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# Expected Return and Standard Deviation

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Dates return on x
1981 2.00%
1982 3.00%
1983 6.00%
1984 9.00%
1985 14.00%

Calculate the expected return and standard deviation.

## SOLUTION This solution is FREE courtesy of BrainMass!

There are two ways of calculating standard deviation. I have shown both of them:

Method 1:
Variance and standard deviation

X= X 2 =
1981 0.02 0.0004
1982 0.03 0.0009
1983 0.06 0.0036
1984 0.09 0.0081
1985 0.14 0.0196
Total= 0.34 0.0326
n=no of observations= 5
Mean=Expected return= 0.068 =0.34/5 or 6.80%

variance={summation of X 2 - n(Mean) 2 }/(n-1)= 0.00237 =(0.0326-5*0.068^2)/(5-1)
standard deviation =square root of Variance= 0.0487 =square root of 0.00237 or 4.87%

Method 2:
Variance and standard deviation

X= (X-Expected Value) 2 =
1981 0.02 0.002304
1982 0.03 0.001444
1983 0.06 0.000064
1984 0.09 0.000484
1985 0.14 0.005184
Total= 0.34 0.00948
n=no of observations= 5
Mean=Expected return= 0.068 =0.34/5 or 6.80%

variance={summation of (X -Mean) 2 }/(n-1)= 0.00237 =(0.00948)/(5-1)
standard deviation =square root of Variance= 0.0487 =square root of 0.00237 or 4.87%

COMMENT FROM STUDENT:
I'm being told the answer should be .0016 for 1981. Your coming up with the answer I came up with.