Calculating Returns and Standard Deviations Based on the following information,
ID: 2650252 • Letter: C
Question
Calculating Returns and Standard Deviations
Based on the following information, calculate the expected return and standard deviation for the two stocks. For this question, you may use the spreadsheet template on the text support website: http://highered.mcgraw-hill.com/sites/0078034752/student_view0/index.html.
State of Probability of Rate of Return if State Occurs
Economy State of Economy Stock A Stock B
----------------------------------------------------------------------------------------------------
Recession .15 .02 -.30
Normal .55 .10 .18
Boom .30 .15 .31
Explanation / Answer
Expected Return=( Probability Of Recession* Return on Stock)+( Probability Of Normal* Return on Stock)+
( Probability Of Boom* Return on Stock)
Standard Deviation=
Square Root of ? Probability Of Recession( Return on Stock-Expected Return) +Probability Of Normal( Return on Stock-Expected Return) +Probability Of Boom( Return on Stock- Expected Return)
Calculation of Expected return and Standard deviation for Stock A:-
Expected Return=(0.15*0.12)+(0.55*0.10)+(0.30+0.15) = 0.103 or 10.3%
Standard Deviation=
? 0.15(0.02-0.103)2 + 0.55(0.10-0.103)2 +0.3 (0.02-0.103)2
= ? 0.15(-0.083)2 + 0.55(-0.003)2 + 0.3(0.047)2
= 0.0412 or 4.12%
Calculation of Expected return and Standard deviation for Stock B:-
Expected Return=(0.15* -0.3)+(0.55*0.18)+(0.30+0.31) = 0.147 or 14.7%
Standard Deviation=
? 0.15(-0.3-0.147)2 + 0.55(0.18-0.147)2 +0.3(0.31-0.147)2
= ? 0.15(-0.447)2 + 0.55(0.033)2 + 0.3(0.163)2
= 0.1963 or 19.63%
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