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After extensive research, you believe the probability distribution for next year's return on FB Inc is:...

After extensive research, you believe the probability distribution for next year's return on FB Inc is:

Return Probability
-1.5% 0.2
20.2% 0.3
-6.3% 0.3
25.8% 0.2


Compute the standard deviation of this return.  

Express your answer as a percentage to three decimal places (the percent sign is not essential). That is, if you compute a standard deviation of 0.12345, enter your answer as 12.345.

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Answer #1

Calculation of standard deviation given the probability and return:Probabilit Return 0.2 0.31 20.20% 0.3 0.21 25.80% 1.50% 6.30% Calculation of Expected Return: Expected return is given by following formula: 10 12 13 14 15 16 17 Expected return(r)- Expected return, r -Sum of product of probability and return in each state :02t-1.50%+0.3*20.20%+0.4*-6.30%+0.2( 25.8%) 9.03% :SUMPRODUCT(C4:C7,D4D7 19 Hence expected return is 9.03% 21 23 24 Variance and standard deviation of stocks can be calculated from following formula: ariance Can- 2P,Gi 26 27 Standard Deviation (O)- p,(r-r)2 29 31 Variance -Sum of product of probability and square of excces return in each state :0.2*((-1.50%-9.03%)^2)+0.3*((20.20%-9.03%)^2)+0.3*((-6.30%-9.03%)^2)+0.2*((25.80%-9.03%)^2) 32 1.86% SUMPRODUCT(C4:C7,(D4:D7-D20)^2) 35 36 37 38 39 Standard Deviation -Sqrt (Variance 13.65%-SQRT(D34) Hence Standard deviation is 13.65%

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