##### First Type of Criticism: Naive Diversification

Proper diversification is seldom achieved. The nature of the tools available to advisors and the color of the investment advice individual investors receive largely derive from Modern Portfolio Theory1 (MPT). MPT is an asset allocation framework fathered in the 1950s by economist Harry Markowitz. It intends to explain the relationship between “market risk,” also referred to as “systemic risk,” and asset returns. It argues that the “optimum” portfolio construction depends crucially on the market risk and return of each asset class and on the correlations between asset classes. MPT provided rules to construct the optimal portfolio that still prevail in the investment industry today. Why is this of concern?

First, because MPT can only be loosely applied. Indeed, future returns and correlations –the two central inputs in MPT– are not observable in the real world. Investment managers need to forecast them ex ante. To illustrate the predicament they find themselves in,** Figure 1 **shows the correlation of monthly returns between the S&P 500 index, a usual proxy for the equity class, and U.S. 10-year Treasury Bond index, a common proxy for the fixed income class. It is blatantly evident that correlation is far from being constant and has a random structure. Such characteristics violate the central assumptions at the heart of MPT. Considering the wild randomness that seems to guide correlations, our investment managers are doomed to severe inaccuracy.

Second, because MPT uses the volatility of asset prices as its sole proxy for risk. Conceptually, volatility can be thought of as the typical deviation observed between an asset’s actual return and its historical average evaluated over an arbitrary period of time. The higher the volatility number, the “riskier” the position according to MPT. Followers of the financial markets will regularly stumble upon such common statements as “ABC Corp. has a 20% vol” which means that, typically, the returns delivered by ABC Corp.’s equity will deviate by about 20% in a given year from their average2 – either downwards or upwards. Does it tell it all about the risk of owning ABC Corp.? Infamous collateralized debt obligations (“CDO”) created from low-quality subprime mortgage-backed securities (“MBS”) had relatively low volatilities in the few years running up to the Great Financial Crisis until the bubble burst in 2008. Their value consistently increased, such that both their actual returns and their average1 returns were equally high, such that the deviation between the two was quite low, and such that the volatility number, or MPT’s “risk” measure, was low. It implied that they weren’t risky from MPT’s point of view. We ask the question again. Did it imply that they weren’t risky in any sense of the word? Clearly, it didn’t. Although their historical returns, the only ones used to forecast volatility, were quite steady, it became obvious after the fact that these CDOs had been bearing a gigantic “left-tail risk.” Left-tail risk is the name given to these threatening events looming over our “neo-liberal”, globalized economy, that have an extremely low probability of occurring but whose impacts on asset prices would be extreme. Think global wars, natural disasters, mass cyberattacks, pandemics, socialist revolutions and other threats that still do not have a name given that they lie outside the realm of regular expectations. The potential impact of the previous events doesn’t show in realized volatilities of asset returns given that they haven’t occurred yet. If you should retain one thing, this should be it: there are numerous shades of risk and all of them should be accounted for when building your investment portfolio. The concept of volatility satisfies our desire to simplify uncertainty but that implies reducing to one single number matters that are too rich to be hollowed out that way. Many serious financial mathematicians will consider investment managers using volatility as their sole measure of risk and randomness as quasi-charlatans.

Third, we also add that market regime diversification should be an essential objective that is ignored by MPT.