The Story of CAGR and XIRR | 5 Jul 2026 | In The Money by Zerodha

Nuggets

The Story of CAGR and XIRR | 5 Jul 2026 | In The Money by Zerodha · Nuggets

The 4,000-Year Historical Legacy of Compounding [00:04:49 - 00:10:40]
- Mesopotamian Foundations: The foundational framework for capital growth was biological, originating from livestock propagation; etymological roots for "interest" in Sumerian, ancient Egyptian, and Greek explicitly trace back to livestock or "the calf" [00:01:20]. A Babylonian clay tablet from 2,000 BC written in Akkadian cuneiform (housed at the Louvre) explicitly models a 20% annual interest rate, calculating the capital doubling timeline at 3 years and 283 days—deviating from modern computing by a marginal 5 days [00:04:56].
- The Usury Prohibitions: Medieval Catholic canonical law completely banned the charging of interest, designating it as the sin of usury based on the theological position that money is inanimate (unlike cattle) and cannot naturally reproduce. Charging for its use over time was viewed as illicitly profiting from time itself, which belonged solely to God. Merchants circumvented this via structured annuities and disguised trade credits [00:05:46].
- Mathematical Formalization:
  - In 1202, Leonardo Fibonacci published Liber Abaci, migrating the Hindu-Arabic positional numeral system (0-9) to Europe. This eliminated the friction of Roman numerals, enabling merchants to compute advanced arithmetic and primitive Discounted Cash Flow (DCF) models [00:06:34].
  - In 1494, Franciscan friar Luca Pacioli (the father of double-entry bookkeeping and mathematics tutor to Leonardo da Vinci) published Summa de arithmetica, formalizing the "Rule of 72" approximation [00:07:26].
  - In 1683, Jacob Bernoulli analyzed continuous compounding frequencies, revealing the mathematical constant e (2.71828), which linked compound finance directly to foundational calculus [00:08:22].
- Wall Street Metric Standardization: During the 1950s quantitative revolution led by Harry Markowitz, William Sharpe, and Eugene Fama, the asset management industry formalized the geometric mean—CAGR—as the baseline institutional standard to normalize time horizons and evaluate fund managers uniformly across global capital markets [00:09:18].

Modern Digital Implementation: Actuarial Roots to Microsoft Excel [00:17:14 - 00:26:22]
- Actuarial Pricing Origins: Throughout the 18th and 19th centuries, British actuaries publishing in the Journal of the Institute of Actuaries (e.g., Francis Baily, George Barrett, Ralph Todhunter) engineered iterative models to solve for internal yields on annuities, bonds, and pension funds. They focused on the backward-looking pricing question: given the fixed price and cash flows, calculate the yield [00:18:05].
- Corporate Capital Allocation: In the 1930s, Yale economist Irving Fisher authored The Theory of Interest, flipping the question to a forward-looking model termed "rate of return over cost." Fisher demonstrated that future cash flows must be heavily discounted due to the opportunity cost of immediate capital deployment [00:19:06]. In 1951, Columbia Business School economist Joel Dean published Capital Budgeting, formalizing this concept as the "Internal Rate of Return" (IRR), which became the default universal metric for corporate treasury capital allocation [00:21:03].
- The Chronological Blindspot: Standard IRR treats time horizons as uniform intervals (Period 1, 2, 3), corrupting performance metrics if capital is deployed at asymmetric dates. Early hand-held hardware like the HP-92 calculator (1977) and the iconic Wall Street cult-standard HP-12C (1981) could execute basic iterative IRR calculations, but remained structurally blind to calendar-specific dates [00:12:46, 00:21:38].
- The Grey Matter Breakthrough: In 1993, Microsoft launched Excel 5.0, bundling an optional Analysis ToolPak add-in. This specific software engine was engineered by a small, now-extinct tech firm in Cambridge, Massachusetts called Grey Matter International Inc. [00:22:45]. Grey Matter wrote the original code that mapped calendar strings into exact incremental day counts from a foundational point (e.g., Day 0, Day 47, Day 183), marrying Simpson's calculus-driven approximation engine to irregular dates to debut the XIRR formula [00:23:49]. Microsoft fully integrated XIRR as a native, built-in function in Excel 2007, solidifying it as the global compliance standard for tracking personal investment portfolios [00:24:21].

The Story of CAGR and XIRR | 5 Jul 2026 | In The Money by Zerodha

1. Executive Briefing (TL;DR)

References

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The Story of CAGR and XIRR | 5 Jul 2026 | In The Money by Zerodha

1. Executive Briefing (TL;DR)

References

More nuggets

BofA: From sports to pop culture: Prediction markets $1 trillion bet | 14 Jul 2026

The Bridge Ep. 13: Good Credit Holds. Bad Credit Breaks | iCapital

Risk, Resilience, and Relationships Ft. Alona Gornick (MD & Senior Investment Strategist, Churchill Asset Management) |16 Jul 2026 | S&P Global Market Intelligence

2. Speaker Profiles & Context

3. Thematic Deep Dives

Metric Architecture: CAGR vs. IRR vs. XIRR [00:02:50 - 00:04:49]

The 4,000-Year Historical Legacy of Compounding [00:04:49 - 00:10:40]

Algorithmic Engine: Newton-Raphson & Simpson’s Refinements [00:10:40 - 00:17:14]

Modern Digital Implementation: Actuarial Roots to Microsoft Excel [00:17:14 - 00:26:22]

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