Question

           Year ​Risk-free    Return Market Return       XYZ Return   

2011   2​%                       5​%                                    9​%  

2012    1​%                     -36​%                                -49​%

a. What was​ XYZ's average historical​ return? ​XYZ's average historical return was ______ ​ (Round to one decimal​ place.) b. Compute the​ market's and​ XYZ's excess returns for each year. The​ market's excess return for 2011 was _______ ​ (Round to the nearest​ integer.) The​ market's excess return for 2012 was ______ ​ (Round to the nearest​ integer.) ​XYZ's excess return for 2011 was _______ ​ (Round to the nearest​ integer.) ​XYZ's excess return for 2012 was _______ ​ (Round to the nearest​ integer.) Estimate​ XYZ's beta. ​XYZ's beta is ______ (Round to two decimal​ places.) c. Estimate​ XYZ's historical alpha. ​XYZ's historical alpha was _______​ (Round to one decimal​ place.

Answer 1

a. XYZ’s return in 2011 was 9% while the return in 2012 was (-) 49%, so the average historical return should be; (+9 – 49)/ 2 = -20%

b. Market’s excess return in 2011 is 3% (Market Return – Risk-free Rate). Market’s excess return in 2012 is -37% (Market Return – Risk-free Rate).

XYZ’s excess return in 2011 is 7% (XYZ Return – Risk-free Rate). Market’s excess return in 2012 is -50% (Market Return – Risk-free Rate).

Beta = 7% - (-50%)/ 3% - (-37%) = 57%/ 40% = 1.425

c. Historical Alpha = (XYZ’s excess return in 2011 + XYZ’s excess return in 2012)/2 – {Beta *[ (Market’s excess return in 2011 + Market’s excess return in 2012)/2]}

Alpha = (7-50)/2 – 1.425(3-37)/2 = -21.5 +24.225 = 2.725