Answer:
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%
