Capital Asset Pricing Model

Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) identifies the link between systemic risk and projected asset return, notably inventories. The goal of the CAPM is to determine whether an investment is fairly valued by comparing risk and expected return.

Systematic and Unsystematic Risk

Prior to understanding the Capital Asset Pricing Model (CAPM), we need to understand the nature of risks. The diversification of portfolio reduces the risk of individual securities. If the number of securities are very large, risk totally vanishes but the risk represented by covariance still remains. So there are two parts of risks: systematic risk which is non-diversifiable and unsystematic risk which is diversifiable.

 systematic risk and unsystematic risk

Systematic risks are economy-wide uncertainty like change in interest rate policy, inflation rates and government taxes. Diversification of portfolio can’t reduce the systematic risk as it moves together with the change in market. This is also known as market risk. On the other hand, unsystematic risks are caused by the unique uncertainties of individual securities and these can be reduced through diversification.

Sensitivity Coefficient (β)

Hence, the risk of an individual security is the systematic risk or the market risk because the unsystematic risk can be reduced by the method of diversification. The return of risky security can be correlated with the volatility of security’s return with relation to the return of the market. This volatility is measured as beta (β) which corresponds to the return of an individual security when the return on market portfolio swings. The shown in chart below is known as the Characteristics Line and it’s slope is called beta (β).

Characteristics Line

Security Market Line (SML)

The Security Market Line (SML) represents the expected return of an individual asset with its risk. The Y intercept represents the risk free interest rate, x axis represents the systematic risk and the slope of SML gives the market risk premium.

Security Market Line (SML) with normalized risk (β):

capital asset pricing model capm

To calculate the expected return using CAPM, we use the following equation:

​E(Rj)​ = Rf ​+ ​(E(Rm) ​− Rf​)βj


E(Rj)​ = expected return of investment

Rf​=risk-free rate

βj ​= beta of the investment

E(Rm)​−Rf​ = market risk premium​

The aim of the Capital Asset Pricing Model (CAPM) formula is to assess the fair value of a stock in comparison with the anticipated value of its risk and its time value of money. Imagine an investor today is planning to pay a 3% dividend stock worth $100 per share. The stock has a beta of 1.3, so it is riskier than a market portfolio. Assume that the risk-free rate is 3% and this investor anticipates that the market will increase by 8% annually. In the format of CAPM, the expected return on the stock is 9.5%:

​9.5%=3%+1.3× (8%−3%)​

In order to reduce the expected stock dividends and the capital appreciation over the expected holding time, the intended return of CAPM formula is used. The CAPM formula states that if the discounted value for future cash flows is $100, the stock is fairly valued as a result of the risk.

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