Capital Asset Pricing Model Homework Help

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Capital Asset Pricing Model

Capital Asset Pricing Model, in finance it is famously known as CAPM. It is defined as

A method of projecting the cost of equity capital of a company. The cost of capital is equal to the return of a risk-free investment made plus a premium that reflects the risk of the company’s equity. Mathematically it is denoted as:

                                  R_a = R_f +β_a (R_m – R_f)

Where the symbol denotes:

                        R_a  = Risk rate of Asset

                        R_F   = Risk-free rate

                        β_{a =} Beta of security

                        R_m = Expected market return

CAPM is basically a model which provides a framework which determines the required rate of return on an asset and indicates the relationship between the risk and return of the asset, which helps in valuing the asset.

The risk involved in the security of an individual’s portfolio is the systematic risk, which is measured as the covariance of an individual risk security with that of the market portfolio.

The Security Market Line (SML) represents the CAPM, which displays the relationship between the asset risk and the required rate of return. The CAPM is based on a number of following assumptions which are:

• Market Efficiency: It implies that the share prices reflect all the available information.
• Risk aversion and mean-variance optimization: Investors are risk averse, they prefer the highest expected returns from the given level of risk.
• Risk-free rate: All the investors lend and borrow at a risk-free rate of interest. They form the portfolios from publicly traded securities like shares and bonds.

It is a very useful tool for determining a reasonable expected return of risk offered by an asset. Individual securities are being plotted on the SML graph. If the return for the security's expected Return vs Risk is plotted above the SML, it is undervalued as the investor has expected a higher return. And if it is plotted below the SML, then it is overvalued then the investor has expected a lower return for the security.

In end, CAPM is based on the idea that the investors demand additional expected return or Risk premium is they are asked to accept the additional risk. CAPM considers only systematic risk and assumes that unsystematic risk can be eliminated by diversification.