Frequency of Disbursements and Variability of Monthly Income
Twice a Month Versus Once a Month Disbursements
Question: A person owns $300,000 of Vanguard MidCap
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 twicemonthly 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 oncemonthly
disbursements and twicemonthly 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 onedisbursement and twodisbursement 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 pvalue 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 twicemonthly 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 twicemonthly 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
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