Quantifying Portfolio Diversification – Part I

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.

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.

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33 thoughts on “Quantifying Portfolio Diversification – Part I

  1. Vinay Maithani Cmrp

    Ultimate post. Now looking forward that 'Magic' distribution numbers for quantitative ways to allocate assets in a portfolio. Will it also include numbers for international and India centric investment as well ?

    1. pattu

      Thanks Vinay. In principle it can include any kind of instrument. Will have to see how to go about this.

  2. Vinay Maithani Cmrp

    Ultimate post. Now looking forward that 'Magic' distribution numbers for quantitative ways to allocate assets in a portfolio. Will it also include numbers for international and India centric investment as well ?

    1. pattu

      Thanks Vinay. In principle it can include any kind of instrument. Will have to see how to go about this.

  3. vignesh


    Very good one. I was actually following the discussion in our fb group.

    Keep writing and waiting for the part 2.

    I think we need to thank nitin who started the discussion in our group.

    Anyway full credits go to you pattu !!!!!

    1. pattu

      Thank you. I was writing the post before that thread began. Hence was able to provide some numbers there easily. Yes thanks to Neerak for asking the question on diversification and Nitin for his insights.

  4. Ramesh

    Diversification gives lower volatility and "better risk adjusted returns", which can mean either of 4 options:

    1. Lower absolute returns with Much Lower risk.
    2. Higher returns with Same risk.
    3. Higher absolute returns with Lower risk.
    4. Much higher absolute returns with slightly higher risk.

    Instead of 3, 1 is more often the case (if not always). The more you diversify, lesser would be the overall returns (and lesser would be the chances of blowout which means much lower risk).

    What do you say?

    1. pattu

      PPFAS LTVF was criticised by jhuhunwala.in for lower returns because of international diversification!!

      Absolutely agree with you. Diversification will lower returns, but that is said with the benefit of hind-sight. In real-time, on a day-to-day basis, it is more important not to lose as much as one index. That is key to peaceful, contended investing.

  5. Ashwani

    Hello Mr Pattabiraman

    Thanks for sharing such useful articles.
    I wanted to know where can I see the correlation coefficient of my funds.
    Is it same as index comparison provided by valueresearchonline.com ?

  6. Banerjee

    Many thanks Pattu. This was enlightening. Eagerly look forward to Part II.

    Need your advise. If one is to start fresh SIP ( or SIP-E as per your definition) , is this the right time or one should wait for the budget / monsoon outcome. What is your view.

  7. Alok Jha

    Can we not invest in gild when equity becomes expensive and buy back the equity when it becomes cheap!

  8. Alok Jha

    Can we not invest in gild when equity becomes expensive and buy back the equity when it becomes cheap!

  9. Alok Jha

    Sir, can we have a tactical asset allocation method among equity-debt and gold asset classes! Can we use Indian and Internationl market experiences in designing this methodology? I personaly feel that ignoring gold completely is not good whiling applying tactical asset allocation strategy. Request an article on this. Rgds,

  10. S Srinivasan

    Missing URL: There's the hyperlink - Diversification equity vs bonds, which is missing. The message was good asking to be notified. I did not have an email to send to, I am marking it as a comment here...


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