Quantifying Portfolio Diversification – Part I

Published: June 23, 2014 at 3:00 pm

Last Updated on May 30, 2016 at 1:41 pm

Survival is a human instinct. The memorable line from Jurassic Park, “life will find a way!”, is relevant not only to all living organisms but also to pretty much everything that we humans do.

Diversification in general, is something that we do by instinct.

We do not fill our wardrobes with only cotton-wear or with only woollen-wear because we do not want to risk wearing the wrong clothes at the wrong time of the year.

The grocer never fills his shop with the same item because he/she does not want to risk losing a steady stream of income by selling the same item which may not have the same demand every day of the month.

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! 🔥

The underlying idea is clean and simple: we diversify to mitigate risk.  It is a survival instinct imbibed in each of us.

Yet, it is baffling that when it comes to investing, very, very few investors diversify their portfolio.

In my opinion, the main reasons behind this, are

  • constantly chasing after returns by looking at short-term performance.
  • abject refusal to concentrate on the net portfolio returns and an obsession with individual performance.

 Why diversify?

  • Reduce portfolio volatility
  • Get better returns with lower risk

Benefits of diversification will take time to appear. So one needs to give it time.

 How to diversify?

Let us consider an unrealistic and naïve example, commission-based selling.

An insurance agent sells endowment policies and also distributes mutual funds.

When there is a stock bull run, he notices sale of diversified equity mutual funds increase (most often after the major rally!).

When there is prolonged sideways market, people tend to buy pension plans and child plans more!

As far as the agent is concerned, mutual funds sales and endowment plan sales, peak at different points of time. That is the sales movement is poorly correlated.

There are risks associated with selling mutual funds and there are risks associated with selling endowment plans.

However, since their sales movement (and therefore risks) is poorly correlated, the fluctuations in the insurance agent’s income is reduced.

That is the agent receives a steady income irrespective of marker conditions compared to sale of mutual funds alone or endowment plans alone.

This is simple commonsense, it is not? Diversify your sales with unrelated products and steady the income stream.

Every action has an associated negative element or risk. The idea is to choose actions with uncorrelated risk. Thus if one fails, chances are the other won’t, and vice-versa. Thus by reducing the chance of both actions failing together, we can reduce the overall risk.

When it comes to investing, the logic remains the same. We choose asset classes which are poorly correlated with each other. Individually they maybe volatile.

However, since their movements are poorly correlated, the overall volatility is lowered.

This may seem counterintuitive. We add volatile, but poorly correlated instruments to reduce overall volatility!

Thus measuring correlation is key to quantifying portfolio diversification.

How to measure correlation?

There is a simple and straightforward way to estimate the correlation between two instruments (from the same or different asset class) – Correlation Coefficient

The square of the correlation coefficient is referred to as R-squared and might be more familiar.

R-squared between an index fund and associated benchmark will ideally be 1. That is, 100% of the index funds returns stem from the benchmarks movement.

R-squared between a large cap fund and associated benchmark will be close to 1. (0.85 -0.99). That is, 85-99% of the funds returns stem from the benchmarks movement.

Many investors have 2-3 large cap funds in the hope to diversifying and reducing risk. However, if the funds are indexed to the same benchmark with identical R-squared, there will absolutely be no benefit from holding the second or third large-cap fund!

See the Value Research list of large cap funds for examples R-squared.

Since the R-squared is always positive, it does not provide information about the nature of the correlation: whether it is

  • positive (two assets classes move in step – peaks and dips coincide) or
  • negative (two asset classes move out of step – peak in one coincide with dip in another)

This where the correlation coefficient steps in.

Diversification among asset classes

You must have heard the refrain, ‘diversify across equity, debt and gold’.

Why do you think they say so?

Equity vs Bonds

Have a look at the CNX 500 plotted with the 10-Ygovernment bond yield


There are regions where they move in step and regions where they move out of step. The correlation coefficient between the indices for the duration shown above (4th Jan 1999 to 23rd Jan 2014) is -0.10.

This indicates that equity and bonds have very little correlation with each other. I choose not to write negative correlation because, the correlation coefficient is a strong function of both the duration and the quantity used for calculating.

If we choose 6 months returns instead of the indices, the correlation coefficient would be 0.05. If we used 4 months or 12 months return, the answer will be very different.

So let us not pay too much attention to the sign or actual number and simply note that the correlation coefficient is much less than 1.

This is a good enough reason to diversify a portfolio with equity and debt (long term gilt funds in this case) for a long term goal in general.

The percentage allocation the would depend on duration. So would the nature of the debt instrument.

Equity vs Gold

The 15  year rolling CAGR for gold and the US broad index, S&P 500 is plotted below. The idea of negative correlation between asset classes can be understood by observing this plot.

Gold stocks correlation

Notice how equity returns peak when gold returns dip and vice-versa.

The correlation coefficient for the above data is -0.52. The square of this, the R-squared is 0.27. That is only 27% of the returns are correlated. The rest is entirely independent of each other.

This is a very good example of negative correlation of two highly risk assets.

Yes! Gold is riskier than stocks!

The average 15-year CAGR for stocks is 11% with a standard deviation of 4.6%

The average 15-year CAGR for gold is 4.6% with a standard deviation of 5.97%.

The standard deviation is a measure of deviations from the average. So higher the value, higher the deviation, and higher the risk.

A standard deviation higher than the average implies, long term gold returns can just about be anything!! Negative or positive!

Gold and Stocks may be a good example of negative correlation between asset classes, but that does not mean gold is a good candidate for diversification.

The risk associated with investing in gold is higher the average return before taxes! Not worth it!

How about bonds?

The average 10-year  bond yield between 4th Jan 1999 to 23rd Jan 2014 is 8.1%. The standard deviation is only 1.7%

Therefore, reasonable reward with low risk, making them very good candidates for diversification.

Diversification within an asset class

People talk of a ‘core’ portfolio consisting of large caps and a ‘satellite’ portfolio consisting of small and mid-caps. Here is why.

Large Cap vs Mid Cap

Diversification mid-cap vs large-cap

Just by visual observation one can tell that the correlation is high. Indeed the correlation coefficient is 0.94!

This is how the 1-year rolling returns look

Diversification returns midcap sensex

The correlation coefficient of the return is 0.93. An R-squared of 0.86. That is 86% of the return movement is correlated.

 Large Cap vs. Small Cap

1-year rolling returns are plotted below.

Diversification returns small cap sensex

The correlation between small cap and large cap is much lower, 0.81. The R-squared is 0.65. So only 65% of the return movement is correlated.

What should we do while diversifying? What should be the large:mid:small cap ratio?

  • 60:20:20
  • 33:33:33
  • 50:25:25
  • etc.

The risk associated with large caps is relative the lowest. For example, between 1st April 2003  to 20th June 2013, the average 1Y return of,

BSE Sensex: 21% . Standard deviation: 29% (low risk)

BSE Mid Cap: 22% . Standard deviation: 41% (medium risk)

BSE Small Cap: 27% . Standard deviation: 54% (high risk)

Hence it makes sense to have something like (large:mid:small cap ratio)

  • 50:30:20 or
  • 60: 25:15

Any other combination can also be chosen depending on risk appetite.

In the second part of this post, we will consider correlation among sectors and correlation between Indian and international stocks. Soon we will also consider quantitative ways to allocate assets in a portfolio.

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!
We also publish monthly equity mutual funds, debt and hybrid mutual funds, index funds and ETF screeners and momentum, low-volatility stock screeners.
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.
🔥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 over 32,000 readers and get free money management solutions delivered to your inbox! Subscribe to get posts via email!

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(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!
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 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!
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!
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

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 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)