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Understanding Correlation of Various Asset Classes – MBA Monday

by Darwin on March 6, 2011

Mirror Image - Correlation Explained

If you’re a DIY investor or if you’ve employed a certified financial professional, it’s likely that you’ve come across the topic of diversification.  The reason for diversification is quite simple – you don’t want to put all your eggs in one basket.  This doesn’t just go owning only 1 stock (or having all your money in company stock), but this also cuts across asset diversification.  You’ll often hear of a cash/stock/bond mix, and these days, with the ease of ETFs replicating numerous asset classes, you can easily invest in REITs (list of dozens by ticker) for real estate exposure, gold ETFs (as well as silver, platinum and more) for precious metals exposure, and even timber.  Without getting into exotic instruments just for the perception of diversification, it’s good to anticipate what sort of diversification these instruments might really bring to your portfolio.

Why Correlation Matters

Aside from just the concept of owning different asset classes or different stocks within an equity portfolio, a goal should be to decrease correlation, such that when one position zigs, another zags.  This isn’t to say you want perfectly inversely correlated investments such that you basically cancel out your gains no matter what happens.  But if you hold multiple investments with very LOW correlation (not necessarily negative), it increases the likelihood that when you actually need to tap your portfolio for cash, some holdings will have done well no matter what the other ones have done.  For instance, if you really needed cash during the 2009-2009 market crash, wouldn’t it have been nice to have some assets in gold or Treasuries to pull from so you didn’t have to liquidate stocks at the pivot bottom?  They have since doubled from March 2009.

For a basic understanding, correlation coefficients span from +1 to -1.  A negative 1 correlation between two assets would mean that they move in perfect opposite directions.  Think of two ETFs like a long and an inverse ETF.  On any given day, if one is up 1%, the other is down 1%.  As correlation coefficients get down below ~0.7, the assets are no longer considered “strongly correlated”.  Below ~04., they aren’t really considered to be correlated much at all (slightly), and at zero, they are perfectly non-correlated.  See example X,Y scatters indicating various correlation coefficients below.  Notice how 1 and -1 are perfectly straight lines.  0.8 shows a reasonably strong, predictable trend.  0.4 is kind of mess and 0 is nothing.  Basically, if I told you Asset A does X next year, how would you expect Asset B to behave over the same period?  Correlation is important to help tell you that.

How to Figure Out Correlation

There are a few ways to understand how various asset classes or stocks are correlated.  I’ll walk you through a step by step example so you can do this yourself for any stock, ETF, mutual fund or commodity. In essence, in excel, we will track daily differences in percentage terms of two ETFs and do a simple correlation function in excel to see how they are correlated.

Example: S&P500 Correlation with Gold

Let’s take a look at how the broad market index (SPY) is correlated with returns of gold bullion as tracked by the ETF GLD.

1. Go into Yahoo!Finance and pull the historical daily prices like this.

2. I picked just since Jan 2010 for a manageable data set.  Export to excel.

3. Do the same for both ETFs.  In the 2 excel files, cut out all columns but date and close.  Cut the close prices from one file into the other.

4. You should now have a single file with dates running down the column and two sets of prices.

5. You should view these in terms of % daily changes in price, so use the following equation (assuming column B has close dates for your first asset) : =(B3-B2)/B2

6. Drag this equation all the way down the file.  Also drag it over one column and down again to capture the daily % changes for the next asset class.

What you have now is two columns side by side showing the daily % changes of each asset class.  Since they are paired for every trading day, you can now run a simple excel function to see how they are actually correlated over time.

7. Use the function “CORREL” and excel will prompt you to input the two data sets.  Just capture the two columns.

Voila!  The result is .14.  This indicates that the returns of gold and the S&P500 are not correlated.  This might seem odd, since they’re both up nicely since early January 2010.  This is a common mispereption.  Two asset classes CAN show similar returns over time but this doesn’t meant that their returns are correlated.  This is just luck.  Over other periods of time, they may diverge significantly.  Like check out a small snapshot and the correlation will be different, or even look at different years.  So, you have to decide what the best proxy for future market conditions will be and select a historical time period to model into the future.

If you don’t think that’s right, well do the same exercise for SPY against the Nasdaq ETF (QQQQ).  Guess what the correlation is?  .95!  Now that’s a strong correlation.  And it makes total sense, right?  Usually, when the S&P500 is up, so is the Nasdaq, and vice versa.  Maybe not to the same degree (That’s Beta – the subject of another post!), but they tend to track together in a correlated fashion.

A final word of caution – correlations break down.  During the financial panic of 2008-2009, investors sold everything that wasn’t nailed down.  So, in a case like that, historical correlations may not stand up.  It would be useful to model various correlations during such a panic like that to see how your portfolio may stand up during a similar crisis.  Additionally, secular changes can alter correlation.  For instance, people used to say that emerging markets weren’t correlated with the US. Well, over the past several years, the world has grown much smaller and global indices have begun tracking much closer together.

Do You Consider Correlation in Your Investment Strategy?

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