Rising correlations & international investing

One of the arguments for international investing is that it lets you diversify away from the US. The US might be doing poorly but Japan and Australia are doing great, so you at least get okay returns. Or vice versa.

But you’ve probably also heard a lot about how, in our modern interconnected world, correlations have increased. “The Nikkei opens lower on worries about the United video and its impact on global air travel!”

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A randomly googled chart showing correlations with the S&P 500

With correlations going up, the diversification benefit has gone down. Right? That makes some kind of intuitive, logical sense.

…But how does that actually affect your investing?

Let’s say that back in 1990 — when correlations were at 0.4 according to the chart above — you had 30% international in your portfolio. Now correlations are at 0.8. So…what should your international holdings be now in order to account for rising correlations? 0%? 10%? 28%?

Before we go further, we should pause and do some introspection about what exactly we’re trying to accomplish here.

Are we just trying to find a justification for not owning any international stocks at all? “Jack Bogle says not to and correlations are so high these days, there’s no real point anymore; I’ll just stick with massively overweighting the US.”

Are we admitting that we were wrong in the 1990s, when correlations were low, but we’ve gotten lucky and correlations have changed such that we don’t need to change our portfolios or our minds? That seems suspiciously lucky but stranger things have happened.

Or are we saying that our allocation between domestic and international should vary based on correlations?

In “Long-Term Global Market Correlations” the authors show how correlations have changed over 140 years.

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Those are some wild swings!

Are we really thinking about a scenario where when correlations are very low (say, under 0.2) then we would overweight foreign equities but when correlations are very high (say, above 0.3) we underweight them?

That’s clearly a kind of tactical asset allocation but I’ve never heard anyone suggest using correlations as a way to determine tactical asset allocation shifts. (Though I’m sure someone has; nearly every investing idea has been proposed by someone before.)

Let’s keep this in the back of our mind as we proceed…

Going back to our original question: if correlations change what does that mean for actual portfolio construction?

A new paper from Viceira, Wang, and Zhou from the Harvard Business School provides an interesting answer in “Global Portfolio Diversification for Long-Horizon Investors”.

Their basic argument is that just talking about correlations alone isn’t useful: you need to also look at what causes the correlations to increase. They split it into two root causes: increased correlations of discount rate shocks and increased correlations of cash flow shocks.

A “discount rate shock” is something that affects (real) interest rates. Inflation is a perfect example: if inflation goes up in many countries at the same time we’d say “their discount rate shock is correlated”.

A “cash flow shock” might be something like “the price of oil crashes…which substantially reduces our cash flow”.

Once you decompose correlations into these two parts a few things happen:

  • There is a fair amount of research showing that shocks to discount rates are transitory but cash flow shocks are more permanent; this means that if rising correlations are due to discount rate correlations then we should also expect the increased correlation to be temporary.
  • Because discount rates vary over time, it means there is a difference between the optimal portfolio for a “short-horizon investor” and a “long-horizon investor”. Essentially, if you can hold the portfolio long enough then the effects of discount rate correlations fade away.

If increased correlations are primarily due to cash flow then the effects are long-lasting and affect everyone equally. But if the increased correlations are due to discount rates then we should expect them to fade away (or at least diminish), meaning they aren’t as relevant to long-term investors.

That leaves the authors with two questions to answer:

  1. How much of the increased correlation is due to discount rates versus cash flows?
  2. How much is the impact on a long-term investor versus a short-term investor?

They do a lot of fancy math to decompose correlations into components: cash flow (CF), real rate (RR), and risk premium (RP). I’ve highlighted the “cash flow” row below:

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You can see that cash flow correlations have increased only a very small amount — 0.06 — while the other correlations have played a much bigger role.

So this is their answer to the first question:

the source of the large increase in correlations […] has been an increase in cross-country correlations of discount rate news


So discount rates became more correlated but cash flow didn’t. That’s good news because the effect of correlated discount rate news subsides at long horizons.

The actual curve looks like this. Look at the red line….

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The impact start off high but falls off over time. The longer our investment horizon, the less important today’s discount rate correlations matter. If we held our portfolio for 700 months (58 years) then it would go away entirely. We won’t hold it that long but even holding for 20 years reduces much of the correlation.

This gives the long-term investor some hope: even though correlations have gone up substantially, it seems like maybe it only matters a little bit?

To try to quantify that, the authors use a variety of models to construct different portfolios and show the optimal portfolio both before and after correlations increased.

I’ve highlighted just the “myopic demand” model but all of them show the same trend, albeit with slightly different numbers.

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You can see that while the allocation to the US increased when global correlations increased, the change was minor. Instead of investing 58.88% in the US, you should invest 59.83% in the US.

The authors argue that difference is negligible and conclude:

Long run portfolio risk [of a globally diversified portfolio] has not increased, optimal long-run equity portfolios are as globally diversified and invest in equities as much as in the prior period with lower cross-country return correlations, and the expected utility from holding global equity portfolios has not declined for long-horizon investors.

So for us that means we can tune out the noise about increased correlations reducing the benefits of a globally diversified portfolio. But that takes us back to what we asked ourselves earlier: This result supports my current beliefs. If it had said there was no longer any benefit to investing globally, would I really have taken action?

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