For several months, we've been posting results for the easy five ETF retirement portfolio series and with each new post we've had several internal conversations about statistics; specifically conversations about standard deviations and correlations. Given daily adjusted closing prices, looking backwards over the last 252 trading days, we compute the minimum absolute deviation (MAD) portfolio, using our universe of Exchange Traded Funds (ETFs):

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

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

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

**U.S. 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

**U.S. Equity Sectors:** XLF, IYM, XLE, VNQ, XLI, XLY, SMH

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:

*(Click to enlarge)*

*(Click to enlarge)*

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 for a well constructed universe:

**A well constructed universe should contain a wide variety of asset classes with a wide range of correlations (i.e. -1 <= correlation <= +1). Always**make sure you are familiar with the correlations among your assets. If not, ask your financial advisor.**Bonds typically have had low negative correlations with commodities, U.S. equities, 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.”**There's a pattern in the correlations with commodity assets (IAU,SLV,DBC,GSG,USO) where commodities exhibit a reduction in the dispersion of correlations within the universe as more data is included (i.e. the number of days back increases).**Over the short term (i.e. 63 days), commodities have maintained low 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.”

**Beware: there are multiple types of correlation.**The type 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.**Again, for a well constructed universe of assets, all correlations should never go to one. Ever.**A well constructed universe and 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 a simple plot like the one presented here should help confirm that.

**Disclosure: **I am long SLV, XLE, AGG, TIP, IAU.