# The magic of equal-weighted portfolios

In Michael McClung’s *Living Off Your Money* he ends up recommending equally-weighted portfolios. That is, if you have 2 asset classes then each one is 50% of your portfolio; if you have 3 asset classes then each one is 33% of your portfolio; if you have 4 asset classes then each one is 25% of your portfolio.

He reaches this conclusion by looking at a wide variety of popular portfolios (Rick Ferri’s Core Four, Bill Bernstein’s No Brainer, Bill Schulteis’s Coffee House, etc). He uses his own metric — Harvesting Ratio — and finds that the best performing of these popular portfolios are equally-weighted.

*(The details of the Harvesting Ratio are perhaps the topic of a future post…)*

When you look around, there are actually a fair number of well-known and popular equally-weighted portfolios.

Sometimes they are equally-weighted across every asset class.

Sometimes they may have unequal weights for the stock/bond allocation but equal-weights within the equity slice.

Equal-weight portfolios have one appealing strength: instead of taking any stances on whether you should have more of X or less of Y, you just say, screw it…I’ll have the same amount of everything!

But McClung’s recommendations, simple as they are and despite a few similar portfolios out there, seem to fly in the face of the recommendations you normally see. Taylor Larimore’s “three-fund portfolio” suggests 50% US, 30% bonds, and 20% international. Rick Ferri’s Core Four has 8% REITs, 48% US, 24% international, and 20% bonds.

Why does equal-weighting work so well? Are there any theoretical arguments underpinning it? Is using equal-weighting a slam dunk case?

It isn’t really surprising but there’s actually a fair bit of academic research on the question. It seems to work that way with academics: chances are *someone* has researched the thing you are interested in. But finding their paper requires knowing the exact magic incantation of search terms (and hoping their paper is publicly available).

“Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?” by DeMiguel, Garlappi, and Uppal in the 2009 *The Review of Financial Studies* looks at 14 models across 7 different datasets and compare them to the “naive” equal-weighting. What they are trying to answer is: is finding the “optimal” portfolio worth it?

From the above discussion, we conclude that of the strategies from the optimizing models,

there is no single strategy that always dominates the 1/in terms of Sharpe ratio. In general, the 1/NstrategyNstrategy has Sharpe ratios that are higher (or statistically indistinguishable) relative to the constrained policies, which, in turn, have Sharpe ratios that are higher than those for the unconstrained policies. In terms of CEQ,no strategy from the optimal models is consistently better than the benchmark1/Nstrategy. And in terms of turnover, only the “vw” strategy, in which the investor holds the market portfolio and does not trade at all, is better than the 1/Nstrategy.

In other words: nothing they looked at was clearly better than equal-weighting. In some situations, with some datasets, a fancy allocation method might do better. But then it might do worse with another dataset.

But *why* do these other models fail to outperform equal-weighting? The authors’ answer is that all of those models require inputs that simply don’t have enough solid data for.

we find that for a portfolio with only 25 assets, the estimation window needed is more than 3000 months, and for a portfolio with 50 assets, it is more than 6000 months

Just FYI, they are saying that you need 500 years of data in order for something like mean-variance optimization to work well. Otherwise the estimation errors overwhelm any “efficiency” you gain.

Their paper includes references to many, many other papers with similar results.

Bloomfield, Leftwich, and Long (1977) show that sample-based mean-variance optimal portfolios do not outperform an equally-weighted portfolio, and Jorion (1991) finds that the equally-weighted and value-weighted indices have an out-of-sample performance similar to that of the minimum-variance portfolio and the tangency portfolio obtained with Bayesian shrinkage methods.

And it appears that normal investors have been doing the “right thing” all along by ignoring all these fancy asset allocation models:

For instance, Benartzi and Thaler (2001) document that investors allocate their wealth across assets using the naive 1/

Nrule. Huberman and Jiang (2006) find that participants tend to invest in only a small number of the funds offered to them, and that they tend to allocate their contributions evenly across the funds that they use, with this tendency weakening with the number of funds used.

What does this mean for *our* asset allocations?

In a lot of ways, this simplifies things. Worrying about getting exactly the right balance of assets is likely wasted stress. Trying to get an optimal asset allocation can actually increase our risk of making our portfolio *worse.*

Including something that we *don’t* equal-weight raises questions about the value of including it in the portfolio at all. All of which pushes us towards simpler portfolios: by following an equal-weighting asset allocation we’re unlikely to have more than maybe 10 different asset classes.

We wish to emphasize, however, that the purpose of this study is

notto advocate the use of the 1/Nheuristic as an asset-allocation strategy, but merely to use it as a benchmark to assess the performance of various portfolio rules proposed in the literature.