# How to calculate CAGR for shares bought at different times?

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. • What's CAGR and what's Qty? – Rudy the Reindeer Apr 8 '12 at 6:40 • And is the mathematica tag correct? – Rudy the Reindeer Apr 8 '12 at 6:44 • Yes Mathematica tag is correct. Here is what CAGR is:en.wikipedia.org/wiki/Compound_annual_growth_rate – meetpd Apr 8 '12 at 12:56 • Qty is quantity – meetpd Apr 8 '12 at 12:57 • 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? – Graphth Apr 9 '12 at 13:15 ## 2 Answers 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.

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.

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