[R] Secant Method Convergence (Method to replicate Excel XIRR/IRR)

[Ravi Varadhan]

Yes, the secant method (like Newton Raphson) is not guaranteed to converge,
unlike the bisection method, but it has a superlinear convergence (not that
this matters much!).  Brent's method, which is used in `uniroot', is a
reliable and fast method, which is why I suggested it in my previous email.

Having said that, I am not sure about the convergence problem that you are
having without seeing the actual example.

Ravi.

-----Original Message-----
From: Adrian Ng [mailto:ang at hamiltonlane.com] 
Sent: Wednesday, August 25, 2010 5:28 PM
To: Ravi Varadhan; r-help at r-project.org
Subject: RE: [R] Secant Method Convergence (Method to replicate Excel
XIRR/IRR)

Hi Ravi,

Thanks for the responses.  I was actually trying to calculate IRR based on
unevenly spaced cash flows, and that's why I decided to use the secant
method.  I'm not sure if my answer isn't converging because I have some
careless mistake in the code, or if it's simply because unlike the bisection
method, the secant method doesn't 'sandwich' the desired root.



-----Original Message-----
From: Ravi Varadhan [mailto:rvaradhan at jhmi.edu] 
Sent: Wednesday, August 25, 2010 5:24 PM
To: Adrian Ng; r-help at r-project.org
Subject: RE: [R] Secant Method Convergence (Method to replicate Excel
XIRR/IRR)

Another approach is to use `uniroot' to find the zero of the NPV function:

npv <- function (cashFlow, irr) {
	n <- length(cashFlow)
	sum(cashFlow / (1 + irr)^{0: (n-1)})
	}

uniroot(f=npv, interval=c(0,1), cashFlow=cashFlow)

However, there may be situations where there are no real zeros or there are
multiple zeros of the NPV function.

Ravi.

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Adrian Ng
Sent: Wednesday, August 25, 2010 8:39 AM
To: r-help at r-project.org
Subject: [R] Secant Method Convergence (Method to replicate Excel XIRR/IRR)

Hi,

I am new to R, and as a first exercise, I decided to try to implement an
XIRR function using the secant method.  I did a quick search and saw another
posting that used the Bisection method but wanted to see if it was possible
using the secant method.

I would input a Cash Flow and Date vector as well as an initial guess.  I
hardcoded today's initial date so I could do checks in Excel.  This code
seems to only converge when my initial guess is very close to the correct
IRR.

Maybe I have some basic errors in my coding/logic? Any help would be greatly
appreciated.

The Wikipedia article to secant method and IRR:
http://en.wikipedia.org/wiki/Internal_rate_of_return#Numerical_solution

Thanks!



ANXIRR <- function (cashFlow, cfDate, guess){
        cfDate<-as.Date(cfDate,format="%m/%d/%Y")
        irrprev <- c(0); irr<- guess


        pvPrev<- sum(cashFlow)
        pv<-
sum(cashFlow/((1+irr)^(as.numeric(difftime(cfDate,"2010-08-24",units="days")
)/360)))
        print(pv)
        print("Hi")


while (abs(pv) >= 0.001) {
        t<-irrprev; irrprev<- irr;
        irr<-irr-((irr-t)*pv/(pv-pvPrev));
        pvPrev<-pv;
 
pv<-sum(cashFlow/((1+irr)^(as.numeric(difftime(cfDate,"2010-08-24",units="da
ys"))/365)))
        print(irr);print(pv)
        }
}





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