. The risk-free rate is 3.0 percent and the expected return on the market is 9 percent. Stock A has a beta of 1.20. For a given year, stock A returned 12.5 percent while the market returned 9.75 percent. The systematic portion of stock A’s unexpected return was percent and the unsystematic portion was percent.

Systematic portion of unexpected return = 0.9%

Unsystematic portion = 1.4%

Explanation:

Expected Return from Stock A :

= +

wherein,

=  Risk free rate

= Expected market return

B= Beta , a measure of sensitivity.

= 3 + 1.2 (9 - 3) =  10.2 %

Actual Return = 12.5%

Excess of actual return over expected return = 12.5 - 10.2 = 2.3%

Actual market return = 9.75%

Excess of actual market return over expected market return

= 9.75 % - 9 % = 0.75%

Excess market systematic return = 0.75%  × B

                                                         = 0.75 × 1.2 = 0.9%

Hence, systematic portion of unexpected return = 0.9%

Thus, unexpected portion = 2.3% (excess security return) - 0.9% (excess market return)

= 1.4 %

they work in some type of way