### Author Topic: How to estimate the expected value of an index fund investment  (Read 2131 times)

#### k290

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##### How to estimate the expected value of an index fund investment
« on: June 22, 2015, 01:00:26 PM »
I'm having difficulty figuring out if my application of exponential compounding here is reasonably accurate. Please help if you have a second...:)

Lets say I have \$1000 invested in an index fund. Historically, it has earned investors  say 6% per annum in growth (including dividend payments).

So I could  just plug in these numbers into the exponential compounding formula A=P(1+r/n)^nt, and just kind of estimate that the investments growth is similar to it being compounded annually, since on average this was its annual growth. Is that really the best we can do for a spreadsheet-able formula though?

Using a fixed compounding calculation seems like it may not be the most reasonable, since shares are not necessarily compounding my money precisely "annually". Selecting annual compounding seems a bit arbitrary. These are stocks. They are volatile. It is only compounding when growth is occuring. This could be a small amount daily or it could be a big leap after a few months of negative 'growth'

Is using the 6% historical average in an annual compounding formula reasonable or not? If not how can I improve its accuracy?

Note: This is a question more about the application of the mathematical equation. This question is NOT about the merits of using historical growth for future predictions so please do not focus on that, but feel free to still comment.

Also lets leave inflation and expenses/fees out of the equation for simplicity.

« Last Edit: June 22, 2015, 01:17:32 PM by k290 »

#### arebelspy

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##### Re: How to estimate the expected value of an index fund investment
« Reply #1 on: June 22, 2015, 01:15:43 PM »
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If you want to know more about us, or how we did that, or see lots of pictures, this Business Insider profile tells our story pretty well.
We (rarely) blog at AdventuringAlong.com. Check out our Now page to see what we're up to currently.

#### forummm

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##### Re: How to estimate the expected value of an index fund investment
« Reply #2 on: June 22, 2015, 01:16:24 PM »
The CAGR (compound annual growth rate) of the S&P 500 is something like 10% over the last 100 years, and about 7% in real (after inflation) terms. The CAGR takes into account all the ups and downs already. So if you went back in time and put 1 dollar into a 100 year zero-coupon bond paying 10% (or whatever the exact number is) and 1 dollar into the hypothetical fee-free S&P 500 index fund, today they would be worth the same amount.

So, yes, you could just use the compounding equation to estimate what you might project your savings to be worth in the future, assuming a particular rate of return.

#### k290

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##### Re: How to estimate the expected value of an index fund investment
« Reply #3 on: June 22, 2015, 01:18:37 PM »
Excellent. Thanks for pointing me in the right direction arebelspy and forummm.

#### forummm

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##### Re: How to estimate the expected value of an index fund investment
« Reply #4 on: June 22, 2015, 01:25:13 PM »
Glad to be of service <tip of the top hat>

#### innerscorecard

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##### Re: How to estimate the expected value of an index fund investment
« Reply #5 on: June 22, 2015, 11:06:04 PM »
This is THE big question. Will the past be like the future? Smart people disagree, and worse still, make it seems as if their opinion is the only right one. In general, the future is somewhat like the past, but people do overindex a lot on the recent past.