CAGR formula translation

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09/21/2016 at 11:30 AM #13470 quote
Stef
Participant

Average
How do I translate this to Probuilder language:
```
cagr=((equity/startcapital)^(1/nryears))-1
```
PRT does not like the “^” (power of) symbol.

Regards
09/21/2016 at 7:30 PM #13509 quote

Nicolas
Keymaster

Legend

I’m sorry, I spent almost 2 hours doing maths formulas to solve the MathPow being not available in math instructions of the platform.. Didn’t solve the formula because of the fractionnal exponent. Seems that I could calculate something if the ‘nryears’ is below 3 but not above.

I have just sent a request to PRT dev team to add the MathPow possibility in the language, as it is not the first time i’m stuck with this! 🙁

If any math genius come here, I’ll be glad to have his opinion 🙂

09/21/2016 at 11:41 PM #13512 quote
JC_Bywan
Moderator

Master
Ok, I guess I’ve become a PRC-addict, even when I’m away from my trading station I feel the need to come and read what happened since last visit, haha

Assuming nryears is an integer, how about a recursive approach, for which the number of iterations would depend on the required precision in the end by the user?

Let’s say to simplify the formula writing that A=equity/startcapital and n=nryears

and let’s name B = (equity/startcapital)^(1/nryears) = A^(1/n)

so B^n = A = B * B^(n-1)

B = A / B ^(n-1)

and if I use i to rank the iterations from 1 to maximum i desired for sufficient precision and {} for index:

B{rank i+1} = ( B{rank i} + B{rank i} ) / 2

B{rank i+1} = ( B{rank i} + A / (B{rank i} ^(n-1) ) / 2

and a code with 2 loops to use the formula:

something like:
```
B=1

for i=1 to 10 //(try 20 and 30 and... to see how much is enough for required accuracy in the end)

previousB=B

den=B

for j=2 to nryears-1
den=den*B
next

B=(previousB + (equity/startcapital)/den)/2

next

cagr=B-1
```
However, I can’t launch prt and test it from here, so it’s probably bugged as I often need to make changes to first writing before getting it right… Also, I have never tried a loop inside a loop in PRT before, don’t know if it can handle it.

Nicolas thanked this post
09/22/2016 at 6:53 AM #13516 quote
Stef
Participant

Average
@Nicolas, I could not solve it either. But, I did come up with the following “indicator” – that can be added to the end of any strategy backtesting code.
```
// yearly and monthly returns
once startcapital=100000 // initial capital amount
once yearstartcap=startcapital // set initial capital for 1st year
once mstartcap=startcapital // set initial capital for 1st month

if day<day[1] and month=1 then // new year
endcapital=startcapital+strategyprofit // ending capital for the year (previous year)
prof=endcapital-yearstartcap // profit for the year (previous year)
yearstartcap=endcapital // set starting capital for the new year
yearreturn=(prof/startcapital)*100 // yearly return as percentage (previous year)
endif

if day<day[1] and month>month[1] then // new month
mendcapital=startcapital+strategyprofit // ending capital for the month (previous month)
mprof=mendcapital-mstartcap // profit for the month (previous month)
mstartcap=mendcapital // set starting capital for the new month
mreturn=(mprof/startcapital)*100 // monthly return as percentage (previous month)
endif


graph 0 coloured(0,0,255) // graph zero line
graph yearreturn coloured(0,200,0) as "Yearly Return %" // graph yearly return (prev year)
graph mreturn coloured(154,0,154) as "Monthly Return %" // graph monthly return (prev month)
```
It calculates yearly and monthly returns, and looks like this (see attachment).

I would appreciate any comments or suggestions for improvements.

Regards

Stef

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Capture.png Capture-1.png
09/22/2016 at 7:06 AM #13522 quote

Stef
Participant

Average

@Noobywan. Tx, will try it.

09/22/2016 at 7:57 AM #13525 quote
Nicolas
Keymaster

Legend
@Noobywan

Your code is good. It successfully returned the good value for the Wikipedia example attached.

Here is the code with the same value:
```
B=1
equity = 13000
startcapital = 9000
nryears = 3

for i=1 to 10 //(try 20 and 30 and... to see how much is enough for required accuracy in the end)

previousB=B

den=B

for j=2 to nryears-1
den=den*B
next

B=(previousB + (equity/startcapital)/den)/2

next

cagr=B-1

RETURN cagr
```
Well done! Fractional exponent gimme headache yesterday, you desserve a beer again! 🙂 Maybe I’ll add a post in the Blog in your own name.

cagr-calculation.png cagr-prorealtime.png
09/22/2016 at 6:26 PM #13555 quote

Nicolas
Keymaster

Legend

@Stef

You add the code about monthly and yearly returns in the Library, but I don’t see any code of ITF file attached to your post. Could you please, gimme here? Thanks.

09/23/2016 at 5:37 AM #13576 quote

Stef
Participant

Average

Here you go…

Nicolas thanked this post

yearmonthreturn.itf

10/01/2016 at 3:06 PM #14037 quote

JC_Bywan
Moderator

Master

No problem for blog post if you think it can be useful to compensate for the lack of mathpow, with or without my name doesn’t matter, I don’t own the rights to recursivity

I am going to write a “carte de fidélité – bières” with squares to stamp the beers on, in case some day I happen to drive near your headquarters 😉

10/01/2016 at 4:05 PM #14038 quote

Nicolas
Keymaster

Legend

Ahaha noobywan, you just have changed my mood from dark to hilarious, thanks a lot. Always got beers at Nicolas’HQ, no worries 😂

05/10/2019 at 8:31 PM #98204 quote

undefined
Participant

Master

codeforpower = exp(5*log(2)) // result = 32 = 2^5
codeforlogarithm = log(32) / log (2) // result = 5

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