A WYSIWYG (pronounced "wiz-ee-wig") editor or program is one that allows a developer to see what the end result will look like while the interface or document is being created. WYSIWYG is an acronym for "what you see is what you get".

The first true WYSIWYG editor was a word processing program called Bravo. Invented by Charles Simonyi at the Xerox Palo Alto Research Center in the 1970s, it became the basis for Simonyi's work at Microsoft and evolved into two other WYSIWYG applications called Word and Excel.

In the game of investments, what you see may not be always what you get. Take a look at these 3 ETFs: Vanguard FTSE All World ex US ETF (NYSEARCA:VEU), Vanguard REIT Index ETF (NYSEARCA:VNQ) and Vanguard Total Stock Market ETF (NYSEARCA:VTI). On the surface, they seem like a well diversified mix. But look at the correlation between these 3 securities and you may realize you are not getting what you bargained for in terms of diversification.

## Correlation and Covariance

Have you heard the saying that it is better to be approximately right than totally wrong?Well, this saying does not hold true when trying to understand the concept of correlation.

Variance is the average squared deviation from the expected value or mathematical mean of a single series of data. The reason it is squared is so that it captures both positive and negative deviations. Covariance, in a similar vein, measures the average deviation of 2 series of data from their respective expected values, taken together. If the 2 series of data are identical, the covariance measure would equal the variance measure.

Correlation is the covariance of A and B divided by the standard deviations of A and B. Dividing by the standards deviations restricts the maximum and minimum value of a correlation measure to +1 and -1 respectively. This enables us to compare the relationships between different pairs of data series on the same footing.

Understanding covariance will help you get a grip on what diversification is all about. Let's say we have 2 data series A and B. Suppose that at a particular instance, series A has a value that is above its expected value and series B has a value that is below its expected value. It is obvious then that the movements in both data series at that instance counteract each other.

Simply put, the 2 series of data move in opposing directions at that instance and it is this out-of-sync movement between the 2 data series that reduces the value of the covariance. The correlation (square root of the covariance) in a situation where series A and series B move perfectly out-of-sync is -1.

On the other hand, if series A and series B were perfectly positively correlated (i.e. have a value equal to +1), then, whenever data series A has a value that is above its expected value, series B will have a value that is also above its expected value. Similarly, each time series A has a value that is below its expected value, data series B will have a value that is also below its expected value.

The correlation between 2 data series in real life situations would fall somewhere between the two extremes of -1 and 1 where a correlation of +1 would be aptly described as "putting all your eggs in one basket".

Now, the total variance of a portfolio that comprises 2 investments A and B is impacted by the variance of series A, the variance of series B, and the covariance of the two data series taken together. In the scenario above where the 2 series move out-of-sync with each other, the reduced covariance between the 2 series will lead to a reduced total variance for that portfolio. Since portfolio volatility is the square root of portfolio variance, a reduced portfolio variance also means lower portfolio volatility.

Any reduction in covariance implies a correlation that is less than +1. So as long as any two securities are less than perfectly positively correlated there will be some diversification benefit.

## Complexity in Simplicity

In the graph on the right (all graphs courtesy of expertGTC3), the x-axis measures portfolio volatility while the y-axis measures average annual return. The Markowitz frontier (red line) charts the portfolio combinations for 2 securities such that each return has the least volatility.

If the 2 securities were perfectly positively correlated, the yellow line would represent the portfolio risk and return results for various combinations of the 2 securities. Since the 2 securities have a correlation near zero, portfolio variance and therefore volatility has been reduced resulting in the frontier represented by the red line. In finance speak, non-systematic risk has been diversified away leaving behind only systematic risk. For the same return, a portfolio on the red line has lower volatility than its corresponding portfolio on the yellow line.

The number of calculations involved can be onerous. Analyzing 10 securities would require you to cycle through 1,013 possible portfolio combinations. If you analyzed 20 securities, it would escalate exponentially to 1,048,555 combinations. And if you looked at 30 securities, it would be a whopping 1,073,741,793 combinations.

Pushing the envelope on this, 49 securities would mean analyzing 562,949,953,421,262 combinations. Fortunately, there are heuristic methods to determine the frontier without cycling through all these combinations.

## What you see MAY NOT be what you get

In my previous article, I mentioned the following stocks: American Express (AXP), ConocoPhillips (COP), Johnson & Johnson (JNJ), Kraft Foods (KFT), Procter & Gamble (PG), Coca Cola (KO), USBanCorp (USB), Walmart Stores (WMT), Wells Fargo (WFC), and Wesco Financial (WSC).

How were these correlated? Take a look at the graph on the right. The graph is a 3-dimensional correlation table taken over the period June 2002 to April 2011. It resembles a skyline of skyscrapers and low rise buildings. Not too bad considering they were all from the same asset class.

Now, let's consider the 3 Exchange Traded Funds (ETFs) we talked about earlier:Vanguard FTSE AW ex-US ETF (VEU), Vanguard REIT Index ETF (VNQ) and Vanguard Total Stock Market ETF (VTI). ETFs are investment funds traded on a stock exchange like stocks.

The graph on the right shows the correlations between each pair of these 3 ETFs. The data used to calculate the correlations were downloaded from Yahoo Finance and is ex-dividend from March 2008 to November 2011.

Judging from what these ETFs say they represent, this portfolio ought to be a well-diversified mix. But a quick glance at their correlation table immediately reveals otherwise.

What do these ETFs represent?

The fund summary in Yahoo Finance for Vanguard FTSE AW ex-US ETF (VEU) is as follows:

*"The investment seeks to track the performance of a benchmark index that measures the investment return of stocks of companies located in developed and emerging markets outside of the United States. The fund employs a passive management or indexing investment approach designed to track the performance of the FTSE All-World ex US Index, a free-float-adjusted, market-capitalization-weighted index designed to measure equity market performance of international markets. The Index includes approximately 2,180 stocks of companies located in 46 countries, including both developed and emerging markets".*

The fund summary in Yahoo Finance for Vanguard REIT Index ETF (VNQ) is as follows:

*"The investment seeks to provide a high level of income and moderate long-term capital appreciation by tracking the performance of a benchmark index that measures the performance of publicly traded equity REITs. The fund employs a passive management or indexing investment approach designed to track the performance of the MSCI US REIT Index. The index is composed of stocks of publicly traded equity real estate investment trusts (known as REITs). It attempts to replicate the index by investing all, or substantially all, of its assets in the stocks that make up the index, holding each stock in approximately the same proportion as its weighting in the index."*

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* *And the fund summary in Yahoo Finance for Vanguard Total Stock Market ETF (VTI) is:

*"The investment seeks to track the performance of a benchmark index that measures the investment return of the overall stock market. The fund employs a passive management strategy designed to track the performance of the MSCI US Broad Market Index, which represents 99.5% or more of the total market capitalization of all the U.S. common stocks regularly traded on the New York Stock Exchange and the Nasdaq over-the-counter market. It holds a broadly diversified collection of securities that, in the aggregate, approximates the full index in terms of key characteristics."*

* *

Reading the fund summaries does not give much clue as to why they are highly positively correlated (see the research done at IndexUniverse on ETF correlations). While the Vanguard FTSE AW ex-US ETF (VEU) does not contain stocks of companies in the US, perhaps companies located outside the US still depend on the US market. Perhaps, the special tax and investment-related features of its component securities are not sufficient to set apart the Vanguard REIT Index ETF (VNQ) as a distinct asset class from the rest.

Perhaps, it does not matter.

Correlation is a statistical measure that tells it like it is. It presents to you a fact --- which is the extent 2 data series move together. The reason why they move in-tandem or out-of-sync may not be immediately obvious.

Diversification will only be achieved if returns on the various securities are not highly positively correlated. Correlation is not a vague notion. It is a precise statistical measure. When you look at correlations, what you see is what you get.

**Additional disclosure:** This article has been approved by Abby

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