Beyond CAGR: How IRR reveals the real impact of investment timing

Two weeks ago, we ex plained the arithmetic average trap and how volatility affects compounding. We also saw why geometric return, or compounded annualised growth rate (CAGR), gives a better picture of long-term wealth creation than a simple arithmetic average (https://bit.ly/4xZ4fyE).

That prompted a practical follow-up question from readers: Where does IRR, or internal rate of return, fit into the picture? This is particularly relevant for mutual fund investors be cause most do not invest all their mon ey on a single day. An investor may put in money every month through a systematic investment plan (SIP), in vest a year-end bonus as a lump sum, or redeem some units along the way to meet expenses such as travel or other consumption needs.

Once money starts moving in and out of an investment at different points in time, calculating returns becomes complicated, and we see CAGR has its limitations. CAGR works well when there is one investment at the begin ning and one value at the end. But it becomes inadequate when an investor makes multiple investments or with drawals at different points in time.


Refer to the illustration. Investor X invests Rs.1 lakh in 2021 at a net asset value (NAV) of Rs.12 and receives 8,333 units. He holds these units for four years and sells them at the end of 2025, when the NAV is Rs.13.26. His invest ment is then worth Rs.1.1 lakh. There is only one investment and one final value. The annualised rate at which Rs.1 lakh grows to Rs.1.1 lakh over four years is 2.53%. That is the CAGR. For sim plicity, we have assumed that there are no other costs or charges (such as brokerage and commissions).

Now consider, instead of investing Rs.1 lakh at one go, an investor puts this sum in two different instalments.

There is no single Rs.1 lakh investment that remains invested throughout the four-year period. The first instalment gets more time in the market than the second instalment. That difference in timing matters. When cash flows oc cur at different points in time, we need a return measure that takes both their size and timing into account. That’s where IRR comes in.

Timing changes your returns

TWR: Time-weighted returns; MWR: Money-weighted returns

Note: All numbers and returns are hypothetical. Assumed no brokerages or commission. Also, it is assumed that investments and withdrawals are made at the end of the period.

Different forms of IRR

Time-weighted returns vs money-weighted returns

To bridge the gap between CAGR and IRR, it is important to understand two fundamental performance concepts: time-weighted returns (TWR) and money weighted returns (MWR).

TWR measures the performance irrespective of when investors invested or withdrew their money. It breaks the perfor mance into individual holding periods, cal culates each period’s compounding growth factor and multiplies them together. Further, it can be annualised by taking the nth root, where ‘n’ is the number of periods.

This is similar to the geometric return that was explained in the previous article. In the illustration, TWR is 2.53%. (For more details on calculations, readers can refer to the pre vious article on the arithmetic return trap.

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Mutual funds employ the principles of TWR to report performance. A fund manag er cannot control when investors put money into the fund or redeem it. If an investor withdraws money during a market crash, for example, that reflects the investor’s cash flow decision rather than the fund manager’s investment performance. TWR removes the impact of such cash flows and focuses on how the underlying portfolio performed.

MWR looks at the same investment from a different perspective. It asks: what return did this particular investor actually earn? Here, both how much money was invested and when it was invested matter.

Suppose two investors put the same total amount into the same fund, but at different times. One puts a large amount into the fund just before a market rally, while the other invests a large amount just before a market decline. The fund’s performance is the same for both investors, but their personal returns can be very different.

Consider investors Y and Z in the illustra tion. Both invest a total of Rs.1 lakh in the fund, but the timing of their investments is differ ent. Investor Y invests Rs.20,000 in 2021 and an other `80,000 in 2023. At the respective NAVs, he acquires a total of 7,941 units. At the 2025 NAV of Rs.13.26, these units are worth Rs.1.05 lakh. His MWR works out to 2.17%, lower than the fund’s TWR of 2.53%. His return is lower because a significant portion of his money was invested in 2023, before the fund fell 20% in 2024.

Now consider investor Z. He invests Rs.20,000 in 2021 and another Rs.80,000 in 2022. He acquires around 9,510 units. At the 2025 NAV of Rs.13.26, his investment is worth Rs.1.26 lakh. His MWR works out to 7.5%, consider ably higher than the fund’s TWR of 2.53%. That is because a significant portion of his money was invested at the lower NAV in 2022, before the fund rallied 25% in 2023.

So, the same fund delivers a TWR of 2.53%, but investor Y earns 2.17%, while investor Z earns 7.5%. This captures the difference between TWR and MWR neatly: TWR tells how the investment performed; MWR tells how your money performed in that investment.

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It is to be noted that for investor X, TWR, MWR and CAGR (or geometric mean) is same as he makes one initial investment and no subsequent external cash flows or withdraw als (see illustration).

Accounting for timing, cash flow

IRR converts a series of investments and withdrawals occurring at different times into a single rate of return. So, IRR takes into account not only how much money went in and came out, but also when each cash flow occurred. The math behind IRR can look intimidating, but investors do not need to calculate it manually. Spreadsheet func tions can do the heavy lifting. What matters is understanding what the number is trying to tell you. There are three types of IRR, which differ on two key factors (see table): the frequency of cash flows and the reinvest ment rate assumed for interim cash flows.