The Perfect Fifth Portfolio: Why Asset Classes Should Harmonize, Not Just Diversify

Every investment committee I’ve dealt with asks the same question sooner or later: “Are we properly diversified?”

The answer usually arrives as a correlation matrix, a dense grid showing how asset classes move relative to each other. Low correlation is good. Negative is better. When one asset zigs, another zags, and the ride smooths out.

I think that answer is useful and incomplete. A correlation matrix measures one thing: how returns have moved together over a sample period. It cannot tell you why two assets move as they do, or whether they will keep doing so when it matters.

That matters more than it sounds. Two assets can show low correlation and still depend on the same underlying thing. Two others can be highly correlated and still respond to quite different forces. Correlation describes the past behaviour of prices. Diversification is a claim about what your holdings depend on.

So I use a different question: are these assets in harmony, or merely out of step?

Where correlation lets us down

Correlation is backward-looking and regime-dependent. Chua, Kritzman and Page showed in 2009 that correlations measured over a full sample often hide how an asset behaves when diversification is needed most. In market declines, many assets that looked independent became far more correlated with equities than their averages suggested.¹

The 2008 crisis is the standard illustration: assets that had been diversifying in calm markets fell together when it counted. And in 2022 the stable stock-bond relationship of the previous two decades gave way. Both stocks and bonds fell by double digits in the same year, the first time that had happened in the Bloomberg Aggregate’s history.²

None of this means correlation is useless. It means a number measured over one period is a symptom. The cause is what each asset is exposed to.

A metaphor, used carefully

Music offers a way to think about those exposures. Two notes sounding together are related by a ratio of frequencies, and some ratios sound consonant while others clash. The perfect fifth is 3:2, the major third 5:4, unison 1:1, and the tritone, in its just form, 45:32.

I want to be plain about what this is. It is a metaphor and a thinking tool, not a measurement. No asset has a frequency, and nobody can compute that a pair is “3:2”. What the metaphor gives me is a vocabulary for three questions I would otherwise ask less clearly:

• Do these assets share a driver, such as earnings, interest rates or inflation?
• Do they respond differently to that driver, or at different speeds?
• When the shared driver dominates, do they converge?

The intervals are shorthand for the answers.

Unison, 1:1: the same driver, the same response. U.S. large-cap growth and the Nasdaq-100 are a standard example. They overlap heavily because the same handful of mega-cap companies sit at the top of both. Holding both adds a second label for one exposure, which is counterfeit diversification. Rebalancing between them is shuffling cards within a single deck.

Perfect fifth, 3:2: a shared foundation with a distinct response. Equities and investment-grade corporate bonds both depend on a company’s capacity to earn. Equities respond to growth and the equity risk premium. Bonds respond to rates and default risk. Here the relationship itself carries information: when credit spreads widen while equities still look calm, the bond market is saying something. I keep one caution close. In a real credit crunch this pair tends toward unison, because the shared earnings driver swamps the difference. That is exactly why the interval is a judgement and not a number.

Major third, 5:4: complementary roles. Long government bonds and real assets such as real estate lean on different sides of the inflation and growth question. One tends to help when growth slows and inflation falls, the other when inflation and income matter. They are not guaranteed to cooperate. The 2022 inflation shock hurt both long bonds and many real assets, which tells me the “complement” holds in some regimes and fails in others.

Tritone, 45:32: productive tension. Equities and a long-volatility or protective strategy pull against each other by design. The tension forces a discipline, selling what has run and buying protection that is cheap after a rally. I want to be honest that this comes at a cost: protection has a carrying cost, and it usually loses money in a rising market. The tension is useful only if the cost is worth paying.

The overlap test

The vesica piscis is the almond shape where two circles overlap. I find it a useful picture for the test.

Draw one circle for what drives asset A and one for what drives asset B. The overlap is the shared driver, and that is where correlation lives. The two crescents outside the overlap are where diversification lives. A pair is only as useful as its crescents.

• Large-cap growth and the Nasdaq-100: circles nearly identical, crescents trivial.
• Equities and investment-grade corporates: a large overlap in earnings capacity, and genuinely different crescents in rates and credit risk. A fifth in calm markets, closer to a unison in stress.
• Equities and art collectibles: hardly any overlap. That is low correlation without any clear relationship, so it tells you little about how they will behave together in a crisis.

You can do a rough version of this with real numbers. Take a few funds, regress each on a small set of common factors such as equity market, rates and credit spread, and look at how much of each one’s return is explained by the same factors. The overlap is a number you can estimate. The musical label is just a way to remember what it means.

What changes in practice

Run the correlation matrix, then ask different questions of it.

1. What are we really exposed to? Not “what asset classes do we hold?” but “what drivers do they depend on?” Holding U.S. equities and Canadian resource stocks is not geographic diversification if both respond to the same commodity prices.
2. Do any holdings sit in unison? Two positions that respond identically are one position. Cutting one costs you nothing in diversification.
3. Which relationships hold under stress? Check how a pair behaved in 2008, 2020 and 2022, not only its average.
4. Where is the tension deliberate? If a position exists to offset another, know the price you are paying for it and what regime it is designed for.

Then watch the relationships, not only the weights. A pair that used to be a fifth and has drifted toward unison is a signal that your diversification has quietly eroded.

Why I think this matters now

The assumptions that supported the old rule of thumb, a steady negative correlation between stocks and bonds, were a feature of a particular era of low and stable inflation. When inflation is uncertain, the two can fall together, and 2022 showed it.² Concentration adds a second problem. A handful of mega-cap names now sit at the top of most broad equity indices, so portfolios that look spread across several equity funds can be leaning on the same few companies.

The same discipline sits under Mental Models Before Financial Models: the number is a prompt for judgement, never a replacement. And where this essay asks what an asset depends on, Five Lenses for Reading Monetary Policy asks what the policy environment is doing to all of those dependencies at once.

The sound of a well-built portfolio

A unison portfolio can feel like skill in good years, because everything rises together. Its drawdowns are all the more severe for the same reason. A portfolio with distinct drivers, honest about where they overlap, tends to be steadier. It cannot promise good outcomes, and no arrangement of intervals does. What it can do is let you see what you own.

Correlation can tell you whether assets have moved together. The better question is whether you understand why.

Next time your committee asks, “Are we properly diversified?”, try following the answer with a second question:

“What does each of these actually depend on?”

This essay extends the harmonic framework I introduced in Resonance vs. Relevance. It is general reflection, not investment advice, and the interval labels are an aid to thinking, not a measurement.

References

Footnotes

1. David B. Chua, Mark Kritzman and Sébastien Page, “The Myth of Diversification”, The Journal of Portfolio Management 36, no. 1 (Fall 2009): 26–35. The paper shows that empirical correlations are asymmetric, with diversification weaker on the downside than full-sample correlations suggest. ↩

2. In 2022 the S&P 500 returned about −18% and the Bloomberg U.S. Aggregate Bond Index −13.0%, the index’s worst year and the first time both fell by double digits (Castle Keep Advisors, 2022 Year in Review). A 60/40 mix of those two indices lost about 16%, its third-worst year since 1950. SPY and AGG, dividend-adjusted, give −18.2% and −13.0%, which agrees. Using U.S. equities and 10-year Treasuries instead, Morgan Stanley Investment Management measured −17.5%, the worst year for that mix since 1937; a 60/40 of the S&P 500 and a 10-year Treasury rolled monthly from FRED yields comes to about −17.5% as well (Return of the 60/40). The Bloomberg U.S. TIPS index also fell, by about 11.9%. ↩ ↩²