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

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

##
This Post Has 3 Comments

### Leave a Reply

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

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%

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

The answer is b i think