The Capital Asset Pricing Model (CAPM) is a model that indicates the relationship between the asset risk and expected return, which is used to price risky securities. The CAPM equation is:
E(Ri) =RF +βi [E(RM) - RF ]
There are several assumptions of the CAPM, which will cause deviation in the application process between the model and reality. It supposes that all investors are risk-averse and select the most efficient portfolio based merely on expected return and variance or standard deviation of asset returns. There are many other significant factors affecting returns of the portfolio, for example, the inflation rate. The variance of returns is assumed to be an adequate measurement of risk. It is certainly satisfied under the assumption of normally distributed returns. Nevertheless, in practice, other risk measures may play an important role in determining the degree of risk. Under the CAPM, asset returns are required to be a normal distribution model. In the real world, asset returns may be irregular and non-normally distributed.
Different investors have different investment ability, so their investment cost is also an aspect to be considered to determine their efficient portfolio. Moreover, the assumption of identical expectations about security returns and frictionless asset markets are impractical. People tend to have multiple portfolios for different goals instead of one portfolio. According to the CAPM, investors choose market portfolios just based on the function of risk-return profile, without other preferences. Not all investors will prefer high returns to low returns and select securities with low risks rather than high risks. Every investor is bound to have his own preference which is different from others, so we cannot simply equate them. Frictionless asset markets mean that there is no transaction cost and no tax or restrictions on trade. The situation won't happen in practice as well. It also assumes that all assets in the market are infinitely divisible so that they can be held or transacted. The market portfolio should include all investment opportunities with marketable value, such as collection of stamps, human capital and real estate. As such diverse investment portfolios are not observable, so people often use stock index as a proxy, leading to incorrect inferences about the validity of CAPM. The model assumes there are only two dates for investor to make the transactions so that they have no extra time to rebalance and consume portfolios over and over.
The Capital Asset Pricing Model (CAPM) thinks, unsystematic risk should not be considered by investors as it can be absolutely diversified away. However, as the returns on all securities are related to the market portfolio return, systematic risk cannot be eliminated by diversification.
(b)Describe Roll's critique of the early empirical tests of the CAPM.
Roll's critique is one of the most popular early empirical tests of the CAPM, concerning the validity of the CAPM equation,
E(Ri) = Rf + βi [ E(Rm) - Rf ]
In the equation, E(Ri) represents the expected return on security i, Rf indicates the risk-free return and βi means the systematic risk for security i. In CAPM, it uses expected returns on the true market portfolio to evaluate the investment portfolio.
Roll criticised the CAPM in two aspects. The first criticism is concluded from one of the properties of the efficient frontier. It is a mathematical fact that there is always a linear cross-sectional relationship between the systematic risk and the expected return to a security, if the beta is calculated in terms of an index portfolio which is on the efficient set. Moreover, the intercept is equal to Rz, the return on the minimum variance zero beta portfolio. Any mean-variance efficient portfolio satisfies the CAPM equation completely, so the efficiency of mean-variance is equivalent to the equation. The assumptions of model become unnecessary. The index portfolio used to estimate the betas may be on the efficient frontier of securities. However, it does not represent that the true market portfolio is efficient. It is proved that the portfolio returns and their betas have an approximately linear relationship, even if an inefficient sample results in a non-linear relationship between the betas of individual securities and their expected returns.
The CAPM uses the stock indices as a proxy for the true market portfolio. We may come to similar conclusions even though stocks are priced differently in respect of risk in the real world. In fact, the market portfolio is made up of every possible and single asset, including commodities, collectibles and anything with market value, such as jewellery, real estate and stamps. However, the returns on these investments are unobservable. Even though we observe a linear relationship between betas and returns based on the NYSE index, it is not shown that the global market portfolios can be efficient as predicted by the CAPM.
Since the validity of CAPM is related with the mean-variance efficiency of market portfolios, and the expected returns on the investment opportunities are not observable, so it is impossible to test the CAPM.
(c) How successfully does the Arbitrage Pricing Theory (APT) address the weaknesses of the CAPM that you have identified in parts (a) and (b)?
The APT is a general theory which states that asset pricing has an influence on the stock price. It believes that the expected return on financial assets can be seen as a linear function to express various macroeconomic factors or the market index, in which the sensitivity of each factor is represented by specific beta. The APT and CAPM are two significant theories on the asset pricing. The CAPM has many specific assumptions about the demand for investors' assets, for instance, they focus only on the mean and variance of return and hold merely traded assets. As the CAPM has a number of assumptions, in order to overcome its weakness, the APT uses factor model which assumes that security returns are driven by a number of factors, more than the expected return of market portfolio. The APT can be viewed as a simplified CAPM which removes the CAPM restrictions and improves the application of theory to be more flexible. Suppose the asset returns are influenced by a few factors
Rit =RF +β1,iF1t +β2,iF2t +…+βk,i Fkt +εit
where
βk,i represents the sensitivity of the return on security i with the influence of factor k
Fkt is the deviation of factor k between its expected value and realised value
εit is the error term or disturbance term of the regression
The common factors which affect the return on assets are multiple and observable, such as GDP, inflation, interest rate and so on, while the CAPM estimates expected returns based on one unobservable factor, the return on market portfolio. According to the CAPM, the systematic risk of assets is based solely on the expected return and variance of asset returns. Under the APT, there is no need to assume that utility functions of investors depend only on the expected returns and variance of return. The assumption of normal distribution of returns is also not required. The APT is satisfied as long as the arbitrageurs in the market make prices approach the equilibrium, while the CAPM is satisfied if all investors select efficient portfolios only.
