Calculate the standard deviations for Roll and Ross by filling in the following

Question

Calculate the standard deviations for Roll and Ross by filling in the following table (verify your answer using returns expressed in percentages as well as decimals): (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your Standard deviation answers to 2 decimal places and other answers to 4 decimal places. Omit the "%" sign in your response.)

Security Returns If State Occurs   State of
  Economy Probability of
  State of Economy         Roll        Ross   Bust .30 –12 % 16 %   Boom .70 23 6

Explanation / Answer

ROLL ROSS
(1) State of Economy (2) Probability of State of Economy (3) Return if State Occurs (4) Product (2) × (3) (5) Return if State Occurs (6) Product (2) × (5)

BUST 0.3 -12% -0.036 16% 0.048
BOOM 0.7 23% 0.161 6% 0.042
E(R) 0.125 E(R) 0.09
Expected return of Ross is 9%
State of    Probability of    Return Deviation     Squared Return      Product (2) × (4)
Economy   State of Economy(2)   from Expected Return Deviation(4)
  Roll
    Bust 0.3 -.245     0.6 0.18
    Boom 0.7 .105     0.11 0.077
   
2 = 0.257
   
  Ross
    Bust 0.3 0.07 0.0049 0.0015
    Boom 0.7 -0.03 0.0009 0.0006
   
2 = 0.0021
   
Taking square roots, the standard deviations are50.6952 % and 4.5826%

Standard Deviations
  Roll 50.6952%
  Ross 4.5826%

(1) State of Economy (2) Probability of State of Economy (3) Return if State Occurs (4) Product (2) × (3) (5) Return if State Occurs (6) Product (2) × (5)

BUST 0.3 -12% -0.036 16% 0.048
BOOM 0.7 23% 0.161 6% 0.042
E(R) 0.125 E(R) 0.09
Expected return of Ross is 9%
State of    Probability of    Return Deviation     Squared Return      Product (2) × (4)
Economy   State of Economy(2)   from Expected Return Deviation(4)
  Roll
    Bust 0.3 -.245     0.6 0.18
    Boom 0.7 .105     0.11 0.077
   
2 = 0.257
   
  Ross
    Bust 0.3 0.07 0.0049 0.0015
    Boom 0.7 -0.03 0.0009 0.0006
   
2 = 0.0021
   
Taking square roots, the standard deviations are50.6952 % and 4.5826%

Standard Deviations
  Roll 50.6952%
  Ross 4.5826%

ROLL ROSS (1) State of Economy (2) Probability of State of Economy (3) Return if State Occurs (4) Product (2) × (3) (5) Return if State Occurs (6) Product (2) × (5) BUST 0.3 -12% -0.036 16% 0.048 BOOM 0.7 23% 0.161 6% 0.042 E(R) 0.125 E(R) 0.09 Expected return of Ross is 9% State of    Probability of    Return Deviation     Squared Return      Product (2) × (4) Economy   State of Economy(2)   from Expected Return Deviation(4)   Roll     Bust 0.3 -.245     0.6 0.18     Boom 0.7 .105     0.11 0.077     2 = 0.257       Ross     Bust 0.3 0.07 0.0049 0.0015     Boom 0.7 -0.03 0.0009 0.0006     2 = 0.0021     Taking square roots, the standard deviations are50.6952 % and 4.5826% Standard Deviations   Roll 50.6952%   Ross 4.5826%

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