In the given problem we need to compute the required performance using CAPM Model

Formula for Required Return Under CAPM Model is

Required Return = R_f + β(R_m -R_f) where R_f is Risk Free Interest β= Beta & R_m = Market Return

a) Given R_f = 7%,   β = 1.3 &  R_m = 8%

R = 7 +1.3( 8-7) = 7+1.3 = 8.3%

Requred Return = 8.3%

Treynor Ratio Return /Beta = 8.3/ 1.3 = 6.38

b) Given R_f = 12% ,  β = -0.2 &  R_m = 12%

R = 12 - 0.2 (12 -12) = 12

Required Return = 12%

Treynor Ratio = Return / beta = 12/(-0.2) = -60

Treynor ratio helps us in udnerstanding how the stock correlates with the index i..e Beta. Lower the Beta ,higher is Treynor ratio & higher the ratio better the stock. Its performance is better.compared to the one with a lower ratiop

From the above it can be observed that Stock b) has a higher return over stock a) . However Stock a) has a higer ratio compared to the Treynor ratio of Stock b) .Hence performace of stock a) in totality is preferred over stock b)