What is the standard deviation of the returns on a stock given the following information? State of Economy

What is the standard deviation of the returns on a stock given the following information? State of Economy Probability of State of Economy Rate of Return if State Occurs Boom .28 .175 Normal .67 .128 Recession .05 .026

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  1. 3.28%

    Explanation:

    Calculation for the standard deviation of the returns on a stock

    The first step is to find the Expected rate of return using this formula

    Expected Return = E[R] = p1*R1 + p2*R2 + p3*R3

    Let plug in the formula

    Expected Return= 0.28*0.175 + 0.67*0.128 + 0.05*0.026

    Expected Return = 0.049 + 0.08576 + 0.0013

    Expected Return= 0.13606

    Second step is to find the Variance using this formula

    Variance = σ2 = p1*(R1-E[R])2 + p2*(R2-E[R])2 + p3*(R3-E[R])2

    Let plug in the formula

    Variance = σ2 = 0.28*(0.175-0.13606)2 + 0.67*(0.128-0.13606)2 + 0.05*(0.026-0.13606)2

    Variance = 0.000424570608 + 0.0000435256119999998 + 0.00060566018

    Variance= 0.0010737564

    Last step is to find Standard Deviation of the returns on a stock

    Note that the Standard Deviation is square-root of variance

    Using this formula

    Standard Deviation =√Variance

    Let plug in the formula

    Standard Deviation = σ =√ (0.0010737564)

    Standard Deviation= 0.032768222411*100

    Standard Deviation= 3.2768222411%

    Standard Deviation =3.28% Approximately

    Therefore the standard deviation of the returns on a stock will be 3.28%

  2. month 1 start amount =$3287.90 interest=(3287.90x0.0145/12)3.97 total to pay=$3291.81 paid =$1200 balance =$2,091.87

    month 2 starting amount= $2,091.87 interest =$25.28 total to pay =$2117.15 paid =$1200 balance $917.15

    month 3 starting amount =$917.15 interest =$11.08 total to pay =$928.23 paid =$928.23 balance =$0 total to pay 1200+1200+928.23 = $3328.23 it will take 3 months to pay a total of $3328.23

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