# Capital Asset Pricing Model (CAPM)

Capital Asset Pricing Model (CAPM), is a theory that explains how asset prices are
formed in the market place. The CAPM is an extension of portfolio theory(Markowitz)
which was developed by William Sharpe, John Lintner and Jan Mossin to examine what
would be the relationship between risk and return in the capital market if investors
behaved in conformity with the prescription of portfolio theory.

The CAPM has implications for:

- Risk-return relationship for an efficient portfolio
- Risk-return relationship for an individual asset or security
- Identification of under and over-valued assets traded in the market
- Pricing of assets not yet traded in the market
- Effect of leverage on cost of equity
- Capital budgeting decisions and cost of capital and
- Risk of the firm through diversification of project portfolio.

**Assumptions of CAPM:**

- Individuals are risk-averse.
- Individuals seek to maximize the expected utility of their portfolios over a single period planning horizon.
- Individuals have expectations that are homogeneous. This essentially means that they have similar subjective estimates of the means, variances and covariances among returns.
- Investors can borrow and lend freely at the riskless rate of interest.
- The market is perfect. The assumption is that there are no taxes, no transaction costs, securities are completely divisible and the market is also competitive.
- The quantity of risky securities in the market is given.

**Elements of the CAPM:**

There are 2 elements of the CAPM. They are:

- Capital Market Line and
- Security Market Line.

**Capital Market Line:**

It depicts the risk-return relationship for efficient portfolios. It serves two functions. Firstly, it depicts the risk-return relationship for efficient portfolios available to investors. Secondly, it shows that the appropriate measure of risk for an efficient portfolio is the standard deviation of return on the portfolio.**Security Market Line:**

It is a graphic representation of CAPM and describes the market price of risk in capital market. Risk averse investors seek risk premium to invest in risky assets. The risk is variability in return and the total risk consists of both systematic risk and unsystematic risk. Generally, the investor can avoid unsystematic risk by diversifying his investment in portfolio. But systematic risk is unavoidable. The market compensates for systematic risk only, according to the capital market theory. The level of systematic risk in an asset is measured by the beta coefficient, represented by the symbol β. The CAPM links beta to the level of required return.

CAPM model: Ke = R
f + β (Km - Rf)

**Where:**

Ke | = | Expected return or cost of equity |

Rf | = | Risk-free rate |

β | = | Beta or Beta coefficient |

Km | = | Expected return on market portfolio (or) equity market required return |

Security Market Line (SML)

**Example 1:**

Given: Required rate of return on a portfolio = 17%; Beta = 1.1; Risk-free rate
= 5%. What is the expected rate of return on the market portfolio?

Ke = R f + β (Km - Rf)

17% = 5% + 1.1 (Km – 5%)

Km = 0.159 or 15.9% or 16%.

Ke = R f + β (Km - Rf)

17% = 5% + 1.1 (Km – 5%)

Km = 0.159 or 15.9% or 16%.

**Example 2:**

Given, the risk-free rate is 8%; Expected return on market portfolio = 14%; Beta
= 1.25. Investors believe that stock will provide an expected return of 17%. What
is the expected return as per CAPM and the "alpha" of the stock?

(The excess return over the expected return according to the CAPM is termed as "alpha").

Expected return as per CAPM | = | 0.08 + 1.25 (0.14 - 0.08) |

=> | 0.155 or 15.5%. | |

Alpha of the stock = 17.00% -15.55% | => | 1.5% |

(The excess return over the expected return according to the CAPM is termed as "alpha").

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