Question

An investment you made 5 years ago has realized the following rates of return.

3 4 Year 1 2 5 Rate of Return 0.50 -0.15 -0.20 0.15 0.08

1. Calculate mean and median of the rates of return using appropriate statistical formulas and show your working.
2. Compute geometric mean using an appropriate statistical formula and show your working.
3. Which one of the three statistics you computed in parts (a) and (b) does best describe the investment return over the 5-year period? Explain why.

Answer 1

Qa) Mean = sum of all the returns / number of observations

= (0.15) + (0.20) + 0.15 + (0.08) + 0.50 / 5

= 0.22 / 5

= 0.044

b) Median

In order to find median, firstly we arrange the returns in ascending order.

Returns are :- (0.15) , (0.20), 0.15, (0.08), 0.50

After rearranging

= (0.20), (0.15) , (0.08), 0.15, 0.50

Median = ( n +1)th item / 2

= ( 5+1) / 2

= 6/2

= 3rd term

Therefore median is -0.08

B) Geometric mean = { (1+r) ×.....× (1+r(n)) } ^ 1/n -1

  = { (1+ (0.15)) (1+(0.20)) (1+0.15) (1+(0.08)) (1+0.50)}^ 1/5 -1

= { (0.85) (0.80) (1.15) (0.92) (1.50) } ^ 0.2 - 1

= { 1.07916 } ^ 0.2 - 1

= 1.01535 - 1

= 0.01535

C) Geometric mean is the best method which describes the investment return over the 5-year period because it takes into consideration the compounding effect from period to period which is not taken by other two measures.