What Is Annualized Return (XIRR)?

For a lump-sum investment, it is simple. If you invested about $7,400 and it became about $10,700 two years later, the CAGR is 20%.

But recurring investing, where you invest about $74 every month, is different. The $74 invested in January and the $74 invested in December have different holding periods. Even if the total contribution is about $8,900 and the final value is about $17,800, saying "the return is 100%" is inaccurate. That's because the January contribution was invested for 12 months, while the December contribution was invested for only 1 month.

XIRR (Extended Internal Rate of Return) is the internal rate of return that accounts for cash flows at irregular points in time. By reflecting each investment date and amount plus the final value, it calculates "what annual interest rate would produce this same result?"

For example, if you invested about $74 every month for 10 years (about $8,900 total) and it became about $17,800, the simple calculation gives a 100% return, but the XIRR is about 13%. That's because later contributions had a short holding period and contributed little to gains, while the effect of early contributions being invested for a long time is reflected.

XIRR finds, through numerical methods, the value of r that satisfies the following equation: the value of r for which the sum of each cash flow divided by (1+r)^(days elapsed / 365) equals 0.

This equation has no analytical solution, so it is solved through iterative methods such as Newton-Raphson. In most cases it converges quickly, but in extreme scenarios (such as a large early loss followed by a dramatic recovery) it may fail to converge. In such cases it is shown as "cannot be calculated."

Even with the same investment period and the same final amount, XIRR varies depending on the timing of the contributions. If you invested a large amount early and less later, the XIRR is lower; the reverse makes it higher.

For recurring installment investing, the XIRR is higher when the market was low early and rose later. This is the "lowering the average purchase price" effect of installment investing.