The mean-variance model, which was developed by Harry Markowitz (1952, 1959), and the capital asset pricing model (CAPM) both play an important role for investors in the equity markets. The portfolio model derives the expected return for a portfolio and an expected risk measure. In addition, the portfolio theory suggests that all portfolios are in the efficient set. As a result of portfolio theory, CAPM is based on the following premise: all investors employ Markowitz theory in order to find the portfolios in the efficient set. Every investor then invests in a portfolio in an efficient set (Haugen, 2001. p.201).
Portfolio theory and the CAPM have been subjected to critical investigation. The purpose of this paper is to critically analyse the relevance of portfolio theory and the CAPM for investors or fund managers in the equity market. This analysis will be carried out by first, briefly presenting a portfolio theory and mentioning some critical points about it. Second, I will introduce the CAPM model generally and present some empirical studies that do not support the model and instead support Fama and French, the alternative model that is suggested.
In summary, even though the CAPM is widely used, an examination of its quantitative perditions reveals that the model fails. Resulting from this, Fama and French is the best-known alternative model that can be used.
Portfolio theory:
The first portfolio theory was devised by Harry Markowitz (1952-1959), who explained how the expected return can be identified. He also showed that the expected risk should be measured using variance or the standard deviation of the rate of return (Pilpeam, 2005. p 166). According to the Markowitz model, expected risk is based on five assumptions regarding investor behaviour:
1-Investors discuss the investment alternative according to the probability distribution of the expected rate of return.
2-The risk of the portfolio as a whole is estimated based on the variability of expected return (Pilpeam, 2005. p 166).
3-Investors prefer a higher return to a lower return.
4-The theory concentrates on the types of existing assets and ignores other issues.
5-Regarding the basis of this theory, the investors are risk-averse (Pilbeam, 2005, p.166).
In fact, using diversification in the portfolio theory improves the risk-return trade-off, which is what the investors need. Actually, there are two formulas for measuring risk. The first is variance (standard deviation) of returns for an individual investment. The other is variance (standard deviation) of return for a portfolio (cuthbertson, and Nitzsche, 2008. Pp 190-204). However, there are two concepts, correlation and covariance, that must be shown before giving the portfolio standard deviation formula. Covariance of return measures two variables moving together regarding their individual mean. Correlation is a statistical concept showing the relationship between two assets, and it gives the range between (-1) to (+1) (Pilbeam, 2005, p.166).
Even though the economy has been changing for a few years, investing long-term is a way to avoid risk. Because of this, many investors prefer to invest long-term. That said, investors as fund managers should not pay attention to the share price volatility of long-term investments. In fact, there are three reasons to invest long-term. First, avoiding taxes, which means more money for investing. Second, saving more money that an investor might spend on a broker. Third, avoiding the spread between the bidding and asking in order to have a high price of shares or stocks (Buffett , 2009).
Although the mean-variance model Markowitz introduced has an important role in modern portfolio theory, there is a criterion problem (Yu et al 2008, p.34-45). This study tested the historical performance of the various series, depending on forecast schemes for the mean-variance and skewness. In addition, the empirical results support the approach of using the neural network-based mean-variance-skewness model to select the optimal portfolio in order to help an investor choose the best portfolio. As a result, the approach can be used as an alternative method to evaluate and test the performance of many forecasting models (Yu et al 2008, p.34-45).
Volatility is a definition of risk that was given according to Modern Portfolio Theory (MPT) and the Efficient Market Hypothesis (EMH). Beyond this, investors are risk-adverse the portfolio theory ignored the risk-loving investors (Buffett, 2009). The next graph shows the kinds of risk clearly:
Source: www.Investopedia.com
One of the disadvantages of the portfolio theory is that it generates the efficient frontier and assumes that investors will accept a portfolio that has an efficient set. Therefore, the portfolio theory should be criticised in this case (Galagedera, 2007, pp.1-2). According to Cuth, Bertson & Nitsuch (2008, pp.154-155), finance as a basic definition is the study of asset prices, and these prices cannot be predicted because they are stochastic. Regarding this view, an alternative theory could be used instead of the classic one: Stochastic Portfolio Theory (SPT) (Science Direct). This theory was devised in 1995. Eventually, it appeared as written by Fernholz (1999) in the Journal of Mathematical Economic. SPT is a framework that analyses portfolio behaviour, especially in an equity market. Since 1999, SPT has been doing well for both practical and theoretical applications. Moreover, this theory has been a source of good strategies for investors in the equity market. While SPT has been used by investors in the equity market, the theory is valid for other financial assets, as long as the asset values are not negative (positive). In fact, there is a difference between SPT and MPT, in which the market structure is analysed under normative assumptions regarding market behaviour. It has been suggested that the difference between normative and descriptive theory separates the social sciences from the natural sciences. Therefore, SPT is a natural science (Karatzas and Femholz, 2009, pp 3-6).
The capital asset pricing model (CAPM):
The CAPM, as developed by William Sharpe (1964), Linter (1965), and Mossin (1966), is the most important development in asset pricing theory. Since that time, CAPM has been widely used in many applications, such as evaluating the performance of many portfolios and estimating the capital cost of companies (Fama, and French, 2004, p.24).
One of the interesting assumptions of the CAPM model is that in the CAPM, there is a linear trade-off between the rate of return and risk, which the Markowitz model does not present in its theory (Pilpearm, 2005, p.193). In fact, the CAPM is built on two essential relationships: the Security Market Line (SML) and Capital Market Line (CML). The former is a useful expression for an individual investor's return. In other words, SML shows a risk-free rate and the risk related to a portfolio or security. The SML is a consequence of the CAPM, and it suggests that a higher beta implies higher expected returns. Moreover, SML can be used to determine whether securities are priced or not (Review of CAPM 2007, p.4). The CML specifies the pricing of an efficient portfolio. In particular, the CML shows an individual investor's return, which estimates the returns on an efficient portfolio (Pilpearm, 2005, p.199).
The aim of the CAPM is for the market portfolio to be on the efficient set. This goal is achieved by following conditions such as a positively, linear, and sloped relationship between the expected returns and beta. In fact, the relationship between the beta and expected return is not necessary as a condition for the market portfolio to be efficient (Haugen, 2001, pp.251). These are critical points to the CAPM, which will be discussed later on in this survey by examining some studies in order to test the CAPM.
The CAPM uses beta (One Factor) in order to compare a portfolio with the whole market. On the other hand, in order to have a better r-squared fit, more factors should be added. The best-known model using three factors is Fama and French. The three-factor model was developed by Gene Fama and Ken French (Haugen, 2001, pp.251-257).
The Fama and French model mentions that two classes of stocks are outperforming the whole market. In other words, the three risk factors explain the average returns on a portfolio formed on 'size' and 'book-to-market' values (Velub and Zhou. 1999, p.236). This model explains an important part of the cross-sectional dispersion in the mean for the rates of return. However, this model has a problem, which is that the factors in Fama and French's model are not based on a theory (Fletcher and Kihanda.2005, pp 2996-2998).
Many studies have been performed in order to test CAPM and to find out whether the alternative model (the Fama and French model) is superior to CAPM or not. To be clear, the next part of this survey will show evidence in the form of empirical studies that support Fama and French's model against the CAPM. In particular, these studies will show the weaknesses of CAPM.
Firstly, the CAPM was tested in the Greek security market. The study examined the CAPM for the Greek stock market. This study was done by using weekly stock returns from 100 companies listed on the Athens stock exchange between January 1998 and December 2002. The tests examined the nonlinearity of the relationship between betas and rates of return. At the end, the results indicated evidence against CAPM by showing that the intercept has a value of around zero. The weakness of the CAPM hypothesis is in estimating the value of correlation between the slope and the intercept ( Michailias et al, 2006. pp.78-88).
Secondly, the CAPM and the Fama and French model were tested in the Turkish stock market. Within this study, the CAPM model and the three-factor model (1993, 1996) were investigated in the Istanbul Stock Exchange (ISE) between 2001 and 2006. The effectiveness of both the models has been analysed using cross-sectional regressions and time series. In addition, the Fama and French model has higher performance than the CAPM regarding pricing errors. Fama and French use a size and book-to-market ratio for 25 portfolios over a 30-year time period. Data within this study gives an optimal instrument for individual investors in Turkey for estimating returns of financial assets. Therefore, the values of the market equity have a critical role in analysing the asset pricing in Turkey. Consequently, Fama and French provided critical evidence for CAPM. In particular, it was observed that there was no relationship between the beta coefficient and the average rate of return (Gokgoz, 2007, pp.131-146).
Third, the Fama and French model was tested in India. This is an important study that supports the Fama and French model strongly. This paper empirically examined the three-factor model on the Indian equity market. In fact, India has approximately 8,000 listed companies. This study used 364 companies between June 1989 and March 1999 as a sample. In addition, the share price data consisted of month-end reports. The study was testing the one-factor linear pricing relationship for both CAPM and the Fama and French model. The results showed that the three-factor model's market, value and size were superior in terms of returns in the Indian equity market. The study also confirmed those results in the US stock market (Connor, and Sehgal, 2001, pp.2-9).
Fourth, another study was performed to test the Fama and French model. This study was performed by using 25 stock portfolios formed on book-to-market, with monthly data from July 1964 to December 1992. The observation was made from 341 companies. This study tested the standard zero version of the three-factor model using the following formula (Velu and Zhou 1999. Pp 219-238):
"Rit = αi +βi1 ƒm,t + βi2 ƒSMB,t + βi3 ƒHML,t + Eit,"
Where Rit is the returns on the portfolios and Æ’m, Æ’SMB and Æ’HML are returns on the three factors.
The pricing restriction is given as follows:
. ''αi = R (1- βi1),'' where: I = 1,.,., N
Where: HML= High Minus Low
SMB= Small Minus Big
The results of this study showed that the Fama and French model explained the average returns on the 25 portfolios (Velu and Zhou 1999. Pp 219-238).
In contrast, the CAPM has never been the subject of any successful empirical study, even though it has had some success in early empirical work when it accommodated an average return for the stock's beta (Fama and French, 2004, p.41-43).
On the other hand, the CAPM is still used widely. However, since the previous evidence supports the Fama and French model, this model can be used as a viable alternative to CAPM, even though it is not derived from theory.
Conclusion:
In summary, this paper has discussed the relevance of the CAPM and portfolio theory using a critical approach for an investor in the equity market. Portfolio theory and CAPM suggested that a market portfolio should be based on the efficient set. In addition, CAPM uses beta to measure the expected returns, which cannot be used alone. These results indicate that the Fama and French model, in combination with the other two factor sizes and book-to-market, is the best alternative model. Indeed, according to the evidence, CAPM is still widely used. This paper has included some analysis of this issue, but it is still an interesting area for future research to investigate.
