Problem 11-4 Expected Returns (LO1, CFA1) Security Returns if State Occurs State

Question

Problem 11-4 Expected Returns (LO1, CFA1) Security Returns if State Occurs State of Economy Bust Boom Probability of State of Economy 0.40 0.60 Roll -15% Ross 15% Calculate the expected returns for Roll and Ross by filling in the following table: (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Calculate the product using the decimal value of the probability and the percentage value of the return. Input all your answers as a percent rounded to 2 decimal places.) Answer is complete but not entirely correct. Roll Ross Probability Return if State Occurs Return if State Occurs State of Product Product State of Economy Bust Boom Economy 0.40 0.60 (15) 22 |96 % (0.06 % 0, % 7.20 % 15 % 5% E(R)-s 0, % E(R) 9.00 %

Explanation / Answer

11-4:

Return = probability of state occurrence x return of the state

Roll return(bust)= 0.4 x -15= -6%

Roll return (boom) = 0.6 x 22= 13.2%

Expected roll return = boom return + bust return

Expected roll return =13.2-6=7.2%

Ross return (bust) = 0.4 x 15 = 6%

Ross return (boom) = 0.6 x 5= 3%

Expected return =6+3=9%

11-6:

Using the same formula as above:

Roll bust return = 0.2*-13=-2.6%

Ross bust return = 0.2*17=3.4%

Portfolio bust return = Roll weight* Roll return+Ross weight * Ross return = 0.6*-2.6+0.4*3.4 = -0.2%

Roll boom return =0.8*24=19.2%

Ross boom return = 0.8*6=4.8%

Portfolio boom return = 0.6*19.2+0.4*4.8= 13.44%

Expected return of portfolio = boom return + bust return =13.44-0.2

=13.24%

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