CAPM

CAPMExtension of the Markowitz Portfolio Theory.

Developed by William Sharpe, John Lintner and Jan Mossin independently.

Markowitzs Portfolio Theory says:

Investors try to minimize risk by investing in an efficient set of portfolio.( they minimise the unsystematic risk by diversification)

However some amount of risk is non-diversifiable and still remaining-- this is the market risk or the systematic risk.

So how risky a security is depends on its systematic risk or its sensitivity to the movements of the market. This degree of sensitivity is measured by Beta.A rational investor will expect higher returns for higher risk. Here the risk we are dealing with is only systematic risk.

Hence the investor expects the return of the security to be + correlated with the systematic risk.

Higher the systematic risk of a security, he will expect higher returns from that security.

CAPM describes two things:

The relationship between risk(systematic risk) and the return.

and thereby also how the securities are priced.

CAPM starts from the Efficient Frontier.

In efficient frontier we are concerned about only the risky securities.

CAPM considers the risk-free securities as well ( Government securities)This is because CAPM states that an investor should be compensated for not only risk but also the time for which he stays invested.

Thus the return of a security has two components- the risk-free return which compensates for the time and

the compensation/ return the investor needs for taking on additional risk.

Risk free Return:Here we consider risk- free securities like government securities.They have zero risk and say gives a return Rf

Suppose the investor invests his funds only in risk-free secrities, that portfolio is represented by RfThis portfolio has no risk, only returns , so it is represented on the Y axis.The investor can change his proportion of funds in the risk-free securities and risky securities.

Eg of risk and return at points B and Rf :

Suppose at point maximum return portfolio B: Rp = 15%Std Dev of P= 8%

Consider a risk free asset with rate of return:Rf = 15%Std Dev = 0%

If an investor invests 40% of his funds in risk free assets and the remaining 60% in portfolio B, the risk and return of the portfoil can be calculated as:Rc = wRm + (1-w)RfCalculate std dev of the combined portfolio as well.

We see that the risk and return of the combined portfolio lies between those of B and Rf.

Similarly the risk and return of all possible combinations of the riskless + risky portfoili can be worked out and they will all lie on the line Rf to B.

This is called riskless lending.

B RfThe capital market lineThe capital market line is the set of portfolios got by mixing risky assets with risk- free assets. All efficient portfolios will lie along this capital market line. It is line which contains portfolios with borrowing and lending.

Expected Return = (Price of time) + (Price of risk)(Amount of risk)The capital market line is got by plotting a graph with expected returns on the y axis and the Portfolio risk or std deviation / variance along the x axis.The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk.

The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time.

The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk.

This is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf).

The capital market line is the basis of the theory capital market theory and explains the returns of only the efficient portfolios.

The inefficient portfolios all lie below the CM line.

In order to find their risk-return relationship, we have to find the security market line. This is got by ploting a graph with Expected return on the yaxis and the Beta along the x axis.The security market lineArmed with two inputs

- the market's overall expected return and

an asset's risk compared to the overall market

the CAPM predicts the asset's expected return and thus a discount rate to determine its price!

To work with the CAPM you have to understand three things. (1) the kinds of risk implicit in a financial asset (namely diversifiable and nondiversifiable risk); (2) an asset's risk compared to the overall market risk -- its so-called beta coefficient (); (3) the linear formula (or security market line) that relates return and -- this is the CAPM equation. Beta coefficient as a measure of volatilityComputing beta () coefficientInterpreting beta () coefficientPortfolio betas

The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf). The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken. Beta coefficientSince it is possible to create a portfolio that virtually eliminates all diversifiable risk, the only question is how much nondiversifiable risk does an asset add to a portfolio. What is a financial asset's systematic risk? Financial economists assume different assets carry different nondiversifiable risks -- depending on how their volatility compares to overall market volatility.

Assumptions of capmInvestors make their investment decisions on the basis of risk-returnsPurchase or sale of security can be undertaken in any divisible units.There are no transaction costs.There are no personal income taxes.The tax rates on the dividend income and capital gains are the same. So investor is indifferent to the from of returns.The investors can all lend/ borrow at the same risk free rate.All investors invest over same time horizons and they have identical expectations regarding expected returns, variances of expected returns and covariances of all pairs of securities.