ITA Wealth Management

Diversification is advocated here at ITA Wealth Management as we look for investments that carry low correlations with each other.  Why is this so important?  Follow the logic below as I attempt to explain why we seek low correlation ETFs and stocks.

Consider a simple two asset portfolio made up of investments ABC and XYZ.  Further, assume the expected return is 10% for each investment and the projected standard deviation is 15%.  This is not unusual for assets in the current market.  In our first example, we will assume the two stocks or ETFs are perfectly correlated to keep this first example simple.  The correlation coefficient is equal to 1.

We first need to calculate something called the covariance.  The covariance for this portfolio is 1 x 0.15 x 0.15 = 0.0225.  Let’s not worry about significant figures at this point in the calculation. 

Here is the calculation of the standard deviation for this portfolio.

SD = Square Root {(.5)^2  x  (.15)^2 + (.5)^2 x (.15)^2 + 2 x (.5) x (.5) x (0.0225)} = 0.15 or 15%

The above calculation makes sense as the stocks are perfectly correlated and both carry a projected standard deviation of 15%.  Mixing two stocks with identical risk has no impact on the portfolios standard deviation.

Now consider two investments where the correlation is 0.5, say a stock and a bond.  Let the standard deviation for each investment remain at 15% even though this is unlikely for a bond ETF.

The covariance for this combination of investments is equal to 0.5 x 0.15 x 0.15 or 0.01125.  Again, do not pay attention to the significant figures.

The standard deviation for this new uncorrelated portfolio is as follows.

SD = Square Root {(.5)^2 x (.15)^2 + (.5)^2 x (.15)^2 + 2 x (.5) x (.5) x 0.01125} = 0.13 or 13%

Only the last value changes do to a new covariance value.  Combining two investments that have a correlation of 0.5 will reduce the portfolio risk by 13.3%, not a trivial reduction.  This is the power of diversification.  If you run out your own calculations, you will see that stocks or ETFs with correlations 80% and higher do not add all that much diversification to a portfolio.

Within a week, I plan to expand on this analysis over on the Premium Content side of the blog.  What asset classes help to lower portfolio volatility or reduce the risk.  Using the QPP program, we are able to see how different ETFs, stocks, and bonds are correlated with each other in a combined portfolio.

Photograph: Lamp post in Cusco, Peru

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