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There are some limitations make the CAPM cannot predict he returns of assets accurately. The assumptions of CAPM do not match with the reality
1.There are transaction costs¼Œinformation costs and taxes. There is asymmetric information in the reality and the market is inefficient and imperfect.
2. All the investor’s expectations are not the same, and they cannot be well diversified. If different investors (perhaps including foreign investors) face different marginal tax rates on income or capital gains, each investor’s after-tax risk-return frontier will be different. Investors may not agree with the expected returns of securities and would like to make positions on their risk-return frontiers, therefore the market portfolio based on the weighted averages of expectations of all investors’ is efficient. Some investors may be unable to sell short without restriction. These investors would operate on a constrained efficient frontier. In this case, the aggregate market index is not efficient
3. The interest rate of lending money is greater than the interest rate of borrowing.
4. The return rate which showed as a normal distribution is different in the reality. The idea that expected return and standard deviation of return are the only two properties of the distribution of returns that matter to investors is based on an assumption that returns are normally distributed. However, in practice returns may be non-normally distributed, and investors may have preferences (for characteristics such as skewness) different to those we have assumed.
5. CAPM only apply to capital assets, human resource may not be traded.
Different investors have different human capital, and they should take this into account in determining their efficient portfolios. A worker in a car factory perhaps should not include shares in car manufacturers in his portfolio. Therefore each investor’s perceived risk-return frontier is different
6. The beta coefficient represents the change of past which is sensitive to the past time period used, but what the investors care about is the price movements of the securities in the future. What’s more the beta may change over time.
7. In real world, risk-free asset and market portfolio do not exist, there are just theoretical concepts. The risk-free rate represents the interest on an investor’s money that he or she would expect from an absolutely risk-free investment over a specified period of time. However, the risk-free rate does not technically exist, even the safest investments with a very small amount of risk.
Although there are so many limitations, the CAPM is still useful to help investors to know the relationship between return and risk.
(b) Describe Roll’s critique of the early empirical tests of the CAPM.
Roll’s critique is has a empirical tests of the CAPM.
This equation state the relationship between the asset expected return E(Ri), the asset covariance Î²im and the market portfolio return Rm. The return is based on the weighted averages of the wealth-weighted total of all investor’s returns in the market.
There are two statements of Roll’s critique:
1. Mean-Variance Tautology:
The mean-variance efficient portfolio Rp meets the CAPM equation, which is equivalent to the CAPM equation. The model assumption is un necessary.
Roll demonstrates that, because the identification of the market portfolio, the CAPM cannot really be tested. We do not include the real estate and human capital in the market proxy, therefore Roll point out that the CAPM is useless since that we cannot text it. The relationship between E(R) and Î² will not hold.
2. The Market Portfolio is unobservable: The market portfolios in the reality contain each available asset. The returns on all possible investments opportunities are unobservable. The effectiveness of the CAPM is equivalent to the market base on all investments. Without looking out all the investments, it is impossible to test if the portfolio is mean-variance efficient. Therefore, it is not possible to test the CAPM.
Roll criticised the tests. The important point is that it is impossible to know a priori which index should be used as a market portfolio.
Any index that is efficient will provide a linear relationship between the systematic risk and the expected return to a security. If we do not know which index is the ‘true’ market portfolio, we can text the efficiency of the index chosen instead of the CAPM. And if there is no risk-free asset, the security market line is:
E (Ri) = (1 – bi)E (RZ) + biE (RM)
RZ represents the return on the minimum variance zero beta portfolio. A relationship of this kind can also be derived starting from any efficient portfolio.
M’ is some other efficient portfolio, and Z’ is the corresponding minimum variance zero beta portfolio (whose returns are uncorrelated with those of M’). Then we get:
E (Ri) = (1 – bi’)E (RZ’) + bi’E (RM’)
bi’ is security i’s beta computed with respect to M’. In Figure 3.5, this line is SML’
The average returns of each security are linear functions of bi and bi’. The average returns lie on the security market line. The only way in which they could fail to do so is if the ‘market’ portfolio that we started from did not form part of the efficient set.This argument implies that the supposed “empirical tests of the CAPM” were really just tests of the efficiency of the chosen market index. Assuming the chosen index was efficient, the tests were tautological. The observed average returns must have been linear functions of the measured betas. The valid way to test the CAPM empirically is to establish whether the ‘true’ market portfolio is efficient. But the ‘true’ market portfolio is impossible to observe, 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 weakness of CAPM:
1 .Need for assumption of normal distribution of returns
2. Need for assumption that utility functions of investors based solely on expected returns and variance of returns
3. Expected returns according to CAPM on one unobservable factor (return on market portfolio)
4. Need for test on the whole market portfolio (which is unobservable)
Arbitrage Pricing Theory
The asset pricing theory predicts the relationship between a portfolio’s returns and a single asset’s returns with a linear combination of independent variables.
APT is better than CAPM
The APT and capital asset pricing model (CAPM) are both important theories on capital pricing. But there is less limitation of the assumptions of APT, which permits for an explanatory model of asset returns. It supposes that every investor would make a unique portfolio with different betas, differing from the identical market portfolio. Sometimes the CAPM is a kind of the APT, at that time, the securities market line is a single-factor model of the asset pricing, and beta is changes in value of the market. The beta coefficients of the APT show the sensitivity of the asset to market element, therefore factor shocks make structural changes in the expected returns of assets, or in the case of stocks, in firms’ profitability. The capital asset pricing model comes from a maximization problem of every investor’s utility function and market equilibrium. APT rely on several factors while CAPM only the market portfolio. What’s more, APT is easier to apply to many other models.
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