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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.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:56 pm ad1c9bdddf
    https://brainmass.com/business/finance/expected-return-standard-deviation-81508

    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

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:56 pm ad1c9bdddf>
    https://brainmass.com/business/finance/expected-return-standard-deviation-81508

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