*By Miguel & Mykola*

Editor's intro: In prepping for your CFA exams, one of the most frustrating things that can happen is that your mind simply refuses to grasp a particular concept. Often, you may be forced into blind memorisation out of desperation.

The purpose of the CFA Topic Deep Dive articles is to help you understand certain CFA concepts. By going deep into detail into a particular example, you'll learn all the nuances about each topic and go into your CFA prep (and exams) better prepared.

We'd love your feedback on this series, so let your views be known in the comments below. For this article, Miguel and Mykola from Financial Analyst Warrior takes us through a detailed example of diversification.

One the most widely known fact about portfolio management is the concept of diversification, which is often summarized as “do not put your eggs in the same basket”.

Finance professionals, and CFA candidates know that the underlying concepts behind portfolio diversification is correlation. The lower the correlation coefficient between assets, the more efficient the portfolio risk reduction through diversification will be. The idea is that when one stock in the portfolio tanks, the other stocks will not follow this stock south if they have low or even negative coefficient of correlation.

Although the general idea behind diversification is usually well understood, we wanted to investigate further and see what it means in real life and how can we apply it when building an actual portfolio. First, let us review the concepts of covariance and correlation:

Although the general idea behind diversification is usually well understood, we wanted to investigate further and see what it means in real life and how can we apply it when building an actual portfolio. First, let us review the concepts of covariance and correlation:

**Covariance**: Measures how much two stocks or portfolios move together. It has two components:- The magnitude of the move(variance)
- The direction of the move (correlation)

**Correlation Coefficient**: Measures if two stocks move in the same direction or opposite direction.Covariance between security X and Y can be easily calculated as:

Once we know the covariance between two securities, we can easily calculate the Correlation Coefficient:

When constructing a portfolio, the bulk of the portfolio risk comes from the covariance between constituents. Since the correlation coefficient is a component of covariance, it thus plays a big role in the risk of the portfolio.

In order to see what asset classes, sectors or geographies offer the best diversification; we selected 50 different exchange-traded funds representing various categories. The list of ETFs used is presented below:

In order to see what asset classes, sectors or geographies offer the best diversification; we selected 50 different exchange-traded funds representing various categories. The list of ETFs used is presented below:

Using the monthly returns of these ETFs, we then constructed a correlation matrix. As you can probably guess, the result was an overwhelming 50X50 matrix with numbers oscillating between -1 and 1 (picture below). However, as financial analysts, your value hinges on how well you can transform columns of charmless and hostile numbers into relevant, actionable and delightful poetry… That is exactly what we did with that correlation matrix (minus the poetry part):

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**Correlation of Global Investment Universe**1.

**Although the VIX index is not an asset classes but rather a tool used by some traders, it offers a remarkable diversification benefit**since it has a strong negative correlation with all asset classes except against long-term U.S. government bonds (positive correlation of 0.63). This makes sense since the volatility of the market is inversely related to the direction of the market. As stocks move down, the volatility index (VIX) increases.2.

**Gold (as represented by GLD) offers great diversification**with an average correlation coefficient of 0.19 against all asset classes (except gold miners and junior gold miners with which it obviously has strong correlation). For instance, the correlation coefficient between gold and the S&P 500 is a lowly 0.0988!3.

**The two U.S. sectors that share the lowest correlation are the consumer discretionary and consumer staple sectors**with -0.48. On the other hand, the industrial sector is strongly correlated with other sectors and thus offers little diversification benefit to a portfolio.4.

**The table below shows the correlation of the S&P 500 against the other asset classes**. We can see that the index is strongly correlated with the other equity asset classes including the different geographies and sectors. In fact, the average correlation between the S&P 500 and the 33 other equity ETFs is 0.79. This is quite interesting since it shows that for investors holding an equity portfolio, they will have a hard time achieving significant diversification by investing in other equities, even if they go international!5.

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We hope this journey in the world of correlation helped you clarify this concept and provide a fresh perspective on portfolio construction. You can build your own matrix easily on excel, using the data analysis package tool. As a CFA candidate, you learn a ton of concepts and theories but we personally find it helpful to apply them in real life using actual data in order to fully grasp their impact.

**Developed nations equities are strongly correlated with each other**. The lower correlation out of the 13 developed markets ETFs selected is achieved by Hong Kong and Japan. For an investor building an international portfolio, this means he may not have to include many developed nations. An index such as EAFA should generally suffice.6.

**Emerging markets do not provide as much diversification as expected**. Given their higher volatility and the fact that their economies are not necessarily synced with developed nations, we expected emerging market ETFs such as Brazil, Mexico, Russia, India or China to provide some diversification benefits. On the contrary, it seems that these nations are very well synchronized with the rest or the world and with each other. The average correlation coefficient between emerging and developed ETF is 0.73 while between emerging nations it is 0.82. This drives home the point made earlier that worldwide equities are well coordinated and investors would have to diversify across asset classes to reduce portfolio risk meaningfully.7.

**The oil and gas commodities are all negatively correlated with bonds ETFs**. The natural gas ETF (UNG) in particular has a negative correlation with the six fixed income categories included in this study.8.

**Excluding the VXX, the two ETFs that display the strongest negative correlation are the consumer staple and consumer discretionary sectors**(-0.48). The second best “couple” in terms of diversification is Treasury bonds versus Israel equities with -0.46! In third place is Treasury bonds and Russian equities (RSX) with a coefficient of -0.41.9.

**The U.S. long-term Treasuries (TLT) turn out to be a great diversifier**. The drawback, of course, is the low yield offered by this asset class. The average correlation between TLT and the 49 other categories is -0.11 and most of the pairs show negative correlations.10.

**The average correlation in the 50 assets matrix is 0.447**. If we do not include the VIX ETF, the coefficient moves to 0.5. Since our universe of ETFs is pretty inclusive, we can use this average correlation as a benchmark when trying to build a diversified portfolio. If an asset provides a correlation coefficient lower than 0.5, we can say it provides more diversification benefit than average.We hope this journey in the world of correlation helped you clarify this concept and provide a fresh perspective on portfolio construction. You can build your own matrix easily on excel, using the data analysis package tool. As a CFA candidate, you learn a ton of concepts and theories but we personally find it helpful to apply them in real life using actual data in order to fully grasp their impact.

*You can download the Excel spreadsheet to see Miguel and Mykola's jumbo correlation matrix below. If you have any questions, just chuck them in the comments below!* diversification.xlsx |