# Correct way to calculate overall CAGR of trades of different lengths?

Let's say you bought 5 stocks on the same day and they performed like this:

Symbol  Return  CalDays   BP/Day    CAGR
AAA       7.4%       42     17.6     86%
BBB       5.1%       41     12.4     56%
CCC       1.9%       26      7.3     30%
DDD      -0.5%       12     -4.2    -14%
EEE      -7.4%       16    -46.3    -83%
Average  1.30%     27.4     -2.6   15.0%


After each trade, the next day a new investment would be made, and it would have the expected return of the trading system overall.

But how do you correctly calculate the overall return of the system? The difference in time periods makes the issue unclear.

At first I thought to use average BP/Day, however that would reward holding losing trades longer, which isn't right.

I'm pretty sure it's not correct to use average CAGR, nor calculating a CAGR from the other averages.

I realize this is a newbie question, but I have not been able to find the answer by searching.

Many thanks in advance!

• What do you mean by 'a new investment would be made', is cash flowing into the system? If so, who controls the flows? Have you looked at the modified Dietz method and time weighted returns? – Bob Jansen Jan 27 at 17:32
• I do not think it is possible to calculate accurate returns from the summary data you have. Information is missing. You need to do a full accounting of all trades, keeping track of both the cash on hand and your holdings of stocks, as you increment the date and process every buy and every sell. Periodically, for example monthly, you need to mark-to-market your holdings, which requires knowing the prices of all stocks you have on that date. – noob2 Jan 27 at 21:30