Question

1. You started your investment with an opening deposit of $1,000. Your portfolio grew as follows:

Beg Yr 1	Beg Yr 2	Beg Yr 3	Beg Yr 4	Beg Yr 5	Beg Yr 6	Beg Yr 7	Beg Yr 8	Beg Yr 9	Beg Yr 10	End Yr 10
$1,000	$1,268	$1,426	$1,497	$1,579	$995	$1,258	$1,447	$1,478	$1,714	$2,270

1. Calculate the average return and geometric return for each year.
2. What is the arithmetic average of your returns?
3. What is your long-term geometric average? (the average at end of year 10).

Answer 1

Part A:

Avg Ret & Geometric ret each Year = [ Ending Value - Begining Value ] / Begining Value

Year	Beginning Value	Ending value	End - Begin	[ End - Begin ] /Begin Value
1	$ 1,000.00	$ 1,268.00	$ 268.00	0.2680
2	$ 1,268.00	$ 1,426.00	$ 158.00	0.1246
3	$ 1,426.00	$ 1,497.00	$    71.00	0.0498
4	$ 1,497.00	$ 1,579.00	$    82.00	0.0548
5	$ 1,579.00	$    995.00	$ -584.00	-0.3699
6	$    995.00	$ 1,258.00	$ 263.00	0.2643
7	$ 1,258.00	$ 1,447.00	$ 189.00	0.1502
8	$ 1,447.00	$ 1,478.00	$    31.00	0.0214
9	$ 1,478.00	$ 1,714.00	$ 236.00	0.1597
10	$ 1,714.00	$ 2,270.00	$ 556.00	0.3244

Part B:

Avg Ret for 10 years = Sum [ Ret ] / n

Year	Beginning Value	Ending value	End - Begin	[ End - Begin ] /Begin Value
1	$ 1,000.00	$ 1,268.00	$ 268.00	0.2680
2	$ 1,268.00	$ 1,426.00	$ 158.00	0.1246
3	$ 1,426.00	$ 1,497.00	$    71.00	0.0498
4	$ 1,497.00	$ 1,579.00	$    82.00	0.0548
5	$ 1,579.00	$    995.00	$ -584.00	-0.3699
6	$    995.00	$ 1,258.00	$ 263.00	0.2643
7	$ 1,258.00	$ 1,447.00	$ 189.00	0.1502
8	$ 1,447.00	$ 1,478.00	$    31.00	0.0214
9	$ 1,478.00	$ 1,714.00	$ 236.00	0.1597
10	$ 1,714.00	$ 2,270.00	$ 556.00	0.3244
Sum of Ret	1.0474
Avg Ret	0.1047

Part C:

Geometric Ret = [ Year 10 Ending Value / Year 1 Beging Value ] ^ ( 1 / 10) - 1

= [ 2270 / 1000 ] ^ ( 1 /100) - 1

= 2.270^ (1/10) - 1

= 1.0854 - 1

= 0.0854 i.e 8.54%

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