When 1 + 1 doesn’t equal 2: The math behind portfolio diversification

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Highlights

• To get the most from diversification, investors should look beyond stocks and bonds and think about other, less-correlated asset classes.
• Diversification isn’t just a buzz word – it impacts how smooth a portfolio’s returns can be.
• Smoother returns don’t just reduce volatility. They can help create wealth over time.

Over the past few years, markets have faced several shocks, from the COVID-19 pandemic to ongoing geopolitical upheaval to prolonged periods of monetary expansion. These shocks have driven investors to look more closely at asset classes such as commodities, precious metals and hedge-fund-like alternatives. Why? Because investors are realizing bonds may not be enough to diversify the equity risk in their portfolios. In turn, we’re seeing an increasing trend in the asset management industry to evolve beyond traditional stocks-and-bonds portfolios.

To enhance your diversification approach, keep these two considerations in mind: 1) correlation,¹ or how different asset classes move relative to each other, and 2) the math behind compounding returns. Investing in a diverse basket of uncorrelated assets can provide a smoother – or less volatile – stream of returns, which, over the long term, is generally more attractive than a volatile one. That’s not only because of the relative stability it can provide, but also because a portfolio’s compound annual growth rate (CAGR) is likely to get boosted over time.

A quick look at correlations

Consider a traditional 60/40 balanced portfolio (60% invested in equities and 40% in bonds), where bonds are included as a way to reduce equity risk. This mix is based on the belief that bond prices don’t usually move in the same direction as equities and that bonds are inherently less volatile. Or at least that’s the usual claim. It’s true that bonds often show less volatility and smaller declines than equities during market downturns, but the direction of their returns is uncomfortably similar to that of equities. In other words, when stock prices fall, bond prices often do too. Stocks and bonds, on average, are positively correlated.

Stocks and bonds can move in the same direction

The first chart below shows that, since 1995, bond prices have – on average – moved in the same direction as equities. In contrast, since 1995, commodities have had a lower correlation with stocks and a negative correlation with bonds. The second chart, meanwhile, shows that there have been periods (such as the 2010s) when all three asset classes have moved in the same direction.

Source: SLGI Asset Management Inc. Stocks – MSCI World Net Total Return Index. Bonds – Bloomberg Global-Aggregate Total Return Value Index. Commodities – Bloomberg Commodity Total Return Index.

A third asset class can boost diversification benefits

The charts above give us a few key takeaways:

• Correlations are unstable, which makes it harder to rely on a single correlation pair (e.g., stocks vs. bonds) to find diversification.
• By adding a third asset to the mix (e.g., commodities), we add more breadth in the search for diversified returns.
• The long-term correlation of stocks and bonds, defined as the last 30-year average, is positive 0.50. This means that, overall, bond prices have moved in the same direction as equity prices.
• Commodities are a good example of how a third asset class can provide more diverse returns. They have a lower 30-year average correlation to equities and slightly negative correlation to bonds.

Although this example used commodities as the third asset class, diversification can be improved by adding any other asset – like precious metals or alternatives – with a low or negative correlation to stocks and bonds.

The idea is that when asset A (e.g., stocks) declines, there is at least some offset from asset B (e.g., bonds) or C (e.g., commodities) that can add a flat or even positive return over a certain period. The less correlated the assets are, the more likely it is that this will happen. And the more it happens, the smoother – or less volatile – a portfolio’s returns.

The power of smooth returns

The charts below compare a traditional 60/40 balanced portfolio (60% MSCI World Index/40% Barclays Global Aggregate Bond Index) with a multi-asset portfolio that allocates 10% to the less-correlated Bloomberg Commodity Index, reducing the equity and fixed income allocations to 55% and 35%, respectively.

Looking at the simple average (or arithmetic mean)² in Chart 2, the 60/40 portfolio’s returns look similar to the multi-asset portfolio. But looking at the next column in Chart 2, annualized return, we see that over time the multi-asset portfolio’s CAGR is 0.16% higher than the 60/40 portfolio’s, even with a lower equity allocation. That’s because investment returns compound over time through multiplication – not through simple addition. Each period’s return builds on the previous period's total balance.

For example, think of an investment that, over two years, returns 50% and then –50%. Adding these numbers together would bring you back to zero, but compound returns are calculated using a different formula – the geometric mean.² In reality, a 50% gain followed by a 50% loss leaves your investment 25% lower than what you started with (1.50 × 0.50 = 0.75).

Chart 1: Calendar year returns of 60/40 portfolio vs. multi-asset portfolio

Chart 2: 7-year figures for 60/40 portfolio vs. multi-asset portfolio

How powerful can a CAGR difference of 0.16% be? Over 20 years, it translates to a 3% advantage for the multi-asset portfolio. Over 40 years, that gap increases to 6%. The secret is smoothing returns. While individual annual returns might seem underwhelming, lower volatility through smoothed returns compounds into higher long-term wealth – a counterintuitive but powerful benefit.

Chart 3: Growth over 20 and 40 years for 60/40 portfolio vs. multi-asset portfolio³

At a portfolio level, this example shows:

• Reducing volatility matters when it comes to asset selection. It not only gives investors more stability, but it also improves the compounding of returns over time.
• With the multi-asset portfolio, investors may see lower returns than a 60/40 portfolio in some periods, and that’s okay – it’s often the cost of including assets less correlated to equities.

The bottom line

The benefits of adding a less-correlated asset class to a diversified portfolio can include lower volatility and therefore higher returns over the long term – even after an apparent yearly cost. That’s why, over the last few years, the Multi-Asset Solutions Team at Sun Life Global Investments has increased its allocation to alternative asset classes. To name just some of our changes, we’ve made dedicated strategic allocations to direct infrastructure, direct real estate and commodities. Our tactical strategies also cover gold and crude oil, which have been relevant in recent markets.

¹ Correlation measures how two things move together on a scale from 1 to -1, where 1 means a perfect same-direction match, -1 means a perfect opposite-direction match, and 0 means no connection.

² Simple average = sum of all values/total number of values.

Geometric mean, used to calculate CAGR = [(1 + r₁) × (1 + r₂) × … × (1 + r_n)]^1/n – 1. In this formula, r is the decimal return for each period and n is the total number of periods.

³ https://www.getsmarteraboutmoney.ca/calculators/compound-interest-calculator/

This commentary is provided for information purposes only and is not intended to provide specific individual financial, investment, tax or legal advice. Information contained in this commentary has been compiled from sources believed to be reliable, but no representation or warranty, express or implied, is made with respect to its timeliness or accuracy.

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