Visualizing Mutual Fund Volatility Measures

Published: December 20, 2013 at 12:08 pm

Last Updated on May 13, 2017 at 6:24 pm

Mutual fund investments are subject to market risk!  Haven’t we heard that one before?!

If we wish to analyze the performance of a mutual fund, we should know how to evaluate returns and how to evaluate volatility.

Volatility, not risk. Risk pertains to your financial goal.  Volatility pertains to the instrument.

There are many ways to evaluate volatility and return.  Here is a list of mutual fund volatility measures:


Join over 32,000 readers and get free money management solutions delivered to your inbox! Subscribe to get posts via email!
🔥Enjoy massive discounts on our robo-advisory tool & courses! 🔥
  1. Alpha
  2. Beta
  3. Standard deviation
  4. R-squared,
  5. Sharpe ratio
  6. Sortino ratio.
  7. Treynor ratio

I had used the first 5 measured in my Step-by-step guide to choosing a mutual fund

Like anything else in life, they have their share of advantages and disadvantages.

Question: Can we get a visual feel for what the mutual fund volatility measures represent without learning the math?

The following is an attempt to answer this question.

Caution: If a man is forced to stand very close to an elephant, his view will depend on where he stands.  The results of these volatility measures are quite like that. So if we wish to take them seriously, we should be aware that results will change with duration and that these measures should be used collectively to evaluate fund performance.

Note: The following is a crude attempt written by a layman, for a layman.  Purists and experts are unlikely to approve the following. If they have a better way of answering the above question, I will be delighted to hear from them.

In order to visualize volatility measures, we will compare the performance of Franklin India Blue Chip Fund (FIBCF) with BSE Sensex. Regular readers will be aware that FIBCF is a regular in the blog and has been featured in the following posts. 

 To compare the performance we will use rolling returns obtained with: mutual fund rolling returns calculator

Rolling returns help to evaluate the consistency of a fund performance with respect to its benchmark.

It is a return in which the start and end dates keep moving. For example, if I wish to find out the 1 year rolling returns, I do the following:

  • Select a start date. Say, 1st Jan. 1997
  • Calculate returns for both fund and benchmark from 1st Jan. 1997 to 31st Dec. 1997.
  • Then calculate returns from 2nd Jan. 1997 to 1st Jan. 1998
  • Repeat until we run out of data!
  • The returns are then plotted with respect to the start date.
  • This gives an idea of how often has delivered better returns than the benchmark.

1. Let us start with 15-year rolling returns of FIBCF and Sensex.

Franklin India Blue Chip 15 year rolling return

The average rolling return is represented by a horizontal line.

The gap between the two lines is a measure of outperformance and can be identified with alpha or Jensen’s alpha, named after Michael Jensen

Notice that the curve deviates from the average both ways (vertical arrows). That is, sometimes the return is more than the average and sometimes less.

The average of the deviations (both positive and negative) is the standard deviation

Standard deviation gives you a measure of how volatile a fund is.

Note: Although the standard deviation takes into account both positive and negative deviations, it is defined such that it is always positive.

2.  Next, we look at 10-year rolling returns of FIBCF and Sensex.

Franklin India Blue Chip volatility

Observe the vertical arrows. These represent times in the past when the Sensex has changed, that is moved up or down, rather suddenly. Notice how FIBCF responds to these changes. Typically, if the Sensex rises/falls, FIBCF rises/falls more.

If we average the difference in the rise/fall, we get an idea of how much more or less volatile FIBCF is with respect to the Sensex. This measure is called beta

3.  Now, let us look at 1-year rolling returns of FIBCF and Sensex.

Mutual fund volatility measures

The 1Y rolling return paints a very different picture! The FIBCF(blue)  curve almost overlaps with that of the Sensex except for a few regions represented by ovals.

The extent of overlap of both the curves gives us a measure of similarity in performance between FIBCF and Sensex. This measure is called R-squared.

It is clear that except for the regions marked by ovals, FIBCF has tracked the Sensex. In the oval regions FIBCF has outperformed the Sensex by a huge extent (except for small period in 1999). So if we had been invested in FIBCF during such periods, our returns would have quite spectacular.

Had we invested in FIBCF after 2004, our returns would have been decent, perhaps a bit above Sensex – nothing sensational.

If you are worried about your investment, you could check returns with this

4.  Let us get back to the 15-year rolling returns of FIBCF and Sensex.

Mutual fund Sharpe Ratio

Notice that I have coloured the regions that have a higher return than the average (horizontal line) in green and regions with returns lower than the average in yellow.

Recall that the average of both deviations is the standard deviation.

Let us briefly digress and consider how post-tax return is computed. The relevance will become clear in a moment.

Suppose I have a FD which offers 10% each year. If I belong to the 30% tax slab, my post-tax interest rate is = 10% X (1-30.9%) = 6.91%. (30.9% is the effective tax rate including cess and surcharges). To summarise

Post-tax return = pre-tax return x (1-tax)

 Now, let us define in a similar manner,

 Post-risk return = Average return x (1-average deviation)

 The post-risk return is calculated by taking into account the average deviation (standard deviation) from the mean return.

Such a measure is called the Sharpe ratio, named after William Sharpe.

The Sharpe ratio is a measure of ‘risk-adjusted performance’.

Note: Sharpe ratio is not defined like the post-risk return.  I have introduced the notion of post-risk return to give us an idea of what it represents. Purists may kind

Now let us rewrite the expression for post-risk return in this way:

Post-risk return (Sharpe) = Average return x (1-average deviation [green and yellow regions] )

That is the post-risk return and the Sharpe ratio are calculated by taking into account the average of both positive deviations (green region) and negative deviations (yellow region) from the mean return.

Wait a minute. Positive deviations are going to give us more returns. So why should we include them in the average deviation and reduce the post-risk return?

Why not include only negative deviations (yellow region) in the average deviation?

Why not indeed!  If we did that, we will be, according to Investopedia, “differentiating between good volatility and bad volatility” and we will get something that resembles the Sortino ratio, named after Dr. Frank Sortino

Post-risk return (Sortino) = Average return x (1-average deviation [yellow regions only] )

Note: Sortino ratio is not defined this way.  I have used this as an illustration.

Limitations

  • The fact that we use the concept of standard deviation implies that both positive and negative deviations occur with same probability (Normal distribution)
  • So are we justified in picking and choosing deviations when both deviations are assumed to occur with equal probability? Debatable!

 

Standard deviation measured deviation with respect to the average. Instead, we could also measure deviation with respect to the benchmark. That is, how does the fund react to changes in the benchmark. As noted above this is called beta.

So why not write?

Post-risk return (Treynor) = Average return x (1- beta)

Why not indeed? We then get something that resembles the Treynor ratio

There is yet another volatility measure, the Fama and French three factor model. This takes into account, risk, return and nature of the underlying asset (market cap) to evaluate performance. I need to understand more about this. So I will leave this out of the present discussion.

Why should a retail investor bother about these volatility measures?

We pick a thorn with a thorn.  If our investment is volatile, we need to know how to evaluate it.  There is no other option, except seek professional help.

What should a retail investor look for?

We should look for a combination of high alpha, low beta, low standard deviation, high Sharpe, Sortino and Treynor ratios in all their mutual fund investments.

As for R-squared it should vary from high (large cap stocks) to low(multi-cap stocks) in the portfolio.

A worked illustration for using these parameters can be found here: Step-by-step guide to choosing a mutual fund

Decent resources on mutual fund volatility measures

  • Beyond the Basics – Modern Portfolio Theory
  • Performance Analysis

Most people (including one of the editors of MoneyLife magazine) dismiss these measures as ‘good for nothing’ mathematical gibberish.

I request people who dismiss time-tested and Nobel-prize winning concepts to show us alternative ways of evaluating volatile financial instruments.

Your take:

  • What do you think?
  • Were you able to get a feel for what these measures represent from this post?
  • What do you to evaluate mutual fund performance?
  • Can you think of better ways to represent these volatility measures?
Do share this article with your friends using the buttons below.

🔥Enjoy massive discounts on our courses, robo-advisory tool and exclusive investor circle! 🔥& join our community of 5000+ users!
Use our Robo-advisory Tool for a start-to-finish financial plan! More than 1,000 investors and advisors use this!
New Tool! => Track your mutual funds and stock investments with this Google Sheet!
Follow Freefincal on Google News
Follow Freefincal on Google News
Subscribe to the freefincal Youtube Channel. Subscribe button courtesy: Vecteezy.
Subscribe to the freefincal Youtube Channel.
Follow freefincal on WhatsApp Channel
Follow freefincal on WhatsApp
Podcast: Let's Get RICH With PATTU! Every single Indian CAN grow their wealth! 
Listen to the Lets Get Rich with Pattu Podcast
Listen to the Let's Get Rich with Pattu Podcast
You can watch podcast episodes on the OfSpin Media Friends YouTube Channel.
Lets Get RICH With PATTU podcast on YouTube
Let's Get RICH With PATTU podcast on YouTube.

  • 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 with 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 over 32,000 readers and get free money management solutions delivered to your inbox! Subscribe to get posts via email!

Explore the site! Search among our 2000+ articles for information and insight!

About The Author

Pattabiraman editor freefincalDr. 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, 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 what 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 you 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!
Both boy and girl version covers of Chinchu gets a superpower
Both the boy and girl version covers of Chinchu gets a superpower.
Most investor problems can be traced to a lack of informed decision-making. We have all 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 and teach him several key ideas of decision-making and money management is the narrative. What readers say!
Feedback from a young reader after reading Chinchu gets a Superpower (small version)
Feedback from a young reader after reading Chinchu gets a Superpower!
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!
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 & it's 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

You can be rich too with goal based investingPublished 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 Gamechanger: Forget Start-ups, Join Corporate and Still Live the Rich Life you wantThis 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

Travel-Training-Kit-Cover-new This is an in-depth dive analysis 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)