# Visualizing Mutual Fund Volatility Measures

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:

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.

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.

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.

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.

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.

• 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?
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## 33 thoughts on “Visualizing Mutual Fund Volatility Measures”

1. Ramesh says:

I am in the ‘these are mathematical gibberish’ group and I believe that it better to be roughly right than precisely wrong.

‘Time-tested’ ? Do you think studies have shown that using these parameters can predict ‘future performance’ of any stock / fund / asset? Please link to any such study.

‘Nobel Prize’ ? That is an argument by authority. And that does not work at all in the finance world (or for that matter in any scientific study). An example is the LTCM blowout managed by these theoretical Nobel Prize winners, if you recall.

Regarding these greek symbols which look good and exact on paper, the biggest issue with them is that they take into account past one year- values only. So, the current beta or alpha, etc will show you the performance of 1 year of FIBCF versus Sensex (and not 15 years). Do you really think making decisions on 1 year is good?

You can yourself find out the various betas, and alphas in the 15 year data and find out for yourself if those values helped you in any way going forward. Or just compare 2003, 2007, 2009 and current values.

Volatility is not the sole criteria for risk. MPT is a failure.

I will quote Warren Buffett here “We bought The Washington Post Company at a valuation of \$80 million back in 1974. If you’d asked any one of 100 analysts how much the company was worth when we were buying it, no one would have argued about the fact that it was worth \$400 million. Now, under the whole theory of beta and modern portfolio theory, we would have been doing something riskier buying stock for \$40 million than we were buying it for \$80 million, even though it’s worth \$400 million — because it would have had more volatility. With that, they’ve lost me.”

1. pattu says:

First, we will have to distinguish between investing in stocks and investing in mutual funds. I don’t think we can evaluate these two in the same way and with the same tools.

The key aspect of stock investing is to assess the value. I don’t think this can be done using any math model. You will need a nose for understanding business. The single most important reason WB is successful.

As for MF investing, we will have to use quantitative tools. Of course it will have to based on existing data and all of them will only evaluate past performance. We take a call based on these and see what happens until the next review.
What tools we use will always be a matter of debate. There is no simple way to evaluate risk. When we use a quantitative tool we must first understand limitations and then only rely on them.
Models will fail. That is the way of nature. We cannot dismiss the math as gibberish or Greek because they fail or is difficult to understand.
These concepts were first published with respect to mutual funds.

If I don’t use math, I will be left with fund house management style and fund manager conviction. Yes, these are important. I prefer to use them as a buffer when the math points to poor performance. I see no justification for dismissing analytical tools. The alternative is not sound enough for me.

Yes all the risk measures will depend on the duration. Morning Star gives you these measures for 3,5,10 and 15 year periods. If you look at these and read them correctly, ‘fund managers conviction’ and ‘AMC style’ can be proven with numbers.

It is all about knowing how to use, interpret and when to remind ourselves of their limitations. Unfortunately, this requires training. The trouble is very few experts in India know to use them properly.

I do understand risk and return are poorly correlated and that there are alternative models. We will have to promote the use of ALL such tools for evaluation. This is what I am hoping to do soon. Only then we will know how to interpret with a level headed mind.

2. Ramesh says:

I am in the ‘these are mathematical gibberish’ group and I believe that it better to be roughly right than precisely wrong.

‘Time-tested’ ? Do you think studies have shown that using these parameters can predict ‘future performance’ of any stock / fund / asset? Please link to any such study.

‘Nobel Prize’ ? That is an argument by authority. And that does not work at all in the finance world (or for that matter in any scientific study). An example is the LTCM blowout managed by these theoretical Nobel Prize winners, if you recall.

Regarding these greek symbols which look good and exact on paper, the biggest issue with them is that they take into account past one year- values only. So, the current beta or alpha, etc will show you the performance of 1 year of FIBCF versus Sensex (and not 15 years). Do you really think making decisions on 1 year is good?

You can yourself find out the various betas, and alphas in the 15 year data and find out for yourself if those values helped you in any way going forward. Or just compare 2003, 2007, 2009 and current values.

Volatility is not the sole criteria for risk. MPT is a failure.

I will quote Warren Buffett here “We bought The Washington Post Company at a valuation of \$80 million back in 1974. If you’d asked any one of 100 analysts how much the company was worth when we were buying it, no one would have argued about the fact that it was worth \$400 million. Now, under the whole theory of beta and modern portfolio theory, we would have been doing something riskier buying stock for \$40 million than we were buying it for \$80 million, even though it’s worth \$400 million — because it would have had more volatility. With that, they’ve lost me.”

1. pattu says:

First, we will have to distinguish between investing in stocks and investing in mutual funds. I don’t think we can evaluate these two in the same way and with the same tools.

The key aspect of stock investing is to assess the value. I don’t think this can be done using any math model. You will need a nose for understanding business. The single most important reason WB is successful.

As for MF investing, we will have to use quantitative tools. Of course it will have to based on existing data and all of them will only evaluate past performance. We take a call based on these and see what happens until the next review.
What tools we use will always be a matter of debate. There is no simple way to evaluate risk. When we use a quantitative tool we must first understand limitations and then only rely on them.
Models will fail. That is the way of nature. We cannot dismiss the math as gibberish or Greek because they fail or is difficult to understand.
These concepts were first published with respect to mutual funds.

If I don’t use math, I will be left with fund house management style and fund manager conviction. Yes, these are important. I prefer to use them as a buffer when the math points to poor performance. I see no justification for dismissing analytical tools. The alternative is not sound enough for me.

Yes all the risk measures will depend on the duration. Morning Star gives you these measures for 3,5,10 and 15 year periods. If you look at these and read them correctly, ‘fund managers conviction’ and ‘AMC style’ can be proven with numbers.

It is all about knowing how to use, interpret and when to remind ourselves of their limitations. Unfortunately, this requires training. The trouble is very few experts in India know to use them properly.

I do understand risk and return are poorly correlated and that there are alternative models. We will have to promote the use of ALL such tools for evaluation. This is what I am hoping to do soon. Only then we will know how to interpret with a level headed mind.

3. AyushP306 says:

Awesome post sir! Very nicely explained. I understood the Standard Deviation, Beta, and R-Squared quite well.

4. AyushP306 says:

Awesome post sir! Very nicely explained. I understood the Standard Deviation, Beta, and R-Squared quite well.

5. AyushP306 says:

Very well explained graphically with the Charts sir. I understood the Sharpe Ratio after reading it for the second time. 😛 Sortino Ratio seems to be the variant of it.

1. pattu says:

Many thanks Ayush. The ratios are tougher to explain. Sharpe, Sortino and Treynor are all variants of each other. I have given an over-simplified illustration.

6. AyushP306 says:

Very well explained graphically with the Charts sir. I understood the Sharpe Ratio after reading it for the second time. 😛 Sortino Ratio seems to be the variant of it.

1. pattu says:

Many thanks Ayush. The ratios are tougher to explain. Sharpe, Sortino and Treynor are all variants of each other. I have given an over-simplified illustration.

7. piyush says:

I think it’s essential to scrutinize the past performance of mutual funds. It will help to showcase the trend of particular fund and the style, fund manager is using for investing.

I also believe that investing in a mutual fund is a lot different from investing in stocks. Direct equity is mostly value investing and no common man has any idea how to measure the value.

Although i believe that lots of advisor in India, recommend those mutual funds, which are top in the chart. They don’t even understand, what is standard deviation.

Mr. pattu you are writing some good blogs, may not be understandable by laymen but good for those advisor, who are looking to gain some knowledge of, how to evaluate funds.

At last your knowledge will transfer to end user.

Regards

1. pattu says:

Many thanks for your frank views Piyush. That is what sets you apart from others. The whole idea of financial literacy is to take complex matters and offer them in a simple way to the layman.

8. piyush says:

I think it’s essential to scrutinize the past performance of mutual funds. It will help to showcase the trend of particular fund and the style, fund manager is using for investing.

I also believe that investing in a mutual fund is a lot different from investing in stocks. Direct equity is mostly value investing and no common man has any idea how to measure the value.

Although i believe that lots of advisor in India, recommend those mutual funds, which are top in the chart. They don’t even understand, what is standard deviation.

Mr. pattu you are writing some good blogs, may not be understandable by laymen but good for those advisor, who are looking to gain some knowledge of, how to evaluate funds.

At last your knowledge will transfer to end user.

Regards

1. pattu says:

Many thanks for your frank views Piyush. That is what sets you apart from others. The whole idea of financial literacy is to take complex matters and offer them in a simple way to the layman.

9. Muthu Krishnan V says:

awesome post, finally understood how these terms work, though i have tried to search the meanings of these terms, never was able to visualize them. Thanks for the post.

1. pattu says:

Thank you very much! You made my day. I was disappointed that this post did not receive the kind of response I expected. I appreciate your support.

10. Muthu Krishnan V says:

awesome post, finally understood how these terms work, though i have tried to search the meanings of these terms, never was able to visualize them. Thanks for the post.

1. pattu says:

Thank you very much! You made my day. I was disappointed that this post did not receive the kind of response I expected. I appreciate your support.

11. satish says:

Dear Pattu,
Thanks for explaining complex terms in such a simple way, though I have been investing for quite some time in mutual funds and equity but never came accross a article which explains some of these terms in such a simple way..
I agree with you that in absence of proven models or formula to predict future performance of mutual funds, we need to rely on anything that can help us pick 3-5 funds among a ocean of 5000 funds and stay above inflation and at the same time not loose money.
Pls dont get disappointed about not getting response, most of the people are lazy by nature to even type a thank you, though they might have thanked you in heart and benefited from your work..Pls keep the good work flowing for people like me who are not from financial or statistical background but trying to make investments work..

1. pattu says:

Thank you very much for your kind word of motivation and encouragement. I appreciate it.

12. satish says:

Dear Pattu,
Thanks for explaining complex terms in such a simple way, though I have been investing for quite some time in mutual funds and equity but never came accross a article which explains some of these terms in such a simple way..
I agree with you that in absence of proven models or formula to predict future performance of mutual funds, we need to rely on anything that can help us pick 3-5 funds among a ocean of 5000 funds and stay above inflation and at the same time not loose money.
Pls dont get disappointed about not getting response, most of the people are lazy by nature to even type a thank you, though they might have thanked you in heart and benefited from your work..Pls keep the good work flowing for people like me who are not from financial or statistical background but trying to make investments work..

1. pattu says:

Thank you very much for your kind word of motivation and encouragement. I appreciate it.

Wonderful work. I was looking for a simple analysis like this. Nowhere I could trace. Finally I got it from you in this article. Thank you so much.

1. pattu says:

Thank you.

Wonderful work. I was looking for a simple analysis like this. Nowhere I could trace. Finally I got it from you in this article. Thank you so much.

1. pattu says:

Thank you.

15. Divya Sugumar says:

Thank You Pattu Sir for explaining all the concepts so clearly. A few months ago, I had no idea on how to select a Mutual Fund. Your blog helped me in taking baby steps. I am a slightly more confident investor now. Thanks to you.! Hoping to learn a lot more. Please do not stop blogging. There are many more people like me who do not comment but are deriving so much knowledge from your blog and the FB group. Kudos and a big thanks to you (And, also Ashal Sir) for selflessly sharing your knowledge.

1. Thank you very much. It is encouragement such as yours that keep me going.

16. Divya Sugumar says:

Thank You Pattu Sir for explaining all the concepts so clearly. A few months ago, I had no idea on how to select a Mutual Fund. Your blog helped me in taking baby steps. I am a slightly more confident investor now. Thanks to you.! Hoping to learn a lot more. Please do not stop blogging. There are many more people like me who do not comment but are deriving so much knowledge from your blog and the FB group. Kudos and a big thanks to you (And, also Ashal Sir) for selflessly sharing your knowledge.

1. Thank you very much. It is encouragement such as yours that keep me going.

17. Srinivasan says:

This is definitely an excellent visualization of the difficult risk measures. As for the relation between past performance and future returns, I would give an example to say how this can be easier with mutual funds. it is difficult to predict the future performance of a player (or even a set of players) based on past alone. However, it more easier to trust the selector of the team based on past performances.. i.e if he (far more he’s than she’s here) has picked winners before, his methods may be useful in the future too… This is of course as long as he sticks to the same game and similar levels.

18. Srinivasan says:

This is definitely an excellent visualization of the difficult risk measures. As for the relation between past performance and future returns, I would give an example to say how this can be easier with mutual funds. it is difficult to predict the future performance of a player (or even a set of players) based on past alone. However, it more easier to trust the selector of the team based on past performances.. i.e if he (far more he’s than she’s here) has picked winners before, his methods may be useful in the future too… This is of course as long as he sticks to the same game and similar levels.

19. vijay says:

I gained good basis of knowledge regarding the risk ratios, hats off to you for spreading the knowledge, respects for guru.