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# Diversification and Correlation

Administrative note: There will be no new post tomorrow–taking the day off for Thanksgiving. And on that note, thanks to each of you for the roles you play here (whether buying one of my books, sharing the blog with others, or participating in the discussion). Being able to do this full-time is literally a dream come true for me. So, thanks. 😀

There appears to be a prevailing sentiment that diversification failed in 2008 because U.S. stocks, international stocks, and REITs all went down at the same time.

The thing is, that’s what usually happens when one of them goes down. They are, after all, positively correlated.

In fact, even bonds–the asset class most frequently used as a diversifier for an otherwise stock portfolio–have a historically positive correlation with the U.S. stock market. If stocks go down in a given year, more likely that not, bonds went down also.

Does this mean bonds are ineffective as a diversifier? Of course not. They’re a helpful diversifier because their correlation to U.S. stocks, while positive, is quite low.

### Math Refresher: Correlation Coefficient

In case it’s been a while since you studied correlations, here’s a refresher:

• If two variables have a correlation coefficient of 1, they move in perfect lockstep. One goes up, so does the other.
• If two variables have a correlation coefficient of 0, they’re completely independent. The movement of one has no value for predicting the movement of the other.
• If two variables have a correlation coefficient of -1, they’re perfectly negatively correlated. When one goes up, the other goes down.

### Negative Correlations: Dream On.

The dream asset class is one that would have a long-term expected return similar to stocks as well as a negative correlation to stocks (such that when one has a bad year, the other usually has a good year).

However, it’s rare that you’ll find asset classes with negative correlation to the stock market (aside from asset classes with negative expected returns). In fact, even looking for a zero correlation is quite difficult. In most cases, a low positive correlation is all we can hope for.

### Seeking Low Correlations

You benefit any time you add an asset class to your portfolio that has:

• A correlation (to the rest of your portfolio) of less than 1, and

That’s why international stocks make a worthwhile diversifier to U.S. stocks even though their correlation is quite high. When one has a bad year, there’s at least a chance that the other had a good year. Or, more likely, when one has a truly terrible year, the other may only have a “sorta bad” year.

And with bonds, even if they lose money in 2/3 years in which stocks lose money, they still provide a diversification benefit because:

• In the other 1/3 bad years, they must have gone up, and
• Even in the 2/3  bad years in which bonds also went down, they likely went down less than stocks.

In other words, all we’re looking for when we diversify is asset classes that will behave differently from stocks (without sacrificing too much expected return), not asset classes that always go up when stocks go down.

### So did diversification fail us?

Just because U.S. stocks, international stocks, and REITs all went down in 2008 doesn’t mean “diversification failed us.” They did, in fact, all perform differently from each other–exactly what we’d hope they would do. And bonds had a great year, with many bond funds putting up double-digit returns.

It seems to me that diversification didn’t fail at all. It worked perfectly according to plan–practically a banner year for the “here’s why you should diversify” message. So what failed? The general public’s expectations and understanding of diversification.

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1. Dylan says

Mike, you are exactly right. Diversification didn’t fail us (neither did indexing or buy and hold investing). Capital markets decided stuff is worth less money. That’s true whether one is diversified or not, and the undiversified investors as a whole cannot do better then the diversified investors. So we cant really say diversification failed and non-diversification did not.

I think historically, ultra-short-term, high-credit (insured muni bonds and 90-day T-Bills) debt has had a slight negative correlation to US equity markets (and much lower return).

“The movement of one has no value for predicting the movement of the other.”

I think this applies to any correlation coefficient, not just zero. It’s never predictive because variations are concurrent. I think a better way to explain zero correlation is that the frequency and degree of positive correlation matches the frequency and degree of negative correlation, resulting in a wash.

2. Mike says

Dylan, you’re right.

When I said “predicting,” I didn’t mean predicting future returns. I really meant something more like this: “if you were told the return of asset class A for a given year, and were asked to guess the return of asset class B for that year, if they have zero correlation, the information about A will be of no use.”

3. >It seems to me that diversification didn’t fail at all. It worked perfectly >according to plan–practically a banner year for the “here’s why you should >diversify” message. So what failed? The general public’s expectations and >understanding of diversification.

Absolutely! Sadly, the general public is likely to abandon diversification, as they expected it to prevent losses- rather than mitigating losses. Happy Thanksgiving!

-Rick Francis

4. Mike, great article once again!

When did you go full time on this? I must be out of the loop!!! 🙂 Congratulations!

Dylan, you’re right about the ultra-short term, high-credit debt having a slight negative correlation to U.S. equities. The info I have shows that 0ne-month CDs and the Vanguard Short-term Bond Index both have a -0.04 to -0.05 correlation to the S&P 500 and about a -0.12 correlation to US Small Caps (based on CRSP data and actual returns). The Lehman Brothers Intermediate Gov’t/Credit Bond index has a slightly positive correlation (~0.10 to 0.15).

5. RJ Weiss says

I was talking to a financial adviser the other day who really believes that buy and hold is dead.

Mike, like you said, it’s exactly the opposite. For whatever reason, the public perceives that buy and hold means you hold the S&P 500 and that’s it.

We seem to forget that buy and hold means indexing not just in stocks but other asset classes as well.

6. Mike says

Paul: I’ve actually been full-time writing since last November–pretty much since before anybody was reading this blog. 🙂

7. Ethan says

I always like to point out that if your careful asset allocation fails to produce a diversification benefit – fails completely and utterly over your entire investing horizon, producing a correlation coefficient of 1 – what have you lost? Nothing. For the careful investor, fees probably aren’t even any higher. And since they performed identically you don’t have any rebalancing costs or time investment.

When failing carries no repercussions, and success has positive repercussions, why would you not try?

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