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A navy topographic contour map whose ridge traces a rising return curve in teal

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.

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

01Read in this order

Six notes that carry the idea.

  1. 01Rolling returns vs CAGR5 min .
  2. 02The volatility tax8 min .
  3. 03Drawdown: depth vs duration7 min .
  4. 04The three year number that changes every day7 min .
  5. 05The since inception trap5 min .
  6. 06The bigger number is the smaller return6 min .

02Every note

20 notes, newest first.

  1. Same returns, different retirementThe same ten annual returns leave a Rs 1 crore corpus drawing Rs 6 lakh a year at Rs 125.66 lakh or Rs 39.08 lakh depending only on their order. . 11 min
  2. The average return is a liePlus 30, minus 20, plus 25, minus 15 averages 5.00 percent and compounds at 2.53, and a 12 percent average at 45 percent volatility compounds at 3.93. . 11 min
  3. The volatility taxFive portfolios averaging 12 percent compound at 11.98 down to 4.00 percent depending only on volatility, so Rs 10 lakh over twenty years ends anywhere from Rs 96 lakh to Rs 22 lakh. . 8 min
  4. The three year number that changes every dayEvery three year window on the Nifty 50 TRI from 2013 to 2025 ranged from 8.8 to 18.3 percent CAGR, and three months in 2020 moved it by 14 points. . 7 min
  5. Sequence of returns: the order you live throughReshuffling the same ten years leaves a lump sum unchanged, ends a retiree with 28 or 140 lakh, and makes an early crash a gift for someone still paying in. . 9 min
  6. The since inception trapA six year old fund's 18.9 percent since inception rode a 75 percent birth year; on the same five years it did 10 against the fifteen year old fund's 13. . 5 min
  7. Rule of 72: count in doublingsRs 10 lakh for thirty years becomes about Rs 3 crore at 12 percent and Rs 1 crore at 8, because four points deletes close to two doublings. . 4 min
  8. The average year mythIn twenty years of Nifty calendar returns only two landed near the 12 percent long run rate, with nine years above 20 percent and 2008 giving back about half. . 5 min
  9. Drawdown: depth vs durationTwo funds with the same 20 percent max drawdown spent seven and twenty six months below their old highs, and the wait is where plans die by quiet quitting. . 7 min
  10. The bigger number is the smaller returnA fund up 214 percent over twelve years earned about 10 percent a year, roughly half the 19 percent a year of the fund with the smaller looking figure. . 6 min
  11. Real vs nominal: the three numbers in a returnA 6.5 percent fixed deposit becomes 4.55 after top slab tax and about 0.6 percent after 4 percent inflation, and turns real negative at the RBI's 6 percent ceiling. . 5 min
  12. After tax and inflation, safe can go backwardsA 7 percent fixed deposit nets about 4.9 after top slab tax and roughly zero after 5 percent inflation, so Rs 10 lakh that doubled on paper buys less than it did. . 5 min
  13. The long run makes the rate safe and the rupees wildTwenty years narrows the annualised range to about 6 to 15 percent while the rupee outcome on Rs 10 lakh fans out from Rs 31 lakh to Rs 1.56 crore. . 5 min
  14. Average return vs CAGRUp 50 then down 50 averages zero and loses a quarter of the money, and two funds averaging 12 percent at 8 and 30 percent volatility end twenty years at Rs 91 lakh and Rs 42 lakh. . 5 min
  15. TRI vs price index: which NiftyThe total return index runs about 1.3 points a year hotter than the TV number, enough to turn a fund that beat the price index by Rs 2.89 lakh into one that trailed by Rs 0.91 lakh. . 5 min
  16. Sharpe, Sortino, Calmar: three leaderboardsThe same three funds rank differently under Sharpe, Sortino and Calmar, and in withdrawal phase Calmar is the bar because drawdown does not average out. . 5 min
  17. Volatility drag: same average, six lakh gapTwo funds printing a 12 percent average return ended at Rs 28.4 lakh and Rs 21.8 lakh on the same Rs 10 lakh, because the drag scales with volatility squared. . 6 min
  18. Sharpe ratio decoded: same CAGR, different rideTwo funds at 14 percent CAGR can carry Sharpe ratios of 0.58 and 0.32, and anything above 1.5 over a real ten year window earns the right to be questioned before it is trusted. . 5 min
  19. Rolling returns vs CAGRA point to point CAGR is a chosen story, and the Nifty 50 TRI's rolling five year windows since 2002 ranged from minus 1.2 to plus 22.4 percent a year. . 5 min
  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. . 5 min

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. 18 index algosEvery RupeeCase strategy, model back tested, in your own demat. All eight topicsBack to the hub: reading paths, search and the latest notes.

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

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

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

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