Question

Year	Yearly Return
1983	11%
1984	9.3%
1985	8.1%
1986	13.6%
1987	10%
1988	12.8%

1A. Please find the arithmetic mean return for this asset.

1B. Please find the geometric mean return for this asset.

1C. Please find the variance for the returns on this asset.

Answer 1

1)A)

Arithmetic return= sum of all returns/ no of observations

= (11+9.3+8.1+13.6+10+12.8)/6

Arithmetic return= 10.8%

1)B)

Geometric return= [(1+r1) * (1+r2) ……*(1+r6)] ^(1/n) -1

r1, r2 .... are returns

= [(1+0.11) * (1+0.093) * (1+0.081) *(1+0.136) *(1+0.10) *(1+0.128)] ^(1/6) -1

Geometric return= 10.7834345407 %

1)C)

There are two types of variances 1. Sample 2. Population. I don’t know which method your college is following so; I’ll write answers for two methods. As per concept we have to use sample observation.

Sample Variance= summation (return- Arithmetic return) ^2/ (n-1)

n is the no of observations

= [ (11-10.8) ^2+(9.3-10.8) ^2+(8.1-10.8) ^2+(13.6-10.8) ^2+(10-10.8) ^2+(12.8-10.8) ^2] / (6-1)

SAMPLE VARIANCE =4.412%

Population variance= summation (return- Arithmetic return) ^2/ n

= [ (11-10.8) ^2+(9.3-10.8) ^2+(8.1-10.8) ^2+(13.6-10.8) ^2+(10-10.8) ^2+(12.8-10.8) ^2] / 6

POPULATION VARIANCE =3.68%