Most investors are aware of the importance of diversification when constructing their portfolios. They know that putting “all of their eggs in one basket” is too risky. Rather, they select investments in different asset classes (bonds, equities, cash, real estate, etc), in different countries, and in different industries. However, choosing different asset classes is often not enough. The best investors know that what really matters is the correlation between investments. Let’s dive in and find out how it works.

The significance of r

Correlation refers to the movement of returns of two or more assets in a specific direction. So, for an effective portfolio, assets should have a negative or inverse correlation with each other. That is, their prices must not all move in the same direction at the same time. The degree to which they do, or do not, do so is measured by the Pearson correlation coefficient, expressed as r (in lower case). Here is how that looks.

Meaning of the Pearson correlation coefficient

A value of exactly 1 means there is a perfect positive relationship between the two variables. For a positive increase in one variable, there is a matching positive increase in the second variable. A value of -1 means there is a perfect negative relationship between the two variables. This shows that the variables move in opposite directions — for a positive increase in one variable, there is a matching decrease in the second variable. If the correlation between two variables is 0, there is no linear relationship between them.

The lower-right graph shows perfect non-correlation, which is nearly impossible to achieve. That is the heart of the difficulty with a quantitative, or mathematical, approach to diversification. Simply expressed, it does not - and cannot - portray an imperfect real world, where relationships between the movements of markets and securities prices are in constant flux.

Further, correlation is based solely on past movements in share prices and, as every investor is warned constantly, past performance is not necessarily an indicator of future returns. Also, we should remember the old investment wisdom that risk is not a number. Known and unknown unknowns are the biggest potential risks but, being unknown, cannot be measured.

Correlation has been rising

However, there is one aspect of market correlations that quantitative metrics reveal clearly. That is the tendency for all markets to become more correlated when faced with a major external shock. The chart, below, tracks three 30-year relationships with US equities: Japan, Europe, and Asia excluding Japan.

Stock market correlations
Source: CAIA Association

The Great Financial Crisis (2007-08) and the coronavirus pandemic (2020) triggered sharp rises in the correlation between the US and both European and Asian ex-Japan markets. Japan by itself, long out of favor with international investors at the time, went in the other direction, seeing an increase in negative correlation, but that was reversed, partially at least, in 2020.

The classic diversification model was the “60-40” portfolio: 60 percent in equities, and 40 percent in bonds. It was based on the premise – hitherto, well proven – that, not only are bonds less volatile than equities, but falling interest rates in a recession underpin bond markets as, simultaneously, they undermine equities. Not any longer, according to the next chart.

Comparison of stocks and bonds performance over the years
Source: Financial Times

One asset class often favored for its non-correlation and superior returns in bear markets is hedge funds. However, the massive growth in the sector over the past 20 years or so has, in effect, brought it into the mainstream. That has made the funds more and more correlated with the major indices. Lately, with the r coefficient rising to almost 0.9 - or 90 percent correlation - there is almost no distinction between the two.

Three-year correlation between HFRI Equity Hedge Total Index and S&P 500 Index
Source: Bloomberg

Are gold & crypto-assets worth it?

The conclusion must be that, if you seek to reduce risk with diversification, you have to look beyond listed securities. Traditionally, many investors have sought refuge from this “curse of correlation” in gold. The World Gold Council produced the chart below to illustrate gold’s correlation with the S&P 500.

Correlation of US equities versus gold, commodities and US treasuries in various environments of US equity market performance since 1973*
Source: World Gold Council

*As of 31 December 2021. Correlations based on weekly returns in US dollars for “US equities”: S&P 500 Index; “commodities”: Bloomberg Commodity Index; “US treasuries”: Bloomberg Barclays US Treasury Index; “gold” LBMA Gold Price PM since January 1973 due to US treasury availability of data.

The top section corresponds to the unconditional correlation over the full period. The middle section corresponds to the respective correlations when the S&P 500 weekly return falls by more than two standard deviations (or “σ”) from the average for the period, while the bottom section corresponds to the respective correlation when the S&P 500 weekly return falls by more than three standard deviations. The standard deviation for the S&P 500 is calculated using weekly returns over the full period.

As we can see from the chart, gold is negatively correlated with the S&P 500 when the index is performing badly. And in the good times, it is only slightly positively correlated.

However, investment managers such as David Henry at Quilter Cheviot have been surprised by the lack of increase in the gold price so far this year: “Gold isn’t working”.

One possible reason is that gold may be “heavy, beautiful and reassuring” but pays no income turning investors to other safe-haven assets that do pay an income. That makes it less appealing today, when interest rates are at last rising after a dozen years, driving up the returns on rival safe havens cash and bonds.

“In this environment, the relative attractiveness of a lump of shiny metal, which does not pay you anything, diminishes,” Mr. Henry says.

Some investors are even turning to crypto-assets, however, those may not be a good alternative to gold.

Taking Bitcoin as a proxy for the entire sector, its correlation has become increasingly close to both US mainstream (S&P 500) and tech equities (NASDAQ). According to TradingView, the 90-day correlation between the largest cryptocurrency by market capitalization and the S&P 500, which includes a strong tech component, reached a value of 0.59 on September 9, 2022 (dark blue area chart below). Furthermore, the link between the bitcoin price and the tech-focused Nasdaq stock index has also tightened, reaching a correlation of 0.62 on September 9, 2022, up from 0.31 on August 15, 2022 (light blue area chart below).

Bitcoin’s correlation with S&P 500 and Nasdaq
Source: CoinDesk

This should make you think twice about using crypto to diversify your portfolio, that is, on top of the crazy volatility of crypto. Uncertainty surrounding the FTX collapse and its potential fallout pushed Bitcoin prices to new two-year lows of around USD 16’977 as of December 1.

However, Bitcoin is not the only crypto suffering. As of December 1, BTC and ETH are both down above 70%, starting from their October 2021 and November 2021 highs respectively.

Private equity has become accessible

Many large and savvy smaller investors have increasingly been turning to alternative assets in their search for lower and negative correlations with traditional assets. Private equity (PE) and debt, infrastructure, real estate, and other so-called alternative assets do not trade in any formal public market and thus do not have the same volatility as public markets nor their immediate reaction to every piece of market news.

Starting with PE, we can see the correlation picture is nuanced, but also not very surprising.

Comparison of US and global private-equity finds’ correlation to US stocks
Source: WP Global Partners

Moreover, the historic availability of PE funds only to professional investors (pension schemes, foundations, insurers, and so forth) and UHNWIs is being transformed by new facilities that make them accessible to the mass affluent. So, we have found another low-correlation asset in addition to gold.

That finding might suggest that, given the shared characteristics of PE and listed smaller companies, there should be a similarly low correlation between those smaller caps and their blue-chip counterparts. You will be disappointed in that assumption. The next chart shows that r has never been below 0.6 in some 40 years and has risen to well over 0.9 more recently for small caps relative to the S&P 500 - this is a fairly strong positive correlation.

However, as the chart below shows there are big differences in the correlation to US stocks depending on the size of the PE fund and whether the fund is US or global-focused. Those PE “megafunds”, as the table captions them, tend to be the buy-out specialists. They try to add value to public companies by taking them private and restructuring them before re-listing, so a correlation between those funds and their listed investment targets is inevitable.

On the other hand, the low correlation between mid-sized and smaller PE funds and the market is encouraging. Predominantly, those funds invest in start-ups (venture capital) and fast-growing enterprises and, thereby, offer higher returns than established (and listed) companies. They are also what most people mean when they think or talk about private equity.

1Y rolling correlation of Russell 2000 vs. S&P 500
Source: CME Group

Bricks and mortar

Finally, there is real estate. The common opinion is that “bricks and mortar” are a more stable asset than equities but are also just as badly affected by rising interest rates or economic recession. Let’s see if that is true.

According to our previous research (made using SIX – Swiss Market Index (SMI) as the Swiss stock market, SXI Real Estate® Fnds Broad TR (SWIIT) as Swiss real estate, and SBI® AAA-BBB Total Return (SBR14T) as the Swiss bond market) real estate has a low correlation, and sometimes no correlation at all, with other major asset classes such as stocks (0.2936) and bonds (0.2825).

Moreover, it has demonstrated strong resilience during economic and market crashes such as that caused by the worldwide pandemic lockdowns which started in early 2020.

However, that’s not really the truth about all real estate as, according to MSCI, the long-run correlations between private real estate and stocks tend to rise up to 66% while the relationship between real estate and bonds is quite low - only 11%.

Be comfortable with risk

Our search has, therefore, found three assets with low correlation to mainstream investments. That does not mean you should allocate your portfolio blindly across gold, private equity, and real estate.

Remember that the aim is to find assets with low positive or negative correlations that will reduce the risk of your portfolio without sacrificing its returns. Ray Dalio calls this the “Holy Grail of Investing.”

This rules out gold because unlike PE and real estate, it produces no income. As Warren Buffett says, “...if you own one ounce of gold for an eternity, you will still own one ounce at its end.”

You also need to consider your personal preferences and your future liquidity needs. PE tends to be riskier than real estate and both are relatively illiquid.

Above all else, you need to keep watching the market and correlations. Correlations change over time and you need to change with them.

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