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‎README.md

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@@ -61,63 +61,60 @@ xirr(['2020-01-01', '2021-01-01'], [-1000, 1200])
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# Multiple IRR problem
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The multiple internal rates of return problem occur when the signs of cash
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flows change more than once. In this case, we say that the project has
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non-conventional cash flows. This leads to situation, where it can have more
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the one (X)IRR or have no (X)IRR at all.
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The Multiple IRR problem occur when the signs of cash flows change more than
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once. In this case, we say that the project has non-conventional cash flows.
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This leads to situation, where it can have more the one IRR or have no IRR at all.
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PyXIRR's approach to the Multiple IRR problem: select the lowest IRR to be conservative
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PyXIRR's approach to the Multiple IRR problem:
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1. It looks for positive result around 0.1 (the same as Excel with the default guess=0.1).
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2. If it can't find a result, it uses several other attempts and selects the lowest IRR to be conservative.
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Here is an example of how to find multiple IRRs:
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```python
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import pandas as pd
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import numpy as np
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import pyxirr
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# load cash flow:
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cf = pd.read_csv("tests/samples/30-22.csv", names=["date", "amount"])
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# check whether the cash flow is conventional:
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print(pyxirr.is_conventional_cash_flow(cf["amount"])) # false
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r1 = pyxirr.xirr(cf)
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print("r1: ", r1) # -0.31540826742734207
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# check using NPV
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print("XNPV(r1): ", pyxirr.xnpv(r1, cf)) # -2.3283064365386963e-10
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# the second root
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r2 = pyxirr.xirr(cf, guess=0.0) # -0.028668460065441048
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print("r2: ", r2)
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print("XNPV(r2): ", pyxirr.xnpv(r2, cf)) # 0.0
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# print NPV profile
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import numpy as np
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# build NPV profile:
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# calculate 50 NPV values for different rates
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rates = np.linspace(-0.5, 0.5, 50)
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# any iterable, any rates, e.g.
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# rates = [-0.5, -0.3, -0.1, 0.1, -0.6]
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values = pyxirr.xnpv(rates, cf)
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series = pd.Series(values, index=rates)
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print("Zero crossing points:")
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for idx in pyxirr.zero_crossing_points(values):
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print(series.iloc[[idx, idx+1]])
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# print NPV profile:
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# NPV changes sign two times:
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# 1) between -0.316 and -0.295
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# 2) between -0.03 and -0.01
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print(series)
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# -0.500000 -8.962169e+08
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# ...
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# -0.336735 -5.895002e+05
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# -0.316327 -1.457451e+04
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# -0.295918 1.801890e+05
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# -0.275510 2.175858e+05
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# ...
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# -0.051020 2.612340e+03
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# -0.030612 1.857505e+02
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# -0.010204 -1.452180e+03
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# 0.010204 -2.533466e+03
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# ...
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# 0.500000 -2.358226e+03
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print("NPV profile:")
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for rate, value in zip(rates, values):
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print(rate, value)
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# plot NPV profile
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import pandas as pd
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series = pd.Series(values, index=rates)
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pd.DataFrame(series[series > -1e6]).assign(zero=0).plot()
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# find points where NPV function crosses zero
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indexes = pyxirr.zero_crossing_points(values)
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print("Zero crossing points:")
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for idx in indexes:
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print("between", rates[idx], "and", rates[idx+1])
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# XIRR has two results:
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# -0.31540826742734207
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# -0.028668460065441048
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for i, idx in enumerate(indexes, start=1):
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rate = pyxirr.xirr(cf, guess=rates[idx])
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npv = pyxirr.xnpv(rate, cf)
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print(f"{i}) {rate}; XNPV = {npv}")
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```
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# More Examples

‎docs/private_equity.md

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@@ -4,51 +4,258 @@
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{% include_relative _inline/pe/dpi.md %}
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```python
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def dpi(amounts: _AmountArray) -> float:
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...
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def dpi_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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) -> float:
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...
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```
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## RVPI
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{% include_relative _inline/pe/rvpi.md %}
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```python
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def rvpi(
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contributions: _AmountArray,
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nav: _Amount,
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) -> float:
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...
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```
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## TVPI
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{% include_relative _inline/pe/tvpi.md %}
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```python
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def tvpi(
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amounts: _AmountArray,
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nav: _Amount = 0,
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) -> float:
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...
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def tvpi_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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nav: _Amount = 0,
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) -> float:
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...
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```
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## MOIC
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{% include_relative _inline/pe/moic.md %}
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```python
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def moic(
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amounts: _AmountArray,
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nav: _Amount = 0,
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) -> float:
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...
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def moic_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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nav: _Amount = 0,
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) -> float:
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...
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```
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## LN-PME
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{% include_relative _inline/pe/ln_pme.md %}
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```python
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def ln_pme(
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amounts: _AmountArray,
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index: _AmountArray,
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) -> Optional[float]:
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...
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def ln_pme_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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) -> Optional[float]:
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...
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```
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## LN-PME NAV
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{% include_relative _inline/pe/ln_pme_nav.md %}
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```python
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def ln_pme_nav(
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amounts: _AmountArray,
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index: _AmountArray,
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) -> float:
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...
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def ln_pme_nav_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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) -> float:
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...
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```
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## KS-PME Flows
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{% include_relative _inline/pe/ks_pme_flows.md %}
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```python
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def ks_pme_flows(
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amounts: _AmountArray,
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index: _AmountArray,
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) -> List[float]:
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...
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def ks_pme_flows_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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) -> Tuple[List[float], List[float]]:
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...
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```
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## KS-PME
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{% include_relative _inline/pe/ks_pme.md %}
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```python
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def ks_pme(
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amounts: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> Optional[float]:
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...
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def ks_pme_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> Optional[float]:
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...
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```
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## mPME
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{% include_relative _inline/pe/m_pme.md %}
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```python
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def m_pme(
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amounts: _AmountArray,
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index: _AmountArray,
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nav: _AmountArray,
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) -> float:
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...
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def m_pme_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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nav: _AmountArray,
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) -> float:
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...
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```
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## PME+ Flows
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{% include_relative _inline/pe/pme_plus_flows.md %}
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```python
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def pme_plus_flows(
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amounts: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> List[float]:
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...
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def pme_plus_flows_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> Tuple[List[float], List[float]]:
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...
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```
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## PME+ Lambda
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{% include_relative _inline/pe/pme_plus_lambda.md %}
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```python
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def pme_plus_lambda(
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amounts: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> float:
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...
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def pme_plus_lambda_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> float:
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...
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```
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## PME+
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{% include_relative _inline/pe/pme_plus.md %}
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```python
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def pme_plus(
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amounts: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> Optional[float]:
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...
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def pme_plus_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> Optional[float]:
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...
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```
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## Direct Alpha
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{% include_relative _inline/pe/direct_alpha.md %}
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```python
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def direct_alpha(
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amounts: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> Optional[float]:
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...
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def direct_alpha_2(
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contributions: _AmountArray,
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distributions: _AmountArray,
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index: _AmountArray,
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nav: _Amount = 0,
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) -> Optional[float]:
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...
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```

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