# GLD and SPY are Uncorrelated, So Good to Mix in a Portfolio, Right?

June 21st, 2012

in gold, syndication

*Written by John Lounsbury*

In an article at *Investing Daily* this week I observed mixing the gold ETF GLD (NYSE:GLD) in a 50:50 ratio with the S&P 500 ETF SPY (NYSE:SPY) did soften the impact of the Great Financial Crisis (GFC) of 2008 when compared to a 100% investment in either GLD or SPY. The conclusions in that article about the effects of the mixed portfolio were summarized in the following table:

Follow up:

There are three conclusions based on the above table:

- The 50:50 portfolio did indeed produce a smaller worst drawdown;
- The 50:50 portfolio produced a smaller average drawdown;
- Perhaps surprisingly, the 50:50 portfolio produced approximately 50% more drawdowns >5% than the individual ETFs.

The drawdown data for SPY is dominated by the colossal market crash from the October 2007 all-time high. If the largest drawdowns are eliminated from all three data sets then the results are:

- SPY – 5 drawdowns, average = -11.8%;
- GLD – 6 drawdowns, average = -12.5%;
- 50:50 – 9 drawdowns, average = - 9.9%.

While the portfolio clearly offered a substantial advantage during the market crash 2007 – 2009, that advantage is less when the remaining time in the sample is examined. One should reasonably question whether a small reduction in average drawdown is worth the cost of such a large increase in the number of drawdowns.

So why has the portfolio introduced a 50% increase in the number of drawdowns? How can this occur when the correlation between the two data sets is essentially zero?

Those who have been following me will be able to make a good guess – It is due to the fact that the average correlation across a long time span is much less important than the fact that very often (and it is true in this case) R = f(t).

The relationship is generally not one for which a simple algebraic function can be written down; f(t) simply represents in the abstract that R can have widely differing values at different points in time.

Notes for the above graph:

- The red dotted lines denote the boundary between what the author defines as poor and negligible correlation (closer to zero) and weak.
- The green dotted lines denote the boundary between the author-defined weal correlation and fair.
- No dotted line has been drawn, but outside of 0.8 the author defines correlation as good, very good and, outside of 0.95, excellent.
- The 200-day moving average for the 30-day correlations is very similar to the 1-year correlation graph (not shown here).

Clearly there are significant amounts of time when the correlation between GLD and SPY is far from zero, both negatively and positively. The most massive period of negative correlation occurred through much of 2008 when the stock market was crashing. This explains the particular effectiveness of the portfolio in calming the fluctuation seen for each of the two individual ETFs during that time. Refer back to the previous graph.

A shorter time span correlation function displays even more of the fluctuation detail of R = f(t). In the graph for the 10-day correlations (not shown here) there are **26 occasions** when R exceeds the value +0.80, including five that exceed 0.90 (the boundary for very good correlation). Of those five, two exceed 0.95 (excellent) and one exceeds 0.99 (almost perfect correlation). One the negative side there are four occasions when R surpasses (negatively) the -0.80 line and two more when it nearly touches -0.80.

With such a wide variation in correlation so many times over the sample time period, it is perhaps surprising that there were not more drawdowns for the 50:50 portfolio.

**Note:** In the future we will cover more case studies of the perverse character of correlation, including demonstrating how R=f(t) not being reognized is one of the fatal flaws of MPT (Modern Portfolio Theory). Understanding correlations is a key factor in making successful investment decisions. But the manner in which correlation has been applied has been primitive, primarily because time variation has been ignored and, perhaps equivalently disastrous, the assumed time invariant value for R has been coupled with an assumption of Gaussian (normal, bell curve) distributions of investment results. Even today, investment professionals (especially executives) will refer to things that went wrong as 9-sigma or 25-sigma events. These statements are dead giveaways that they are still not recognizing that Black Swans (Taleb) do exist. As far as investing is concerned, they are still living with a discredited stone-age set of concepts.

**Related Articles**

Gold's Persistent Allure by John Lounsbury (at *Investing Daily*)

Correlation Concepts by John Lounsbury

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