“How should individual investors diversify?”

A few months ago I looked at a 2009 paper that found that, even though there are tons of fancy ways to determine an asset allocation, a naive equal-weighting — where you just split your money up evenly — seems to do just as well anything else…and with a lot less effort.

I’ve become interested in this because it seems to stand in stark contrast to how people actually act. That research suggests, “Your asset allocation won’t matter much” while, in the real world, people obsess over whether they should have 5% in Emerging Markets or 10%.

It seems complete counterintuitive that asset allocation is, it not unimportant, at least substantially less important than we normally treat it.

The 2013 paper “How should individual investors diversify? An empirical evaluation of alternative asset allocation policies?” is another entry in the genre. And it also finds that a wide variety of “naive” asset allocation heuristics are all good enough when compared against 11 mathematical optimisation methods.

Country allocation of equities

The first is deciding how to split up your equity investment among countries. How much do you invest in the US versus the UK versus Ireland? In addition to the sophisticated mathematical optimisations they also consider: equal-weighting, market cap-weighting, and GDP-weighting.

They find that none of the optimising models significantly outperforms any of the three simple heuristics. Interestingly, they find that the GDP-weighting does better than the far more popular market cap-weighting. You can see that there’s a big difference between market cap- and GDP-weighting. GDP-weighting, in general, will give you a lot more emerging markets in addition to shielding you a bit from bubbles (notice the lack of the Japanese bubble when GDP-weighting).

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Market cap-weighting 1973–2012
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GDP-weighting 1973–2012

Asset allocation between stocks and bonds

Next they look at the asset allocation between stocks, bonds, and commodities. They look at a wide variety of literature to determine a “consensus” recommendation which forms the basis of their naive portfolio: 60% stocks, 25% bonds, 15% commodities.

They find that, while there are some performance differences, the p-values are so low that there’s not much confidence in the results. In the end they find that

The evidence from the asset allocation thus again supports the conclusion that optimizing portfolio choice models are not able to outperform a passive benchmark.

Sensitivity checks: 5,151 portfolios

So far, all the authors have shown is that the fancy mathematical models don’t provide any real value when tested with real-world out-of-sample data. That’s not nothing! But they provide two other interesting bits of information along the way.

They note that the 60/25/15 portfolio performs well. But that was a “consensus” portfolio based on surveying the literature. Maybe the literature was biased and suggested portfolios like that based on past performance. In other words, maybe 60/25/15 wasn’t “naive” but was actually optimised based on the historical data. Maybe 60/25/15 was great but slight deviations from it — say 55/30/15 — would have been horrible.

So they test every combination of assets in steps of 1%. From 0% stocks to 100% stocks. From 0% bonds to 100%. From 0% commodities to 100% commodities. 5,151 portfolios in total. While around 60% of those 5,151 portfolios perform worse, it is usually because they were heavily tilted towards a single asset (i.e. 80% commodities). The authors write

This is good news for individual investors. Although it is not possible to identify the best performing portfolio ex ante, almost any form of well-balanced allocation of asset classes already offers Sharpe ratios similar to the best performing strategy.


For most of the portfolios they generate, they perform factor regressions to look into the causes of the performance. They perform “10-factor regressions”.

  • 3 factors for bonds: “market”, value, and momentum
  • 3 factors for commodities: market, value, and momentum
  • 4 factors for equtiies: market, value, momentum, and size.
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None of the fancy mathematical models provided any alpha beyond those 10 factors. In many cases they actually had (substantial) negative alpha. By contrast, the simple heuristics had the most alpha (albeit still only small amounts).

What I learned

  • More evidence that all of the fancy asset allocation methods don’t appear to work in the real world; simple & naive rules of thumb appear fine.
  • Within those simple rules of thumb, there is wide latitude when it comes to making a “good enough” portfolio. Whether you put 30% into something or 35% into something isn’t something you should stress over.
  • GDP-weighting seems to have some advantages over market cap-weighting. (Though I’m not sure it is really actionable; are there any ETFs that do this for you? Would anyone really hold a dozen country ETFs and rebalance themselves?)
  • More evidence that factors are (or should be) the fundamental building block of a portfolio. Though I still haven’t really wrapped my head around how factors interact with things like international diversification or commodity/REIT type diversification.

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