Question

5) Assume a fictitious world where there are four stocks:

General Electric (GE)

CitiGroup (C)

British Petroleum (BP)

FaceBook (FB)

The market is in equilibrium where CAPM assumptions hold (e.g. homogeneous expectations, efficient markets, zero transaction costs, etc.)

Express the equilibrium condition for this universe of stocks in terms of each stock’s return contribution and risk contribution. For notation purposes, you can use the symbols r_mkt & σ_mkt to represent the market’s return & risk and r_f to represent the risk-free rate. (Note: Students can either type or neatly hand-write the relationship and upload a picture or file containing the expression.)

Answer 1

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.

Assumptions

Basic assumptions of the CAPM model are as follows.

1. Markets are ideal—no transaction fees, taxes, inflation, or short selling restrictions.
2. All investors are averse to risk.
3. Markets are highly efficient. All investors have equal access to all available information.
4. All investors can borrow and lend unlimited amounts under a risk-free rate.
5. Beta coefficient is the only measure of risk.
6. All assets are absolutely liquid and infinitely divided.
7. The amount of available assets is fixed during a given period of time.
8. Markets are in equilibrium. All investors are price takers, not price makers.
9. 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

The risk premium of a given security (RP_i) can be assessed as follows:

RP_i) = β_i × (E(R_M) - R_F)

CAPM and market equilibrium

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.