Capital Assets Pricing Model was developed by William F. Sharpe. In portfolio theory he emphasised that the risk factor is a combination of two types of risks

**(1)** Systematic Risk

**(2)** Unsystematic Risk.

Systematic risk is non-diversifiable in nature while non-systematic risk is diversifiable. In other words, systematic risk cannot be controlled while unsystematic risk can be controlled. The systematic risk attached to each security is the same irrespective of any number of securities in the portfolio. But we know that the total risk of a portfolio is reduced with the increase in the number of securities. This happens due to the reduction in the unsystematic risk distributed over the number of securities in the portfolio.

Capital Assets Pricing Model describes the relationship between the risk and expected (required) return. In this model the expected (required) return of a security is the risk free rate plus a risk premium based on the systematic risk of a security. There is no premium based on the unsystematic risk as it can mostly be eliminated by diversification. Therefore, it will have no effect on the return of individual securities. There will be a premium only for the systematic risk which cannot be eliminated by diversification.

According to the CAPM model: Expected Return = Risk Free Rate + Risk Premium

Risk Premium = (Market Return - Risk Free Rate) X Beta

**Ri = Rf + (Rm - Rf) Bi**Ri = Expected return of the security-i

Rf = Risk free rate

Rm = Market return

Bi = Beta of security-i

## What is Beta (B)?

Beta denotes the systematic risk. Beta of a security measures the sensitivity of the returns of of that security with respect to the returns of the market poerfolio or the index. The market portfolio or the index has a beta of 1. Given the betas of individual securities, calculating the beta of the portfolio is very simple. It is nothing but the weighted average of the betas of the individual securities. A risk free security has a beta of 0 as it carries no systematic risk.

When the beta of a security is 1, its systematic risk is equal to the aggregate market risk. When the beta of a security is less than 1, its systematic risk is less than the aggregate market risk. When the beta of a security is more than 1, its systematic risk is more than the aggregate market risk.

**Negative Beta:** Theoritically the beta of a security can be negative. As the risk free securities have a beta of 0, a security with negative beta will give less returns than the risk free securities. Practically securities with negative beta do not exist as there are no inverstos for them.

**Security Market Line:** The security market line describes the expected returns of all the securities and portfolios in the economy. In equilibrium, every security / portfolio lies on the security market line. There is a perfect balance between the risk and return of a security / portfolio in equilibrium. Any given point on the security market line represents a security / portfolio having only two dimentions i.e., the expected rate of return and the beta.

There is a linear relationship between the expected rate of return and beta i.e., expected rate of return increases linearly with increase in risk, as measured by beta. The security market line expresses the basic theme of the CAPM i.e., the required rate of return on a security is equal to the risk free rate plus risk premium.

## Assumptions of the Capital Assets Pricing Model

**(1)** Capital Assets Pricing Model assumes that capital markets are efficient. It means that security prices reflect all the available information and the individual investors are not able to affect the prices. Therefore, there is no scope for any abnormal gains or losses in the efficient market.

**(2)** Investors are risk averse in nature. They evaluate the return of a security in terms of expected rate of return. Risk is evaluated in terms of Standard deviation or variance. Investors want the highest expected rate of return for any given level of risk.

**(3)** All investors have the same expectations about returns and risks of securities over a given period or time frame.

**(4)** Capital Assets Pricing Model is time specific in nature i.e., all investment decisions are based on a single given time period.

**(5)** Risk free rate of return is certain or fixed over a single given time period and all investors can lend and borrow at this rate.

**(6)** Market portfolio or the index contains only the systematic risk. SENSEX, NIFTY or a similar portfolio should be used as a proxy.

## Implications of the Capital Assets Pricing Model

**(1)** Investors will always combine a risk free security with a mark portfolio of risky securities. Investment in risk free securities will be in proportion to their market values.

**(2)** Investors will be compensated only for that risk which cannot be diversified. This is the systematic risk which is denoted by beta.

**(3)** Investors can expect returns from their investments according to the associated risk. This shows a linear relationship between the expected rate of return of a security and its beta.

## Limitations of the Capital Assets Pricing Model

**(1)** Capital Assets Pricing Model is based on the expected rate of return. Future returns cannot be known but we have access to the past returns. Practically historical data regarding past returns is significant in forecasting the expected rate of return.

**(2)** The systematic risk denoted by beta is unstable. It varies from period to period. Hence it may not reflect the true risk involved or may not be a good estimate of the future risk.

**(3)** Capital Assets Pricing Model takes into account only the systematic risk while the total risk consists of unsystematic risk as well. Both the risks have an impact over returns and hence both should be taken into account.

(4) Capital Assets Pricing Model may not hold good in case the investors do not diversify their portfolios in a planned manner.