XIRR Tool

In Properties of Money we have seen the importance of "r" - or annualized returns. As an investor, how would you assess your investments across various assets and compare their relative returns?

MS Excel's "Extended Internal Rate of Return"-XIRR function is one such metric.

XIRR is a money-weighted annualized return (as opposed to time-weighted returns). In addition to calculating returns of individual portfolios with irregular cash-flows, XIRR can also easily blend multiple heterogeneous portfolios and calculate returns of "super-portfolios".

XIRR is the solution to the equation

$$\sum ^{n}_{i=1}\dfrac {p_{i}}{\left( 1+x\right) ^{\left( di-d_{1}\right)/365 }}=0$$

Where $p_{1}$ .. $p_{n-1}$ represents the transactions in and out of the portfolio. $p_{n}$ represents the final balance or the amount you will get back when you completely liquidate the portfolio on day $d_{n}$. This date should be greater or equal to than all dates entered before it. The equation simply applies discounting to a chronological stream of investments. By convention, opening balance/initial deposit i.e $p_{1}$, on day $d_{1}$ and all other deposits into the portfolio are considered negative. Withdrawals, dividends and final balance amounts are considered positive.

There are a few numerical methods that may be used to solve this equation. We may use the Newton-Raphson method or the Secant method. These are root finding methods that essentially start with a guess and iteratively refine it till the computed value falls within an acceptable tolerance. I use another root finding method the Bisection method to converge my guesses in the tool below.

Data entered never leaves the browzer. I use copy/paste buttons to save/retrieve my work as text in txt files/mail drafts.