When people say, “Over the long term, equity will provide good returns”, they often forget or do not want to consider how monthly or annual return sequences combine to result in the final annualized return (CAGR). Sometimes, the sequence of returns can be good or bad.
This is known as sequence of returns risk, sequence risk or timing luck. Understanding and minimising this is essential to investing success. With a simple example, we discuss what is a sequence of returns risk and how it affects the corpus during the accumulation phase (when we are investing towards it) and during the withdrawal phase (when we use the corpus to generate an income from it, after retirement)
Sequence of returns risk essentially means the following: We plan with an annualized return on a spreadsheet. This implies that the annual return year after year is the same in the calculation. There is no other way around it. The annual returns in equity (or gold or bonds) are different. Sometimes, you get + 25% and sometimes -40%. When these annual returns combine, they produce high, low or mediocre returns. How does this happen? What is the solution?
Lump sum investment growth at a constant return
Suppose you wish to invest Rs. one lakh for 15 years and assume an annualized return of 10% (from equity alone). This means that you assume Rs. one lakh will grow yearly.
| Year | Return Assumed | Year-end corpus |
| 1 | 10% | 1,10,000 |
| 2 | 10% | 1,21,000 |
| 3 | 10% | 1,33,100 |
| 4 | 10% | 1,46,410 |
| 5 | 10% | 1,61,051 |
| 6 | 10% | 1,77,156 |
| 7 | 10% | 1,94,872 |
| 8 | 10% | 2,14,359 |
| 9 | 10% | 2,35,795 |
| 10 | 10% | 2,59,374 |
| 11 | 10% | 2,85,312 |
| 12 | 10% | 3,13,843 |
| 13 | 10% | 3,45,227 |
| 14 | 10% | 3,79,750 |
| 15 | 10% | 4,17,725 |
Reality: Sequence of returns risk
It should be clear that 10% year on year is pure fantasy. Consider a real 15-year sequence considered in a past study – How to reduce risk in an investment portfolio:
-18%, -5%, 20%, -27%, 52%, -18%, -22%, -3%, 69%, 22%, 43%, 95%, 35%, -55%, 86%
Now, that Rs. 1 lakh would “grow” as follows
| Year | Actual return | Year-end corpus |
| 1 | -18% | 82,000 |
| 2 | -5% | 77,900 |
| 3 | 20% | 93,480 |
| 4 | -27% | 68,240 |
| 5 | 52% | 1,03,725 |
| 6 | -18% | 85,055 |
| 7 | -22% | 66,343 |
| 8 | -3% | 64,352 |
| 9 | 69% | 1,08,756 |
| 10 | 22% | 1,32,628 |
| 11 | 43% | 1,89,657 |
| 12 | 95% | 3,69,832 |
| 13 | 35% | 4,99,273 |
| 14 | -55% | 2,24,673 |
| 15 | 86% | 4,17,892 |
Notice something bizarre? The final amount is the same in both cases!! How is this possible?
1 L x (1+10%)^15 = 4.17 Lakh. Here, ^15 means (1+10%) is multiplied by itself 15 times, just as 2^3 = 2 x 2 x 2.
Instead of multiplying the same assumed return each year, it could be different for each year.
1 L x (1-18%)x(1-5%)x(1+20%)x(1-27%)x(1+52%)x(1-18%)x(1-22%)x(1-3%)x(1+69%)x(1+22%)x(1+43%)x(1+95%)x(1+35%)x(1-55%)x(1+86%) = 4.17 Lakh.
The math in both cases may have resulted in the same corpus, but there is one big difference – human emotions and behaviour. The return after one year is – 18%. How many people will still stick with equity?
Even if they do, the return after year 2 is -5%!! When investing or during the accumulation phase, the sequence of returns risk governs human behaviour. The corpus will be the same if the final annualized return is the same as the one assumed. However, the annual returns decide whether we stay invested or exit.
Deriving income from Rs. 50 lakh for 15 years
Suppose we have Rs. 50 lakh with us, and we wish to derive an income that increases each year at 6% (assumed inflation). Before the start of each year, we withdraw the annual expenses required for that year and assume the rest of the amount grows at an assumed return of 10%. The year-end corpus will decrease, as shown below.
| Annual Expenses | Assumed Return | Year-end corpus |
| 3,60,000 | 10% | 51,04,000 |
| 3,81,600 | 10% | 51,94,640 |
| 4,04,496 | 10% | 52,69,158 |
| 4,28,766 | 10% | 53,24,432 |
| 4,54,492 | 10% | 53,56,934 |
| 4,81,761 | 10% | 53,62,690 |
| 5,10,667 | 10% | 53,37,226 |
| 5,41,307 | 10% | 52,75,511 |
| 5,73,785 | 10% | 51,71,898 |
| 6,08,212 | 10% | 50,20,054 |
| 6,44,705 | 10% | 48,12,884 |
| 6,83,387 | 10% | 45,42,446 |
| 7,24,391 | 10% | 41,99,861 |
| 7,67,854 | 10% | 37,75,207 |
| 8,13,925 | 10% | 32,57,410 |
Even if the expenses increase 6% yearly, since the corpus grows at the same annual return of 10%, we will still have 32 Lakh left after 15 years.
The reality: How varying returns can diminish a corpus
Now, introduce variable returns as discussed above.
| Expenses | Actual Returns | Actual end corpus |
| 3,60,000 | -18% | 38,04,800 |
| 3,81,600 | -5% | 32,52,040 |
| 4,04,496 | 20% | 34,17,053 |
| 4,28,766 | -27% | 21,81,450 |
| 4,54,492 | 52% | 26,24,976 |
| 4,81,761 | -18% | 17,57,436 |
| 5,10,667 | -22% | 9,72,480 |
| 5,41,307 | -3% | 4,18,238 |
| 5,73,785 | 69% | |
| 6,08,212 | 22% | |
| 6,44,705 | 43% | |
| 6,83,387 | 95% | |
| 7,24,391 | 35% | |
| 7,67,854 | -55% | |
| 8,13,925 | 86% |
The corpus has now run out in 8 years!!
Notice that a sequence of returns risk can fail when you are accumulating a corpus due to bad portfolio management and investor behaviour. The withdrawal phase after retirement results in an error in the actual calculation! This is far more dangerous as one could get away with an assumed return in the accumulation phase.
Video version
What is the solution?
Proper asset allocation and step-wise reduction in equity well before the goal deadline. The Freefincal Robo Advisor Tool takes care of this automatically and gives you clear directions on how much to invest in which asset class and how to vary your asset allocation each year, depending on your personal circumstances. It helps effectively minimise sequence risk in both the accumulation and withdrawal phases of investing.
🔥Enjoy massive discounts on our courses, robo-advisory tool and exclusive investor circle! 🔥& join our community of 7000+ users!
Use our Robo-advisory Tool for a start-to-finish financial plan! ⇐ More than 2,500 investors and advisors use this!
Track your mutual funds and stock investments with this Google Sheet!
We also publish monthly equity mutual funds, debt and hybrid mutual funds, index funds and ETF screeners and momentum, low-volatility stock screeners.
Podcast: Let’s Get RICH With PATTU! Every single Indian CAN grow their wealth!
You can watch podcast episodes on the OfSpin Media Friends YouTube Channel.
🔥Now Watch Let’s Get Rich With Pattu தமிழில் (in Tamil)! 🔥
- Do you have a comment about the above article? Reach out to us on Twitter: @freefincal or @pattufreefincal
- Have a question? Subscribe to our newsletter using the form below.
- Hit ‘reply’ to any email from us! We do not offer personalized investment advice. We can write a detailed article without mentioning your name if you have a generic question.
Join 32,000+ readers and get free money management solutions delivered to your inbox! Subscribe to get posts via email! (Link takes you to our email sign-up form)
About The Author
Dr M. Pattabiraman(PhD) is the founder, managing editor and primary author of freefincal. He is an associate professor at the Indian Institute of Technology, Madras. He has over ten years of experience publishing news analysis, research and financial product development. Connect with him via Twitter(X), Linkedin, or YouTube. Pattabiraman has co-authored three print books: (1) You can be rich too with goal-based investing (CNBC TV18) for DIY investors. (2) Gamechanger for young earners. (3) Chinchu Gets a Superpower! for kids. He has also written seven other free e-books on various money management topics. He is a patron and co-founder of “Fee-only India,” an organisation promoting unbiased, commission-free investment advice.
Our flagship course! Learn to manage your portfolio like a pro to achieve your goals regardless of market conditions! ⇐ More than 3,000 investors and advisors are part of our exclusive community! Get clarity on how to plan for your goals and achieve the necessary corpus no matter the market condition is!! Watch the first lecture for free! One-time payment! No recurring fees! Life-long access to videos! Reduce fear, uncertainty and doubt while investing! Learn how to plan for your goals before and after retirement with confidence.
Our new course! Increase your income by getting people to pay for your skills! ⇐ More than 700 salaried employees, entrepreneurs and financial advisors are part of our exclusive community! Learn how to get people to pay for your skills! Whether you are a professional or small business owner who wants more clients via online visibility or a salaried person wanting a side income or passive income, we will show you how to achieve this by showcasing your skills and building a community that trusts and pays you! (watch 1st lecture for free). One-time payment! No recurring fees! Life-long access to videos!
Our new book for kids: “Chinchu Gets a Superpower!” is now available!
Most investor problems can be traced to a lack of informed decision-making. We made bad decisions and money mistakes when we started earning and spent years undoing these mistakes. Why should our children go through the same pain? What is this book about? As parents, what would it be if we had to groom one ability in our children that is key not only to money management and investing but to any aspect of life? My answer: Sound Decision Making. So, in this book, we meet Chinchu, who is about to turn 10. What he wants for his birthday and how his parents plan for it, as well as teaching him several key ideas of decision-making and money management, is the narrative. What readers say!
Must-read book even for adults! This is something that every parent should teach their kids right from their young age. The importance of money management and decision making based on their wants and needs. Very nicely written in simple terms. – Arun.
Buy the book: Chinchu gets a superpower for your child!
How to profit from content writing: Our new ebook is for those interested in getting side income via content writing. It is available at a 50% discount for Rs. 500 only!
Do you want to check if the market is overvalued or undervalued? Use our market valuation tool (it will work with any index!), or get the Tactical Buy/Sell timing tool!
We publish monthly mutual fund screeners and momentum, low-volatility stock screeners.
About freefincal & its content policy. Freefincal is a News Media Organization dedicated to providing original analysis, reports, reviews and insights on mutual funds, stocks, investing, retirement and personal finance developments. We do so without conflict of interest and bias. Follow us on Google News. Freefincal serves more than three million readers a year (5 million page views) with articles based only on factual information and detailed analysis by its authors. All statements made will be verified with credible and knowledgeable sources before publication. Freefincal does not publish paid articles, promotions, PR, satire or opinions without data. All opinions will be inferences backed by verifiable, reproducible evidence/data. Contact information: letters {at} freefincal {dot} com (sponsored posts or paid collaborations will not be entertained)
Connect with us on social media
Our publications
You Can Be Rich Too with Goal-Based Investing
Published by CNBC TV18, this book is meant to help you ask the right questions and seek the correct answers, and since it comes with nine online calculators, you can also create custom solutions for your lifestyle! Get it now.
Gamechanger: Forget Startups, Join Corporate & Still Live the Rich Life You Want 
This book is meant for young earners to get their basics right from day one! It will also help you travel to exotic places at a low cost! Get it or gift it to a young earner.
Your Ultimate Guide to Travel
This is an in-depth dive into vacation planning, finding cheap flights, budget accommodation, what to do when travelling, and how travelling slowly is better financially and psychologically, with links to the web pages and hand-holding at every step. Get the pdf for Rs 300 (instant download)
