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