(1) The Capital Asset Pricing Model (CAPM) is one tool investors and financial advisers use to try to determine how investments will perform and to try to price and assess them accordingly. However, like all mathematical models that seek to predict events in the real world, it suffers from some methodological limitations.
Many of the limitations to the CAPM lie in its methodological assumptions. Under these assumptions, “the only difference between investors is the amount of wealth they must invest and the personal trade-off they make between portfolio mean and portfolio variance”(Levy and Post). However, it is not possible in the real world. There are many other factors influence returns of the portfolio, for example, the inflation rate.
Different investors make different choices. According to Levy and Post, one of these assumptions requires that all investors have access to the same information. Their investment cost is an aspect to determine their efficient portfolio. In additional, the assumption of the expectations regarding asset returns and frictionless asset markets are unreasonable. All investors choose their portfolio according to the mean-variance criterion, without other preferences (Levy and Post). The fact is that not all investors will prefer high returns to low returns and choose securities with low risks rather than high risks. It cannot simply equate them because every investor is bound to have his own preference.
As the returns on securities are related to the market portfolio return, the CAPM cannot be applied in a diversified environment.
（2）Roll’s critique is a famous analysis of early empirical tests of the Capital Asset Pricing Model by Richard Roll.
E(Ri) = Rf + βi [ E(Rm) – Rf ]
In the equation, E(Ri) means the expected return on security I, Rf represents the risk-free return, βi states the asset covariance and Rm indicates the market portfolio return. The expected return on the true market is used to assess the investment portfolio.
Roll’s critique argues two statements regarding the market portfolio. Firstly, the market portfolio is unobservable. Every security’s observed average return is βi ‘s linear functions. According to Levy and Post, “the market portfolio will almost always be ex-post mean-variance-inefficient, even if the market portfolio is ex-ante efficient’. It is a mathematical fact that observed average return would be located on a measured security market line. The only way to avoid this situation is that the market portfolio is not in efficient set at the start. However, it does not represent that the empirical tests of the...