For several months, we've been posting results for the easy 5-ETF retirement portfolio series. Given daily adjusted closing prices, looking backwards over the last 252 trading days, we compute the minimum absolute deviation portfolio with the formulation presented by Konno and Yamazaki using our universe of ETFs:

**Fixed-Income/Bond Assets:** TIP, SHY, IEF, TLT, AGG

**Commodities:** IAU, SLV, GSG, BDC, USO

**Global Equities/Emerging Markets:** FXI, EFA, EEM, IEV, [[IOO]

**US Equities:** OEF, IVV, ISI, IYY, JKD, JKG, JKJ

**Leveraged Assets (i.e. Double Longs):**DDM, SSO, QLD, MVV

**Inversely Correlated Assets (i.e. Shorts):** DOG, SH, PSQ, MYY

**Inversely Correlated and Leveraged Assets (i.e. Double Shorts):** DXD, SDS, QID, MZZ

**US Equity Sectors:** XLF, IYM, XLE, VNQ, XLI, XLY, SMH

Below we plot the correlations among the asset classes. While there are multiple types of correlations, the type of correlation we present here describes how different assets are correlated with each other (i.e. cross-correlation). Another type of correlation (e.g. serial correlation) can be used to describe the relationship of a single asset's returns over time. For these posts, I'll only focus on cross-correlation.

It's very easy to compute the correlations (a 41 X 41 matrix) and generate a correlation plot of all possible correlations among the assets within our universe. Here, I'll post the correlations for the past 63, 126, and 252 trading days to represent the previous one, two, and four quarters:

These plots presents all possible correlations for all possible combinations of assets in our universe of ETFs for the three time periods. The solid blocks represent combinations of assets that behave similarly (i.e. similar correlations).

Here are today's take home messages:

**A well constructed universe should contain a wide variety of asset classes with a wide range of correlations (i.e. -1 <= correlation <= +1) and all correlations should never go to one during any period. Ever**. A well constructed universe and the resulting portfolio should include groups of assets (e.g. bonds, stocks, and commodities) that range in correlation from +1, 0, and -1 with the other groups of assets. Having simple plots like the ones presented here should help you confirm that. Make sure you are familiar with the correlations among your assets. You shouldn't need to know the exact correlation values, but you should be familiar with how correlation influences your portfolio. If not, ask your financial advisor, financial planner, or your handy dandy applied econometrician.**Bonds traditionally have had low negative correlations with commodities, US equities, and global equities**. Conversely, they have low positive correlations with shorts, which seems to reinforce their role as shock absorbers during downturns in equities. That's why bond ETFs show small positive returns when equities decline sharply. It's indicative of a “flight to safety.” and these relationships will be interesting to watch in the coming months.**There is a pattern in the correlations among commodity assets (IAU, SLV, DBC, GSG, USO) where commodities exhibit small changes in magnitude as the number of days looking back decreases.**Over the longer term (i.e. last 252 days), commodities have exhibited low positive correlations with just about everything in our universe. This pattern supports statements like, “Gold (NYSEARCA:IAU) is practically uncorrelated with any other asset. Buy gold to hedge against inflation.”**As the time window decreases and more data is included (e.g. 63 and 126 days), the boundaries of blocks of correlation appear to dissolve for some asset classes.**This typically indicates changes in the relationships among the different classes and certainly within individual assets. When plotted over longer periods of time, these blocks remain constant with very minor variations and it's these relationships that are good for guiding simplified portfolio construction (e.g. TLT, IVV, and IAU)A well constructed universe should include individual assets within a group that, when the market does correct, will have correlations that change slightly with each other, and may tend towards 1, but should have correlations that remain low or negative against other assets in other groups.

The market will correct again, and while it's possible that we may have a catastrophic failure like we saw in the recent past (i.e. 2007-2009), a decent retirement portfolio should be able to pass a simplified stress test, by asking what does my correlation matrix look like. Having a picture like this one helps.