**CAPITAL ASSET PRICING MODEL**

The CAPM developed by William F Sharpe, John Linter, and Jan Mossin establishes a linear relationship between the required rate of return of a security and its beta. Beta, as we know is the non-diversifiable risk in a portfolio. A portfolio’s standard deviation is a good indicator of its risk. Thus if adding a stock to a portfolio increases its standard deviation, the stock adds to the risk of the portfolio. This risk is the un-diversified risk that can not be eliminated. Beta measures the relative risk associated with any individual portfolio as measured in relation to the risk of the market portfolio.

Beta = Non-diversifiable risk of asset or portfolio/risk of the market portfolio

Thus Beta is a measure of the non-diversifiable or systematic risk of an asset relative to that of the market portfolio. A beta of 1 indicates an asset of average risk. If beta is more than 1, then the stock is riskier than the market. On the other hand, if the beta is less than one, the market is riskier.

Recall that portfolio theory implied that each investor faced an efficient frontier. In general, the efficient frontier will differ among investors because of differences in expectations. When we introduce riskless borrowing and lending there are some significant changes involved. Lending is best thought of as an investment in riskless security. This security might be a savings account, Treasury bills, or even high-grade commercial paper. Borrowing can be thought of as the use of margin. Borrowing and lending options transform the efficient frontier into a straight line.

**CAPM assumptions**

The CAPM is often criticized as unrealistic because of the assumptions on which the model is based, so it is important to be aware of these assumptions and the reasons why they are criticized. The assumptions are as follows:

**1. Diversified portfolios**

This assumption means that investors will only require a return for the systematic risk of their portfolios since unsystematic risk has been diversified and can be ignored.

**2. Single-period transaction horizon**

A standardized holding period is assumed by the CAPM to make the returns on different securities comparable. A return over six months, for example, cannot be compared to a return over 12 months. A holding period of one year is usually used.

**3. Investors can borrow and lend at the risk-free rate of return**

This is an assumption made by portfolio theory, from which the CAPM was developed, and provides a minimum level of return required by investors. The risk-free rate of return corresponds to the intersection of the security market line (SML) and the y-axis. The SML is a graphical representation of the CAPM formula.

**4. Perfect capital market**

This assumption means that all securities are valued correctly and that their returns will plot on to the SML. A perfect capital market requires the following: that there are no taxes or transaction costs; that perfect information is freely available to all investors who, as a result, have the same expectations; that all investors are risk-averse, rational, and desire to maximize their own utility; and that there are a large number of buyers and sellers in the market.