Capital Asset Pricing Model (CAPM) is a theory which is used to price an asset in the context of its risk. CAPM is a model that illustrates the relationship between systematic risk and expected rate of return of a portfolio of financial assets (for example shares and bonds). CAPM can be used to price an investment, to evaluate the risks and the rate of return of this investment.

The CAPM formula is the risk free rate plus the beta of the investment, multiplied by the different of the expected return of the market and the risk free rate.

$$ER = R_{f} + \beta(ER_{m} - R_{f})$$

Where ER = expected return, Rf = risk-free rate, B = beta of the investment, and ERm = the expected return of a market.

In this formula ERM – Rf is a risk premium.  The risk premium is the risk premium of the market portfolio, i.e. the surplus of the expected rate of return from the market over the risk-free rate.

• when β = 1 (market portfolio), then R = Rm
• when β = 0 (risk-free instruments), then R = Rf
• when β> 1 (aggressive portfolio), then R> Rm
• when 0 <β <1 (defensive portfolio), then Rf <R <Rm
• when β <0, then R <Rf.

Note: the beta of the investment is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. It’s calculated using regression analysis, and you can think of beta as the tendency of a security’s returns to respond to swings in the market.

• Systematic risk is a type of market risk that is non-diversifiable.
• Unsystematic risk is a risk that can be diversified away if the number of stocks in the investor’s portfolio increase.

### Capital Asset Pricing Model Assumptions

CAPM is based on the following assumptions:

• All investors can choose between individual portfolios based on two characteristics: expected rate of return and beta (a measure of risk).
• All investors have the same investment horizon, and their expectations of return rates on individual securities are homogeneous.
• All investors are rational and aim to maximize economic utilities.
• The capital market:
• Has no transaction costs,
• There is no dividend, interest income and capital gains tax,
• Has no restrictions on short sales,
• Has excellent divisibility and liquidity of financial instruments,
• All instruments can be easily bought and sold on the market

Under these conditions, CAPM shows that the cost of equity capital is determined only by beta. Beta signifies whether the investment is more or less volatile (volatility is a measure of security stability) than the market or benchmark

### Example of Capital Asset Pricing Model

An investor wants to determine the expected return on the shares of ABC Company. At the moment, the yield on a 10-year treasury bond is 2.5%. According to forecasts, a return on the market index of 10% per year can be expected. In the past, changes in ABC’s prices were more rapid than changes in the index value.: the value of β was estimated using the CAPM model, and its value is 1.5.

• Risk-free rate – 2.5%
• β – 1.5
• The rate of return from the market – 10%
$$ER = 2.5\% + 1.5 \times (10\% - 2.5\%) = 13.75\%$$

### Security Market Line

Security Market Line is a line that represents CAPM formula. The x-axis represents beta and the y-axis represents the expected return. The market risk premium of an investment is determined by where it is plotted on the chart in relation to the SML.

### Types of portfolios in CAPM

• Correctly-priced portfolios – these are portfolios on the SML line, which means that the expected rate of return is equal to the rate of return on the SML.
• Undervalued portfolio – a portfolio above the SML, the expected rate of return is higher than the rate of return from other portfolios with the same beta. It is an attractive portfolio for investors, which is why they will try to buy it. This will increase the price, which will cause a drop in the rate of return. As a result, the portfolio will reach the position on the SML.
• Overvalued portfolio – a portfolio that is below the SML, which means that the expected rate of return is lower than the rate of return that can be achieved by a portfolio with the same beta. This portfolio is not attractive; therefore, investors will try to sell it. As a result, the price will decrease which will cause an increase in the rate of return. As a result, the portfolio will reach the position on the SML.