

Roll and Ross (1980)37 try to ascertain the dissimilarities between APT and the CAPM. The APT is founded on a linear return-generating process fundamentally, and it does not require the assumptions of utility neither is it limited to a single period. Even though it is consistent with every imaginable component for portfolio diversification, not one

35 Reinganum, M. R. (1981), “The Arbitrage Pricing Theory: Some Empirical Results”, Journal of Finance 36: 313–21 36 K. C. John Wei, “An Asset-Pricing Theory Unifying the CAPM and APT”, The Journal of Finance, Vol. 43, No. 4 (Sept. 1988), pp. 881-892 37 Roll, Richard W., and Stephen A. Ross (1980), “An Empirical Investigation of Arbitrage Pricing Theory”, Journal of Finance 35:5 1073–1103

specific portfolio plays a role in the APT. There is no stipulation that the market portfolio must be mean-variance efficient as in the CAPM. Furthermore, there are two significant differences between the actual Sharpe diagonal model which is a single- factor producing model and the APT. Firstly, the APT permits a few more generating factors. Secondly, since there must be a consistency between all market equilibrium and no arbitrage profits, the APT shows that all equilibrium is to be denoted by a linear correlation between the expected return on each asset and the response proportion of its return, or loadings, on the single factor.

Figure 4: Arbitrage Pricing Theory

Source: viking.som.yale.edu

Supposing that the security A plotted off the SML. According to the CAPM, this is not allowed. If investors were to realize that security A's expected return is higher than that of security B, then most of the investors would seize the opportunity to exploit the

situation. If security A lies above the security market line (in whichever dimension) then this would imply that A, relative to its beta, is underpriced. Investors will become aware this and buy security A. This transaction may be financed by selling (that is, shorting) security B, a portfolio with equivalent systematic risk.

The APT states that, if there are sufficient securities, it must be possible to construct a diversified portfolio that has zero senility to each factor. Such a portfolio would be effectively risk-free and therefore it should offer a zero risk premium. According to the APT, securities’ risk premium depends upon two things- the risk premiums associated with each other and the securities’ sensitivity to each of the factors (Brealey and Myers, 1981)38. But in case of the CAPM, the risk premium is determined by the product of the market price of risk and the securities’ systematic (undiversifiable) risk level. This later value is given by the product of the securities’ total risk and the degree to which the returns on securities are correlated to the returns on the market portfolio. But, if the expected risk premium of each of the portfolios is proportional to the portfolios’ market risk, then the CAPM and the APT are equivalent (Brealey and Myers, 1981).

The APT is very similar to the CAPM in the sense that the expected return of any security is equilibrium will be equal to the risk-free rate plus a risk premium. Not only that, the APT is similar to the CAPM in the application of the, model that it can be used in exactly the same way as the CAPM for determining the cost of capital, for valuation and for capital budgeting (Weston and Copeland, 1986)39.

2.4 THE THREE FACTOR MODEL Fama and French (1993)40 proposed a three-factor model for determining expected returns. They added two more factors to their model which were not in the CAPM to better explain portfolio returns. In their three-factor model, Fama and French (1993) incorporate the size factor and book-to-market ratio to market risk so as to measure the stock returns better. Small capitalization stocks and stocks with a high book-to-market ratio substitute for firm value and reflects risks that beta, the market systematic risk and

38 Richard Brealey and Stewart Myers, “Principles of corporate finance”, Mcgraw-Hill Book Company, New York (1981) pp. xxii + 794 39 John Fred Weston and Thomas E. Copeland, “Managerial finance”, Dryden Press (1986), 8th Edition 40 Fama, E. F., & French, K. R. (1993), “Common risk factors in the returns on stocks and bonds”, Journal of Financial Economics, 33(1), 3–56

market return do not explain. In fact, they showed proof that for small cap stocks, the covariance between returns is higher than it is for large cap stocks. Likewise, the covariance of returns, measured by the book-to-market ratio, is higher for high value stocks than the covariance of returns for stocks with a low book-to-market ratio. Therefore, the three-factor model comprises the firms’ size, firms’ value and also, the market risk factor as in CAPM.

Figure 5: Three-Factor Model – Risk Axes

Source: bogleheads.org

In more detail, the Fama-French three-factor model separates stock returns into three distinct risk factors:

Beta – a measure of volatility of a stock in comparison to the market; the risk of owning stocks in general; or an investment’s sensitivity to the market. A beta of 1 means that the security will move with the market. If the beta of any investment is higher than the market, then the expected volatility is also higher and vice versa.

Size – the extra risk in small company stocks. Small company stocks (small cap) tend to act very differently than large company stocks (large cap). In the long run, small-cap stocks have generated higher returns than large-cap stocks; however, the extra return is not free since they have higher risk.

Value – the value in owning out-of-favor stocks that have attractive valuations. Value stocks are companies that tend to have lower earnings growth rates, higher dividends and lower prices compared to their book value. In the long run, value stocks have generated higher returns than growth stocks, which have higher stock prices and earnings, albeit because value stocks have higher risk.

Fama and French found that on average, a portfolio’s beta is the reason for 70% of its actual stock returns. They discovered that figure jumps to 95% with the combination of beta, size and value. Their research showed the premium provided by small-cap and value stocks as well as the small, if any, influence active trading has on stock returns.

2.5 INTERTEMPORAL CAPITAL ASSET PRICING MODEL (I- CAPM)414243 Merton (1973)44 derived a version of the CAPM that relaxes the single time period assumption. In the ICAPM, trading takes place continuously.

In contrast to the standard CAPM, in the context of ICAPM, investors are concerned not only with end of period wealth, but also with the opportunities of consumption and investment throughout the life of the stock. Therefore, when choosing a portfolio at

41 Andros Gregoriou, “Asset Pricing”, BS2551 Money Banking and Finance 42 Adelina Barbalau, Cesare Robotti and Jay Shanken, “Testing Inequality Restrictions in Multifactor Asset- Pricing Models, June 2015. 43 Mona A. Elbannan, “The Capital Asset Pricing Model: An Overview of the Theory”, International Journal of Economics and Finance; Vol. 7, No. 1; 2015 44 Merton, R. C. (1973), “An intertemporal capital asset pricing model”, Econometrica, 41(5), 867–887

43 period t-1, ICAPM investors consider how their wealth at period t might vary with future state variables, including income from labour, price of consumption goods and the nature of investment opportunities. The ICAPM continuous time framework suggests that we should make further assumptions concerning the evolution of the risk- free rate over time. If the risk-free rate of interest is non-stochastic (i.e. fixed) then the ICAPM is a replicate of the standard CAPM and the model becomes:

E[Ri] = rf + {E[Rm] – rf} ɣ1 + {E[Rn] – rf} ɣ2

Since investors are exposed to the risk of unfavorable risk due to the stochastic interest rate, they to hedge their position by including portfolio N in the set of funds that they consider for portfolio formation (in addition to the portfolio M and the risk-free asset). Thus, the model exhibits three-fund separation.

The ICAPM of Merton (1973) extends the CAPM to a multi-period framework. Unlike the single-period maximizer of the CAPM who does not take into account events beyond the current period, the intertemporal maximizer of the ICAPM also takes into account the relationship between current returns and returns that will be available in the future. This gives rise to additional sources of risk that an investor should hedge against. According to the ICAPM, the expected return on an asset is not only proportional to the asset’s covariance with the market portfolio return, but also to the asset’s covariance with changes in the investment opportunity set.

Merton's ICAPM as an extension of the standard CAPM has an alternate assumption about the investors aim. Investors, in the CAPM, think only about the added wealth they will gain from their portfolio at current period end. In contrast, investors, according to the ICAPM, are not just worried about the end-of-period result, but also with consumption or investment opportunities of the resulting pay-off. Therefore, in selecting a portfolio now, investors under the ICAPM examine how their future wealth might fluctuate with future factors like their income, consumption costs and the behavior of future portfolio opportunities. Therefore, the ICAPM demonstrates that investors behave in such a way as to maximize the expected utility of their lifetime consumption and which they can continuously through time. This assumption of

continuous asset trading in time is not the case in the standard model. Unlike in the single-period model, Merton shows that the demands of the present are influenced by the likelihood of uncertainty in investment opportunities available in the future.

Merton’s (1973) study, in which he advanced the ICAPM that makes use of maximization of utility to get precise multi-factor forecasts of the expected returns securities, earned him comments from Fama (1996)45. Fama demonstrates that Merton obtains precise results without the assumption of perfect diversification of market portfolio. Fama considers Merton’s methods burdensome because of the time- continuous approach he used, and infers that like the CAPM, the relationship between expected returns and the multi-factor risks of this intertemporal model is the specification of securities weights that holds in any efficient portfolio with multiple factors and that is applied market portfolio M. Just as in the CAPM market equilibrium requires that the market portfolio is the efficient portfolio that trades-off between return and risk, in the ICAPM, the market portfolio is multifactor-efficient as indicated market prices. Fama shows that the ICAPM as postulated by Merton can be built on intuition like the CAPM’s influential intuition centered on Markowitz’s (1959)46 theory of mean- variance efficiency.

Investors, in the ICAPM, hold portfolios that are multifactor-efficient and generalize the concept of efficient portfolios. Similar to the CAPM investors, investors in the ICAPM dislike uncertainty of wealth, but they are also care about hedging certain parts of future consumption-investment opportunities, like consumption goods’ relative prices and the return to risk trade-offs they might encounter in the capital market. In addition, the ICAPM investors expect low risk and relatively high expected returns like investors in the CAPM. Nevertheless, the ICAPM investors are also concerned about the variations of the portfolio returns with other variables. Consequently, the optimal portfolio will factor in many of the variables and will have the widest span of possible expected returns.

45 Fama, E. F. (1996), “Multifactor portfolio efficiency and multifactor asset pricing”, Journal of Financial and Quantitative Analysis. 31(4), 441–465 46 Markowitz, Harry (1959), “Portfolio Selection: Efficient Diversification of Investments”, New York: Wiley

3. CRITICISMS, TESTS AND THE EMPIRICAL EVIDENCE The standard CAPM has continuously faced criticism in many a study for its assumptions that investors are maximize single-period investment, no restriction to risk-free lending and borrowing, and that investors only focus on return and risk of single-period portfolio, and if expected returns are explained by market betas, and the appropriate proxy for the market portfolio of all risky assets. On the other hand, there are also numerous studies in support of the CAPM. This section proceeds as follows: a review of the major criticism of the CAPM, then an analysis of some recent tests and finally some evidences for and against the CAPM.

3.1 ROLL’S (1977) CRITIQUE OF TESTS OF ASSET PRICING THEORY Roll (1977) demonstrated that, while testing two-parameter asset pricing theory is conceivable on a basic level, ‘no correct and unambiguous test of the theory has appeared in the literature’ to that time and that ‘there is practically no possibility that such a test can be accomplished in the future’. These suggestions are as yet legitimate today. Be that as it may, as Diacogiannis and Feldman (2011, p. 5) note, ‘it is not clear that . . . the essential implication – that LBPE [linear beta pricing with efficient benchmark] regressions [that are fitted] with inefficient benchmarks are meaningless – has been sufficiently internalized’ by critiques. Roll (1977) built up that ‘there is only a single testable hypothesis associated with the generalized two-parameter asset pricing model of Black (1972). This hypothesis is: “the market portfolio is mean- variance efficient”.’

As indicated by Roll (1977), a wrongly determined intermediary for the market portfolio can have two impacts which are: (i) The beta computed for alternative portfolios would be wrong because the market portfolio is inappropriate, (ii) the SML derived would be wrong because it goes from the risk-free rate through the improperly specified market portfolio.

Besides, when contrasting the performance of portfolio administrators with the "benchmark" portfolios, the above elements will tend to overestimate the performance

46 of portfolio administrators as the intermediary market portfolio utilized won't be as effective as the genuine market portfolio to such an extent that the slope of the SML will be underestimated.

Several related conclusions were drawn, some being condensed underneath:

• The best known purported ramifications of the CAPM, that beta is directly identified with expected return, is not freely testable.

• Asset pricing theory is not testable unless the exact composition of the true market portfolio is known and utilized as a part of the tests.

• Using an intermediary for the market portfolio has two difficulties. First, the intermediary may be mean-fluctuation efficient notwithstanding when the true market portfolio is not. On the other hand, the intermediary may be inefficient, and can't be utilized to test the efficiency of the true market portfolio.

Roll (1977) points out that tests performed by using any portfolio other than the true market portfolio are not tests of the CAPM but are tests of whether the proxy portfolio is efficient or not. Intuitively, the true market portfolio includes all the risky assets including human capital while the proxy just contains a subset of all assets. Furthermore, for a given sample of mean returns, there always exist an infinite number of ex-post mean-variance portfolios. For these portfolios there will be an exact linear relationship between sample returns and sample betas. This linearity will hold whether or not the true market portfolio is efficient. Thus, the two-parameter asset pricing theory is not testable unless all assets are included in the sample. He emphasized that the true test of CAPM is only possible if true market portfolio is observable

Campbell et al. (1997) suggest that Roll's worry is: (a) a legitimate hypothetical concern, however not an experimental issue (Stambaugh, 1982); or (b) decreased, given that the relationship between the intermediary and the true market portfolio surpasses 0.70, in which case acknowledgment/dismissal of the CAPM with

a market intermediary suggests acknowledgment/dismissal of the CAPM with the true market portfolio.

3.2 MAYUR AGRAWAL, DEBABRATA MOHAPATRA, AND ILYA POLLAK (2012) Agrawal, Mohapatra and Pollak (2012) empirically analyze the CAPM in the context of the U.S. stock market by constructing and tracking over time, several portfolios consisting of shares of large publicly traded U.S. companies. They propose a novel statistic to test CAPM, using the statistic to show that one of the conclusions of CAPM can be rejected with a high level of conﬁdence. Agrawal, Mohapatra and Pollak (2012) constructed and analysed an implementable investment strategy based on their test statistic. Their strategy outperformed the market over the testing period (1971–2010) and had low correlation with the market. They show that their strategy is robust to the size and price-to-book ratio of the underlying assets, and to the transaction costs. However, the strategy’s performance signiﬁcantly degrades during the last 20 years of the period, as compared to the 1970s and 1980s. The CAPM consists of a number of assumptions on the structure of the market and the preferences of the market participants. And, one consequence of the model is that, for any portfolio,

αs = 0 ………………………………….. (1)

µs = βsµm ………………………………….. (2)

Agrawal, Mohapatra and Pollak (2012) describe several experiments which show that the empirical behaviour of the U.S. stock market over the past four decades disagrees with (1) and (2) in a statistically significant manner. They had several difficulties with empirically evaluating (1) and (2) as none of the quantities involved were directly observable. Besides, they claim that there is no single, universally accepted definition for one crucial ingredient of (2): the market return. They used the return of a broad stock index, the S&P 500, as a proxy for the market return.

In addition to testing whether alphas are equal to zero, they proposed another test

statistic. Suppose that β1 and β2 are two portfolios, with respective betas and, and

respective expected returns µ1 and µ2.

Then (2) implies

µ1 = β1µm

µ2 = β2µm

And after multiplying the ﬁrst of these equations by β2 and the second by β1, their right-hand sides become the same, and hence the left-hand sides are equal:

β1µm - β2µm = 0 …………………………… (3)

Hence, if the stock market is consistent with (2), then (3) would hold. In this case, an estimate of the quantity obtained through the five-step procedure outlined in their paper, will not deviate from zero in a statistically significant way. In fact, as shown in the remainder of the paper47, they observe the opposite: both (3) and (1) can be rejected with high confidence.

One of authors’ mechanisms for testing the CAPM was to construct an investment strategy which had zero theoretical beta. If the CAPM holds, then (2) would mean that such strategy must have zero expected profit and loss. On the other hand, if the zero- beta strategy has non-zero expected profit and loss, then (2) is violated, which is inconsistent with the CAPM. Therefore, in order to ﬁnd out whether historical observations of their strategy’s profit and loss are consistent with the CAPM, they must have a procedure for determining whether the mean profit and loss is different from zero by a statistically signiﬁcant margin. They develop the procedure subject to some constraints which is fully detailed in their paper.

47 Mayur Agrawal, Debabrata Mohapatra, and Ilya Pollak, “Empirical Evidence Against CAPM: Relating Alphas and Returns to Betas”, IEEE Journal of Selected Topics in Signal Processing (August2012), Vol.6, No.4

Agrawal, Mohapatra and Pollak’s (2012) conclusion that empirical data from the U.S. stock market contradicts the CAPM has been previously pointed out and discussed in literature outlined in their paper. They proposed a new statistic for testing this conclusion and analysed an implementable investment strategy based on this statistic. If the CAPM applied to the U.S. stock market, then the strategy’s expected profit would be zero. Actually, the sample mean of the profit surpassed zero by a statistically significant amount. The finding is not explained by the trading costs or by other factors—company size and price-to-book ratio—that have been proposed as improvements to the CAPM. They furthermore show that, even though the strategy’s profits are heavy-tailed and temporally dependent, the t-statistic of their sample mean is well modelled as a normal distribution. This justified their calculations of significance levels. Their strategy outperforms the market and has a low correlation with the market. The low correlation with the market is important, as it implies that the strategy can provide diversification compared to a pure market portfolio. Additionally, the strategy is less volatile than the market, in the sense that its largest daily loss over the 40-year testing period is about 12 daily standard deviations, whereas the market’s largest loss is about 21 standard deviations.

The dramatic reduction of the profitability of the strategy over the last 20 years suggests that the U.S. stock market became much more consistent with CAPM than it used to be. This point is confirmed by their analysis of yearly alphas which fail to reject the hypothesis that alpha is zero at significance level 1% in any pf the years starting with 1994. Based on these results, they conclude that there is economically and statistically significant evidence contradicting the CAPM in the U.S. stock market over the 40-year period.

3.3 PHILIP BROWN AND TERRY WALTER (2013) Brown and Walter (2013) give practical evidence of the CAPM’s continued relevance. They argue that the CAPM is an ex-ante48 concept, whereas the so-called ‘tests’ of the CAPM are conducted ex-post49. The CAPM is a partial equilibrium model in which

48 Ex-ante: based on forecasts rather than actual results 49 Ex-post: based on actual results rather than forecasts

agents view the risk-free return (Rf) and the probability distribution of the future return on risky assets (Rj) as exogenous. According to Brown and Walter (2013), the CAPM, which is basically an ex-ante concept, is used widely by corporations in their forward-looking capital budgeting and capital structure decisions, and by academics when considering adjustments for differences in risk. They outline the following points50:

a. Corporations Use the CAPM in Capital Budgeting: Graham and Harvey (2001) surveyed the CFOs of 392 U.S. firms and found that large firms rely heavily on present value techniques and the CAPM in their capital budgeting, while small firms are more likely to use a payback method. The CAPM was used always or almost always by 73.5% of respondents when estimating the cost of capital. Graham and Harvey (2005) reported quarterly estimates by U.S. CFOs made between June 2000 and June 2005 of the 10-year market risk premium over 10- year U.S. Treasury Bonds. The average 10-year bond yield was 4.6%, and the average market risk premium was 3.7%.

b. Regulatory Agencies Use the CAPM in Price Setting: The CAPM has become the ‘industry standard’ for regulatory decisions on the cost of capital and price determination for utilities (see Romano, 2005, for U.S. and Grayburn et al., 2002, for U.K. evidence). Gray and Hall (2006, 2008) refer to more than 10 Australian bodies that regulate infrastructure assets, worth more than $A100bn in total, where those assets were acquired after evaluation using CAPM-derived cost of capital estimates.

c. Market Efficiency Tests Are Joint Tests: Tests of market efficiency have, since Fama’s (1970, 1991) review articles, been recognized as joint hypothesis tests that (a) the market is efficient and (b) the correct model describing the expected return on an asset has been specified. Fama (1991) asks whether the joint-hypothesis problem makes empirical work on asset-pricing models uninteresting. His answer is ‘an unequivocal no’. He states (1991, p. 1576) ‘The empirical literature on efficiency and asset-pricing models passes the acid test of

50 These points are exactly as listed and stated in Brown and Walter (2013)

scientiﬁc usefulness. It has changed our views about the behaviour of returns, across securities and through time . . .The empirical work on market efﬁciency and asset- pricing models has also changed the views and practices of market professionals.’ We agree with his answer.

d. Academics and Practitioners Continue to Estimate Rm-Rf, and to Use the CAPM in Teaching Corporate Finance: Fernandez et al. (2011b) reports survey results for academics’ and practitioners’ estimates of the market risk premium. Estimates are provided for 56 countries, with the largest number of responses coming from the U.S. (1,503 responses) and Spain (930). The mean ex ante market risk premium for the U.S. is 5.5% with a standard deviation of 1.7%, while the mean Spanish estimate is 5.9% (1.6% standard deviation). The mean estimate for Australia is 5.9% (1.9% standard deviation). Similar surveys have been conducted previously, with U.S. premiums being estimated by academics at 6.3%, 6.4%, 6.0% and 5.7% in 2008, 2009, 2010 and 2011 respectively (Fernandez et al., 2011a). Brealey et al. (2011) is one of the most widely used textbooks in corporate ﬁnance classes. While the Fama–French three factor model and APT are mentioned, Brealey et al. (2011) and Ross et al. (2010) advocate that the CAPM be used to estimate the expected cost of capital.

In summary, they emphasize that the CAPM is elementally an ex-ante concept that provides a way of thinking about the risk–return trade-off, in the context of efficiently diversified portfolios of investments. They refute Dempsey’s (2013) argument that the empirical evidence against the CAPM is so compelling that it should be abandoned and perhaps be replaced by an assumption that investors expect the same return on all assets. They find two problems with Dempsey’s (2013) argument. Problem one being the presumption that the evidence is valid. However, valid tests of the CAPM require efficient benchmarks, which they argue have so far proven elusive. The second is that the idea of investors expecting to be compensated for unavoidable risk is inconsistent with the beliefs of theorists and practitioners, namely that risk matters to investors such that, ex-ante, a risk premium must exist. Beta, in numerous instances, has been declared dead; yet researchers and practitioners continue to use the CAPM, mostly ‘because of the strength of the intuition behind it’.

3.4 AHMAD ALQISIE AND TALAL ALQURRAN (2016) The study of Alqisie and Alqurran (2016) aimed at testing the validity of CAPM in the Amman Stock Exchange (ASE) during the period (2010 – 2014), which they divided into three sub periods. They used monthly returns of 60 stocks of Jordanian companies listed in the ASE. The Black, Jensen and Scholes (1972) and Fama and MacBeth (1973) methods were used by Alqisie and Alqurran (2016) to test the CAPM in different study sub-periods. The results showed that higher risk (beta) is not associated with higher levels of return, which is a violation of the CAPM assumption. Results of their study contradicts the CAPM’s assumption that beta coefficient is a ‘superior’ tool for predicting the relationship between risk and return; therefore, the beta coefficient of some portfolios in the three sub periods were insignificant. Moreover, in all three sub-periods, the results they got from testing the security market line was in violation of the CAPM assumption that the slope should be equal to the average risk premium. Lastly, tests of nonlinearity of the relationship between return and betas validated the CAPM hypothesis that the expected return-beta relationship is linear. They could not find conclusive evidence in support of CAPM in the ASE. Alqisie and Alqurran (2016) state that all previous studies regarding CAPM were aimed to achieve two objectives: how to test the validity of CAPM using statistical analysis to reach conclusive results in order to accept or refuse the model and how to provide information about financial assets or projects in order to help investors take financial decisions. However, there are still deliberations on the empirical validity of CAPM in finance literature. Therefore, they attempt to see if systematic risk beta as an independent variable can explain the variation in stock returns in the ASE.

The specific objectives of their study are as follows: • to examine whether a higher/lower risk stocks yields higher/lower expected rate of return. • to examine whether the slope of security market line equal to the average risk premium. • to examine whether the expected rate of return is linearly related with the stock beta, i.e. its systematic risk.

Alqisie and Alqurran (2016) conclude by reiterating that the purpose of the study was to investigate the validity of CAPM in Amman Stock Exchange (ASE) for the period

(2010 – 2014), by using monthly rate of return of 60 stocks of Jordanian companies listed in ASE. The researchers tested the CAPM for different study sub-periods by using 6 portfolios each have 10 stocks. The findings of the study led to the following conclusions51:

• The test for the CAPM hypothesis that higher risk beta is associated with higher rate of return is violated in the three sub periods. This result is in line with studies results of (Grigoris et al. 2006; Choudhary and Choudhary, 2010).

• The test for the CAPM hypothesis that alpha coefficient is significantly not different from zero is accepted in the three sub periods, thereby we accept the null hypothesis for all constants. This result is not in line with studies results of (Grigoris et al. 2006; Yang and Donghui, 2006; Choudhary and Choudhary, 2010).

• The test for the CAPM hypothesis that beta coefficient is a good toll to predict the relationship between risk and return did not fully support the CAPM, hence the beta coefficient of some portfolios in the three sub periods was not significant, which means it is not different from zero, and this violated the CAPM assumption. This result is in line with studies results of (Yang and Donghui, 2006; Choudhary and Choudhary, 2010; Bilgin and Basti, 2011).

• Test for the Security Market line52, the intercept λ0 was significantly not different from zero in all sub periods which is consistent with CAPM hypothesis, but regarding the slope λ1, it was not significantly different from zero in all sub periods. As CAPM assumes that, λ1 should be equal to the average risk premium, which should be greater than zero, thereby the result is inconsistent with the CAPM hypothesis, and accordingly, the CAPM is rejected in the three sub periods. This result is in line with studies results of (Yang and Donghui, 2006; Loukeris, 2009; Choudhary and Choudhary, 2010; Bilgin and Basti, 2011).

51 The conclusions are exactly as listed and stated in Alqisie and Alqurran (2016) 52 The study also also test the Non-Linearity between the total portfolio returns and its beta by using the 2 following equation: rp = λ0 + λ1βp + λ2β p + ep. According to the theory, if the CAPM is true, the portfolio returns and its beta are linearly related with each other and (λ2) will be equal to zero.

• Test for Non-linearity53, the intercept λ0 is not significantly different from zero in the three sub periods; thereby, it is consistent with the argument of CAPM. In the case of λ1, the test results show that the λ1 is not significantly different from zero in the three sub periods, as CAPM assumes that λ1 should be equal to the average risk premium, the results here are inconsistent with CAPM hypothesis. But concerning the coefficient λ 2, the results show that coefficient λ 2 is not significantly different from zero in the three sub periods, which means that these results are consistent with the CAPM hypothesis and betas are linearly related with rate of return. This result is in line with studies results of (Black, et. al, 1972; Fama and MacBeth, 1973; Yang and Donghui, 2006; Choudhary and Choudhary, 2010). On the other hand, results of other studies contradicted our results (Fama and French, 1992; Bilgin and Basti, 2011), thus, CAPM can be accepted in the three sub periods, but still the results show weakness to fully explain the model.

According to their results above, Alqisie and Alqurran (2016) did not find conclusive evidence in support of validity of CAPM in the Amman Stock Exchange (ASE) for the period (2010 – 2014).

3.5 OTHER TESTS AND CRITICISMS (CAPM) is the most famous asset pricing model in finance literature. It states that the return of a stock is influenced by only one single factor, i.e. the return on the market. The risk of an asset can be measured by its responsiveness to that single factor. If the systematic risk and return relationship implied in this basic model could be validated in real world stock markets that would be a true revolution in finance (Bilgin and Basti, 2014). Since CAPM was developed half a century ago, many researchers in finance field tries to test its validity in order to evaluate its ability in explaining risk- return relationship in stock markets. Some of these studies results supported the model while others contradicted the supportive results. These studies, in no particular order, are outlined below:

53 Please refer to note 6.

3.5.1 Black, Jensen and Scholes (1972) This is one of the earliest studies and it supports the CAPM. Black, Jensen and Scholes (1972) performed another classic test of the Capital Asset Pricing Model employing time-series regression. Black et al. used the return on portfolios of assets rather than individual securities. In their study, they formed portfolios of all stocks of the New York Stock Exchange over the period 1931- 1965, instead of individual stock return, to eliminate or reduce the company unsystematic risk in order to deal with effect of systematic risk on returns, which can be measured by beta coefficient. Based on monthly return data and an equally-weighted portfolio of all stocks traded on the NYSE as their proxy for the market portfolio, they find evidence in support of a significant positive linear relation between beta and expected return. This method purported to reduce the statistical errors that may appear when estimating beta coefficient. Their findings showed a linear relationship between average excess portfolio return and the beta, and portfolios with high beta have higher returns, while portfolios with lower beta have lower returns.

3.5.2 Fama and MacBeth (1973) Fama and Macbeth (1973) extended the work of Black et.al (1972) and reached the same results. They provide confirming evidence based on a two-pass regression approach. The two-pass regression approach (FM approach)54 has become a dominant methodology in empirical tests of the CAPM. They examine whether there is a positive linear relation between average return and beta and whether the squared value of beta and the volatility of the return on an asset can explain the residual variation in average returns across assets that is not explained by beta alone. They combined the time series and cross- sectional steps to investigate whether the risk premium of the factors in the second pass regression were non-zero. Forming 20 portfolios of securities, they estimated betas from a time-series regression similar to Lintner’s methodology. Using return data for the period from 1926 to 1968, for stocks traded on the NYSE, they find that the data generally supports the CAPM.

54 The Fama-MacBeth regression is a method used to estimate parameters for asset pricing models

Fama and MacBeth (1973) highlighted the evidence (i) of a larger intercept term than the risk-free rate, (ii) that the linear relationship between the average return and the beta holds and (iii) that the linear relationship holds well when the data covers a long period.

3.5.3 Banz (1981) Banz (1981) tested the CAPM to measure the effect of company size in explaining the rest of return which beta couldn’t explain. Banz (1981) tests the CAPM by checking whether the size of the firms involved can explain the residual variation in average returns across assets that is not explained by the CAPM's beta. Banz challenges the CAPM by showing that size does explain the cross-sectional variation in average returns on a particular collection of assets better than beta. He finds that during the 1936-75 period, the average return to stocks of small firms (those with low values of market equity) was substantially higher than the average return to stocks of large firms after adjusting for risk using the CAPM. This observation has become known as the size effect. Banz (1981) concluded that company size explained the return for some stocks better than beta coefficient, and he found that return of stock of small companies is higher than return of large companies.

3.5.4 Blume and Husic (1973) Further supporting evidence is provided by Blume and Husic (1973), who confirm linearity of the beta risk-return relation on the NYSE over three different periods of the Second World War. Blume and Husic (1973) find that price is, in some sense, a better predictor of future returns than the historically estimated beta. They express the annual returns in 1969, on the NYSE and the American Stock Exchange, as a function of 1968 year-end price and the historically estimated beta. In order to assess how adequately price measures beta, the correlation between price and historically estimated beta is calculated for American listed securities for each of the years from 1964 to 1968. They find that the correlations are unexpectedly close to zero. Therefore, this early study illustrates the more

general observation that, while the CAPM may hold true in some markets sometimes, it does not hold true in all markets at all times.

3.5.5 Basu (1977) Basu (1977) observes that low P/E ratio portfolios earn higher absolute and risk adjusted rates of return than those of high P/E ratio portfolios during the period from April 1957 to March 1971. Basu (1983) provides evidence that shares with high earnings yield (low price to earnings ratio) experience on average higher subsequent returns than shares with low earnings yield. Firms with low price-earnings ratio yielded higher sample return and firms with higher price-earnings ratio produced lower returns than justified by beta. Basu (1977) observes that the price-earnings ratio gives a different evaluation for the equities from the CAPM, and argues that the equities with high earnings to price ratio have higher expected returns than the CAPM estimates.

3.5.6 Fama and French (1992) In 1992, Fama and French adopted Banzs’ findings in their study; they found that results of Banz study could be very important in explaining the relationship between risk and return, although they used the same methodology used in the Fama and MacBeth (1973) study, which supported the CAPM. They considered the ability of other attributes to account for this cross-sectional variation. Fama and French (1992) provide evidence that CAPM has no ability to predict stock returns depending on beta coefficient; the results of their study showed that, additional factors besides beta effect company return such as, company size, book -to- market ratio. Fama and French (1992) in their influential paper entitled, “The cross-section of expected stock returns”, show that two easily measured variables, size and book-to-market equity combine to capture the cross-sectional variation in average stock returns associated with market beta, size, leverage, book-to- market, and earnings-to-price ratios. They argued that portfolios formed on the basis of ratio of book-value of equity to market value and size (market capitalization) earn higher returns than what is predicted by CAPM. They even suggest that the B/M ratio is more powerful than the size effect in explaining cross sectional average returns. Moreover, they find that when allowing for

variations in beta that are unrelated to size, the relationship between beta and average return is flat. Hence, they naturally argue that the CAPM is dead.

3.5.7 Kothari, S., Shanken, J., & Sloan G. (1995) Kothari et al (1995) said that Fama and French (1992) results depend basically on explaining the statistical results only i.e. it depends critically on how one interprets their statistical tests, arguing that using annual returns yields betters beta estimates. They highlighted the survivorship bias in the data used to test the validity of the asset pricing model specifications. Kothari et al (1995) re- examine the risk-return relation using a longer measurement interval of returns and alternative market data (the S&P industry portfolios). They argue that since failing (excluded from the sample) stocks would be expected to have low returns and high book market ratios, the average return of the included (in the sample) high book-to-market ratio stocks would have an upward bias. They assert that selection bias in the construction of book-to-market portfolio could be the cause of premium reported by Fama and French. They present evidence that average returns do indeed reflect substantial compensation for beta risk, provided that betas are measured at an annual interval.

3.5.8 Jagannathan and Wang (1996) Jagannathan and Wang (1996) showed that specifying a broader market portfolio can affect the results. They said that results of Fama and French (1992) are not important, they assumed that lack of practical evidence on validity of CAPM may refer to the basic assumptions which were adopted to test CAPM for example, most of studies which tested CAPM assumed that indexes return in financial markets are the best measures of assets returns in macroeconomics, but this assumption is not accurate. Jagannathan and Wang (1996) argue that because of the nature of the real options vested with firms their systematic risk will vary depending on economic condition, and the stock returns of such firms will exhibit option like behaviour.

3.5.9 Choudhary and Choudhary (2010) Choudhary and Choudhary (2010) tested the validity of the CAPM for the Indian stock market. The study used monthly stock returns from 278

companies of BSE 500 index listed on the Bombay stock exchange from January 1996 to December 2009.The findings of the study are not supportive of the theory’s basic hypothesis that higher risk (beta)is associated with a higher level of return. They used Black et al (1972) methodology through constructing portfolios and conducting time series test of the CAPM and concluded that the CAPM does not hold on the BSE. This is despite evidence suggesting the CAPM does explain excess returns, which supports the linear structure of the CAPM equation. They allude to the fact that the theory’s prediction for the intercept is that it should equal zero and the slope should equal the excess returns on the market portfolio. Their results showed that; (1) higher risk (beta) is not associated with a higher level of return and this result don’t support the CAPM theory. (2) The CAPM’s prediction for the intercept and the slope of the equation is contradictory with the CAPM hypothesis. (3) The relationship between beta and expected return is linear.

3.5.10 Bilgin and Basti (2011, 2014) Bilgin and Basti (2011) tested the validity of CAPM in Istanbul stock exchange during 2006 – 2010 for 42 company stock, they adopted Fama and McBeth’s (1973) unconditional testing approach, and they used monthly returns of stock. Their results indicated that there is no meaningful relationship between betas and risk premiums, which means CAPM is not valid in (ISE). Bilgin and Basti (2014) gave further evidence on the validity of CAPM in Istanbul stock exchange by testing both the unconditional and conditional versions of CAPM during the period 2003-2011, through dividing the test period into four sub-periods, their results indicated that unconditional CAPM is rejected for the sample period, while the test of conditional CAPM indicated a statistically significant conditional relationship during some sub-periods. But since the relationship between risk and return in up and down markets is not symmetric, this conditional relationship doesn’t indicate a positive relation between risk and return, according to these results, CAPM may not be a useful tool to measure the relationship between risk and return in ISE.

Grigoris et al. (2006) tested the validity of CAPM in Athens securities market by using weekly return of 100 companies. They constructed 10 portfolios, each portfolio contains 10 companies in order to calculate beta for each portfolio, they tested the relationship between beta and portfolios returns, their results showed that portfolios with high beta didn’t earn high returns, and the intercept (α) of the model is not equal to zero, which means that CAPM is not valid in explaining the relationship between risk and return in Athens security market.

Hasan et al. (2013) use monthly stock returns on the Bangladesh Stock Exchange for the period from January 2005 to December 2009. The all share price index (DSI) is used as the proxy for the market portfolio and the Bangladesh 3-month government treasury bill as the risk free asset. The results of the coefficients of squared beta and unique risk indicate that the expected return-beta relationship is linear in portfolios and that firm specific risk has no effect on the expected return of the portfolios. The intercept terms for the portfolios are not significantly different from zero. These findings support the validity of CAPM.

Yang and Donghui (2006) tested CAPM in the Shanghai stock exchange during 2000 – 2005. They used weekly stock returns from 100 companies, methods of time-series test and cross-sectional test were used, and they found linear relation between expected returns and betas, which implies a strong support of the CAPM hypothesis. But in testing the intercept and the slope, the results proved that CAPM is not valid in Chinese stock market.

Dzaja and Aljinovic (2013) test the CAPM using data from Romania, Hungary, Bulgaria, Serbia, Poland, Turkey, Czech Republic, and Bosnia and Herzegovina. They use monthly returns from the period of January 2006 to December 2010. Based on regression analysis, they find that higher yields do not mean higher beta. Also by applying the Markowitz portfolio theory they determine the efficient frontier for each market, and find that the stock market indices do not lie on the efficient frontier and therefore cannot be regarded as a good proxy for the market portfolio, as is usually assumed. The authors conclude that the CAPM beta alone is not a valid measure of risk.

Loukeris (2009) tested the validity of CAPM in London stock market for the period 1980 – 1998 by using two step regression procedures of 39 stocks, the results showed

61 that the cross section of average excess security return is positively related to beta. But when using the two-step regression procedure into CAPM, the result showed that the slope of the security market line is different from the slope of SML indicated by CAPM, which means that CAPM hasn’t a statistical significance in portfolio selection.

Reddy and Thompson (2011) use quarterly returns to test the CAPM on the Johannesburg Stock Exchange (JSE) for the period from June 1995 to June 2009. They use regression analysis to test the validity of the model on both individual sectoral indices and portfolios constructed from the indices according to their betas. They conclude that, on the assumption that the “residuals of the return generating function are normally distributed,” the CAPM could be rejected for certain periods, though the use of the CAPM for long-term actuarial modelling in the South African market can be reasonably justified.

4. CAPM AND THE CURRENT ECONOMY 4.1 CAPM AND LOW/NEGATIVE INTEREST RATES The CAPM is a model for determining the price of risky securities and expected return on assets and estimating the cost of capital.

Basic formula:

E(Ri) = Rf + β*[E(RM) – Rf]

Risk premium

where:

E (Ri) = the expected return on asset i β = the market beta of asset i that measures the sensitivity of the asset’s return to variation in the market return.

Rf = the risk-free rate of return, and

RM =the market return

The risk-free rate (Rf) is an important input in the CAPM. It is also the starting point for all expected return models. The risk-free rate is the building block for estimating both the cost of equity and capital. The cost of equity is computed by adding a risk premium to the risk-free rate, with the magnitude of the premium being determined by the risk in an investment and the overall equity risk premium (for investing in the average risk investment).

For an investment to be risk free, it must meet two conditions. The first is that there can be no risk of default associated with its cash flows. The second is that there can be no reinvestment risk in the investment. The risk-free rate is said to be an illusion however, as there is no such thing as a risk-free asset. In practice, the risk-free rate does not technically exist as even the safest investments carry a very small amount of risk. Thus, the interest rate on either short-term Treasury bills or long-term Treasury bonds is commonly used as a proxy for the risk-free rate because these securities have virtually zero risk of default.

One central result of the CAPM is the so-called Security market line (SML). It displays the expected rate of return of an induvial security as a function of systematic, non- diversifiable risk.

Figure 6: The Security Market Line

Source: Wikipedia

In theory, if there are negative interest rates then according to the CAPM equation you would have a negative intercept. The risk-free rate is the y-intercept of the Security market line. If the risk-free rate goes negative the y-intercept of the Security market line would simply be below the x-axis. So, if the risk-free rate decreases the whole line shifts

down. Economically speaking this means that the return on the risk-free asset is negative. This basically means people are willing to pay for safety.

Once Rf and RM are defined points along SML (understanding that by definition, Rf has 55 zero β and RM has β = 1), the effect of, ceteris paribus , changing Rf is clearer. If the

market’s return, RM is unaffected, the slope of the line increases so securities are ever

more sensitive to risk (β) under a negative interest rate regime. So, if Rf moves down the Y-axis of the Security Market Line, to a negative intercept, it is conceivable that equity returns would move down somewhat in parallel.

Another effect of a negative risk free rate is, that the risk premium would go up by the amount of risk free rate. A higher risk premium implies that, while the expected real returns on government bonds are low, the long-run real returns implied by current equity valuations remain relatively high (Daly, 2016)56.

However, low risk free rates, and especially negative rates encourage corporate borrowing for share buybacks, thus artificially boosting returns.

4.2 CURRENT OPINIONS ON THE CAPM57 Few theories are more influential or important in driving financial markets as the capital asset pricing model. Yet its application continues to spark vigorous debate, even in the present day.

Tassell (2007)58 in his article quotes James Montier, an analyst at Dresdner Kleinwort, saying that the CAPM is empirically bogus - it does not work in any way, shape or form. "The CAPM is, in actual fact, Completely Redundant Asset Pricing (CRAP)," he says, claiming that financial markets are in denial of this fact.

55 All other things being equal 56 Daly, K (2016), “A Secular Increase in the Equity Risk Premium”, International Finance, 19: 179–200. 57 Tests, Evidences and Criticisms in the last decade 58 Tony Tassell (2007), “The time has come for the CAPM to RIP”, The Financial Times Limited. Retrieved from http://www.ft.com/cms/s/0/12ed9dd0-b8ab-11db-be2e- 0000779e2340.html?ft_site=falcon&desktop=true#axzz4gFj4eq5z

Tassell points out that some of the most damning evidence against the CAPM came from ‘an exhaustive 2004 study by Eugene Fama and Kenneth French, the academics who helped develop the efficient markets theory in the early 1970s, that argued stocks are always correctly priced as everything that is publicly known about the stock is reflected in its market price’. As Montier states, this study demonstrates that the CAPM “woefully” understates the profits to low beta stocks and greatly exaggerates the profits to high beta stocks. “Over the long run there has been essentially no relationship between beta and return,” he says. Fama and French themselves concluded that while CAPM was a theoretical “tour de force59”, its empirical track record was so poor that its use in “applications” was probably invalid. In others words, CAPM is a fine theory but useless in the real world. A similar study of the 600 largest US stocks by Jeremy Grantham, a value investor in 2006 yielded similar results. It showed from 1969 to the end of 2005, the lowest decile of beta stocks - notionally the lowest risk - outperformed by an average 1.5 per cent a year. The highest beta stocks, or the riskiest, actually underperformed by 2.7 per cent a year. The problems in the CAPM, Tassell claims, lie in its assumptions, particularly those used to derive the efficient portfolio that is used as a benchmark for the model in theory. The most commonly-cited criticism is an implicit assumption that that all investors can borrow or lend funds on equal terms.

Other assumptions that have been criticized include: that there are no transaction costs, that all investors have a “homogeneity” of expectations and risk appetites and that investors can take any market exposure without affecting prices. It also assumes no taxes so investors are indifferent between dividends and capital gains. “Markowitz himself noted that the CAPM is like studying "the motions of objects on Earth under the assumption that the Earth has no air. The calculations and results are much simpler if this assumption is made. But at some point, the obvious fact that on Earth, cannonballs and feathers do not fall at the same rate should be noted,” he says. Current market conditions might be exacerbating problems. Vineer Bhansali, head of portfolio management analytics at Pimco, adds that the increasing availability of leverage for some investors may actually drive all risky security prices higher.

59 An achievement or performance that shows great skill and attracts admiration

The concept of pursuing absolute returns rather than relative performance is now widely debated. There needs to be a similar evolution in market thinking on how risk is defined, measured and dealt with. Montier cites a quote from legendary investor Ben Graham: "What bothers me is that authorities now equate the beta with the concept of risk. Price variability, yes; risk, no. Real investment risk is measured not by the per cent a stock may decline in price in relation to the general market in a given period but by the danger of a loss of quality and earning power through economic changes or deterioration in management."

Loukeris (2009) tested the validity of CAPM in London stock market for the period 1980 – 1998 by using two step regression procedures of 39 stocks, the results showed that the cross section of average excess security return is positively related to beta. But when using the two-step regression procedure into CAPM, the result showed that the slope of the security market line is different from the slope of SML indicated by CAPM, which means, he concludes, that CAPM does not have a statistical significance in portfolio selection.

Choudhary and Choudhary (2010) tested the validity of the CAPM for the Indian stock market. The study used monthly stock returns from 278 companies of BSE 500 index listed on the Bombay stock exchange from January 1996 to December 2009.The findings of the study are not supportive of the theory’s basic hypothesis that higher risk (beta)is associated with a higher level of return. They used the Black et al (1972) methodology through constructing portfolios and conducting time series test of the CAPM and concluded that the CAPM does not hold on the BSE. This is despite evidence suggesting the CAPM explains excess returns, which supports the linear structure of the CAPM equation. They touch on the fact that the theory’s prediction for the intercept is that it should equal zero and the slope should equal the excess returns on the market portfolio. Their results showed that; (1) higher risk (beta) is not associated with a higher level of return and this result don’t support the CAPM theory. (2) The CAPM’s prediction for the intercept and the slope of the equation is contradictory with the CAPM hypothesis. (3) The relationship between beta and expected return is linear.

Dreman (2010)60 stated, “When it comes to popular investing gospel, the Capital Asset Pricing Model (CAPM) ranks right up there with its elder cousin the Efficient Market Hypothesis. As a value investor, I don’t think much of either of these. I make my living investing in market inefficiencies.” The CAPM says that the only way to outperform the stock market averages is by taking greater risk. Risk, according to the theory, is synonymous with volatility and is typically expressed by beta. Thus, a manager who outperforms the market by five percentage points a year, by the CAPM’s logic, must be taking more risk or have a high beta portfolio. After adjusting for risk, he may be doing worse than someone who outperforms by only two points. Higher betas translate into higher returns, lower betas into lower returns. Dreman propses that the CAPM be deleted from business school textbooks. He insists that the theory has done more harm than good for investors. Ever since the 1980s CAPM has been widely accepted by almost all sophisticated trading and money management firms practicing Modern Portfolio Theory to price stocks. It’s rooted into most Wall Street computer models. Indeed, most of the big firms and their chief risk officers focus on beta but have, until recently, ignored most other types of risks - like leverage and liquidity. He believes that this contributed to the severity of at least three major crashes since the 1980s: the Crash of 1987, Long-Term Capital in 1998 and the 2008 subprime debacle the world is still working through. In the years leading up to the 2007–08 crash leverage and liquidity were not considered risky on subprime bonds. After all, the beta of these bonds was relatively low, despite the garbage they were holding and the leverage they piled on. When housing prices fell, the markets collapsed.

Dreman points out that Eugene Fama began distancing himself from this famous theory years ago. In 1992, he, Fama, and Kenneth French wrote a paper stating that there was no link between volatility (risk) and return. Fama said, “Beta as the sole variable in explaining returns on stocks is dead.” A year later Fama and French came up with a new risk theory factoring two other risk measures to accompany beta. These were market capitalization (smaller caps are riskier) and high book to market (a value

60 David Dreman (2010), “Debunking Beta”, Forbes. Retrieved from https://www.forbes.com/forbes/2010/0927/finance-david-dreman-fixed-income-watch-debunking-beta.html

68 measurement). Dreman asserts that this was a “desperate attempt” to save their discredited Efficient Market Hypothesis.

Bilgin and Basti (2011) tested the validity of CAPM in Istanbul stock exchange (ISE) during 2006 – 2010 for 42 company stock. They adopted Fama and McBeth’s (1973) unconditional testing approach, and they used monthly returns of stock. Their results indicated that there is no meaningful relationship between betas and risk premiums, which means CAPM is not valid in (ISE).

In their 2014 study, Bilgin and Basti gave further evidence on the validity of CAPM in Istanbul stock exchange by testing both the unconditional and conditional versions of CAPM during the period 2003-2011, through dividing the test period into four sub- periods, their results indicated that unconditional CAPM is rejected for the sample period, while the test of conditional CAPM indicated a statistically significant conditional relationship during some sub-periods. But since the relationship between risk and return in up-and-down markets is not symmetric, this conditional relationship doesn’t indicate a positive relation between risk and return, and according to these results, CAPM may not be a useful tool to measure the relationship between risk and return in ISE.

Reddy and Thomson (2011) use quarterly returns to test the CAPM on the JSE for the period from June 1995 to June 2009. They use regression analysis to test the validity of the model on both individual sectoral indices and portfolios constructed from the indices according to their betas. They conclude that, on the assumption that the “residuals of the return generating function are normally distributed,” the CAPM could be rejected for certain periods, though the use of the CAPM for long-term actuarial modelling in the South African market can be reasonably justified.

Agrawal, Mohapatra and Pollak’s (2012) conclusion that empirical data from the U.S. stock market contradicts the CAPM is clearly pointed out and discussed in literature outlined in their paper. They proposed a new statistic for testing this conclusion and analysed an implementable investment strategy based on this statistic. If the CAPM is applicable to the U.S. stock market, then the strategy’s expected profit would be zero. Actually, the sample mean of the profit surpassed zero by a statistically significant

69 amount. The finding is not explained by the trading costs or by other factors—company size and price-to-book ratio—that have been proposed as improvements to the CAPM. They furthermore show that, even though the strategy’s profits are heavy-tailed and temporally dependent, the t-statistic of their sample mean is well modelled as a normal distribution. This justified their calculations of significance levels. Their strategy outperforms the market and has a low correlation with the market. The low correlation with the market is important, as it implies that the strategy can provide diversification compared to a pure market portfolio.

Additionally, the strategy is less volatile than the market, in the sense that its largest daily loss over the 40-year testing period is about 12 daily standard deviations, whereas the market’s largest loss is about 21 standard deviations. The dramatic reduction of the profitability of the strategy over the last 20 years suggests that the U.S. stock market became much more consistent with CAPM than it used to be. This point is confirmed by their analysis of yearly alphas which fail to reject the hypothesis that alpha is zero at significance level 1% in any pf the years starting with 1994. Based on these results, they conclude that there is economically and statistically significant evidence contradicting the CAPM in the U.S. stock market over the 40-year testing period.

Hasan et al. (2013) use monthly stock returns on the Bangladesh Stock Exchange for the period from January 2005 to December 2009. The all share price index (DSI) is used as the proxy for the market portfolio and the Bangladesh 3-month government treasury bill as the risk-free asset. The results of the coefficients of squared beta and unique risk indicate that the expected return-beta relationship is linear in portfolios and that firm specific risk has no effect on the expected return of the portfolios. The intercept terms for the portfolios are not significantly different from zero. These findings support the validity of CAPM.

Brown and Walter (2013) summarily emphasize that the CAPM is elementally an ex- ante concept that provides a way of thinking about the risk–return trade-off, in the context of efﬁciently diversiﬁed portfolios of investments. They refute Dempsey’s (2013) argument that the empirical evidence against the CAPM is so compelling that it should be abandoned and perhaps be replaced by an assumption that investors expect the same return on all assets. They find two problems with Demsey’s (2013) argument.

Problem one being the presumption that the evidence is valid. However, valid tests of the CAPM require efﬁcient benchmarks, which they argue have so far proven elusive. The second is that the idea of investors expecting to be compensated for unavoidable risk is inconsistent with the beliefs of theorists and practitioners, namely that risk matters to investors such that, ex-ante, a risk premium must exist. Beta, in numerous instances, has been declared dead; yet researchers and practitioners continue to use the CAPM, mostly ‘because of the strength of the intuition behind it’.

Lai and Stohs’s (2015)61 paper uses algebraic analysis to prove that “CAPM is dead,” because they believe that it is “either beset62 with a serious endogeneity problem or is circular.” Given the expected excess return vector, whether or not the market is in equilibrium, the non–singular covariance matrix implies that there must exist one and only one portfolio, such that the expected excess rate of return on assets can be rewritten as the product of its beta and the market risk premium. This leads to the mathematical conclusion that the market portfolio in CAPM must be the optimal mean–variance efficient portfolio and must depend on the expected excess return. The optimal mean– variance efficient market portfolio is a necessary and sufficient condition for CAPM. This proposition entails the problem of endogeneity. Endogeneity by itself, they say, may not prove the death of CAPM, but it does point to the well–known difficulties with obtaining reliable betas or costs of capital. That is, the CAPM appears to be almost useless for predicting the rate of return for an asset in the real world, as claimed by Levi and Welch (2014). Even if endogeneity problems can be resolved, the fundamental argument for CAPM appears circular, which alone is an obstacle that appears insurmountable. Their argument is not empirical in nature, but rather based on the logic and mathematics of CAPM, which distinguishes the argument from the many other empirical or econometric critiques of CAPM. So, Lai and Stoh conclude that the CAPM is a contradiction unto itself.

The results of the study of Alqisie and Alqurran (2016) contradicts the CAPM’s assumption that beta coefficient is a ‘superior’ tool for predicting the relationship between risk and return; therefore, the beta coefficient of some portfolios in the three

61 Lai, T. and Stohs, M. H. (2015), “Yes, CAPM Is Dead”, International Journal of Business, 20(2): 144 – 158 62 Plagued or troubled or afflicted

71 testing sub-periods were insignificant. Moreover, in all three sub-periods, the results they got from testing the security market line was in violation of the CAPM assumption that the slope should be equal to the average risk premium. Lastly, tests of nonlinearity of the relationship between return and betas validated the CAPM hypothesis that the expected return-beta relationship is linear. They could not find conclusive evidence in support of CAPM in the ASE.

Table 1: Summary of Findings

AUTHOR(S) YEAR TEST MARKET TEST TESTED MAIN FINDINGS PERIOD MODEL Fischer Black, 1972 U.S. - New York 1926 - Standard Their results supported the CAPM. Michael C. Stock Exchange 1966 CAPM They find evidence in support of a Jensen and (NYSE) significant positive linear relation Myron between beta and expected return. Scholes Their findings showed a linear relationship between average excess portfolio return and the beta, and portfolios with high beta have higher returns, while portfolios with lower beta have lower returns. Eugene F. 1973 U.S. - New York 1926 - Standard They provide confirming evidence that Fama and Stock Exchange 1968 CAPM the data generally supports the CAPM. James D. (NYSE) Fama and MacBeth (1973) highlighted Macbeth the evidence (i) of a larger intercept term than the risk-free rate, (ii) that the linear relationship between the average return and the beta holds and (iii) that the linear relationship holds well when the data covers a long period. Marshall E. 1973 U.S. - New York 1964 - Standard Blume and Husic (1973) find that price Blume and Stock Exchange 1968 CAPM is, in some sense, a better predictor of Frank Husic (NYSE) and the future returns than the historically American Stock estimated beta. They find that the Exchange correlations are unexpectedly close to (AMEX) zero. Therefore, this early study illustrates the more general observation that, while the CAPM may hold true in some markets sometimes, it does not hold true in all markets at all times.

S. Basu 1977 U.S. - New York 1956 - Standard Basu (1983) finds evidence that shares Stock Exchange 1971 CAPM with high earnings yield (low price to (NYSE) earnings ratio) experience on average higher subsequent returns than shares with low earnings yield. Firms with low price-earnings ratio yielded higher sample return and firms with higher price-earnings ratio produced lower returns than justified by beta. This provides evidence against the CAPM as beta alone fails to explain stock returns. Rolf W. Banz 1981 U.S. - New York 1936 - Standard Banz challenges the CAPM by Stock Exchange 1975 CAPM showing that size does explain the (NYSE) cross-sectional variation in average returns on a particular collection of assets better than beta. He finds that the average return to stocks of small firms (those with low values of market equity) was substantially higher than the average return to stocks of large firms after adjusting for risk using the CAPM. This observation has become known as the size effect. Banz (1981) concluded that company size explained the return for some stocks better than beta coefficient, and he found that return of stock of small companies is higher than return of large companies. Eugene F. 1992 U.S. - New York 1962 - Standard Fama and French (1992) provide Fama and Stock Exchange 1990 CAPM evidence that CAPM has no ability to (NYSE), the predict stock returns depending on beta

Kenneth R. American Stock coefficient; the results of their study French Exchange showed that, additional factors besides (AMEX) and beta effect company return such as, National company size, book -to- market ratio. Association of Moreover, they find that when Securities Dealers allowing for variations in beta that are Automated unrelated to size, the relationship Quotations between beta and average return is flat. (NASDAQ) Hence, they naturally argue that the CAPM is dead. S. P. Kothari, 1995 U.S. Stock Market 1927 - Standard They assert that selection bias in the Jay Shanken 1990 CAPM construction of book-to-market and Richard portfolio could be the cause of G. Sloan premium reported by Fama and French. They present evidence that average returns do indeed reflect substantial compensation for beta risk, provided that betas are measured at an annual interval. Ravi 1996 U.S. - New York 1962 - Conditional They found that when betas and Jagannathan Stock Exchange 1990 CAPM63 expected returns are allowed to vary and Zhenyu (NYSE) and the over time by assuming that the CAPM Wang American Stock holds period by period, the size effects Exchange and the statistical rejections of the (AMEX) model specifications become much weaker. When a proxy for the return on human capital is also included in measuring the return on aggregate wealth, the pricing errors of the model are not significant at conventional levels. More importantly, firm size does not have any additional

63 The standard CAPM with conditional beta, conditional expected returns and conditional market risk premium

explanatory power. We find that the conditional version of the CAPM explains the cross-section of stock returns rather well. Grigoris 2006 Greece - Athens 1998- Standard Their results showed that portfolios Michailidis, Stock Exchange 2003 CAPM with high beta didn’t earn high returns, Stavros and the intercept (α) of the model is not Tsopoglou, equal to zero, which means that CAPM Demetrios is not valid in explaining the Papanastasiou relationship between risk and return in and Athens security market. Mete Feridun Xi Yang and 2006 Chinese Stock 2000 - Standard Yang and Donghui found linear Donghui Xu Market - Shanghai 2005 CAPM relation between expected returns and Stock Exchange betas, which implies a strong support of (SSE) the CAPM hypothesis. But in testing the intercept and the slope, the results proved that CAPM is not valid in Chinese stock market. Loukeris 2009 U.K. - London 1980 - Standard Loukeris’ results showed that the cross Nikolaos Stock Market 1998 CAPM section of average excess security return is positively related to beta. But when using the two-step regression procedure into CAPM, the result showed that the slope of the security market line is different from the slope of SML indicated by CAPM, which means that CAPM does not have a statistical significance in portfolio selection. Kapil 2010 India - Bombay 1996 - Standard The findings of the study are not Choudhary Stock Exchange 2009 CAPM supportive of the theory’s basic (BSE) hypothesis that higher risk (beta)is

76 and Sakshi associated with a higher level of return. Choudhary Their results showed that; (1) higher risk (beta) is not associated with a higher level of return and this result don’t support the CAPM theory. (2) The CAPM’s prediction for the intercept and the slope of the equation is contradictory with the CAPM hypothesis. (3) The relationship between beta and expected return is linear. Taryn Leigh 2011 South Africa - 1995 - Standard They conclude that, on the assumption Reddy and Johannesburg 2009 CAPM that the “residuals of the return Robert John Stock Exchange generating function are normally Thomson (JSE) distributed,” the CAPM could be rejected for certain periods, though the use of the CAPM for long-term actuarial modelling in the South African market can be reasonably justified. Mayur 2012 U.S. Stock Market 1971 - Standard They foundeconomically and Agrawal, 2010 CAPM statistically significant evidence Debabrata contradicting the CAPM in the U.S. Mohapatra Stock Market in the testing period. and Ilya Pollak Philip Brown 2013 Standard Brown and Walter find that since the and Terry CAPM CAPM is firmly an ex-ante concept, Walter and the ‘tests’ of the CAPM are continuously conducted ex-post, then the ‘tests’ and any resulting evidences or finding are not valid.

Md. Zobaer 2013 Bangladesh Stock 2005 - Standard The results of the coefficients of Hasan, Anton Market 2009 CAPM squared beta and unique risk indicate Abdulbasah that the expected return-beta Kamil, Adli relationship is linear in portfolios and Mustafa and that firm specific risk has no effect on Md. Azizul the expected return of the portfolios. Baten The intercept terms for the portfolios are not significantly different from zero. These findings support the validity of CAPM. Josipa Džaja 2013 Central and 2006 - Standard They found that higher yields do not and Zdravka South-East 2010 CAPM mean higher beta. Also by applying the Aljinović European Markowitz portfolio theory they emerging determine the efficient frontier for each securities markets market, and find that the stock market - Romania, indices do not lie on the efficient Hungary, frontier and therefore cannot be Bulgaria, Serbia, regarded as a good proxy for the market Poland, Turkey, portfolio, as is usually assumed. The Czech Republic, authors conclude that the CAPM beta and Bosnia and alone is not a valid measure of risk. Herzegovina Rumeysa 2014 Turkey - Istanbul 2003 - Standard Their results indicated that Bilgin and Stock Exchange 2011 CAPM and unconditional CAPM64 is rejected for Eyup Basti (ISE) Conditional the sample period, while the test of CAPM conditional CAPM indicated a statistically significant conditional relationship during some sub-periods. But since the relationship between risk and return in up and down markets is not symmetric, this conditional relationship doesn’t indicate a positive

64 Unconditional CAPM here refers to the Standard CAPM

relation between risk and return, according to these results, CAPM may not be a useful tool to measure the relationship between risk and return in ISE. Ahmad 2016 Amman Stock 2010 - Standard They found that higher risk (beta) is not Alquise and Exchange (ASE) 2014 CAPM associated with higher levels of return, Talal Alqurran which is a violation of the CAPM assumption. Results of their study contradicts the CAPM’s assumption that beta coefficient is a ‘superior’ tool for predicting the relationship between risk and return; therefore, the beta coefficient of some portfolios in the three sub periods were insignificant. Moreover, the results they got from testing the security market line was in violation of the CAPM assumption that the slope should be equal to the average risk premium. Lastly, tests of nonlinearity of the relationship between return and betas validated the CAPM hypothesis that the expected return-beta relationship is linear. They could not find conclusive evidence in support of CAPM in the ASE.

CONCLUSION

The aim of this work was to five a general overview of the standard capital asset pricing model (CAPM). The first section summarily describes the theory of the CAPM and how it is formulated, outlining and explaining its assumptions. As observed by critiques, most of these assumptions do not encourage real-world application of the model. Therefore, section two of his study outlines alternative models for asset pricing which were developed in response to the shortcomings of the standard CAPM. The greater part of them were gotten by barring of some supposition out of the fundamental model.

The CAPM is condemned for its assumptions, for example, the unrestricted risk-free borrowing and lending, investors care only about the risk and return of one-period portfolio returns, market Betas explain the expected returns. In any case, it is generally utilized and numerous industries and investors and portfolio managers rely on upon this model in decision-making. In spite of the empirical evidence which suggests the failure of the CAPM, and the problems concerning the model’s assumptions, the CAPM remains a useful tool for estimating the cost of capital, evaluating the investment performance and event studies of efficient market (Moyer, McGuigan, & Kretlow, 2001 and Campbell, Lo, & MacKinlay, 1997).

The criticisms of and evidences against the standard model is a result of a multitude of empirical tests carried out by numerous researchers. Notable among the challenges to the validity of the CAPM are the findings that the average returns on stocks is related to firm size (Banz (1981)), earnings to price ratio (Basu (1983), book-to-market value of equity (BM) (Rosenberg, Reid, and Lanstein (1985)), cash flow to price ratio, sales growth (Lakonishok, Shleifer and Vishny (1994)), past returns (DeBondt and Thaler (1985) and Jegadeesh and Titman (1993)), and past earnings announcement surprise (Ball and Brown (1968)). Subsequent studies also confirm the presence of similar patterns in different datasets, including those of international markets. Fama and French (1993) surmise that two other risk factors, in addition to the stock market factor used in empirical implementations of the CAPM, are necessary to fully characterize economy wide pervasive risk in stocks. The Fama and French (1993) three-factor model has received wide attention as a replacement for the CAPM.

The evaluation of these studies questions the sufficiency the CAPM’s beta. It is difficult to take a definitive stand on this issue in view of the inconclusive nature of debates surrounding the model (Chan and Lakonishok, 1993). Therefore, it would be premature and extremely presumptuous to declare that beta is undoubtedly dead. Daniel and Titman (1997) summarize this debate as follows: “Thus, while the literature does not directly dispute the supposition that the return premia of high book-to-market and small size stock can be explained by a factor model, the debate centres on whether the factors can possibly represent economically relevant aggregate risk.” Though not effectively destroying the CAPM, collectively, these criticisms and empirical evidences pose a challenge to CAPM.

It is recommended that the CAPM be used carefully when estimating the required rate of return of a stock or as a supplement to other asset pricing models.

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List of Figures

Figure 1: CAPM with Risk-Free Borrowing and Lending ...... 20 Figure 2: Investment Opportunities ...... 22 Figure 3: The Security Market Line ...... 29 Figure 4: Arbitrage Pricing Theory ...... 40 Figure 5: Three-Factor Model – Risk Axes ...... 42 Figure 6: The Security Market Line ...... 64

List of Tables

Table 1: Summary of Findings ………………………………………………………………….… 20