Market beta and required return

EXERCISE 01

Correlation with the market is 0.6; asset volatility is 20.000%, market volatility 16.000%, risk-free return 4.000% and market risk premium 8.000%.

A.Calculate beta and the CAPM required return.

A.

\beta_i=\rho_{iM}\frac{\sigma_i}{\sigma_M},\quad E[R_i]=r_f+\beta_i(E[R_M]-r_f)

\beta_i=0.6\frac{0.2}{0.16}\approx 0.75

E[R_i]=0.04+(0.75)(0.08)\approx 0.1

Beta = 0.75000; required return = 10.000%.

Market beta and required return

EXERCISE 02

A.What does beta measure? Is it proportional to the correlation with market returns?

A.

\beta_i=\frac{Cov(R_i,R_M)}{Var(R_M)}=\rho_{iM}\frac{\sigma_i}{\sigma_M}

Beta measures the sensitivity of a security’s return to the market return, or its contribution to systematic risk. It equals correlation multiplied by the ratio of security volatility to market volatility. It is proportional to correlation only with those volatilities held fixed; a high-volatility stock need not have a high beta.