# How to retroactively calculate what the return on an investment in an index fund with monthly contributions would have been

If I had invested \$1000 on 1/1/2000 in the S&P500 and each month I invested a further \$1000 in to the same fund for 10 years, how would I calculate the return on investment I have made, accounting for the fluctuations in the value of the S&P500.

I am interested to see what the basic formula would be, ignoring inflation, and how the formula for including inflation would differ.

I'm going to assume you have some sort of fund that invests in the S&P500 for you, and it automatically subtracts its fee from your holdings in the fund every now and then. You then need a list of the value of the fund for each month since 1/1/2000.

Let's say the fund went something like

``````jan 1 2000 \$100
feb 1 2000 \$110 +10%    (+10/100)
mar 1 2000 \$90  -18.2%  (-20/110)
apr 1 2000 \$130 +44.4%  (+40/90)
may 1 2000 \$120 -7.7%   (-10/130)
``````

Now the total value of your investment always goes in two steps: add \$1000, then apply the percentage for a month, then add \$1000 again:

``````1. \$0 + \$1000 = \$1000
2. \$1000 +10% = \$1100  # Your holdings after january
3. \$1100 + \$1000 = \$2100
4. \$2100 - 18.2% = \$1718  # Your holdings after february
5. \$1718 + \$1000 = \$2718
6. \$2718 + 44.4% = \$3926  # Your holdings after march
7. \$3926 + \$1000 = \$4926
8. \$4926 - 7.7% = \$4547  # Your holdings after april
``````

At this point, you have added \$1000 four times, so your total investment was \$4000. Profit is \$547. Of course you'll want to do this with a script, not by hand.

To know how it was with inflation included, you also need a list of inflation per month. Then you do the same calculation, but if say inflation was 0.3% in a month then you add that instead of the change to the index. It's also reasonable to just do that by year, apply the yearly inflation and add \$12000, because the number doesn't change a lot during a year. The difference between the two calculations is your inflation adjusted profit.

• Distributions/dividends would also need to be factored in somehow. – Chris W. Rea Oct 24 '16 at 18:03
• This is great thanks, but I don't understand what you mean when you say " if say inflation was 0.3% in a month then you add that instead of the change to the index." - specifically I don't get what you mean when you say instead of the change to the index. Please could you elaborate on this or perhaps give and example? – user283471 Oct 24 '16 at 20:25

If I were doing this, I'd write down the following information:

``````Date       Amount Price Shares  CPI
2000/01/01 \$1000  \$100  10.000  168.800
2000/02/01 \$1000  \$110   9.091  168.900
2000/03/01 \$1000   \$90  11.111  171.200
2000/04/01 \$1000  \$130   7.692  171.300
Total      \$4000        37.894
``````

You can get the CPI information from a table. The other information is available as part of the purchase transaction.

Without inflation, we have a \$4000 investment that is currently worth the modern price times the number of shares. Let's use a modern (2010/01/01) price of \$200.

``````37.894 * \$200 = \$7578.80
``````

That's the current value on January 1st, 2010.

So the return is

``````(\$7578.80 - \$4000) / \$4000 = .8947 = 89.47% increase
``````

It's more complicated with inflation, as we can't just multiple \$1000 by the number of months. We have to normalize on some specific point in time. For example, we might calculate everything in January 1st, 2010 dollars. The CPI on that date was 216.687.

So now we take \$1000 in 2000/01/01 and convert it to 2010/01/01 currency:

``````\$1000 * 216.687 / 168.800 = \$1283.70
``````

And three more times

``````2000/02 \$1282.93
2000/03 \$1265.70
2000/04 \$1264.96
``````

That gives a total of \$5097.29 invested in 2010/01/01 dollars.

``````(\$7578.80 - \$5097.29) / \$5097.29 = .4868 = 48.68% increase after inflation
``````

Note that it would probably be easier to do this in a spreadsheet, which may even have functions to calculate these things for you.

Also, inflation numbers are usually a little out of date. For example, the October 1st numbers aren't out yet (on October 24th). So you wouldn't have been able to do this exact calculation until February of 2010. Or you'd only be able to do the equivalent calculation now (October 2016) through September 1st, 2016.

I just used the prices from the other answer (except the \$200, which I made up myself). I made no attempt to get accurate data on that. For the CPI information, I used the real data. Mostly because it was easier than making it up. Note that a real investment would likely have additional fees and dividend reinvestments. Perhaps those would get hidden in the share price. Perhaps not.

• This was very helpful, thanks. What if instead of the actual CPI I just had the inflation as a percentage. e.g 3.38% in 2000, 2.83% in 2001 etc. How would that change the calculation? – user283471 Oct 24 '16 at 19:50