CAPM & Arbirage

 

Introduction and definition 

A model 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

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

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Relationship between expected return and systematic risk of individual assets or securities or portfolios

 

Introduction and definition 

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

and Jan Mossin independently, independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. 

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Harry Markowitz Markowitz is the father of the modern portfolio portfolio theory theory..

William F Sharpe developed the CAPM. He emphasized that risk factor in  portfolio theory is a combination combination of two risk , systematic systematic and uns unsystematic ystematic risk .

 

Introduction and definition 

Under CAPM, 

This implies a liner relationship between the asset’s expected return and its beta.

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Investors will be compensated only for that risk which they cannot diversify.. This is the market related (systematic) risk diversify

 

 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 i n market is giv given. en.

7.

No transaction cost.

 

Elements of CAPM Capital Market Line – risk return relationship for efficient portfolios. Security Market Line – Graphic depiction (representation) of CAPM and market price of risk in capital capita l markets.

1. 2. a) b)

Systematic Risk Unsystematic Risk

3. 4.

Risk Return Relationship Risk Free Rate

5. 6.

Risk Premium on market portfolios Beta -  - Measure the risk of an individual asset value to market portfolio.  Assets. a) b)

Defensive Assets  Aggressivee Assets.  Aggressiv

 

Total Risk = Systematic Risk + Unsystematic Risk 

   N    R    U    T    E    R      O    I    L    O    F    T    R    O    P    F    O    V    E    D    D    T    S

Unsystematic risk Total Risk Systematic risk

NUMBER OF SECURITIES IN THE PORTFOLIO

 

  Systematic risk or Un diversifiable risk  

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It cannot be eliminated through diversification diversificat ion It can be measured measured in relation relat ion to the risk of a diversif diversified ied portfolio market.  Ac  Accor cording dingortothe CAPM, the the Non-Div Non-Diversifiable ersifiable risk of an investment or security or asset is assessed in terms of the beta co-efficient

 

Unsystematic or Diversifiable Risk  

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It cannot be eliminated through diversification diversificat ion It can be measured measured in relation relat ion to the risk of a diversif diversified ied portfolio market.  Ac  Accor cording dingortothe CAPM, the the Non-Div Non-Diversifiable ersifiable risk of an investment or security or asset is assessed in terms of the beta co-efficient

 

CAPM formula 

   + βi (E(R m) – R f f)  E (ri) = R f f + 

E(r i) = return required on financial asset i

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R f f  =  = risk-free rate of return

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βi = beta value for financial asset i

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E(r m) = average return on the capital market

 

   BETA A  BET Also known as "beta coefficient coefficient." ."   

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Beta measures non-diversifiable risk, or volatility of a security or a portfolio in comparison to the market as a whole  It shows how the price of a security responds to market forces. In effect, the t he more responsive the price of a security is to changes in the market, the higher will be its b beta. eta.

 

 BET  BETA A  

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Investors will find beta helpful in assessing systematic risk and understanding the impact

market movements can hav havee on the return expected from a share of stock. CAPM uses beta beta to viewed both as a mathematical mathematical equati equation (SML).on and graphical, as the security market line Betas can be positive or negative however, all betas are positive and most most betas lie between 0.4 to 1.9.

 

   BETA A  BET VALUE OF BETA 

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 β= 1

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 β <1

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  β>1 

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

 

The theory limitations  

CAPM has the following limitations: 

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It is based on unrealistic assumptions. It is difficult diff icult to test the validity of CAPM. CAPM. Betas do not remain stable sta ble over over time.