CAPM and the Characteristic Line

The Characteristic Line  Total risk of any asset can be assessed by measuring variability of its returns  Total risk can be divided into two parts— diversifiable risk (unsystematic risk) and non- diversifiable risk (systematic risk)  The characteristic line is used to measure statistically the undiversifiable risk and diversifiable risk of individual assets and portfolios

 Characteristic line for the ith asset is:  r i,t = a i + b i r m,t + e i,t OR  r i,t = b i r m,t + a i + e i,t  Take Variance of both sides of Equation  VAR (r i,t ) = VAR(b i r m,t ) +VAR(a i ) + VAR(e i,t )  VAR(b i r m,t ) = VAR (r i,t ) - VAR(e i,t ) OR  VAR(e i,t ) = VAR(r i,t ) - VAR(b i r m,t )

Beta Coefficients  An index of risk  Measures the volatility of a stock (or portfolio) relative to the market

Beta Coefficients Combine  The variability of the asset’s return  The variability of the market return  The correlation between –the stock's return and –the market return

Beta Coefficients  Beta coefficients are the slope of the regression line relating –the return on the market (the independent variable) to –the return on the stock (the dependent variable)

Beta Coefficients

Interpretation of the Numerical Value of 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

Interpretation of the Numerical Value of Beta

 Beta < 1.0 Stock's return is less volatile than the market return

Interpretation of the Numerical Value of Beta

High Beta Stocks  More systematic market risk  May be appropriate for high-risk tolerant (aggressive) investors

Low Beta Stocks  Less systematic market risk  May be appropriate for low-risk tolerant (defensive) investors

Individual Stock Betas  May change over time  Tendency to move toward 1.0, the market beta

Portfolio Betas  Weighted average of the individual asset's betas  May be more stable than individual stock betas

How Characteristic Line leads to 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  The portion of total risk not explained by characteristic line is called unsystematic risk

 Assets with high degrees systematic risk must be priced to yield high returns in order to induce investors 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 Model (CAPM)  For a very well-diversified portfolio, beta is the correct measure of a security’s risk.  All investments and portfolios of investments 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 ]   i

The Capital Asset Pricing Model (CAPM)  The CAPM has –A macro component explains risk and return in a portfolio context –A micro component explains individual stock returns –The micro component is also used to value stocks

Beta Coefficients and The Security Market Line  The return on a stock depends on –the risk free rate (r f ) –the return on the market (r m ) –the stock's beta –the return on a stock: k= r f + (r m - r f )beta

Beta Coefficients and The Security Market Line  The figure relating systematic risk (beta) and the return on a stock

Beta Coefficients and The Security Market Line

 CAPM can be used to price any asset provided we know the systematic risk of that asset  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 StocksExpected ReturnBeta A16%1.2 B19%1.3 C13%0.75 E(rm) = 18%rf = 14% Which of these stocks is correctly priced?

Example of CAPM  Given the following security market line E(r i ) =  I What must be the returns for two stocks assuming their betas are 1.2 and 0.9?