**Capital Asset Pricing Model:-** Before going into detail of capital asset pricing model (CAPM), let’s discuss some of the basic concepts of **Risk and Return** theory that are helpful in understanding CAPM.

**Risk**

Risk is the combination of dangers and opportunities, or the volatility or spread, or uncertainty of the future outcomes over investment is called risk. Risk is measured in terms of standard deviation. A risk of a project is composed of two types.

**Diversifiable Risk**

It is the **Risk** that can be reduced through diversification in of investments in uncorrelated projects. The unfavorable random events of one projects are equalize through the favorable events of other project.

**Market Risk:**

It is that part of total risk which cannot be reduced through diversification. It is related to the unfavorable socio-political and economic events that are taking place globally and that affect almost all the companies of the industry in a country like inflation, market interest rates, war etc.

**Return:**

If there is a risk than definitely there must be some return against that risk, which is a logical thing to understand. An investor only takes additional risk, if certain additional return is offered against that risk.

**Beta:**

Beta is the building block of CAPM theory. In case of a stock market, the inclination of a stock to accelerate with the market is called beta.

**Capital Asset Pricing Model**

Sharpe and Markowitz are professors who had develop of capital asset pricing model, which is considered to an important theory in the risk & return portion. Every rational investor wants to maximize the return on his investment at the lowest possible risk. The investor diversifies his investments over a number of uncorrelated projects in order to eliminate his company specific (diversifiable) risk. So, the remaining portion of the risk in the portfolio of the investor is only market risk that cannot be reduced by diversification. In case of portfolio of stocks, there is an index that reflects the **Weighted Average** of all the transactions on that stock market. The index is a measure of the relative strength of the stock exchange. In reality there is no stock exchange that is fully diversified.

In CAPM Model, it is assumed that the beta of the market is equal to +1. There are betas of different stocks of a company that are published by rating agencies and stocks brokerages. These individual stock betas are compared with the market beta of the stock exchange.

**Example:**

Suppose in the New York stock exchange there is a trading of stocks of different companies. If the beta of a share A is equal to +1.0, then this means that the share is exactly as risky as the market is. In other words, if the market index, that is 100, goes up to 5% after one year, then the stock A’s beta also goes up to 5% based on the historical data.

If beta of a stock B is +2, then the stock B is double risky as beta of the New York stock exchange.

If a stock has a beta of -1, then this stock is as much risky as the market of the stock exchange, But in the opposite direction. In other words if the stock exchange goes up by 5% in a year then the stock goes down by 5%.

If a stock of beta E is +0.5, then this stock is half as risky as the market of the stock exchange.

**Formula of the Beta of a Stock:**

In a stock exchange there is some risk of the market that is indicated through the movements in the index of stock exchange. There is also a stock X whose price also changes from one year to another. The movement in the value of a stock relative to the market index is ascertained from one year to another.

**Capital Asset Pricing Model Graph**

The above graph shows the beta of the stock X in a stock exchange of index 100. The value of the stock X is shown as expected return (r_{A}) on y-axis where as the market price is also represented as expected return (r_{M}), but on the x-axis. The risk free rate of return is treated as the starting point to measure the movement in the value of both the individual stock X and the market price of stock exchange (Index). There are points on the graph that shows the relative movement of stock X each year. A best line of linear regression is made to fit in the graph in order to that passes through these points. If a slope is drawn on the two points of the regression line, then this slope gives the relative risk of the stock X to the overall stock market which is called the beta coefficient.

The formula of beta coefficient of stock X is given below.

Beta = Slope = ΔY/ ΔX

= %r_{A }/ %r_{M}

= (r_{A}^{*} – r_{RF}) / (r_{A}^{*} – r_{RF})

In the light of above formula, the coefficient beta is defined as the difference between the expected rate of return of Stock X and the risk-free rate of return whole divided by the difference of market rate of return and risk-free rate of return.

**Portfolio Beta of CAPM:**

**01- **For the calculation of stock beta, there are two ways which are as follow.

First method is similar to the above least square method of stock beta. On the basis of historical data the movements in the portfolio returns and market returns are shown on the graph on x-axis and y-axis respectively. After fitting a regression line through the points, the slope of the line gives the portfolio beta.

**02-** In the second method the published stock betas of the individual stocks in a portfolio are averaged on the weighted average basis to give the portfolio beta of all the stocks. Numerically

β(P) = X_{A} β_{A} + X_{B} β_{B} + X_{C} β_{C} + … β