The valuation of assets in the financial market is no doubt a challenging task as it is closely correlated with risks and uncertainties embodied in the assets which provide the possibility that the investment outcomes would differ from the expected value (Grundy and Malkiel, 1995). In other words, the valuation of assets is actually linked to the qualification of risk-return trade-off. Up until the introduction of Capital Asset Pricing Model (CAPM) in 1964, the estimation of risk was largely based on the historical performances of individual security rather than a precise geometric or mathematic relationship. Therefore, this essay would contribute a lot to the discussions on CAPM and the Arbitrage Pricing Model as well as their comparison.
One fundamental theory behind CAPM and other asset pricing models is the portfolio selection theory which is contributable to Markowitz (1959), Tobin (1959 and 1966). Markowitz points out that under mean-variance criterion, the optimal portfolio should be the set of securities that provide the preferable expected rate of return with the minimum volatility. In addition to this theory, James Tobin proposed that every investor has his own individual preference for liquidity which can be achieved by the combination of the efficient risky portfolio presented by Markowitz and a set of risk-free investment. At the same time, the implement of expected utility hypothesis by John von Neumann and Oskar Morgenstern and the concept of risk adverse have remarkable impact of risk pricing models as well.
Capital Asset Pricing Model
Enlighted by the previous foudations by Markowitz and Tobin, a general equilibrium capital asset pricing model was developed by Sharp(1964), Linster(1965) and Mossin independantly. With a series of assumptions (attached in appendix), the CAPM model claims a linear relationship between return of any asset and how it co-varies with the market portfolio. Under the assumptions listed above,
βi = =
The linearity of the SML depicts the idea that a higher risk would be induced with a higher expected rate of return. As it is shown in the graph, under the condition of market equilibrium, the market clears when all investors hold the same optimal proportion of assets. The β coefficient represents the correlation coefficient between the expected return of individual portfolio and the market portfolio.
First of all, the mean-variance framework is worthwhile being doubted in the first place as it assumes the rates of return are normally distributed which is unachievable in reality. In addition, under this criterion, the utility function is considered quadratic which, as well, does not seem plausible as investors hold identical sense of adverse towards deviations. At the same time, the single measure of systematic risk, β, requires assets to be linearly dependent as all returns in the market are assumed to be correlated and it clearly ignores these assets which are not sensitive to the market behaviour (Krause, 2001).
Some other critical points rely on the restrictiveness of the assumptions under CAPM. There is no doubt that short sale is strictly limited under the regulation in USA. After 2007, it is only permitted when the price is higher than the national best bid (www.sec.gov[->0], 2012). More importantly, as transaction costs and taxes would affect the trade-off between risks and expected returns ie encouraging possible swaps, the absence of such costs may invalid the outcomes of CAPM to some extent. In the meantime, it is argued that capital market line is nothing but a “fuzzy amalgamation” of investors as the theory ignores the heterogeneity of risk preferences (Krause, 2001).
Another significantly fundamental critique from Richard Roll (1977) argues that it is...