# Expected Return and Standard Deviation

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.

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## 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.

FOLLOW UP FROM OTA:

Please indicate the source which says that the answer should be 0.0016 for 1981. Your reasoning and the answer which I have provided are correct. Please also check the data . The answer provided is correct for the data given

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