Question

Consider the following for a portfolio:

Year	Beginning value	Dividend	Ending value
1	$100	$1.46	$110
2	$110	$1.12	$112
3	$112	$1.27	$115

What is the geometric mean annual return?

Answer 1

Step-1, Calculation of Return for each of 3 years

Return for Year 1 (r1)

Return for Year 1 = [{(Ending Value – Beginning Value) + Dividend} / Beginning Value] x 100

= [{($110 - $100) + $1.46} / $100] x 100

= [($10 + $1.46) / $100] x 100

= [$11.46 / $100] x 100

= 11.46%

Return for Year 2 (r2)

Return for Year 2 = [{(Ending Value – Beginning Value) + Dividend} / Beginning Value] x 100

= [{($112 - $110) + $1.12} / $110] x 100

= [($2 + $1.12) / $110] x 100

= [$3.12 / $110] x 100

= 2.84%

Return for Year 3 (r3)

Return for Year 3 = [{(Ending Value – Beginning Value) + Dividend} / Beginning Value] x 100

= [{($115 - $112) + $3.00} / $112] x 100

= [($3 + $1.27) / $112] x 100

= [$4.27 / $112] x 100

= 3.81%

Step-2, Calculation of Geometric Mean Annual Return

Geometric Mean Annual Return = [(1 + r1) x (1 + r2) x (1 + r3)]^1/n – 1

= [(1 + 0.1146) x (1 + 0.0284) x (1 + 0.0381)]^1/3 – 1

= [1.1145 x 1.0284 x 1.0381]^1/3 – 1

= [1.18992694]^1/3 – 1

= 1.05967682 – 1

= 0.05967682 or

= 5.97% (Rounded to 2 decimal place)

“Hence, the Geometric Mean Annual Return will be 5.97%”