Re: [Help-glpk] IRR (Internal Rate of Return) using MathProg

[Jeffrey Kantor]

This was intriguing enough that I spent some time trying to get it to
work. Turns my advice wasn't very good after all. IRR is found as the
root to a function that is simply too poorly behaved to yield a
consistently useful linear or linear fractional approximation.  Noli's
data turns out to be a great example where there a significant
convexity confounds any attempt at a linear approximation.  The
citation I provided purports to find approximations good to four
digits. But when stressed, these approximations don't even give sign
much less four digit accuracy.

So please disregard my advice. It was an intriguing thought at the
time but doesn't hold up practice except for the most benign cases.

Jeff

For the data given in Noli's original inquiry, the

On Sun, Sep 16, 2012 at 5:14 PM, Jeffrey Kantor <address@hidden> wrote:
> If you can get by with a close approximation to the IRR, then there
> may be another way to approach this problem. The so-called Dietz
> formula is used to estimate returns on a portfolio.  You can derive
> the Dietz formula from an expression for NPV by taking the first two
> terms in a Taylor series expansion with respect to return r about the
> point r = 0, then solving for r.  The Dietz return is the ratio of two
> affine terms in the cash flows.  Once you have that, then use a
> Charnes-Cooper type transformation to convert this express into a
> linear objective for an LP.  The net result is that you could then
> include return in the the objective or constraints of your
> calculation.
>
> I've not done actually done this but it might be worth exploring. Here
> is some background
>
> http://www.shestopaloff.ca/yuri_eng/articles_subject/finance/HIGH_ACCURACY_METHODS_FOR_IRR_Web.pdf
> http://en.wikipedia.org/wiki/Linear-fractional_programming
>
> On Sun, Sep 16, 2012 at 3:06 PM, Andrew Makhorin <address@hidden> wrote:
>>
>>> It is well known, and your links show how, to use Newton's algorithm
>>> (aka Newton Raphson's algorithm) to find the IRR, since it's really
>>> find a root of a polynomial (see the other post by Jeffery Kantor,
>>> which also describes the fact that depending on the cash flows, there
>>> could be multiple solutions).
>>>
>>
>> Newton-Raphson's method is not a good choice in this case because
>> i) it requires an initial guess, ii) it is able to find only one root;
>> iii) it may not converge. To find all roots of a polynomial it is much
>> better to use a specialized algorithm, for example, QD-algorithm or
>> Bairstow's algorithm. Note also that roots of polynomials of high degree
>> are extremely sensible to round-off errors in specifying the polynomial
>> coefficients, so I belive that there should exist another formulation
>> of IRR.
>>
>>
>>
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