Systematic risk

And The

CAPM

Topics Covered



  • Measuring Systematic Risk: Beta
  • The Security Market Line

Measuring Systematic Risk


  • There are two components of risk:
    • Systematic
    • Non-Systematic
  • Systematic risk is measured by a stock's beta
  • Beta ($\beta$) is estimated over a period of time through a regression

The (estimated) beta coefficient is the slope of the line of best fit

Security Market Line

  • Under CAPM, diversifiable risk is completely eliminated
  • Only the systematic risk determines the required rate of return
  • A stock's risk premium is proportional to the market risk premium
  • Beta measures this proportion:

$\dfrac{E(R_i)-R_F}{\beta_i} = \dfrac{E(R_m)-R_F}{\beta_m}$



$\dfrac{E(R_i)-R_F}{\beta_i} = \dfrac{E(R_m)-R_F}{1}$

Security Market Line


Rearranging our equation gives us
the Security Market Line (SML):


$E(R_i) = R_F + \beta_i \times [E(R_m)-R_F]$

Example 1

Suppose a stock had a $\beta$ of $0.74$. The expected market return is $12\%$ and the risk free rate is $4\%$. What is the expected return on the stock?



$E(R_i) = 0.04 + 0.75 \times (0.12-0.04)$$ = 0.10$

Example 2

Suppose the expected return on the market were $11\%$, the risk free $4\%$, and the stock's expected return $15\%$. What is the stock's beta coefficient?



$0.15 = 0.04 + \beta_i \times (0.11-0.04)$

$\beta_i=1.57$

Summary



  • Beta
  • The Security Market Line