CAPM & Arbirage

8/10/2019 CAPM & Arbirage

1/15


2/15

Introduction and definition

A model that describes the relationship between risk and expected return and that is

used in the pricing of risky securities behind that investors need to be compensated

in two ways: time value of money and risk

CAPM is an framework for determining the equilibrium expected return for risky

assets.

Relationship between expected return and systematic risk of individual assets or

securities or portfolios


3/15


The model was introduced by Jack Treynor, William Sharpe, John Lintner

and Jan Mossin independently, building on the earlier work of Harry Markowitz

on diversification and modern portfolio theory.

Harry Markowitz is the father of the modern portfolio theory.

William F Sharpe developed the CAPM. He emphasized that risk factor in

portfolio theory is a combination of two risk , systematic and unsystematic risk.


4/15


Under CAPM,

This implies a liner relationship between the assets expected return and

its beta.

Investors will be compensated only for that risk which they cannot

diversify. This is the market related (systematic) risk


5/15

Assumptions

1. Market is perfect

2. Individuals are risk averse.

3. Individuals seek maximizing the expected return

4. Homogeneous expectations

5. Borrow or Lend freely at risk less rate of interest.

6. Quantity of risky securities in market is given.

7. No transaction cost.


6/15


7/15

Total Risk = Systematic Risk + Unsystematic Risk

Total

Risk

Unsystematic risk

Systematic risk

STD

DEVO

FPORTFOLIO

RETURN

NUMBER OF SECURITIES IN THE PORTFOLIO


8/15

Systematic risk or Un diversifiable risk

It cannot be eliminated through diversification

It can be measured in relation to the risk of a diversifiedportfolio or the market.

According to CAPM, the Non-Diversifiable risk of aninvestment or security or asset is assessed in terms of thebeta co-efficient


9/15

Unsystematic or Diversifiable Risk

It cannot be eliminated through diversification

It can be measured in relation to the risk of a diversifiedportfolio or the market.

According to CAPM, the Non-Diversifiable risk of aninvestment or security or asset is assessed in terms of thebeta co-efficient


10/15

CAPM formula

E (ri) = Rf+ i (E(Rm) Rf)

E(ri) = return required on financial asset i

Rf= risk-free rate of return

i= beta value for financial asset i

E(rm) = average return on the capital market


11/15

BETA Also known as "beta coefficient."

Beta measures non-diversifiable risk, or volatility of asecurity or a portfolio in comparison to the market asa whole

It shows how the price of a security responds to marketforces.

In effect, the more responsive the price of a security isto changes in the market, the higher will be its beta.


12/15

BETA Investors will find beta helpful in assessing

systematic risk and understanding the impact

market movements can have on the returnexpected from a share of stock.

CAPM uses beta to viewed both as a mathematicalequation and graphical, as the security market line

(SML). Betas can be positive or negative however, all betas

are positive and most betas lie between 0.4 to 1.9.


13/15

BETA VALUE OF BETA

=1

1

For example, if a stock's beta is 1.2, it's theoretically 20% more

volatile than the market


14/15

The theory limitations CAPM has the following limitations:

It is based on unrealistic assumptions.

It is difficult to test the validity of CAPM. Betas do not remain stable over time.


15/15

CAPM & Arbirage

Documents

Transcript of CAPM & Arbirage