atoti.experimental.finance.irr module#

atoti.experimental.finance.irr(*, cash_flows, market_value, date, precision=0.001)#

Return the Internal Rate of Return based on the underlying cash flows and market values.

The IRR is the rate r that nullifies the Net Present Value:

\[\begin{split}NPV = \\sum_{i=0}^{T} CF_i (1 + r)^{\\frac{T - t_i}{T}} = 0\end{split}\]

With:

  • \(T\) the total number of days since the beginning

  • \(t_i\) the number of days since the beginning for date i

  • \(CF_i\) the enhanced cashflow for date i:

    • CF of the first day is the opposite of the market value for this day: \(CF_0 = - MV_0\).

    • CF of the last day is increased by the market value for this day: \(CF_T = cash\\_flow_T + MV_T\).

    • Otherwise CF is the input cash flow: \(CF_i = cash\\_flow_i\).

This equation is solved using the Newton’s method.

Parameters

  • cash_flows (MeasureDescription) – The measure representing the cash flows.

  • market_value (MeasureDescription) – The measure representing the market value, used to enhanced the cashflows first and last value. If the cash flows don’t need to be enhanced then 0 can be used.

  • date (Hierarchy) – The date hierarchy. It must have a single date level.

  • precision (float) – The precision of the IRR value.

See also

The IRR Wikipedia page.

Example

With the following data:

Date

MarketValue

CashFlows

2020-01-01

1042749.90

2020-01-02

1099720.01

2020-01-03

1131220.24

2020-01-04

1130904.32

2020-01-05

1748358.77

-582786.257893061

2020-01-06

1791552.54

The IRR can be defined like this:

m["irr"] = irr(cash_flows=m["CashFlow.SUM"], market_value=m["MarketValue.SUM"], date=h["Date"])
cube.query(m["irr"])
>>> 0.14397
Return type

MeasureDescription