Visualising The Annualized Return and Volatility

Last Updated on

I discuss ways in which we can visualise and interpret the annualised return, also known as the compounded annualised growth rate or the CAGR and volatility of returns. Franklin India Prima Fund had a NAV of 201.75 on April 3rd, 2006 and a NAV of 878.5 on 12th April 2017. What is the annualised return?

To compute this, we first realise 11 years is the intervening time period – 11.033 to be precise. The annualized return is given by,

878.5 = 201.75 x (1+ CAGR)^11.033

CAGR = (878.5/201.75)^(1/11.033)-1 = 14.26%.

Here ^ refers to “the power of” ( eg. 2^4 = 2 x 2 x 2 x 2)

This means that if we treat the mutual fund investment as a fixed income instrument providing annual interest on the account balance then the annual interest is 14.26%.

Of course, any market-related instrument does not provide interest or compound. It grows up or down in value. We make this kind of calculation to compare the “growth” with a risk-free instrument (that does compound) to ascertain the risk premium.

Now, suppose we decide to simulate the NAV growth from April 2006 to 2017, with only the above-mentioned information, then we will have to assume that the NAV grows by the same amount every day, and there are 2709 business days.

So we have,

NAV on April 12th 2017 = (NAV on April 3rd 2006) x (1+R)^2709

R = daily growth rate (I don’t want to call it interest rate!)

R = 0.054%.

This is how it will pan out.

Naturally, this is nonsense. The actual NAV movement is shown below.

The point of this exercise is to illustrate how the annualised return calculation sweeps the NAV ups and downs under the carpet and focusses only on the initial NAV and final NAV. There are literally millions of smooth curves that I can draw between the end points and what is shown above is just one.

When you buy something from Amazon, you don’t care whether the delivery guy braved the hot sun or floods. All you care about is the condition of the package.  You ordered something at a price and you got it in one piece – only the start and end points matter.

When you buy anything that is market-linked, you are not the end-user. You are in charge of the delivery department. You need to deliver your own net worth to where it needs to be. Therefore, the route matters. In other words, the ups and downs matter – not just the end result which is unpredictable. The volatility associated with a return matters.

Suppose we assume each month has about 21 business days and computed the “monthly” returns from April 2006 to April 2017, we would get 129 months.

This is an absolute view of the volatility. When we invest in equity, it is better to temper ourselves that -20% monthly returns are more than possible. When such returns occur will decide the wealth we create – early, middle or later in the investment schedule. More on that later.

Problems arise when we start to replace this view with a single number.  If we bin the returns into compartments, this is what we get.

This is anything but a bell curve or a normal distribution. Therefore the idea of an “average” monthly return is not valid. And by extension, the “average” deviation from the “average return”, also known as the standard deviation is also invalid. The standard deviation is the “industry standard” representation of volatility and it is wrong.

IF we assume that NAV grows by the same amount each month, then 

final NAV = initial NAV x (1+monthly_return)^129

monthy_return ~ 1.15%

Instead of the standard deviation, a simpler way to depict volatility is to define it as:

No of negative monthly returns/Total monthly returns

For the present case, this is 45/129 ~ 35%.

This gives me an idea of what to expect from this fund (or this category of funds) over the next 10 years: Expect NAV to fall for at least 1/3 rd of the months invested. Now let us try selling mutual funds with statistic!


Kolkata DIY Investor Workshop May 28th, 2017

Register for the Kolkata DIY Investor Workshop May 28th, 2017

You Can Be Rich Too With Goal-Based Investing

You can be rich too with goal based investing is my new book with PV Subramanyam. If you have not yet got the book, check out the reviews below and use the links to buy.

Reader Quotes:

Gift it to your Friends and Relatives whom you care more. Already follower of Pattu and Subra’s forum. Ordered 4 more copies to give gift to my friends and eagerly waiting to read

The best book ever on Financial Freedom Planning. Go get it now!

Your first investment should be buying this book

The (nine online) calculators are really awesome and will give you all possible insights

Thank you, readers, for your generous support and patronage.

Amazon Hardcover Rs. 317. 21% OFF

Kindle at (Rs. 307)

Infibeam Now just Rs. 307 24% OFF.

If you use a mobikwik wallet, and purchase via infibeam, you can get up to 100% cashback!!

Bookadda Rs. 344. Flipkart Rs. 359 ($ 3.70 or Rs. 267)

Google Play Store (Rs. 244.30)

  • Ask the right questions about money
  • get simple solutions
  • Define your goals clearly with worksheets
  • Calculate the correct asset allocation for each goal.
  • Find out how much insurance cover you need, and how much you need to invest with nine online calculator modules
  • Learn to choose mutual funds qualitatively and quantitatively.

More information is available here: A Beginner’s Guide To Make Your Money Dreams Come True!

What Readers Say

Do share if you found this useful

About the Author M Pattabiraman author of freefincal.comM. Pattabiraman(PhD) is the author and owner of  He is an associate professor at the Indian Institute of Technology, Madras since Aug 2006. Pattu” as he is popularly known, has co-authored two print-books, You can be rich too with goal based investing (CNBC TV18) and Gamechanger and seven other free e-books on various topics of money management.  He is a patron and co-founder of “Fee-only India” an organisation to promote unbiased, commission-free investment advice. Pattu publishes unbiased, promotion-free research, analysis and holistic money management advice. Freefincal serves more than one million readers a year (2.5 million page views) with numbers based analysis on topical issues and has more than a 100 free calculators on different aspects of insurance and investment analysis. He conducts free money management sessions for corporates  and associations(see details below). Previous engagements include World Bank, RBI, BHEL, Asian Paints, TamilNadu Investors Association etc. Contact information: freefincal {at} Gmail {dot} com (sponsored posts or paid collaborations will not be entertained)
Want to conduct a sales-free "basics of money management" session in your office?
I conduct free seminars to employees or societies. Only the very basics and getting-started steps are discussed (no scary math):For example: How to define financial goals, how to save tax with a clear goal in mind; How to use a credit card for maximum benefit; When to buy a house; How to start investing; where to invest; how to invest for and after retirement etc. depending on the audience. If you are interested, you can contact me: freefincal [at] Gmail [dot] com. I can do the talk via conferencing software, so there is no cost for your company. If you want me to travel, you need to cover my airfare (I live in Chennai)

Connect with us on social media

Content Policy

Freefincal has original unbiased, conflict-of-interest-free,  topical reports, reviews, commentary and analysis on all aspects of personal finance like mutual funds, stocks, insurance etc. All guest authors and contributors to the site also do not have any conflict of interest. If you find the content useful, please consider supporting us by (1) sharing our articles and (2) disabling ad-blockers for our site if you are using one. No promotional content We do not accept sponsored posts and link exchange requests from content writers and agencies. This is our privacy policy Our website is non-profit in nature. The revenue from the advertisement will only be used for hosting charges, domain registration charges, specific plugins necessary for traffic growth and analytics services for search engine optimisation.

Do check out my books

You Can Be Rich Too with Goal-Based Investing

You can be rich too with goal based investingMy first book is meant to help you ask the right questions, seek the right answers and since it comes with nine online calculators, you can also create custom solutions for your lifestyle! Get it now.  It is also available in Kindle format.
Gamechanger: Forget Startups, Join Corporate & Still Live the Rich Life You WantGamechanger: Forget Start-ups, Join Corporate and Still Live the Rich Life you wantMy second book is meant for young earners to get their basics right from day one! It will also help you travel to exotic places at low cost! Get it or gift it to a young earner

The ultimate guide to travel by Pranav Surya

Travel-Training-Kit-Cover This is a deep dive analysis into vacation planning, finding cheap flights, budget accommodation, what to do when travelling, how travelling slowly is better financially and psychologically with links to the web pages and hand-holding at every step.  Get the pdf for ₹199 (instant download)

Free Apps for your Android Phone

All calculators from our book, “You can be Rich Too” are now available on Google Play!
Install Financial Freedom App! (Google Play Store)
Install Freefincal Retirement Planner App! (Google Play Store)
Find out if you have enough to say "FU" to your employer (Google Play Store)

Blog Comment Policy

Your thoughts are vital to the health of this blog and are the driving force behind the analysis and calculators that you see here. We welcome criticism and differing opinions. I will do my very best to respond to all comments asap. Please do not include hyperlinks or email ids in the comment body. Such comments will be moderated and I reserve the right to delete the entire comment or remove the links before approving them.


  1. “This gives me an idea of what to expect from this fund (or this category of funds) over the next 10 years: Expect NAV to fall for at least 1/3 rd of the months invested. Now let us try selling mutual funds with statistic!”

    doesnt this mean you are suggesting “past performance will be indicative of future perfomance” 🙂

    it can be 35 or 15 or even 65 .. no one can say for sure…..

    also the period matters…. would you get 35% if you took it between 2006 and 2013 ? ….

    you wouldnt is my guess … for the same reason it wont happen in future too…

    1. I am saying that past risk is the indicator of minimum future risk. Yes period and durations matter and can one can easily do this over rolling durations.

  2. Ok i understand but still i feel just like we cannot predict mininum future performance in the same vien we cannot comment on minimum future risk as well based on past risk… but thanks for this insight …

Leave a Reply

Your email address will not be published. Required fields are marked *