Correlation Illusion

One of the key tenets of portfolio construction is diversification. And as Curt LaChappelle discussed in a recent article, one the key tenets of diversification is correlation.

The New Rules of Diversification: Correlation Matters

LaChappelle is correct … if you have a portfolio of assets that tend to all rise and fall together, you’re going to experience more overall portfolio volatility than if they don’t. But the intent of this post isn’t to rehash the diversification canon. That’s been more than thoroughly covered by conventional finance. Rather the focus here is on its flaws.

One is the tendency to overly emphasize statistics over fundamentals. Modern Portfolio Theory (MPT) is based on statistical analysis. Correlation isn’t merely a component of diversification, it is diversification. Lock, stock and barrel.

The weakness of this purely empirical approach is evident from the article itself. Correlations aren’t reliable. They do tend to be more persistent than returns, but that’s far from saying they’re reliable. As LaChappelle discusses, the correlation between stocks and bonds has sometimes been positive, sometimes negative. So the pursuit of diversification through seeking low correlations alone becomes an exercise in guessing what the markets will do next … something that if you could do reliably, would make diversification unnecessary in the first place.

I’ve hinted that statistics are not the only approach. Diversification on the basis of fundamentals is at least as valuable, arguably both more valuable and more reliable.

Let me explain what I mean. Suppose you own shares of XYZ Corp common stock. As a first step in diversification, you might add some of its bonds. To the extent stocks and bonds aren’t correlated, you will have improved your portfolio diversification. But it’s not just statistical. If the company runs into financial trouble, your stock is likely to be affected more than your bonds, just because of its lower position in the capital structure. If the company goes bankrupt, common stock takes the losses first. Bond holders lose last.

The same thing applies between issuers. Owning the stocks of two companies rather than one is less risky because the odds of them both going bankrupt are less than those of either one. The same goes for owning the bonds of both companies. The risk is further reduced if they are not in the same industry. Likewise if they’re not domiciled in the same country.

This is likely to also show up in a statistical analysis of correlations. But you don’t need to do one in order to be confident your risk is reduced. And you don’t have to worry that the results of your statistical analysis will fail to persist. As long as the fundamental facts don’t change, you will have reduced your risk.

The tendency to define risk in terms of volatility itself is flawed. It just happens to be readily reduced to numbers.

If volatility is all you’re concerned about, then by all means statistical analysis is all you need do. But since correlations change, it’s not reliable. And most investors are, in reality, not concerned so much about volatility as risk of loss. Volatility treats risk of gain and of loss alike.

But wait … conventional statistical analysis suffers from an even more fundamental flaw. It tacitly assumes that its measures of volatility and correlation are those of the assets themselves under consideration.

But we don’t know that. All we ever know is the relative value of pairs of assets.

Finance is not physics. In physics, we have solid, reliable units of measurement. A kilogram today is the same as it was five years ago. A meter today is the same as it was ten years ago. If we measure the mass or length of an object and find it to have changed, we can be certain that something about the object itself has changed. We’re still only comparing one thing with another, but confident the value of one of them itself is unchanging.

The remarkable thing about finance is that virtually everyone in the field knows that units of financial value are not at all like this, but nevertheless proceeds with elaborate and precise analyses as if they are.

Thats exactly what you’re doing when you perform, report, or rely on correlation studies.

The article cited at the outset is a case in point. It maintains that the correlation between stocks and bonds has changed, from positive to negative and back again. But considering that there is no reliable unit with which to measure these quantities, the conclusion is fiction. In truth, no data are cited demonstrating that the volatility of stocks and bonds alone is, was, or will be anything.

It doesn’t exist. All we know is the relative value of one asset and another; the relative value of stocks and dollars, bonds and dollars, etc.

A thought experiment illustrates. Suppose that the value of stocks and bonds were both invariant. Absolute and unchanging.  But that the value of the measurement unit was not. It fluctuated. Because of the fluctuations in the value of the measuring unit, the prices of stocks and bonds would be seen to fluctuate. And these fluctuations would be synchronized. It would appear that stocks and bonds are both fluctuating in value, and perfectly correlated.

Next suppose that, perhaps over some other time frame, the value of the measuring unit did not fluctuate. Instead the value of stocks and bonds fluctuated. And suppose they fluctuated in mirror image, so that when stocks rose, bonds fell, and vice versa. In this case you would observe that stocks and bonds are fluctuating in value, and that they are negatively correlated.

Of course, both of these are idealized scenarios not observed in the real world. But what if the real world was made up of combinations of cases intermediate the two? That stocks and bonds were always negatively correlated, but sometimes their price fluctuations were dominated by fluctuations in the value of the measuring unit, and others by their own changes in value?

You might observe that the correlation between stocks and bonds was sometimes positive, sometimes negative. Some occult metaphysical phenomenon was causing the correlations to flip between positive and negative from one time frame to the next.

But that would only be due to the above cited invalid assumption:

The remarkable thing about finance is that virtually everyone in the field knows that units of financial value are not at all like this, but nevertheless proceeds with elaborate and precise analyses as if they are.

The implication is this: Despite all the ink spilt on using correlations to establish what is diversified, it is best to regard it as for amusement only. True, reliable, diversification is built on fundamentals. A genuinely diversified portfolio is built from assets that derive their value from fundamentally independent sources. Stocks and bonds of different issuers in different industries in different parts of the world. Commodities like gold that don’t even have an issuer in the first place. Not only financial assets but real assets.

This isn’t to say that there is no value in considering statistical volatility. It may provide a measure of psychological comfort in those rare times when the currency we use to price our other assets in rises, causing them to appear to fall in value together. As in parts of 2008, for example. But such times are rare and fleeting … most of the time our currency is falling in value, and in those exceptional times the managers of those currencies engage in prompt and vigorous efforts to return it them to their falling state. It’s not a stretch to say even that the main reason we “invest” in other things is to sidestep the resulting losses. So undue focus on reducing apparent volatility comes at the expense of long term returns.

This is expressed in the MPT maxim that there is a tradeoff between risk and return.  But it’s based on an assumption that virtually everyone uses even while recognizing that it’s invalid.

10 thoughts on “Correlation Illusion

  1. jk says:

    for information purposes i’d like to share for anyone who might be interested an alternative approach altogether. instead of using asset class allocation with index funds in order to create a diversified portfolio, i have chosen to invest idiosyncratically in what i think are undervalued niches.
    such niches exist because, contrary to modern portfolio theory, the market is not efficient. distortions may arise because of fashionable political and economic beliefs, misunderstandings or inattention by important market players, and because some sub-markets are too small to accommodate large pools of capital.
    so, for example, i have about 15% invested in sruuf [uranium] which i started accumulating about a year ago. sruuf has approximately doubled in the past year [my own positions are up over 40%] but i believe it has a lot of runway ahead of it. .
    basically it was in oversupply for a while and mines shut down. now demand is exceeding new production while inventory is disappearing. it will take [4-5?] years to re-open old mines and more years [?8-10?] to create new mines. in the meantime power plants need fuel.
    whatever you think about nuclear in the u.s., china for example has 55 nuclear plants under construction, and existing plants in the u.s., france, etc need to be periodically refueled. the utilities have no choice – they MUST find supply. this is headed for a spike before new supply can be brought on line.
    this trade benefits from 2 inefficiencies: 1. inattention by nuclear consumers. the utilities have been able to procure supply very easily in recent years. also the cost of their fuel is de minimus versus the huge capital expenditures that went into their facilities. for these reasons the utilities have not paid much heed to the shrinking supply problems. they are only now beginning to awaken – there are about a dozen rfp’s out currently, soliciting offers for nuclear fuel. no one is responding to these rfp’s. oops. 2. small niche- this market is too small for endowments, insurers, p.e. firms and the like. it has thus been neglected.
    another set of opportunities exist in oil and gas. because of fashionable esg limitations on investment mandates, o&g capex has been severely restricted for some time. o&g, however, is not going away. [i will skip discussion of o&g demand both in oecd and developing countries, and also skip my belief that full battery ev’s represent a severely misguided wrong turn in policy which won’t significantly reduce o&g demand in any case.] anyway, if you’re willing to put up with some [i think/hope minor] geopolitical risk, you can buy pbr/a and ec and get 20% dividends as well as direct exposure to o&g. the price of o&g will spike when we hit the fossil fuel singularity, i.e. when rising global demand bumps up against the lack of capex to produce new supply. somewhat related, you can buy offshore drillers and offshore service companies for pennies on the dollar. these rigs are in increasing demand, are not about to face newly constructed competitor rigs, and are commanding escalating day rates in the hundreds of thousands of dollars. they require patience, however, as it will take years for this thesis to play out.
    another neglected niche is gold, and precious metals more generally. we may have discussed it a fair amount in these environs, but it currently is only 0.5% of portfolios while historically it has been 2%. meanwhile we are all aware of the enormous deficits currently flooding the economy with more spending. [look at the dollar index on this website]
    gold is also, importantly, insurance. it’s up about 9% compounded since 2000, and i expect it to grind higher in fits and starts. for it to really spike to, say, $8000 [it’s now a bit over $2000] would mean really bad things are happening in terms of runaway inflation- that’s when its insurance function would be useful
    another, more conservative, option is tips [i recommend buying individual bonds, not an etf. you can currently get a bit over 2% on top of cpi. cpi is fake, of course, but it’s something to partially offset the inflation experienced in your own life]. another is multi-family real estate, though this will require being mindful of your chosen vehicle.
    you’ll notice that ALL the options i’ve presented represent real things, and would be expected to hold purchasing power value in the face of inflation. inflation is, according to official measures, subsiding at the moment, but i think it’s got a great future.
    the risk in your index funds is that the u.s. indices have been held up by the soaring “magnificent 7”- apple, amazon, alphabet, meta, microsoft, nvidia and tesla. the s&p 493 [i.e. the s&p 500 minus these 7 stocks] has basically done nothing.
    the mag 7 have become the safety trade for portfolio managers. if they don’t own them, they are lagging the market. therefore they must own them, in size. but this is reminiscent of the nifty 50 in the ’70s and the tmt stocks in the late ’90s. eventually all the “must own” stocks were taken out and shot.
    i think there is more risk in the s&p 500 than in the niches i’ve described. of course, only time will tell.

    1. Bill Terrell says:

      Thanks, JK. I don’t disagree with your views, but am puzzled that they’re framed as an alternative investment approach. Just so there’s no reader confusion, my post doesn’t advance an investment approach; no themes, no index funds, etcetera … rather it compares two ways of assessing diversification, statistical and fundamental, particularly critical of the former. Either can be applied independently of economic outlook, style, themes, vehicles, priorities, and degree of concentration or diversification. Aside from the specific ways of measuring diversification, there is no “there” there to be an “alternative” to.

    1. Bill Terrell says:

      I still remember the first Earth Day back in 1970. Our middle school had us in some sort of parade for the planet. It seemed artificial even at the time. And ever since, it’s been reinvented seemingly every few years, as if “the environment” had just been discovered.

      More like Groundhog Day.

  2. jk says:

    i suppose what i outlined could be viewed as “fundamental” diversification, in the sense that there are several different [?unrelated, ?partially related] themes, but i don’t think it fits the notion of “diversification” at all. diversification usually implies a mix of standard asset classes, whether chosen on a statistical or fundamental basis.
    my point is that one doesn’t have to diversify in either of those senses. my holdings each stand alone, at least in my own mind. they are not chosen to bear any particular relationship to one another. i think what i’m doing is orthogonal to diversification as ordinarily conceived.

    1. Bill Terrell says:

      Orthogonal is a good word for it. Diversification is one dimension of the investment space. I would say that there is nearly always some degree of diversification … the only questions are what kind and how much. The only time I can recall having none at all would be before I bought my first stock, when the only assets I had were dollars. Once I bought a few shares in the regional power utility, I then had at least moved off the zero axis.

      At the opposite extreme, maximum diversification would be with the Global Market Portfolio. It corresponds to a position of zero risk due to investment choices. It’s not an actual or recommended portfolio but a theoretical ideal useful as a benchmark or metric to assess exactly what risks an investor is taking.

      If there is any implied message, it would be for those who buy an S&P 500 index fund and think they’re fully diversified. A few hundred securities in one asset class, in one market, with much of that concentrated in a handful of names in one economic sector. My guess is we would both agree that circumstance would be markedly improved by taking half of that and putting it into the portfolio you just outlined…