2.1 The Capital Asset Pricing Model
The CAPM is one of the most influential theories in finance, and it is widely used in applications (e.g. estimating the cost of the capital for firms) . Meanwhile, the CAPM is probably the most tested model. The beauty of the CAPM comes from its parsimony and elegance in establishing a linear relationship between risk and return. The CAPM indicates that if an investor wants to obtain a higher expected rate of return, he has to bear additional risk. It is derived on the basis of the mean-variance approach, which is first proposed by Markowitz (1959). The mean-variance approach claims that mean is a proxy of the asset’s return and variance stands for the risk which the asset bears. If two assets have the same return, the investor will choose to invest in the asset with lower degree of risk. If two assets have the same degree of risk, the investor will choose to buy the asset with higher return.
Sharpe (1964) is the first one who applies the mean-variance approach to construct a market equilibrium theory about asset prices under conditions of risk. First, Sharpe defines investor’s utility function with only two parameters – the expected value and standard deviation.
U=f(E_w,σ_w)
where E_w is the expected future wealth and σ_w indicates the predicted standard deviation of the possible divergence of actual future wealth from the expected future wealth E_w. Thus, for risk-averse investors, dU⁄(dE_w )>0 and dU⁄(dσ_w )<0. In the presence of two risky assets, the investment opportunity curve is determined by assets’ expected rate of return, risk and the correlation between different assets. The same analysis also applies to determining the utility of an investor who invests in the combination of ri...
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Capital Asset Pricing Model (CAPM) is an ex ante concept, which is built on the portfolio theory established by Markowitz (Bhatnagar and Ramlogan 2012). It enhances the understanding of elements of asset prices, specifically the linear relationship between risk and expected return (Perold 2004). The direct correlation between risk and return is well defined by the security market line (SML), where market risk of an asset is associated with the return and risk of the market along with the risk free rate to estimate expected return on an asset (Watson and Head 1998 cited in Laubscher 2002).
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The Modern portfolio theory {MPT}, "proposes how rational investors will use diversification to optimize their portfolios, and how an asset should be priced given its risk relative to the market as a whole. The basic concepts of the theory are the efficient frontier, Capital Asset Pricing Model and beta coefficient, the Capital Market Line and the Securities Market Line. MPT models the return of an asset as a random variable and a portfolio as a weighted combination of assets; the return of a portfolio is thus also a random variable and consequently has an expected value and a variance.