State of Probability of Economy State of Economy Roll Ross Bust .30 -10 % 14 % B
ID: 2745569 • Letter: S
Question
State of Probability of Economy State of Economy Roll Ross Bust .30 -10 % 14 % Boom .70 21 5 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 amounts should be indicated by a minus sign. Round your Economy and Standard deviation answers to 2 decimal and other answers to 4 decimal places. Omit the "%" sign in your response.) State of Economy Probability of State of Economy Return Deviation from Expected Return Squared Return Deviation Product Roll Bust Boom 2 = Ross Bust Boom 2 = Standard deviations Roll % Ross %
Explanation / Answer
Here first we need to compute expected return
ER = sum of P x R
ER (Roll) = 0.30 x -0.10 + 0.70 x 0.21
= 0.117
ER( Ross) = 0.30 x 0.14 + 0.70 x 0.15
= 0.147
Roll
State
Probability
R
R- ER
P x (R-ER)^2
Bust
0.3
-0.1
-0.217
0.0141267
Boom
0.7
0.21
0.093
0.0060543
0.020181
Standard deviation =( sum of P x (R-ER)^2)^0.50
= (0.020181)^0.50
= 14.21%
Ross
State
Probability
R
R- ER
P x (R-ER)^2
Bust
0.3
0.14
-0.007
1.47E-05
Boom
0.7
0.15
0.003
6.3E-06
2.1000000000E-05
Standard deviation =( sum of P x (R-ER)^2)^0.50
= (2.1000000000E-05)^0.50
= 0.46%
State
Probability
R
R- ER
P x (R-ER)^2
Bust
0.3
-0.1
-0.217
0.0141267
Boom
0.7
0.21
0.093
0.0060543
0.020181
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