Frequency of Disbursements and Variability of Monthly Income
Twice a Month Versus Once a Month Disbursements
Question: A person owns $300,000 of Vanguard Mid-Cap
fund VMGRX at the beginning of 2003.
The price of the fund is $5.92.
This amounts to 50,675.7 shares.
The person is considering two different disbursement
strategies. The first involves monthly
disbursement on the start of the first week of the month. The second involves twice-monthly disbursements
on the first day of the first week of the month and the first day of the third
week of the month.
Does the movement to twice a month disbursements decrease
the variance of monthly income derived from disbursements from this fund over
the 2003 to 2005 time period.
Analysis: The monthly income from once-monthly
disbursements and twice-monthly disbursement from the Vanguard Midcap fund over
the 2003 to 2005 time period are presented in the table below.
Monthly Income and
Frequency of Fund Disbursements
|
||||
Year
|
Month
|
Week
|
Monthly Income from One
Disbursement
|
Monthly Income from Two
Disbursements
|
2003
|
1
|
1
|
$1,000
|
$967
|
2003
|
2
|
1
|
$889
|
$905
|
2003
|
3
|
1
|
$894
|
$939
|
2003
|
4
|
1
|
$953
|
$972
|
2003
|
5
|
1
|
$1,042
|
$1,044
|
2003
|
6
|
1
|
$1,119
|
$1,119
|
2003
|
7
|
1
|
$1,165
|
$1,156
|
2003
|
8
|
1
|
$1,104
|
$1,152
|
2003
|
9
|
1
|
$1,243
|
$1,247
|
2003
|
10
|
1
|
$1,251
|
$1,245
|
2003
|
11
|
1
|
$1,308
|
$1,281
|
2003
|
12
|
1
|
$1,273
|
$1,278
|
2004
|
1
|
1
|
$1,367
|
$1,369
|
2004
|
2
|
1
|
$1,415
|
$1,418
|
2004
|
3
|
1
|
$1,393
|
$1,383
|
2004
|
4
|
1
|
$1,377
|
$1,351
|
2004
|
5
|
1
|
$1,325
|
$1,341
|
2004
|
6
|
1
|
$1,374
|
$1,378
|
2004
|
7
|
1
|
$1,420
|
$1,427
|
2004
|
8
|
1
|
$1,440
|
$1,439
|
2004
|
9
|
1
|
$1,475
|
$1,458
|
2004
|
10
|
1
|
$1,442
|
$1,427
|
2004
|
11
|
1
|
$1,479
|
$1,503
|
2004
|
12
|
1
|
$1,527
|
$1,526
|
2005
|
1
|
1
|
$1,566
|
$1,568
|
2005
|
2
|
1
|
$1,586
|
$1,604
|
2005
|
3
|
1
|
$1,596
|
$1,621
|
2005
|
4
|
1
|
$1,666
|
$1,684
|
2005
|
5
|
1
|
$1,710
|
$1,646
|
2005
|
6
|
1
|
$1,520
|
$1,521
|
2005
|
7
|
1
|
$1,524
|
$1,475
|
2005
|
8
|
1
|
$1,459
|
$1,477
|
2005
|
9
|
1
|
$1,502
|
$1,516
|
2005
|
10
|
1
|
$1,574
|
$1,578
|
2005
|
11
|
1
|
$1,609
|
$1,636
|
2005
|
12
|
1
|
$1,675
|
$1,654
|
The standard deviation estimates of the monthly income from
the one-disbursement and two-disbursement strategies are presented below.
Standard Deviation of
Income from
Two Disbursement Strategies
|
|
One Monthly Disbursement
|
Two Monthly Disbursements
|
$224
|
$220
|
The reduction in the standard deviation of monthly income by
increasing disbursements from once a month to twice a month appears really
small.
I used the FTEST command in Excel to see if the standard
deviations differ. I got a p-value of
around 0.9. They don’t differ.
Conclusions: Results pertain to this security and this
relatively narrow time period. The sample
involves three strong market years and a fairly diversified fund. Simply increasing the number of monthly
disbursements does not accomplish much in terms of reduction in the variability
of monthly income in this instance.
A Technical Note: It took me awhile to figure out how to
manipulate the data for this post.
The twice-monthly distribution data looked like this.
Year
|
Month
|
Week
|
Price VMGRX
|
Shares Sold
|
Disbursed Value
|
2003
|
1
|
1
|
5.92
|
84.5
|
$500
|
2003
|
1
|
3
|
5.54
|
84.3
|
$484
|
2003
|
2
|
1
|
5.28
|
84.2
|
$466
|
2003
|
2
|
3
|
5.48
|
84.0
|
$468
|
2003
|
3
|
1
|
5.33
|
83.9
|
$443
|
2003
|
3
|
3
|
5.88
|
83.8
|
$446
|
2003
|
4
|
1
|
5.70
|
83.6
|
$458
|
2003
|
4
|
3
|
5.93
|
83.5
|
$456
|
2003
|
5
|
1
|
6.25
|
83.3
|
$444
|
2003
|
5
|
3
|
6.28
|
83.2
|
$454
|
The twice-monthly disbursement data table looks like this.
There is no by statement in Excel to get monthly totals I
sorted by week and added week 1 to week 3 for every month.
Readers interested in this post might like my new book on
Kindle.
Solving Financial Problems in Excel by David Bernstein on
Kindle
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