Portfolio Strategy

# Diversity Orthogonality Theory: The Key Ingredient to a Free Lunch

While the concept of diversification as a benefit is widely understood, the degree to which the correlation of those assets can impact a portfolio is often underestimated. In this article, Cameron Hight and Chris White discuss the Diversity Orthogonality Theory.

Before we get to the Diversity Orthogonality Theory, a primer on Diversification, from an investment perspective, is an important context.

Why Diversity Matters…in a Portfolio

“Diversification is the only free lunch.” – Harry Markowitz, Nobel Laureate Economist

Markowitz is right but with two important caveats. Diversification is great if the amount of return per unit of risk is improved (Sharpe Ratio) and the investor can take advantage of the risk reduction, usually with leverage, to improve overall returns.

While the concept of diversification as a benefit is widely understood, the degree to which the correlation of those assets can impact a portfolio (and, thus, profitability) is often underestimated. A correlation of 1 means that the two assets move perfectly in sync, while a correlation of -1 means that they move perfectly in opposite directions. A correlation of 0 means that the two assets are not correlated at all). Let’s imagine that we build three equal-weight portfolios where each asset produces a 10% return with 10% volatility. In the first portfolio, the average correlation amongst the assets is 0.9, the second is 0.5, and the third is 0.1. With just one asset, the return and volatility of each portfolio is 10% and 10%, for a Sharpe of 1.0x. See what happens as we move to two assets and beyond (diversification):

Ray Dalio does a great job of explaining the uncorrelated diversification benefit in this video.

The effect on portfolio volatility is profound; the portfolio with the lowest average correlation has a volatility under half that of the one with the highest average correlation. Moreover, for the portfolios with the higher average correlations, the benefits have largely been realized by the time the 3rd asset has been added, whereas the lowest correlation version is still benefiting even as the 16th asset is added.

Remember, every portfolio generates the same 10% return, so as the volatility drops, their relative Sharpes are markedly different:

As mentioned above, both portfolios have the same (unleveraged) return, yet the lowest correlation portfolio has a much lower volatility outcome. In turn, this offers the potential to leverage that portfolio to achieve the same volatility profile as the higher correlation versions, radically transforming the return outcome. You can see the direct relationship between the Sharpe Ratio graph above and the leveraged returns chart below.

One final note before moving on to the practical implications. It is worth examining just how transformative the impact is on Sharpe (leverage-adjusted returns) for our 16 asset portfolios as the average correlation drops:

Multi-Managers Are Eating the World

For fundamental equity managers, diversification clearly brings benefits. However, as the charts above show, the impact is relatively muted for the simple reason that it is hard to find stocks that have a low correlation with everything else in your portfolio; in equities, the majority of the volatility and correlation component is connected to the underlying equity market. It is extremely rare for stocks to consistently correlate at the sub-0.5 level to everything else in a portfolio.

However, the understanding of the power of diversification and low correlation is the force that has allowed the multi-manager model to attract the majority of capital flows in the public equity space over the past ten years. Whereas it is hard to find low-correlation stocks for a portfolio, finding (or building) low-correlation portfolios is a viable prospect. Driving down the correlations within a stable of portfolio managers, whether it be by addressing different markets/asset classes/strategies or through the reduction of the drivers of cross-correlation among managers (such as market or factor exposure) has been the secret to unlocking consistent performance and high Sharpe ratios for these platforms. In turn, this has allowed them to apply increasing amounts of leverage and create a virtuous cycle of expanding gross exposure with which to entice and reward managers.

However, there are still limits to this approach. The war for talent rages across most markets and the operating model for these businesses has led to a prevalence of “cookie-cutter” managers, stocks with investment characteristics that cause them to be labeled “pod favorites”, and the ever-present specter of idea crowding and risk of chaotic unwinds.

Diversity Orthogonality Theory

As we saw above, if we think of Portfolio Managers (PMs) as assets, then adding a PM to a portfolio is increasingly beneficial as their correlation to other managers falls. It seems reasonable to assume that PMs with similar life experiences are more likely to have higher correlation return streams than PMs with different life experiences.

The Diversity Orthogonality Theory is this; PMs that are different (diverse) should have lower correlations to one another than PMs that are similar and thus, assuming similar return generation skills, combining diverse PMs will result in better risk-adjusted returns.

This could apply to fields other than investing. If we think of running a business as a series of decisions with expected returns. Decisions made by people with similar backgrounds will be more correlated than those with diverse backgrounds. Imagine a situation where non-diverse decisions result in groupthink and over-investment in similar ideas where a diverse group may make decisions (returns) from multiple sources, thus reducing the overall volatility of the combined decisions (returns). Indeed, research has shown that diversity can lead to better returns for corporates1.

This is all predicated on finding orthogonality without sacrificing return. It's important to find orthogonality without sacrificing return because otherwise, you're just diversifying for the sake of diversifying. The goal is to find a group of PMs that are different from each other but still generate good returns. While we know of no comprehensive studies of returns by background, there are numerous studies measuring women’s returns and, they are generally as good, if not better than their male counterparts2. The lesson is this: if you can find people with similar amounts of return-generating potential, combining those who think a little differently may provide the best overall strategy.

If we think of diversification as the free lunch of finance, then a key ingredient for this dish should be a preference for creating a cohort of managers who work well together but where the shared sum of their backgrounds and life experiences are greater than the whole.

The Diversity Orthogonality Theory underscores the intrinsic link between diversification in investment and tangible economic outcomes. By integrating portfolio managers from diverse backgrounds, we not only champion inclusivity but also position ourselves for potentially superior risk-adjusted returns. This isn't about diversification for its own sake, but about leveraging the power of lower correlation. As the financial industry recognizes and harnesses this value, it paves the way for a more inclusive future, beckoning talents from all walks of life to enrich the world of finance.

Footnotes

1 “How Diverse Leadership Teams Boost Innovation”, Boston Consulting Group: above average diversity of management teams produces 19% higher innovation revenue (https://www.bcg.com/publications/2018/how-diverse-leadership-teams-boost-innovation)

“The Other Diversity Dividend”, Harvard Business Review: homogenous teams with respect to background and ethnicity produce profoundly worse investment outcomes in the venture capital world (https://www.bcg.com/publications/2018/how-diverse-leadership-teams-boost-innovation).

“Why diversity matters”, McKinsey: companies with both racial and gender diversity  are 25% more likely to have financial returns above national industry medians (https://www.mckinsey.com/capabilities/people-and-organizational-performance/our-insights/why-diversity-matters).

2 “Diversity Matters: The Role of Gender Diversity on US Active Equity Fund Performance”, Stephen Lawrence, Senior Investment Strategist at The Vanguard Group: (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4081494).

“Fund Managers by Gender “, MorningStar: (https://assets.informa.com/MarketingImages/WM-NREI-Portal/FundManagerByGenderPerformanceLens.pdf)

“The CS Gender 3000: Women in Senior Management”, Credit Suisse Research Institute: firms with at least 15% women in top management outperform in terms of share price, ROE, PB, and payout (https://www.credit-suisse.com/about-us-news/en/articles/media-releases/42376-201409.html).

“Hedge Funds Run by Women, Minorities Outperform Market Peers”, Bloomberg: (https://www.bloomberg.com/news/articles/2021-11-08/hedge-funds-run-by-women-minorities-outperform-market-peers)

“The performance of female hedge fund managers”, Rajesh Aggwal and Nicole Boyson: (https://www.sciencedirect.com/science/article/abs/pii/S1058330016000148)