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I have bought shares at following times:

    Buy - 5th March 2006 - Price > $ 70 - Quantity - 10
    Buy - 2nd May 2007 -   Price > $ 33.5 - Quantity - 100
    Buy - 1st Oct 2008 -   Price > $ 57.7 - Quantity - 17
    Buy - 5th Jan 2012 -   Price > $ 94.8 - Quantity - 27

Assuming current share price to be $ 100, how can I find CAGR (cumulative) for the total investment I made till now?

PS: Sorry but I am unable to format this. Adding two spaces does not seem to add line breaks.

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    $\begingroup$ What's CAGR and what's Qty? $\endgroup$ – Rudy the Reindeer Apr 8 '12 at 6:40
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    $\begingroup$ And is the mathematica tag correct? $\endgroup$ – Rudy the Reindeer Apr 8 '12 at 6:44
  • $\begingroup$ Yes Mathematica tag is correct. Here is what CAGR is:en.wikipedia.org/wiki/Compound_annual_growth_rate $\endgroup$ – meetpd Apr 8 '12 at 12:56
  • $\begingroup$ Qty is quantity $\endgroup$ – meetpd Apr 8 '12 at 12:57
  • $\begingroup$ A better question might be, why exactly did you tag it Mathematica? Because, I think it's probably not a correct tag. So, can you explain why you think it is? $\endgroup$ – Graphth Apr 9 '12 at 13:15
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If you had made just one investment, calculating the CAGR is not hard. Say you bought it for 100, held it 30 months (or 5/2 years), and sold it for 200. r, the CAGR, would be found by solving $100(1+r)^{\frac 52}=200$, which gives $1+r=2^{\frac 25}\approx 1.32$, so the CAGR is about 32%. If you have multiple buys (and even multiple sales) you want a common $r$ that makes it come out. Say you bought some for 100 at day 0, some more for 200 18 months later, it is now 42 months in (7/2 years) and worth 500. The first batch has been compounding for 7/2 years, the second for 2, so we solve $100(1+r)^{\frac 72}+200(1+r)^2=500$. Usually you cannot solve for $r$ algebraically, you have to do it numerically. Excel has the function IRR for this. I get $r \approx 0.222$ in this example. If you have sales along the way, just enter them as negative investments. If you do, there may be more than one value of $r$ that satisfies the equation.

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Your stock portfolio works just like a mini-fund.

You define an initial amount of money (Assets Under Management, AUM) equal to the 1st position (Price*Qty). Your NAV is 100. The gains on your position would be your returns, until you add a new position.

Each time you add your position, your AUM sees capital inflows. The gains on all the positions open would be spread over a bigger AUM in the return calculation.

The returns for the periods determine the evolution of your NAV. The CAGR over a chosen time window is just the standard CAGR formula applied to NAV(t-1), NAV(t).

Hope this helps understand the general idea.

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  • $\begingroup$ Thank you for your answer. But can you please explain me with an example. I am little dumb in these things. Thanks! $\endgroup$ – meetpd Apr 14 '12 at 4:02
  • $\begingroup$ I am sorry, I do not have enough reputation to post a printout of the answer. $\endgroup$ – IcannotFixThis Apr 16 '12 at 9:06
  • $\begingroup$ Can you send me email? send it to succeedebay@gmail.com..Thanks! $\endgroup$ – meetpd Apr 16 '12 at 15:50

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