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:

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

With:

\(T\) the total number of days since the beginning
\(t_i\) the number of days since the beginning for date \(i\)
\(CF_i\) 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

Example

With the following data:

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