CAPM

 

Characteristic CAPM and the Characteristic  Line

 

T he he Characteristic Line 

Total risk of any asset a sset can be assessed by measuring variability variability of its returns



Total risk can be divided into two parts²  diversifiablee risk (unsystematic risk) and nondiversifiabl diversifiablee risk (systematic risk) diversifiabl



The characteristic line is used to measure statistically statisticall y the undiversifi undiversifiable able risk and diversifiablee risk of individual assets and diversifiabl  portfolios

 

 Characteristic 

line for the ith asset is: r  = a + b r  + e OR 



r i,t = bir m,t + ai + ei,t



Take Variance of both sides of Equation E quation



VAR (r i,t) = VAR(bir m,t ) +VAR(ai) + VAR(ei,t) VAR(bir m,t ) = VAR (r i,t) - VAR VAR(ei,t) OR  VAR(ei,t) = VAR(r i,t) - VAR VAR(bir m,t )

 

i,t

i

i m,t

i,t

 

Beta Coefficients  An 

index of risk

Measures the volatility of a stock (or  portfolio) relative to the market

 

Beta Coefficients Comb Combine ine  The

variability of the asset¶s return

 The

variability of the market return

 The

correlation between  ±the  ± the stoc stock's k's return and and

 ±the  ± the marke markett retu return rn

 

Beta Coefficients  Beta

coefficients are the slope of 

the regression line relating  ±the  ± the retur return n on the market (the independent variable) to  ±the  ± the retur return n on the stock (the dependent variable)

 

Beta Coefficients

 

I nterpretation nterpretation

of the

Numerical Nume rical Value of Beta Beta  Beta

= 1.0 Stock's return has

same volatility as the market return  Beta

> 1.0 Stock's return is more

volatile than the market return

 

I nterpretation nterpretation

of the

Numerical Nume rical Value of Beta Beta

 

I nterpretation nterpretation

of the Numer Numerical  ical 

Value of Beta  Beta

< 1.0 Stock's return is less

volatile than the market return

 

nterpretation I nterpretation Value of Beta

of the Numer Numerical  ical 

 

H 

igh Beta Stocks



More systematic market risk



May be appropriate for high-risk tolerant (aggressive) investors

 

L

ow Beta Stocks

 Less 

systematic market risk

May be appropriate for low-risk tolerant (defensive) investors

 

I 

ndividual Stock Betas



May change over time

 Tendency

to move toward 1.0, the market beta

 

P 

ortfolio Betas

 Weighted

average of the individual

asset's betas 

May be more stable than individual stock betas

 

 How Characteristic Line leads t o CAPM? 



The characteristic regression line of an asset explains the asset¶s systematic variability of returns in terms of market forces that affect all assets simultaneously simultaneously The portion of total risk not explained by characteristic line is called unsystematic unsystematic risk 

 



Assets with high degrees systematic

risk musttobe pricedinvestors to yield high returns in order induce to accept high degrees of risk that are undivesifiable in the market  CAPM illustrates positive relationship  between systematic risk and return on an asset

 

Capital Asset Pricing M odel  (CAPM)  For 

 

a very well-diversified portfolio, beta is the correct measure of a security¶s risk. All investments investments and portfolios of  investments investm ents must lie along a straight-line in the return-beta space Required return on any asset is a linear  function of the systematic risk of that asset E(r i) = r f + [E(r m) ± r f ] v Fi

 

T he he

Capital Asset P ricing  ricing  P 

Model (CA M)  The

CAPM has

 ±A  ± A macro component ex explains plains risk and return in a portfolio context  ±A  ± A micro component explains explains individual stock returns  ± The micro component is also used to value stocks

 

Beta Coefficients and  T 

L

he Security Market  ine

 The

return on a stock depends on

 ± the ris  ±the risk k free rate (r ff )   ±the  ± the retur return n on the market (r m)  ±the  ± the st stock's ock's be beta ta  ±the  ± the retu return rn on a stock: k= r f + (r m - r f )beta

 

Beta Coefficients and  T 

L

he Security Market  ine

 The

figure relating systematic risk

(beta) and the return on a stock

 

Beta Coefficients and  T he he

Security Market Line

 

 CAPM

can be used to price any asset

 provided that asset we know the systematic risk of  

In equilibrium, every asset must be priced so that its risk-adjusted required rate of  return falls exactly on the straight line



If an investment were to lie above or below that straight line, then an opportunity for  riskless arbitrage would exist.

 

 Examples

of  CAPM  CAPM 

Stocks

Expected Return

Beta

A B

16% 19%

1.2 1.3

C

13%

0.75

E(rm) = 18% rf = 14% Which of these stocks is correctly priced?

 

 Example  Given

of  CAPM  CAPM 

the following security market line

E(r i) = 0.07 + 0.09 FI What must be the returns for two stocks assuming assum ing their betas are 1.2 and 0.9?