Question

8. You are the treasurer for your company's actuarial club. The club's account had a fund balance of $1,050 on January 1 and $1,160 on December 31. At the end of every month, the club receives $90 in membership dues. There were withdrawals of $600 on May 1 and $400 on June 15. Calculate the dollar-weighted (money-weighted) rate of return for the year, expressed as an annual rate compounded monthly. (A) 3.00% (B) 3.23% (C) 3.46% (D) 3.69% (E) 3.92%

Answer 1

Using the Modified dietz approximation method to calculate the dollar weighted rate of return:

Rate of return =

(EMV - BMV - c) (no.ofdays fromcash flowtillenddate/Totalnumberofdays) * C;) (BMV +

where

EMV = Ending Market Value = 1160

BMV = Beginning Market Value = 1050

Ci = cash flow after Di days i.e. after 31 days if the first cash flow is on Jan 31.

No. of days from cash flow till end date = 365 - Di = 365 - 31 = 334 for the first cash flow

Total number of days = 365 (since we are considering a year)

The values are calculated in excel and the table is copied below. The formula is copied in the table below:

The answer is option B: 3.23%

Date	No. of days	Fund value	Deposit	Withdrawal	Mod Dietz	Cash flow
01-01-07	364.00	1050
01-31-07	334.00		90		82.35616	90
02-28-07	306.00		90		75.45205	90
03-31-07	275.00		90		67.80822	90
04-30-07	245.00		90		60.41096	90
05-01-07	244.00			600	-401.096	-600
05-31-07	214.00		90		52.76712	90
06-15-07	199.00			400	-218.082	-400
06-30-07	184.00		90		45.36986	90
07-31-07	153.00		90		37.72603	90
08-31-07	122.00		90		30.08219	90
09-30-07	92.00		90		22.68493	90
10-31-07	61.00		90		15.0411	90
11-30-07	31.00		90		7.643836	90
12-31-07	0.00	1160	90		0	90
				Total	-121.836	80
					Return	3.232%

Date	No. of days	Fund value	Deposit	Withdrawal	Mod Dietz	Cash flow
39083	=DAYS($A$39,A3)	1050
39113	=DAYS($A$39,A4)		90		=(D4-E4)*(B4/365)	=D4-E4
39141	=DAYS($A$39,A5)		90		=(D5-E5)*(B5/365)	=D5-E5
39172	=DAYS($A$39,A6)		90		=(D6-E6)*(B6/365)	=D6-E6
39202	=DAYS($A$39,A7)		90		=(D7-E7)*(B7/365)	=D7-E7
39203	=DAYS($A$39,A8)			600	=(D8-E8)*(B8/365)	=D8-E8
39233	=DAYS($A$39,A9)		90		=(D9-E9)*(B9/365)	=D9-E9
39248	=DAYS($A$39,A10)			400	=(D10-E10)*(B10/365)	=D10-E10
39263	=DAYS($A$39,A11)		90		=(D11-E11)*(B11/365)	=D11-E11
39294	=DAYS($A$39,A12)		90		=(D12-E12)*(B12/365)	=D12-E12
39325	=DAYS($A$39,A13)		90		=(D13-E13)*(B13/365)	=D13-E13
39355	=DAYS($A$39,A14)		90		=(D14-E14)*(B14/365)	=D14-E14
39386	=DAYS($A$39,A15)		90		=(D15-E15)*(B15/365)	=D15-E15
39416	=DAYS($A$39,A16)		90		=(D16-E16)*(B16/365)	=D16-E16
39447	=DAYS($A$39,A17)	1160	90		=(D17-E17)*(B17/365)	=D17-E17
				Total	=SUM(F4:F17)	=SUM(G3:G17)
					Return	=(C17-C3-G18)/(C3+F18)