Question

A firm you are analyzing has had the following returns the past 5 years: 27.0%, 33.0%, -40.0%, -14.0% and 32.0 %. What are the standard deviation and variance of the past five year returns?

Answer 1

Mean return = sum of all returns/ no of years

=(27+33-40-14+32)/5

Mean return = 7.6 % or 0.076

Note: There are two methods to calculate varaince i.e, SAMPLE VARIANCE and POPULATION VARIANCE. I doesnt know which method your professor is following. I will write answers for both.

Method 1:

Sample Variance = SUMMATION ( (Return - Mean return) ^2)/(N-1)

N is no of observations

((0.27 – 0.076) ^2 + (0.33 - 0.076) ^2 + (-0.40 - 0.076) ^2 + (-0.14 - 0.076) ^2 + (0.32- 0.076) ^2)/(5-1)

Sample Variance = 0.10873

Standard deviation= sqrt(Sample Variance)

=Sqrt(0.10873)

Standard deviation = 32.97%

Method 2

Population Variance= SUMMATION ( (Return - Mean return) ^2)/(N)

((0.27 – 0.076) ^2 + (0.33 - 0.076) ^2 + (-0.40 - 0.076) ^2 + (-0.14 - 0.076) ^2 + (0.32- 0.076) ^2)/(5)

Population Variance = 0. 086984

Standard deviation= sqrt (Sample Variance)

=Sqrt(0. 086984)

Standard deviation = 29.49%