Question

Assume you invest $10,000 in Charles Fund. It expects to return 5% annually.

i. Based on an operating expense of 1.25% on the average fund balance for each year, calculate the operating expenses for three years.

Beginning Balance	Annual Return	Ending Balance Before Expenses	Average Balance	OperatingExpense Percentage	Operating Expenses	Ending Balance after Expenses
$10,000	5%			1.25%
	5%			1.25%
	5%			1.25%

ii. Calculate your actual (geometric) return.

Answer 1

i. For year 1 Beginning balance = $10000, Ending balance before expenses = Beginning balance(1+ Annual return) = 10000(1+5%) = 10500, Average Balance = (Beginning balance + Ending balance before expenses) / 2 = (10000+10500) / 2 = 10250, Operating Expense = 1.25% x Average balance = 1.25% x 10250 = 128.125, Ending balance after expenses = Ending balance before expenses - Operating expenses = 10500 - 128.125 = 10371.875

For year 2 Beginning balance = Ending balance after expenses for year 1 = 10371.875, Ending balance before expenses = Beginning balance(1+ Annual return) = 10371.875(1+5%) = 10890.46875 , Average Balance = (Beginning balance + Ending balance before expenses) / 2 = (10371.875+10890.46875) / 2 = 10631.171875, Operating Expense = 1.25% x Average balance = 1.25% x 10631.171875 = 132.889648, Ending balance after expenses = Ending balance before expenses - Operating expenses = 10890.46875 - 132.889648 = 10757.579102

For year 3 Beginning balance = Ending balance after expenses for year 2 = 10757.579102, Ending balance before expenses = Beginning balance(1+ Annual return) = 10757.579102(1+5%) = 11295.45805 , Average Balance = (Beginning balance + Ending balance before expenses) / 2 = (10757.579102 + 11295.45805) / 2 = 11026.51858, Operating Expense = 1.25% x Average balance = 1.25% x 11026.51858 = 137.83148, Ending balance after expenses = Ending balance before expenses - Operating expenses = 11295.45807 - 137.83148 = 11157.62657

Rounding the above balances to two decimal places, we get

Beginning Balance	Annual Return	Ending Balance Before Expenses	Average Balance	Operating Expense Percentage	Operating Expenses	Ending Balance After Expenses
							10000.00	5%	10500.00	10250.00	1.25%	128.13	10371.88
10371.88	5%	10890.47	10631.17	1.25%	132.89	10757.58
10757.58	5%	11295.46	11026.52	1.25%	137.83	11157.63

ii. Actual Geometric return

Actual (Geometric) return = (Ending balance after expenses for year 3 / Beginning balance for year 1)^1/3 - 1 = (11157.62657 / 10000)^1/3 - 1 = (1.115762657)^1/3 - 1 = 1.0371875 - 1 = 0.0371875 = 3.71875%

So Actual (Geometric) Return = 3.71875%