bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

[Ting Boon Ghee]

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Using Calc to compute the rate of return on an investment, negative returns will result in error.

;; Extract from manual on the description of this function

8.6.4 Related Financial Functions
---------------------------------
The ‘b T’ (‘calc-fin-rate’) [‘rate’] command computes the rate of return on an investment.  This is also an inverse of ‘pv’: ‘rate(N, PAYMENT, AMOUNT)’ computes the value of RATE such that ‘pv(RATE, N, PAYMENT) = AMOUNT’.  The result is expressed as a formula like ‘6.3%’.

;; Example of positive return working correctly
;; Calculations for N=1, Payment=110 Amount=100
;; Answer is 10% as expected

;; Using the calculator
M-x calc <RET> 1 <RET> 110 <RET> 100 <RET> b T
Answer is 10%

;; Evaluating the original function from calc-fin.el
(calcFunc-rate 1 110 100) 
Answer : (float 1 -1)

;; Negative returns result in error
;; Calculations for N=1, Payment=90 Amount=100
;; Answer should be -10%

;; Using the calculator
M-x calc <RET> 1 <RET> 90 <RET> 100 <RET> b T
Result : rate(1, 90, 100)

Pressing '=' in the calculator subsequently gives the following message
Working... widen = (-1.59974 .. 199261559.20347)
Unable to bracket root: (-1.599740 .. 199261559.203470)

;; Evaluating the original function from calc-fin.el
(calcFunc-rate 1 90 100)

Evaluating the function produces this Backtrace message

Debugger entered--Lisp error: (wrong-type-argument "*Unable to bracket root" (intv 0 (float -159974 -5) (float 19926155920347 -5)))
  math-reject-arg((intv 0 (float -159974 -5) (float 19926155920347 -5)) "*Unable to bracket root")
  math-search-root((- (calcFunc-pv (var DUMMY var-DUMMY) 1 90 0) 100) (+ (/ 90 (* (var DUMMY var-DUMMY) (^ (+ (var DUMMY var-DUMMY) 1) 2))) (/ (- (/ 90 (+ (var DUMMY var-DUMMY) 1)) 90) (^ (var DUMMY var-DUMMY) 2))) (float 1 -4) (float -1000899910009 -11) (float 1 0) (float -55 0))
  math-newton-search-root((- (calcFunc-pv (var DUMMY var-DUMMY) 1 90 0) 100) (+ (/ 90 (* (var DUMMY var-DUMMY) (^ (+ (var DUMMY var-DUMMY) 1) 2))) (/ (- (/ 90 (+ (var DUMMY var-DUMMY) 1)) 90) (^ (var DUMMY var-DUMMY) 2))) nil nil nil nil (float 1 -4) (float -1000899910009 -11) (float 1 0) (float -55 0))
  math-find-root((calcFunc-eq (calcFunc-pv (var DUMMY var-DUMMY) 1 90 0) 100) (var DUMMY var-DUMMY) (intv 3 (float 1 -4) 1) t)
  math-compute-rate(1 90 100 nil calcFunc-pv)
  calcFunc-rate(1 90 100)
  elisp--eval-last-sexp(nil)
  eval-last-sexp(nil)
  funcall-interactively(eval-last-sexp nil)
  command-execute(eval-last-sexp)

;; Original definition of calcFunc-rate and math-compute-rate copied from calc-fin.el as follows
(defun calcFunc-rate (num pmt amount &optional lump)
  (math-compute-rate num pmt amount lump 'calcFunc-pv))

(defun math-compute-rate (num pmt amount lump func)
  (or (math-objectp num)
      (math-reject-arg num 'numberp))
  (or (math-objectp pmt)
      (math-reject-arg pmt 'numberp))
  (or (math-objectp amount)
      (math-reject-arg amount 'numberp))
  (or (null lump)
      (math-objectp lump)
      (math-reject-arg lump 'numberp))
  (let ((root (math-find-root (list 'calcFunc-eq
				    (list func
					  '(var DUMMY var-DUMMY)
					  num
					  pmt
					  (or lump 0))
				    amount)
			      '(var DUMMY var-DUMMY)
			      '(intv 3 (float 1 -4) 1)
			      t)))
    (if (math-vectorp root)
	(nth 1 root)
      root)))

;; My modified function definitions
(defmath my/rate (num pmt amount &optional lump)
  (my/compute-rate num pmt amount lump 'calcFunc-pv))

(defmath my/compute-rate (num pmt amount lump func)
  (or (math-objectp num)
      (math-reject-arg num 'numberp))
  (or (math-objectp pmt)
      (math-reject-arg pmt 'numberp))
  (or (math-objectp amount)
      (math-reject-arg amount 'numberp))
  (or (null lump)
      (math-objectp lump)
      (math-reject-arg lump 'numberp))
  (let ((root (math-find-root (list 'calcFunc-eq
				    (list func
					  '(var DUMMY var-DUMMY)
					  num
					  pmt
					  (or lump 0))
				    amount)
			      '(var DUMMY var-DUMMY)
			      '(intv 3 -1 1)
			      t)))
    (if (math-vectorp root)
	(nth 1 root)
      root)))

By changing the interval from '(intv 3 (float 1 -4) 1) to '(intv 3 -1 1), the correct answer of -10% for above example can be computed.

;; Evaluating my modified function
(calcFunc-my/rate 1 90 100)
Answer : (float -1 -1)

That is -10% as expected.

I am not sure if this is a bug or due to some restrictions or constrains elsewhere that the interval cannot be negative in the original function definition of math-compute-rate. Other than Rate, IRR function is also facing the same issue as the interval for math-compute-irr is also set as '(intv 3 (float 1 -4) 1).

Calculations can also be crosschecked with spreadsheets. Results should be same.

-- 
Best regards,
Boon Ghee

bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

[Eli Zaretskii]

> Date: Tue, 10 Dec 2024 00:44:04 +0800
> From: Ting Boon Ghee <tingbg@gmail.com>
> 
> Using Calc to compute the rate of return on an investment, negative returns will result in error.

Isn't it true that in the financial world there are no negative rates,
only positive rates written in red color?  Maybe this explains what
you see?

bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

[Ship Mints]

[-- Attachment #1: Type: text/plain, Size: 1132 bytes --]

Negative rates do indeed exist in the real world. Central banks, for
example, have set their very short-term rates negative to deter savings
(depositor pays bank to save rather than the bank paying the depositor) and
encourage credit growth and reduce longer-term rates (lending or investing
in longer-term instruments). Of course, you won't get a negative-rate
mortgage, this scheme is focused on money-center banks, not retail
consumers. In other places like the commodity markets, you can also see
negatives for things you might not expect. Oil prices were driven negative
for a short time when there was no excess shipping capacity and the cost of
shipping hyperinflated.

On Tue, Dec 10, 2024 at 8:23 AM Eli Zaretskii <eliz@gnu.org> wrote:

> > Date: Tue, 10 Dec 2024 00:44:04 +0800
> > From: Ting Boon Ghee <tingbg@gmail.com>
> >
> > Using Calc to compute the rate of return on an investment, negative
> returns will result in error.
>
> Isn't it true that in the financial world there are no negative rates,
> only positive rates written in red color?  Maybe this explains what
> you see?
>
>
>
>

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bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

[Michael Heerdegen via Bug reports for GNU Emacs, the Swiss army knife of text editors]

Eli Zaretskii <eliz@gnu.org> writes:

> Isn't it true that in the financial world there are no negative rates,
> only positive rates written in red color?  Maybe this explains what
> you see?

It's probably not related but: this part of `calc-fin-rate' is clearly
suspicious:

      (calc-to-percentage
       (calc-normalize
	(cons (if (calc-is-hyperbolic) 'calcFunc-ratel
		(if (calc-is-hyperbolic) 'calcFunc-rateb ;; !@?!
		  'calcFunc-rate))
	      (calc-top-list-n n))))

Looks like one of those two identical `calc-is-hyperbolic' tests
must be replaced with `calc-is-inverse' (the second one?).


Michael.

bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

[Michael Heerdegen via Bug reports for GNU Emacs, the Swiss army knife of text editors]

Hello,

could you please post a recipe?


TIA,

Michael.

bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

[Manuel Giraud via Bug reports for GNU Emacs, the Swiss army knife of text editors]

Michael Heerdegen via "Bug reports for GNU Emacs, the Swiss army knife
of text editors" <bug-gnu-emacs@gnu.org> writes:

> Hello,
>
> could you please post a recipe?

Hi,

The recipe is at the end of the mail.
-- 
Manuel Giraud

bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

[Michael Heerdegen via Bug reports for GNU Emacs, the Swiss army knife of text editors]

Ting Boon Ghee <tingbg@gmail.com> writes:

> I am not sure if this is a bug or due to some restrictions or
> constrains elsewhere that the interval cannot be negative in the
> original function definition of math-compute-rate.

It could be that the original authors just did not have this special
case in mind when writing the code, and there is no such reason.

Michael.

bug#74760: 29.4; Calc : calcFunc-rate does not produce negative results

[Ting Boon Ghee]

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Thanks everyone for response.

These financial functions (and more) are available in spreadsheets such as
Libreoffice Calc. There is no restriction for Rate to be negative in
Libreoffice Calc. One way to look at this is, from investment perspective,
it just means the series of payments is less than the initial outlay,
resulting in negative return.

The Info manual describes the Rate function as an inverse of ‘pv’:
‘rate(N, PAYMENT, AMOUNT)’ computes the value of RATE such that ‘pv(RATE,
N, PAYMENT) = AMOUNT’. So let's try PV.

If Rate = -0.1, N = 1, PAYMENT = 90, calculate PV. Thus,

M-x calc <RET> _0.1 <RET> 1 <RET> 90 <RET> b P
Answer : 100

This means PV function can accept Rate as a negative number.

I stumbled upon this issue because I was trying to recreate a table that I
had done previously in Libreoffice Calc into an Org Table. The table uses
Rate function to calculate a series of returns with a range of negative to
positive returns. The negative returns generated errors in the table fields.

I suppose Emacs Calc was developed long ago to mimic handheld calculators.
I'd wonder whether anyone is still using it as a "handheld" financial
calculator. Such functions are most useful in spreadsheets. Emacs now has
an implementation of a spreadsheet in the form of Org Table that uses Emacs
Calc. This does mean that it is restricted to what Emacs Calc can provide.
A missing function that I wish for is the XIRR function available in other
spreadsheet softwares.

-- 
Best regards,
Boon Ghee

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