Linked IRR Calculator

Linked IRR (Linked Internal Rate of Return) is a performance measurement technique that geometrically chains together multiple sub-period returns to produce an accurate cumulative return over a longer period. Unlike a simple sum of returns, geometric linking correctly accounts for compounding — meaning that gains and losses in each sub-period affect the base from which the next sub-period is calculated.

The concept is widely used in investment performance reporting, particularly under the Global Investment Performance Standards (GIPS) framework published by the CFA Institute. GIPS requires that portfolio managers report time-weighted returns, and linked IRR is the standard method for combining sub-period Modified Dietz or other sub-period returns into a composite time-weighted return.

Why does geometric linking matter? Consider a portfolio that gains 50% in year one and loses 50% in year two. A naive arithmetic approach says the average return is 0%, implying no change. But the geometric calculation correctly reveals a cumulative loss of 25%, because the 50% loss in year two applies to a larger base. Linked IRR captures this reality precisely.

This calculator accepts any number of sub-periods, each with its own return percentage and duration in months. The linked return is computed as the product of each period's growth factor minus one. It then annualizes that result based on total elapsed months, and provides the geometric mean return per sub-period alongside the arithmetic mean for comparison.

A cumulative linked return by itself is hard to compare across portfolios measured over different time horizons. A 7% return over six months is very different from a 7% return over three years. Annualizing converts any cumulative return into an equivalent rate that would have been earned if the performance sustained for exactly one year, enabling apples-to-apples comparison.

The annualization formula used by this calculator is:

Annualized Return = (1 + Linked Return)^(12 ÷ Total Months) − 1

For example, if the linked return over nine months is 5.99%, the annualized equivalent is approximately 8.06%, because the same compounding rate sustained for twelve months would produce a higher cumulative result. Conversely, a return earned over more than twelve months will annualize to a lower figure than the raw cumulative return.

This approach matches the time-weighted return (TWR) annualization convention used in GIPS-compliant reporting. It is appropriate when the sub-periods together span a coherent investment horizon, such as all quarters within a calendar year or all months within a multi-year evaluation window.

This calculator reports both the geometric mean and the arithmetic mean per sub-period, and the difference between them is practically important for investment analysis.

The geometric mean per sub-period is calculated as:

Geometric Mean = (1 + Linked Return)^(1 ÷ n) − 1

where n is the number of sub-periods. It represents the constant rate that, compounded over all n sub-periods, produces the same final value as the actual sequence of returns. This is the theoretically correct "average" for multiplicative processes like investment growth.

The arithmetic mean is simply the sum of all sub-period returns divided by the number of periods. It is always equal to or greater than the geometric mean when returns vary — a mathematical consequence of Jensen's inequality. The larger the volatility across sub-periods, the bigger the gap between arithmetic and geometric means.

In practice, the arithmetic mean overestimates long-run compound growth. If a fund reports "average returns" using the arithmetic mean, investors can be misled about actual wealth accumulation. The geometric mean — and by extension the linked IRR — tells you what your money actually grew to. Investment managers following GIPS exclusively use geometric (time-weighted) figures in performance reports to prevent this confusion.

One of the most common workflows for this calculator is linking Modified Dietz returns. Modified Dietz is an approximation of the time-weighted return for a single sub-period that adjusts for external cash flows without requiring daily portfolio valuation. For each sub-period, the Modified Dietz return is:

Modified Dietz = (EMV − BMV − CF) ÷ (BMV + Weighted CF)

where EMV is ending market value, BMV is beginning market value, CF is net external cash flows, and weighted CF weights each cash flow by the fraction of the period remaining when it occurred.

Once you have Modified Dietz returns for each sub-period (for example, each month within a quarter, or each quarter within a year), you feed them into this linked IRR calculator to chain them geometrically. This two-step process — compute Modified Dietz for each sub-period, then link — is the standard GIPS-recommended approximation for time-weighted return when daily valuations are unavailable.

The linked result is a much better approximation of the true time-weighted return than simply adding Modified Dietz figures together. Portfolio managers, performance analysts, and compliance teams use this workflow to produce GIPS-compliant composite returns, attribution reports, and benchmark comparisons on a monthly, quarterly, or annual basis.

This calculator handles any number of sub-periods, making it suitable for linking monthly returns into a quarter, quarterly returns into a year, or yearly returns into a multi-year track record.

The linked IRR calculator is the right tool whenever you need to combine sequential return figures into an accurate cumulative or annualized performance measure. Common scenarios include:

• GIPS-compliant performance reporting: Investment managers must chain sub-period returns to produce official composite returns for presentation to prospective clients.
• Quarterly to annual roll-up: Combining four quarterly returns into a full-year figure using proper geometric linking rather than simply adding percentages.
• Manager evaluation: When comparing two fund managers whose track records span different date ranges, converting both to annualized linked returns puts them on equal footing.
• Portfolio attribution: Segment-level linked returns can be aggregated and compared against benchmark linked returns to identify where the portfolio over- or underperformed.
• Personal finance tracking: Individual investors who track monthly or quarterly brokerage returns can use this tool to get an accurate multi-period cumulative view.
• Alternative investment reporting: Private equity, hedge funds, and real estate funds often report sub-period returns that must be chained to produce meaningful IRR-like metrics.

The key limitation of linked IRR versus a full cash-flow-based IRR is that linked IRR assumes you are working with already-computed sub-period returns rather than raw cash flows. If you have the actual cash flows (amounts invested, distributions received, and ending value), a standard IRR or XIRR calculation may be more appropriate. Linked IRR shines when sub-period return estimates are already in hand and need to be combined efficiently.