Don't put all your eggs in one basket! … Fair enough but what baskets should we use?

Learning objectives:

Introduce the asset correlation matrix and show how to use it.


In the previous section, we explained the concept of correlation between two assets, here we will extend this concept to a basket of assets. Correlation between assets is the foundation of portfolio theory. By selecting investments that have low correlation to one another you can reduce the volatility of a portfolio. The importance of building a portfolio by selecting assets that are not well correlated is universally accepted. There is not much investment strategy that makes such unanimity amongst the financial professionals. Asset correlation analysis is the cornerstone of Markowitz’s Efficient Frontier theory that will be introduced in the next section.

First, we will explain how to read the table, called correlation matrix that is used to illustrate the correlations between all the pair of assets that composed an investment portfolio.

Select Matrix 1 and you will see a very basic example that corresponds to the correlation matrix of our three key assets that we used so far namely, stocks, bonds and cash. The diagonal of a correlation matrix is always composed of ones. This is because a variable is always perfectly correlated with itself. Also the values located in the upper right region of the correlation matrix are not shown since there are equal to the values shown below the diagonal (a correlation between variable A and variable B is equal to the correlation between variable B and variable A). A correlation matrix is always symmetric. The correlation between two assets is located at the row and column intersection of the two assets. For instance correlation between stocks and bonds has been equal to 0.045. Even if, correlation between two assets varies over time, this low correlation between stocks and bonds is quite common and this is why bonds are attractive in a portfolio.


As we already mentioned in previous sections, in addition to stocks, bonds and cash, investors have also access to a plethora of financial products that offer exposure to real estate, commodities, hedge funds, private equity, derivatives, managed futures and distressed securities.

We can for instance use the following list of ETFs, SPY to replicate the S&P500, AGG for US Investment Grade Bonds, GSG for commodities (Energy, Metals, and Agriculture), ICF for real-estate, PSP offers some exposure to private equity, QAI for hedge-funds, EFA for stocks from Europe, Australia, Asia and Far East, VWO Emerging markets, GLD for gold and TIP US Treasury inflation protected securities.

Matrix 2 shows the correlation of daily percent changes of asset’s returns over the two years period from May 22, 2009 to May 24, 2011. It is interesting to note that bonds (AGG) exhibit negative correlation (-0.315) with stocks (SPY). Negative correlation is very attractive to better manage portfolio risk. Bonds actually show negative or very low correlation with all assets included in this matrix except with TIP which has also very correlation with most of the assets.
Both commodities (GSG) and gold (GLD) also exhibit low correlation with stocks (SPY). But correlation between assets does not tell you anything about their respective volatilities. Gold in particular tends to have very high volatilities and risk.
Also it is interesting to mention that over this 2-year period, correlations between US large-cap stocks (SPY) and international stocks (EFA and even VWO) have been quite high (0.910 and 0.877 respectively).


In Graph 1, we highlight one important characteristic of the correlation between two assets: correlation varies over time. Actually like volatility, correlation is not stable and it may experience significant changes over time. In the top part of the graph we show together the volatility of SPY and AGG, as well as their correlation from 2003 to 2011. On the bottom, for reference you can see the asset price of SPY and AGG. Correlation and standard deviations are based on daily changes of asset returns and are calculated using a rolling three month period. Standard deviations have been annualized (multiplied by the root square of the number of trading days in a year, 252). Most of the time correlation is on the negative side, but you can observe some peaks above zero, especially during the 2008 financial crisis.

The first matrix shown in Matrix 3 picture highlights the correlations of the same assets as before but from August 28, 2008 to March 9, 2009. During this period the stock market lost about 50% of its value. We selected this period to illustrate how the asset correlations changed during the so called subprime crisis. The second matrix shows the difference between the correlation of the two periods, ie from August 28, 2008 to March 9, 2009 and from May 22, 2009 to May 24, 2011. Correlations that have increased during the financial crisis are shaded in red and those that have decreased are shaded in blue, then in dark yellow are those that have experienced very little changes. As shown, bonds’ correlations have generally increased with most of the assets. On the other TIPS and gold correlations with other assets decreased. Also notice that correlations between US stocks and non-US stock increased as well.

Each crisis has its specificities, but it has been shown that correlation between assets tend to increase during severe price corrections. In other words, you loose some benefits from diversification when you need it the most. This does not mean that you should get rid of diversification.

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