The Diversification Ratio

Quantifying diversification benefits.

Most advisors manage risk by reducing exposure to risky assets. The problem with this approach is that it lowers your expected return. This is true because risk and return are linked (lower risk = lower return).?

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The better approach is to find risky assets whose risks partially cancel out. This allows you to lower a portfolio’s risk without necessarily sacrificing expected returns. The technical term for risks that cancel each other out is “diversification”.

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But how do you know the extent to which a portfolio is diversified?

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The Diversification Ratio

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The Diversification Ratio tells you how much lower a portfolio’s risk is compared to the sum of its parts.

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For example, if you equally allocated across two assets, each with a risk (standard deviation) of 10%, the sum of their standard deviations would simply be 10%. However, because these risks might partially cancel out, the portfolio’s risk may only be 6%.

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In this example, the Diversification Ratio would be 40%. The portfolio’s risk (6%) is 40% lower than the sum of its parts (10%).

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There are two types of risk that can be reduced through diversification: specific asset risk (also known as “idiosyncratic risk”) and market risk (also known as “systematic risk”).

Specific asset risk is easy to diversify. Take, for example, the S&P 500, which essentially eliminates company specific risk, leaving investors with the returns of the US Large Cap Equity market.

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If you added up the weighted average standard deviations of the S&P 500 constituents over the past year, you would get a summed standard deviation of 24.12%. The S&P 500, however, realized a standard deviation of only 10.98%. (Source: Ycharts. Period: 3/31/2023 through 3/31/2024).

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The Diversification Ratio of the S&P 500 over the past year is therefore 55%. This represents a very large diversification benefit and speaks to the reason why a diversified portfolio of stocks is likely to outperform a concentrated portfolio over time.

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But! Investors in the S&P 500 are still left with systematic risk, or the risk of the US Large Cap Equity market. Whenever the U.S. enters the next recession and company earnings drop, the value of US equity prices will likely fall 20-50%+.

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To diversify the systematic risk of the US Equity market, we need to allocate portfolio risk to other markets like bonds and commodities, whose systematic risks will offset the declining value of the Equity market.

What about the “Balanced” 60/40 Portfolio?

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Practically the entire financial services industry uses the Total US Bond Market, or aggregate “agg” bonds, to reduce the systematic risk of equities. Asset allocation is taken to mean the mix between equities and aggregate bonds. Clients receive some mix of these assets based on their risk tolerance, be it 80/20, 60/40, 30/70, etc.

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The problem is that aggregate bonds provide essentially no diversification benefits to equities.

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As proof, the Diversification Ratio of the 60/40 portfolio over the past year is a paltry 3%! (Source: Ycharts. Period: 3/31/2023 through 3/31/2024. Vanguard Balanced Index “VBINX” used as proxy for 60/40 Portfolio)

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You might be thinking to yourself… “We have been in a rising interest rate environment recently, but over the long term, the 60/40 is diversified”.

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Not really.

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The 30-year Diversification Ratio of the 60/40 Portfolio, in a period of low inflation and falling interest rates, is not much better at less than 9%. (Source Ycharts. Period 3/31/1994 through 3/31/2024)

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Maximizing the Diversification Ratio

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The Diversification Ratio is maximized when (1) assets have the same standard deviation, and (2) exhibit a correlation of -1.

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In theory, a two-asset portfolio with these characteristics would completely diversify away risk. In reality, this is impossible to achieve, as both the risks and correlations of assets vary greatly through time and changing economic conditions.

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The reason aggregate bonds are a poor diversifier to equities is that they exhibit neither of the optimal characteristics. The long-term standard deviation of aggregate bonds is around 4.5% versus 16% for US Large Cap Equities. So, the risk profiles do not offset. Also, the correlation between these assets is close to 0, unlike other bonds which have a correlation closer to -1 in certain environments.

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The type of bonds that exhibit a risk profile closest to stock, along with a correlation closer to -1 in certain market environments, is 20+ Year US Treasury bonds.

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Of course, there are certain market environments when both stocks and bonds are highly correlated. We therefore need to mix in another asset that tends to have negative correlations with stocks and bonds during these periods and has a similar risk profile.

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Gold is just such an asset. Gold’s longer-term standard deviation is around 16%, matching that of stocks, and it tends to rally during inflationary periods that are bad for stocks and bonds.

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We could greatly improve the diversification benefits of the 60/40 portfolio by replacing the 40% allocation to aggregate Bonds with a 20% allocation to 20+ Year US Treasuries and 20% allocation to physical gold.

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The weighted average sum of this 60% US Large Cap Equity, 20% 20+ Year Treasury, and 20% Gold allocation is 15.35%, while the portfolio risk is only 10.28%. This translated to a Diversification Ratio of 33%. (Source Ycharts. Period 3/31/1994 through 3/31/2024)

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Notice that we were able to triple the diversification benefits of the 60/40 portfolio by replacing aggregate Bonds with better diversifiers, while keeping total portfolio risk the same at 10.3%.

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These diversification benefits translate to higher expected returns at the same level of risk, since the expected returns of both 20+ Year US Treasuries and Gold are higher than aggregate Bonds.

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Summary

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When building a portfolio of assets, I would encourage you to look at the Diversification Ratio of the final portfolio. The entire purpose of asset allocation is to reduce risk through diversification, and a manager’s goal should be to maximize these benefits first, before looking to other forms of risk management or value-add.

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Take the free lunch of diversification before paying for other forms of risk management.

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Making simple changes to the underlying allocation can translate to real benefits for investors without needing any active management skills or market timing luck.