By Yuriy Smirnov Ph.D.

The capital asset pricing model (CAPM) is the equation that describes the relationship between the expected return of a given security and systematic risk as measured by its beta coefficient. Besides risk the model considers the effect of risk-free interest rates and expected market return.

Basic assumptions of the CAPM model are as follows.

- Markets are ideal—no transaction fees, taxes, inflation, or short selling restrictions.
- All investors are averse to risk.
- Markets are highly efficient. All investors have equal access to all available information.
- All investors can borrow and lend unlimited amounts under a risk-free rate.
- Beta coefficient is the only measure of risk.
- All assets are absolutely liquid and infinitely divided.
- The amount of available assets is fixed during a given period of time.
- Markets are in equilibrium. All investors are price takers, not price makers.
- Return of all available assets is subject to normal distribution function.

The CAPM model allows you to assess the expected return of a given security using the following formula:

E(R_{i}) = R_{F} + β_{i} × (E(R_{M}) - R_{F})

where E(R_{i}) is an expected return of a security, R_{F} is a risk-free rate, β_{i} is the beta coefficient of a security, and E(R_{M}) is an expected market return.

Market risk premium (RP_{M}) can be calculated as follows.

RP_{M}) = E(R_{M}) - R_{F}

RP_{i}) = β_{i} × (E(R_{M}) - R_{F})

Let’s assume an investor is thinking of buying one of three stocks: Stock A with a beta of 0.85, Stock B with a beta of 1.25, and Stock C with a beta of 1.65. If the risk-free rate is 4.50% and the expected market return is 12.35%, the expected return of each security can be assessed under CAPM.

E(R_{A}) = 4.50 + 0.85 × (12.35 - 4.50) = 11.17%

E(R_{B}) = 4.50 + 0.85 × (12.35 - 4.50) = 14.31%

E(R_{C}) = 4.50 + 0.85 × (12.35 - 4.50) = 17.45%

Thus, a relationship exists between risk and the expected return of a security. So, the higher the beta, the higher the expected return and vice versa.

The capital asset pricing model is a widely used concept, but some assumptions can’t be met in real market conditions.

- Real markets have transaction costs; moreover, they can differ significantly for market participants, e.g., institutional investors have lower transaction costs than other investors.
- Several taxes are present on invested capital, e.g., capital gains tax and income tax. Investors try to maximize their economic utility by considering the effect of taxation. Such behavior reduces the efficiency of investments and affects the pricing of assets.
- Real markets are not always efficient, so investors do not have homogeneous expectations.
- No asset is free of risk. Even T-bills are exposed to inflation risk, liquidity risk, and reinvestment risk.
- Investors have different abilities to borrow at a risk-free rate. For institutional investors, the interest rate is lower than it is for private investors.
- The beta coefficient isn’t the only risk measurement in CAPM because it only reflects the ratio between a given security’s return volatility and market return volatility.
- Empirical studies have shown that the return of a security doesn’t follow any normal distribution function.

Stock market equilibrium is one CAPM model basic assumption, which means that the expected rate of return is equal to the required rate of return, and the current price of a given security is equal to its intrinsic value. If the stock market is in equilibrium, no securities are undervalued or overvalued. The actual stock market, however, is not in equilibrium, so both undervalued and overvalued stocks are present, and their expected return is different from the CAPM assessment.

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