Question

The following equally likely outcomes have been estimated for the returns on Portfolio P and Portfolio Q: Scenario Portfolio P Portfolio Q 1 4.0% 11.0% 2 7.0% -7.0% 3 -3.0% 15.0% 4 9.0% -9.0% Calculate the standard deviations of the rate of return for the two portfolios. Round your answer to the nearest tenth of a percent.

Stdev(P): 6.13%; Stdev(Q): 12.01%

Stdev(P): 5.31%; Stdev(Q): 11.29%

Stdev(P): 5.25%; Stdev(Q): 11.24%

Stdev(P): 4.55%; Stdev(Q): 10.62%

Answer 1

Standard Deviation of returns of Portfolio P

Expected Return

Expected Return = Sum of Returns x ¼

= [4% + 7% -3% + 9%] x ¼

= 17% x ¼

= 4.25%

Standard Deviation

Variance = [(4 – 4.25)² + (7 - 4.25)² + (-3 – 4.25)² + (9 - 4.25) ²] x ¼

= [0.06 + 7.56 + 52.56 + 2.56] x ¼

= 82.75 x ¼

= 20.69

Standard Deviation = Square Root of 20.69 or (20.69)^1/2

Standard Deviation = 4.55%

Standard Deviation of returns of Portfolio Q

Expected Return

Expected Return = Sum of Returns x ¼

= [11% - 7% + 15% - 9%] x ¼

= 10% x ¼

= 2.50%

Standard Deviation

Variance = [(11 – 2.50)² + (-7 – 2.50)² + (15 – 2.50)² + (-9 – 2.50) ²] x ¼

= [72.25 + 90.25 + 156.25 + 132.25] x ¼

= 451 x ¼

= 112.25

Standard Deviation = Square Root of 112.25 or (112.25)^1/2

Standard Deviation = 10.62%

Therefore, the standard deviations of the rate of return for the two portfolios would be “Stdev(P): 4.55%; Stdev(Q): 10.62%”