Frequency of Disbursements and Variability of Monthly Income

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.

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