### 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.

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).

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

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:

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.

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 SharesPrice Purchased01/31/2004 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 Total1/31/2004Initial Purchase0.9566 104.54 $100

2/29/2004Purchase0.9436 105.98 $100

Previous Balance0.9566 105.98 $101

Total 1.9001$2013/31/2004Purchase0.9614 104.01 $100

Previous Balance1.9001 104.01 $198

Total 2.8616$2984/30/2004Purchase0.9768 102.37 $100

Previous Balance2.8616 102.37 $293

Total 3.8384$3935/31/2004Purchase0.9638 103.76 $100

Previous Balance3.8384 103.76 $398

Total 4.8022$4986/30/2004Purchase0.9487 105.41 $100

Previous Balance4.8022 105.41 $506

Total 5.7509$6067/31/2004Purchase0.9812 101.92 $100

Previous Balance5.7509 101.92 $586

Total 6.7320$6868/31/2004Purchase0.9774 102.31 $100

Previous Balance6.7320 102.31 $689

Total 7.7095$7899/30/2004Purchase0.9710 102.99 $100

Previous Balance7.7095 102.99 $794

Total 8.6804$89410/31/2004Purchase0.9565 104.55 $100

Previous Balance8.6804 104.55 $908

Total 9.6369$1,00811/30/2004Purchase0.9193 108.78 $100

Previous Balance9.6369 108.78 $1,048

Total 10.5562$1,14812/31/2004Purchase0.8957 111.64 $100

Previous Balance10.5562 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.

<< Home