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.
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 risky assets and a risk-free asset. The two most important assumptions of the equilibrium pricing model are: i) investors can borrow or lend money at the same rate (i.e. the risk-free rate) and ii) investors have the same opinion about the prospects of various investments (i.e. homogeneous expectations). Under these assumptions, Sharpe (1964) shows that, in equilibrium, the relationship between the expected return and the standard deviation of return on efficient combination of risky assets should be linear. Another important implication of the outlined equilibrium conditions is that the expected return on an asset is related to part of the asset’s risk which cannot be diversified away (i.e. systematic risk).
Almost simultaneously, Lintner (1965), and Mossin (1966) came up with similar results which are later on acknowledged as the Capital Asset Pricing Model (CAPM). The CAPM is developed on the basis of following assumptions :
There is no transaction cost in the market;
All assets in the market are infinitely divisible;
Investors do not suffer from personal income tax;
An individual investor cannot affect the price of an asset by his buying or selling action, and investors are all price takers;