Answers
Solution :
a. Arithmetic Return for the stock:
The formula for calculation of arithmetic return is
Arithmetic Return = Total of returns / No. of years
= [13 % + 17 % + 17 % + ( - 4 % ) + 13 % + 8 % ) ] / 6
= 64 % / 6 = 10.6667 %
= 10.67 % ( when rounded off to two decimal places )
Thus the arithmetic return for the stock = 10.67%
Thus the solution is option 3 = 10.67 %
b. Geometric Return for the stock:
The formula for calculation of geometric return is
Geometric mean = [ ( 1 + Return 1 % ) * ( 1 + Return 2 % ) * .( 1 + Return 3 % ) * ( 1 + Return 4 % ) * ( 1 + Return 5 % ).. ( 1 + Return n % ) ] 1/n - 1
Where Return 1 % = Return in year 1 = 13 % = 0.13
Return 2 % = Return in year 2 = 17 % = 0.17
Return 3 % = Return in year 3 = 17 % = 0.17
Return 4 % = Return in year 4 = ( - 4 % ) = - 0.04
Return 5 % = Return in year 5 = 13 % = 0.13
Return 6 % = Return in Year 6 = 8 % = 0.08
n = 6
Applying the values in the formula we have
= [ ( 1 + 0.13 ) * ( 1 + 0.17 ) * ( 1 + 0.17 ) * ( 1 - 0.04 ) * ( 1 + 0.13 ) * ( 1 + 0.08 ) ] 1/6 - 1
= [ ( 1.13 ) * ( 1.17 ) * ( 1.17 ) * ( 0.96 ) * ( 1.13 ) * ( 1.08 ) ] 1/6 - 1
= [ 1.812273 ] 1/6 - 1
= [ 1.812273 ] 0.1667 - 1
= 1.104195 - 1 = 0.104195
= 10.4195 %
= 10.42 % ( when rounded off to two decimal places )
Thus the geometric return for the stock = 10.42 %
Thus the solution is option 3 = 10.42 %
Note : ( 1.812273 ) 0.1667 is calculated using the excel formula
=POWER(Number,Power) = POWER(1.812273,0.1667) = 1.104195
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