Merge pull request #99 from yatshunlee/main

Updated irr function [issue 98]

Author: Kai-Striega

numpy_financial/_financial.py

@@ -710,7 +710,7 @@ def rate(
     return rn
 
 
-def irr(values, *, guess=None, tol=1e-12, maxiter=100, raise_exceptions=False):
+def irr(values, *, raise_exceptions=False):
     r"""Return the Internal Rate of Return (IRR).
 
     This is the "average" periodically compounded rate of return
@@ -726,14 +726,6 @@ def irr(values, *, guess=None, tol=1e-12, maxiter=100, raise_exceptions=False):
         are negative and net "withdrawals" are positive.  Thus, for
         example, at least the first element of `values`, which represents
         the initial investment, will typically be negative.
-    guess : float, optional
-        Initial guess of the IRR for the iterative solver. If no guess is
-        given an heuristic is used to estimate the guess through the ratio of
-        positive to negative cash lows
-    tol : float, optional
-        Required tolerance to accept solution. Default is 1e-12.
-    maxiter : int, optional
-        Maximum iterations to perform in finding a solution. Default is 100.
     raise_exceptions: bool, optional
         Flag to raise an exception when the irr cannot be computed due to
         either having all cashflows of the same sign (NoRealSolutionException) or
@@ -799,13 +791,6 @@ def irr(values, *, guess=None, tol=1e-12, maxiter=100, raise_exceptions=False):
                                       'cashflows are of the same sign.')
         return np.nan
 
-    # If no value is passed for `guess`, then make a heuristic estimate
-    if guess is None:
-        positive_cashflow = values > 0
-        inflow = values.sum(where=positive_cashflow)
-        outflow = -values.sum(where=~positive_cashflow)
-        guess = inflow / outflow - 1
-
     # We aim to solve eirr such that NPV is exactly zero. This can be framed as
     # simply finding the closest root of a polynomial to a given initial guess
     # as follows:
@@ -823,20 +808,40 @@ def irr(values, *, guess=None, tol=1e-12, maxiter=100, raise_exceptions=False):
     #
     # which we solve using Newton-Raphson and then reverse out the solution
     # as eirr = g - 1 (if we are close enough to a solution)
-    npv_ = np.polynomial.Polynomial(values[::-1])
-    d_npv = npv_.deriv()
-    g = 1 + guess
+    
+    g = np.roots(values)
+    eirr = np.real(g[np.isreal(g)]) - 1
 
-    for _ in range(maxiter):
-        delta = npv_(g) / d_npv(g)
-        if abs(delta) < tol:
-            return g - 1
-        g -= delta
+    # realistic IRR
+    eirr = eirr[eirr>=-1]
 
-    if raise_exceptions:
-        raise IterationsExceededError('Maximum number of iterations exceeded.')
+    # if no real solution
+    if len(eirr) == 0:
+        if raise_exceptions:
+            raise NoRealSolutionError("No real solution is found for IRR.")
+        return np.nan
 
-    return np.nan
+    # if only one real solution
+    if len(eirr) == 1:
+        return eirr[0]
+    
+    # below is for the situation when there are more than 2 real solutions.
+    # check sign of all IRR solutions
+    same_sign = np.all(eirr > 0) if eirr[0] > 0 else np.all(eirr < 0)
+    
+    # if the signs of IRR solutions are not the same, first filter potential IRR
+    # by comparing the total positive and negative cash flows.
+    if not same_sign:
+        pos = sum(values[values>0])
+        neg = sum(values[values<0])
+        if pos >= neg:
+            eirr = eirr[eirr>=0]
+        else:
+            eirr = eirr[eirr<0]
+    
+    # pick the smallest one in magnitude and return
+    abs_eirr = np.abs(eirr)
+    return eirr[np.argmin(abs_eirr)]
 
 
 @nb.njit

tests/test_financial.py

@@ -860,12 +860,3 @@ def test_irr_no_real_solution_exception(self):
 
         with pytest.raises(npf.NoRealSolutionError):
             npf.irr(cashflows, raise_exceptions=True)
-
-    def test_irr_maximum_iterations_exception(self):
-        # Test that if the maximum number of iterations is reached,
-        # then npf.irr returns IterationsExceededException
-        # when raise_exceptions is set to True.
-        cashflows = numpy.array([-40000, 5000, 8000, 12000, 30000])
-
-        with pytest.raises(npf.IterationsExceededError):
-            npf.irr(cashflows, maxiter=1, raise_exceptions=True)