Question

Calculate annual arithmetic rate of return and annual geometric rate of return of stock A and B. Consider the data in table below, which show the movements in price for two stocks over two successive holding periods. Both stocks have a beginning price of $10. Stock A rises to $40 in period 1 and then declines to $30 in period 2. Stock B falls to $8 in period 1 and then rises to $25 in period 2.

Answer 1

to find arithmetic rate of return, we need to find the normal rate of return

rate of return    =   Current price - Previous Price / Previous Price X100

period 1 wont have a rate of return , since it is the starting point.

The average of the above rate of returns arrived will give the arithmetic rate of return,

           i.e.     =    (rate of return of period 2+rate of rate of return of period 3)/2

computation as below

excel formulas

geometric rate of return is given by,

the normal return is calculated in decimals points = Current price - Previous Price / Previous Price

to this return in decimal1 is added to get 1+r

these 1+r are multiplied across periods

Nth root of above multiplied values is taken,, where n is the number of periods for which return is available,

and from the resultant figure 1 is subtracted to arrive at Geometric mean

  

excel formulas :