# How to optimally calculate return / compound interest

Hello Mustachians,

I am just trying to simply understand (with practical examples) how is best way to simply calculate my profit/loss from share’s investments and the concept of compound interest.

The simple example assuming the underlying economical growth and companies growth concept is like: A \$10,000 investment earning 5% a year will be worth \$26,533 in 20 years because of the compound interest. Interest paid on the initial investments plus interest paid on the yearly earnings year over year on top.

However this is actually not the real case for a share price, right? The company can go up 5% the first year, down 10% the second year, up 20% the third year and so on…
Also the shares are not practically paying interests year over year, so how can I actually estimate for example my “average compounded” year over year interest got after 10 or 20 years ? or that is practically of non-sense…? which ratio / factors would be of more sense?

…or how I could best assess if it would be better for me to invest for instance on quarterly small instalments over 10 years or with a fixed large initial capital upfront for the next 10 years?

For example 40000 -CHF on share A today vs 1000 -CHF per quarter for share A every quarter over the next 10 years??

I mean even if we assume that after 10 years there is a 100% growth on the share price, I cannot really understand how I will benefit myself from the compound interest concept as far as of course there is no interest paid annually or whatsoever …(let’s assume no dividends in the meantime just for simplification)

Also for the case that you are keeping the shares for many years, how can you consider also inflation on the final calculation on your return?

Also what’s different in the case of ETFs?

Let’s not consider transaction / administration fees, foreign exchange profits/losses for the examples just for the sake of simplification for the case.

Sorry for my very large post in advance,

Leonidas

Check CAGR that’s the metric used. But this is a backward looking metric (you can only compute it after the fact), there’s no guarantee for equity investment to have specific returns (you can see historical returns, but they don’t promise anything and have large variations)

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It is not a stupid question. Performance calculation is a complex topic.

Say that you invested 1k 10 years ago and that is worth 3k today. You can compute the equivalent compound interest rate (CAGR) as (final/initial)^(1/years)-1 = (3000/1000)^(1/10)-1 = 0.116 = 11.6%. So it doesn’t matter whether it went up or down, that is the equivalent rate.

You can also calculate the geometric average. Say one year you made +10%, then -5% and then +10%. Then after 3 years the equivalent performance would be (1.1 * 0.95 * 1.1)^(1/3)-1 = 0.475 = 4.75%

The problem with portfolio performance is that you buy and sell stocks or ETFs or whatever you trade during the holding period. And these technique only work if you buy once and hold forever. Depending on what you want to measure you should use a TWR (time weighted return) or a MWR (money weighted return). Only the former corresponds to a real “compounded rate of growth”.

TWR will eliminate the effect of cash flows and is my preferred method. It will measure how the portfolio did disregarding the cash flows timing. The usual recommendation is TWRR. Otherwise you can use a MWR calculation, of out which I find the XIRR (internal rate of return) the most relevant.

Here are some slides that I found googling around on the topic, hope it helps: https://www.slideshare.net/social_citadelle/xirr-vs-twrr-55490971

And mind you: there are people whose sole job is computing these things (or rather programming these things so that they get computed correctly).

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Thanks a lot Ed,

basically that’s most what I was looking for very simply explained!
I will dig a bit further down based on your inputs and I might come with more questions than answers

Thanks again,
Leonidas