## If RP has a secret ingredient, it is correlation: the degree to which two assets move in relation to each other. It comes up everywhere in this blog and elsewhere in the Risk Parity literature, so perhaps a step back to officially define and explain it is important. Sorry for the length of the following explanation, but it really is that important!

When it comes to the mindsets of RP, correlation connects them all. For the first, where the advice was to think of the recipe, not just the ingredients, correlation is the figure which tells us how those ingredients blend. When we pursue true diversification, not just variety, it is correlation that we look at. Finally, when we seek to put together a portfolio like a decathlete, it is correlation, or really, negative correlation, which tells us whether we are adding adaptability to new environments or just doubling, or tripling, down on what there already is.

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In mathematical terms, correlation is expressed by the correlation coefficient which is a statistical measure of the relative movements of two variables compared to their respective means. The range for the coefficient is between positive one to negative one, with numbers close to zero indicating a weak relationship, and numbers at the end indicating a strong relationship. By the way, unlike â€śbeta,â€ť a related but distinct measurement, the correlation coefficient canâ€™t be greater than 1 or lower than -1.

### Positive, Non-, and Negative Correlations

To put it in simple terms, I think of correlation as the â€śzigzagâ€ť number. Two assets with a positive correlation will tend to â€śzigâ€ť together, and carry a correlation coefficient at or close to one. It is slightly confusing, but positive correlation just means that whatever direction one goes relative to its own mean, so too, will the other according to its mean, whether this is up or down. A good example of positive correlation would be the relationship between VXUS, Vanguardâ€™s Total International Stock Index ETF, and VOO, Vanguardâ€™s S&P 500 Index ETF. The correlation between them is .86, meaning a strong tendency to move together. In this case, this is not surprising, as the 500 equities that dominate VOO resemble the types of companies that dominate VXUS, despite geographic differences. What is surprising is when you hear that people have bought both to diversify. Holding both improves variety, but not dissimilarity.

When there is no apparent pattern to the up or down movements of two assets, those two assets are said to be non-correlated. In such a case, the correlation coefficient would hover around zero, maybe .2 on either side, but essentially close to zero. A good example of this might be VOO and GLD, a gold ETF. Their correlation right now is .09, so basically no coordinated zigging and zagging, just the wandering of two cats around the house.

Negative correlation is when there is a â€śzigzagâ€ť effect - when one moves, the other moves in the opposite direction. In this case, the coefficient would be at or approaching negative one, though in the real world, it is very rare to find negative correlations anywhere beyond -.5. A good example of this relationship would be the pair of VOO and EDV, Vanguardâ€™s Extended Duration Treasury Bond ETF. The pair's coefficient is -.35, signifying a moderate oppositional pattern between the two. When one â€śzigs,â€ť the other â€śzags.â€ť

A very important point: Â the correlation coefficient between two assets is always changing, and it is best to think of it as a measure of a relationship at a particular time, not as an inherent quality of the assets. There will even be times when assets for which you typically see a negative relationship suddenly turns positive. This can happen in times of market crisis, or a "risk off" Â scenario when people just want to be in cash. In a crisis, they say, the only thing goes up is correlation, as everything tanks together. The good news is that this situation tends to be temporary. If you have patience, the relationships should return as market sentiment settles.

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Think of correlation a bit like you think of expected returns. We expect that the stock market will return between 6 and 10% most of the time, with some years far above that, and some years way worse, even negative. For correlation, we expect that most of the time, Long-term treasuries and the S&P 500 will be negatively correlated in the -.3 to -.5 range. There will indeed be weeks and even months where they sink together (and times where they rise together!), so it's important to focus on the big picture.

### The Holy Grail of Investing

The latter types of asset pairs, non-correlated and negatively correlated, are the building blocks of a Risk Parity portfolio. Ray Dalio once said that the search for multiple, non- and negatively correlated asset streams was the â€śHoly Grailâ€ť of investing. Combine enough of them and you could have high returns with low risk, as the volatility of one asset would be canceled out by others, with lots of other assets unaffected.

Of course, as the name implies, the search for assets with these relationships is not easy, what with all the knights and killer rabbits, (oh wait, wrong â€śHoly Grailâ€ť). Still, if we consider equities the bedrock of any portfolio, non-correlated assets are few, and negatively correlated assets even rarer. Most of the assets people talk about tend to be equities, which generally have highly positive correlations with each other, whether large-cap or small, American or non-American, growth or value, or whatever sub-category you wish to talk about. There are some exceptions, such as utilities (currently a correlation of .39 with VOO), but in general, most equity ETFs will have a number at .6 or higher.

### How to Find Correlations

To find the correlation between assets, you can figure it out yourself if you have the data, but the far easier method is to use the â€śasset correlationsâ€ť tool on Portfolio Visualizer. You enter in the assets you wish to calculate, then hit â€śview calculationâ€ť and you get a matrix like this:

Another similar tool on the site is the â€śasset class correlationâ€ť display, which is basically the same but pre-loaded with fifteen asset classes. This is worth spending some time with, as you can get a sense of how the different assets interact. While Iâ€™m at it - a big thank you to the creators of this site, and if you really get into creating RP portfolios, this is definitely a site you should bookmark.

Correlation is related to but slightly different from â€śbeta,â€ť though beta can be helpful too when thinking of RP portfolios. Beta is essentially a measure of the volatility of any asset compared to the market as a whole. Since the market is the most common Â thing people want to compare to, the popularity of beta makes sense, and indeed you can find beta on whatever site you use for looking at financial information. I use Barchart, by the way, and the 60-month beta is on the splash page for stocks and ETFs. I typically use beta as a rough estimate of correlation and use it as a criterion in my stock/ETF screeners, then follow up by double-checking on it on Portfolio Visualizer, since it can have a longer timeframe.

In sum, if you are interested in creating risk-balanced portfolios, then getting familiar with correlation between assets is a crucial step. If most investors only pay attention to return, and more sophisticated investors incorporate an understanding of risk, then the next step is to understand how different assets interact with each other - and for that, correlation is key.

Ahh, you paid attention to the end. Your reward is this classic: