"The Myth of Diversification Reconsidered"

*Interesting paper with a neat take on correlation: its asymmetric and we should focus on downside more than overall correlation. Treasuries still most dissimilar to equities; commodities, not so much.*** Not exactly a must read, but provides food for thought for the RP investor.**

**Not exactly a must read, but provides food for thought for the RP investor.****Read the original:**

**Important Points for the RP Investor**:

This paper caught my eye as a possible answer to 2022’s big portfolio question: what do we do when stocks and bonds go down together? For the past four decades, it's been orthodoxy that US Treasury bonds are the best diversifier for an equity portfolio, but 2022 shook that belief to the core. Not only did Treasuries fail to soften the blow felt by declining equities, they actually added even more pain. Suddenly, we’re all now awash in stories of the death of the 60/40, the death of bond investing, and the death of diversification. Yes, all hyperbole, but still.

Given the title, “The Myth of Diversification,” and placement in a prominent journal, I wondered if this paper by William Kinlaw, Mark Kritzman, Sebastien Page, and David Turkington might offer a perspective of why diversification seemed to fail when it was most needed. After digesting it, the paper doesn’t quite get to what I hoped, but there are some interesting points in it worth sharing.

The paper begins with a critique of standard portfolio theory regarding mean-variance optimization (the idea of weighing risk and reward to find the best portfolio) and correlation. The typical view:

*makes two implicit assumptions about diversification that warrant careful consideration. Because it relies on a single parameter to approximate the way each pair of assets co-vary, mean–variance optimization assumes that correlations are symmetric on the upside and downside. Moreover, the approach assumes that diversification is desirable on the upside as well as the downside. The first assumption is occasionally correct, but the second assumption never is (page 3).*

The authors show that correlation really is asymmetric, different on the upside and the downside, as asset classes act differently when the main driver of returns (equities) are going up versus going down. Furthermore, this asymmetry is often the exact opposite of what an investor wants, since when equities are rising, we’d actually prefer more unification of returns. When equities decline, we’d like the diversifying asset classes to put on the brakes, but that's when you get unification as everything goes down.

You wait around with sub-par returns from diversifying assets in strong equity markets, only to have them abandon you when you need them, in the same way a banker charges you to borrow an umbrella on a sunny day, but then takes it back when it rains (either from Mark Twain or Robert Frost, quoted on page 3). Its a familiar story.

The authors argue for a better way of measuring correlation that will zero in on diversification when it is needed, i.e., when equities decline. The authors then lay out a method for analyzing the degree to which a given asset diversifies the main growth engine when it underperforms (pages 10 through 12). Instead of comparing two assets with each other and getting a symmetrical correlation pattern (X is correlated with Y as Y is to X), they instead look at how Y’s correlation to X when X is at particular deviations from its mean, particularly below. In this case, recognizing that equities are the central asset class in most portfolios, they focus on the times when equities are in decline and then see how the other asset classes perform.

The results of their analysis are a bit different than the traditional analysis of symmetrical correlation. You can read the main part of the paper for all the nitty-gritty math, but the key table (exhibit 8) is on page 11 and describes correlations of six asset classes compared to equities when equities are down.

The main finding is that Treasury Bonds and Corporate Bonds are the best to provide good diversification in that case. This is somewhat to be expected in the case of Treasuries, but I was a bit surprised to see that corporate bonds did well in this analysis. My thinking going in was that corporate bonds were too susceptible to equity risk to offer much protection when equities declined.

Interestingly, the authors find that commodities are not that helpful when equities decline. In their analysis, the diversification impact of commodities seems most likely to occur when you don’t want it to, when their presence in a portfolio with equities creates drag from positive equity performance. Very interesting.

The last few pages of the paper (12 to 14) are where the authors take those lessons and apply them to portfolio construction. They create two portfolios:

- a “full-scale optimal portfolio” (they cite the work of Cremers, Kritzman, and page from 2005). They employ a “kinked utility function” located at -25%, meaning the portfolio weights are adjusted so that the portfolio is as safe as possible beyond a -25% decline. This approach sacrifices some safety for a more profitable mix at most times.
- a mean-variance optimal portfolio using only the downside correlations. This is the “safer” version for handling downturns, but may be overly so and lack expected returns for when equities are climbing.

In short, the “full-scale optimal” portfolio is a 78/22, with a sliver of commodities, and the mean-variance optimal is a 69/23/8.

I do wish the paper had looked at gold, as well, and to get greedy, it’d be great to see this approach applied to preferred shares, min. vol. equities, trend-following managed futures, or other asset classes in the Risk Parity toolbox. As I was reading, I couldn’t also help but think that this could be a standard number that could appear alongside market beta. If the Sortino ratio is the Sharpe ratio focused on the downside, it seems like there could be some sort of downside-specific correlation number as well.

All in all, an interesting paper that had some new perspectives on correlation worth considering. Not exactly a “must-read” for Risk Parity aficionados, and a little bit complicated for the average DIY investor, but worth the time if you enjoy this sort of thing!