Tuesday, December 29, 2015

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.

Readers interested in this post might like my new book on Kindle.

Solving Financial Problems in Excel by David Bernstein on Kindle