How to Calculate Personal Rate of Return When Dollar-Cost Averaging

Let's say you are in the accumulation phase and are dollar-cost-averaging into a mutual fund. You get your mutual fund statement at the end of the year and it tells you that the fund returned X amount that year. Was that YOUR actual return? Most likely not. Why? Because you invested at different times during the year. The mutual fund's reported rate of return is based on the assumption that you invested on January 1st and held it until December 31.

So, what is a Personal Rate of Return? It is the ACTUAL rate of return that you receive.

How do you calculate it? There are a number of ways. I'll show you a way that I learned about. I must warn you, this is a pretty involved method for calculating personal ROR (also known as a time-weighted ROR). Also, some of you will notice that there are shortcuts that can be taken in some of the steps. I'm going to go the long way around so that hopefully everyone can understand this.

EXAMPLE

For this example, we will say that you started on January 1, 2004 with zero dollars in your account. We will assume that you set up your account for automatic investments of $100 to be made on the last day of each month. For this example, we will use Vanguard's S&P 500 Index Fund (VFNIX).

Step 1. Calculate the number of shares purchased for each time period.

Here are the monthly closing prices and number of shares purchased for VFNIX:

              Purchase      Shares
                Price     Purchased
01/31/2004       104.54    0.95657165
02/29/2004       105.98    0.94357426
03/31/2004       104.01    0.96144601
04/30/2004       102.37    0.97684869
05/31/2004       103.76    0.96376253
06/30/2004       105.41    0.9486766
07/31/2004       101.92    0.9811617
08/31/2004       102.31    0.97742156
09/30/2004       102.99    0.97096806
10/31/2004       104.55    0.95648015
11/30/2004       108.78    0.91928663
12/31/2004       111.64    0.8957363

Step 2. Figure out a running total for each purchase. This step is pretty involved.

                              Shares   Price   Total
1/31/2004   Initial Purchase   0.9566  104.54    $100
2/29/2004   Purchase           0.9436  105.98    $100
            Previous Balance   0.9566  105.98    $101
                       Total   1.9001            $201
3/31/2004   Purchase           0.9614  104.01    $100
            Previous Balance   1.9001  104.01    $198
                       Total   2.8616            $298
4/30/2004   Purchase           0.9768  102.37    $100
            Previous Balance   2.8616  102.37    $293
                       Total   3.8384            $393
5/31/2004   Purchase           0.9638  103.76    $100
            Previous Balance   3.8384  103.76    $398
                       Total   4.8022            $498
6/30/2004   Purchase           0.9487  105.41    $100
            Previous Balance   4.8022  105.41    $506
                       Total   5.7509            $606
7/31/2004   Purchase           0.9812  101.92    $100
            Previous Balance   5.7509  101.92    $586
                       Total   6.7320            $686
8/31/2004   Purchase           0.9774  102.31    $100
            Previous Balance   6.7320  102.31    $689
                       Total   7.7095            $789
9/30/2004   Purchase           0.9710  102.99    $100
            Previous Balance   7.7095  102.99    $794
                       Total   8.6804            $894
10/31/2004  Purchase           0.9565  104.55    $100
            Previous Balance   8.6804  104.55    $908
                       Total   9.6369          $1,008
11/30/2004  Purchase           0.9193  108.78    $100
            Previous Balance   9.6369  108.78  $1,048
                       Total  10.5562          $1,148
12/31/2004  Purchase           0.8957  111.64    $100
            Previous Balance  10.5562  111.64  $1,178
                       Total  11.4519          $1,278

Step 3. Calculate the individual returns for each time period.

To do this, you simply use this formula:

[(This month's closing balance - Current month's purchase)/Previous month's balance]-1

For the month of February, the numbers would like this (I rounded the numbers for simplicity's sake):

[(201 - 100)/100]-1
[101/100]-1
[1.01]-1
.01

You would repeat this process for March - December. Here's what your numbers should look like not rounded:

Feb     0.013775
March   -0.01859
April   -0.01577
May     0.013578
June    0.015902
July    -0.03311
Aug     0.003827
Sept    0.006646
Oct     0.015147
Nov     0.040459
Dec     0.026292

Step 4. Calculate the Personal Rate of Return

Here's the formula for this step:

{[(1 + Feb Rate) X (1 + March Rate) X ...]-1} X 100

It should look like this:

{[(1 + 0.013775) X (1 + (-0.01859)) X (1 + (-0.01577)) X ...]-1} X 100

Your final answer should look like this:

{[1.067917] - 1} X 100
.067917 X 100
6.7917%

WHEW! That's a lot of work to find out that your personal rate of return for this example is 6.8%! Now you know why a stockbroker doesn't furnish this information!

If you are interested, send me an email and I'll send you a copy of the Excel file I used to calculate this example.