---
title: "Returns and risk maths | RupeeCase Blog"
description: "CAGR, rolling windows, Sharpe, drawdown, volatility drag, sequence risk and real returns: how a return number is built and what it hides."
source_url: "https://www.rupeecase.com/blog/topic/returns-risk-maths/"
---

RupeeCase notes . Topic

# Returns and risk maths

      CAGR, rolling windows, Sharpe, drawdown, volatility drag, sequence risk and real returns: how a return number is built and what it hides.

* **20**notes in this topic
* **6**to read in order
* **3**questions answered

        01Read in this order

## Six notes that carry the idea.

1. [06The bigger number is the smaller return6 min . 5 Jul 2026](/blog/2026-07-05-morning-total-return-vs-cagr/)
2. [06The bigger number is the smaller return6 min . 5 Jul 2026](/blog/2026-07-05-morning-total-return-vs-cagr/)
3. [06The bigger number is the smaller return6 min . 5 Jul 2026](/blog/2026-07-05-morning-total-return-vs-cagr/)
4. [06The bigger number is the smaller return6 min . 5 Jul 2026](/blog/2026-07-05-morning-total-return-vs-cagr/)
5. [06The bigger number is the smaller return6 min . 5 Jul 2026](/blog/2026-07-05-morning-total-return-vs-cagr/)
6. [06The bigger number is the smaller return6 min . 5 Jul 2026](/blog/2026-07-05-morning-total-return-vs-cagr/)

        02Every note

## 20 notes, newest first.

1. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
2. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
3. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
4. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
5. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
6. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
7. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
8. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
9. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
10. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
11. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
12. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
13. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
14. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
15. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
16. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
17. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
18. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
19. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)
20. [SIP returns: XIRR vs the absolute numberThe same 60 month SIP statement shows 33 percent absolute, a 14 percent factsheet CAGR and an 11.4 percent XIRR, and only the last one is the return you earned.8 May 2026 . 5 min](/blog/2026-05-08-evening-sip-xirr-vs-absolute/)

        03Go deeper

## From the notes to the course, and to the cards.

          [Learn path 1The free Learn course on the same ground, with a certificate at the end.](/learn/path-1/)
          [18 index algosEvery RupeeCase strategy, model back tested, in your own demat.](/strategies/)
          [All eight topicsBack to the hub: reading paths, search and the latest notes.](/blog/)

        04Questions, answered with figures

## Three questions readers ask about returns and risk maths.

        Why does the same fund show different CAGRs on different factsheets?Because a point to point CAGR depends on the window. Every three year window on the Nifty 50 TRI from 2013 to 2025 ranged from 8.8 to 18.3 percent a year, and the same fund printed 18.3 percent in December 2021 and 11.4 percent in December 2024 without changing. [Read the note: The three year number that changes every day](/blog/2026-07-29-morning-three-year-number/)

What is the difference between average return and CAGR?Average return adds the years and divides; CAGR multiplies them. Up 50 then down 50 averages zero and leaves Rs 75 of Rs 100. The gap is roughly half the variance a year, so doubling volatility quadruples the drag. [Read the note: The volatility tax](/blog/2026-07-31-evening-volatility-tax/)

Does the order of returns matter?Not for a lump sum left alone, where any order ends at the same number. It decides everything once money flows out: the same ten returns leave a retiree drawing Rs 6 lakh a year from Rs 1 crore with Rs 125.66 lakh or Rs 39.08 lakh. [Read the note: Same returns, different retirement](/blog/2026-09-05-morning-same-returns-different-retirement/)

    Explore next

## Where to go next.

* [Free module 2.3Risk Metrics That Matter8 min read](/learn/path-2/module-2-3-risk-metrics-that-matter)
* [Free module 4.4Performance Measurement9 min read](/learn/path-4/module-4-4-performance-measurement)
* [CalculatorCAGR calculatorFree, with the formula and a worked example](/learn/tools/cagr-calculator)
* [CalculatorLumpsum calculatorFree, with the formula and a worked example](/learn/tools/lumpsum-calculator)
* [LearnLearn systematic investing, free11 paths, 70 modules, certificates](/learn/)