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:

$$NPV=\sum _{i=0}^{T}C{F}_i(1+r{)}^{\frac{T-t_i}{T}}=0$$

With:

• $T$ the total number of days since the beginning

• $t_i$ the number of days since the beginning for date $i$

• $C{F}_i$ the enhanced cashflow for date $i$

  • CF of the first day is the opposite of the market value for this day: $C{F}_0=-M{V}_0$.

  • CF of the last day is increased by the market value for this day: $C{F}_T=cash\mathrm{\_}flo{w}_T+M{V}_T$.

  • Otherwise CF is the input cash flow: $C{F}_i=cash\mathrm{\_}flo{w}_i$.

This equation is solved using the Newton’s method.

Parameters:

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

• market_value (NonConstantMeasureConvertible) – 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.

Return type:

MeasureDescription

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