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"Shadow Convexity" Means The Death Of Modern Portfolio Theory

Excerpted from Artemis Capital Management letter to investors,

Do not call upon spirits you are not capable of controlling… risk in risk parity

The story of the sorcerer’s apprentice is a tale about the dangers of non-linearity and ‘shadow’ convexity. In the story, the apprentice became massively short “broom” convexity resulting in a dangerous overflow of liquidity. In fixed income terminology, the word ‘convexity’ describes the degree to which a bond is negatively exposed to rising interest rates in a non-linear fashion. Central banks and regulators have decided to invoke their own sorcery by buying bonds through quantitative easing and requiring stringent capital requirements for ‘too big to fail’ banks. The unintended consequence is that systemically important institutions are now warehousing massive amounts of convexity risk in assets with negative real returns. What would happen if rates increased 300 basis points in a year the way they did between 1979 and 1980? The result would be a -20% mark-to-market loss on a portfolio of supposedly “safe haven” securities!

Now imagine if that crash in ‘safe haven’ bonds occurs simultaneously with a decline in equity prices...
...all of a sudden we have a big global problem.

Modern portfolio theory ignores massive ‘shadow’ convexity from a potential correlation breakdown in the relationship between stocks and bonds. Let us assume I have a little money to invest and I go to a qualified financial advisor for advice on investing for retirement. The adviser would likely tell me to diversify those assets according to a 60/40 split between stocks and bonds. The theory is that when times are good stocks go up but bonds underperform and vice versa.

Therefore, I put my money in a 60/40 split, supposedly, because there is anti-correlation between stocks and bonds. Now let us assume I run an institution with hundreds of millions to invest and I can afford a more expensive financial advisor. The expensive financial advisor agrees with the general principal of a 60/40 stock and bond split but feels that we can do much better by leveraging the bonds so they match the stock portfolio weighted by their respective volatilities. The theory is that bonds outperform stocks on riskadjusted basis while exhibiting strong anticorrelation. The financial advisor calls this “risk parity” and shows me an incredible 20-year record of returns including gains in 2008.

The entire global financial system is leveraged to the theory that stocks and bonds are always anti-correlated. Risk parity funds currently manage approximately $1.4 trillion of institutional assets globally based on this theory.  It is impossible to estimate how many trillions of dollars are managed according to the simple 60/40 mantra… but let us just assume something north of $1.4 trillion and something south of “more money than God”.

Given the unfathomable amount of assets leveraged to this simple relationship, I decided to test the anti-correlation between equity and fixed income, or positive correlation between yields and stock prices, based on over 132 years of price data. The truth about the historical relationship between stocks and bonds is scary.

Between 1883 and 2015 stocks and bonds spent more time moving in tandem (30% of the time) than they spent moving opposite one another (11% of the time). It is only during the last two decades of falling rates, accommodative monetary policy, and globalization that we have seen an extraordinary period of anti-correlation emerge between stocks and bonds unmatched by any other regime in history. Not only are stocks and bonds positively correlated most of the time but also there is a precedent for multi-year periods whereby both have declined.

In the event stocks and bonds simultaneously lose value, the classic 60/40 portfolio will become a 100% loser and volatility will be the only asset class that is capable of protecting your portfolio.

Risk parity strategies are viewed as defensive in nature by the institutional investor community due to their outperformance during the 2008 financial crisis. While the strategy can be very effective the thirty year track record hides significant risks. Risk parity derives alpha through a form of ‘shadow’ short convexity that includes leveraged exposure to:

  1. Short correlation between equity and fixed income;
  2. Short portfolio gamma through volatility rebalancing.

To understand this risk we looked backward by estimating the performance of a classic 60/40 and a simple risk-parity portfolio across 100+ years of financial data. Risk parity faces significant tail risk 1 out of every 50 years. In the 20th and 21st century simultaneous positive returns occurred 63% of the time with negative stock and bond returns occurring in 2% of the years. The danger scenario whereby stocks and bonds decline in tandem (see lower left quadrant) occurred in the 1970s, late 1950s, 1940s, and between 1906 and 1909.

Although simultaneous negative returns in both equities and fixed income is rare, the impact on the classic 60/40 and risk parity portfolios is potentially devastating. The chart below shows the worst rolling years for each portfolio since 1800. We only include periods when stocks and bonds fell simultaneously.

The nightmare period for negative correlation occurred between 1906 and 1909 when the 60/40 portfolio experienced a -67% peak-to-trough drawdown and a simple risk parity strategy would have gone bankrupt. This analysis is not taking into account the harder to measure second ‘shadow’ convexity exposure of risk parity described herein as portfolio gamma. What is portfolio gamma? During periods of rising volatility risk parity portfolios are forced to deleverage. If $1.4 trillion of risk parity assets are deleveraging at the same time during a period of sustained stress in bonds and then stocks we would likely face a self-reflexive spiral of selling. The portfolio gamma is the hard to measure cost of reducing your risk exposure when everyone else is doing the exact same thing. Risk parity, like portfolio insurance in 1987, is self-reinforcing when widely adopted and arguably introduces fragility to markets. The size of the risk parity market questions whether the product may pose a systemic risk during a sustained period of negative stock and bond returns like 1906 to 1909, the late 1940s, or late 1970s. 

The $1.4 trillion dollar question is...
what would cause the relationship between stocks and bonds to completely melt down?

The volatility of inflation appears to be a core driver of higher correlation between stocks and bonds. When inflation, as gauged by the consumer price index, is more volatile we tend to experience higher levels of stock and bond correlation as evidenced by data from 1885 to 2015. The early part of the 20th century, which experienced the most debilitating periods of stock and bond underperformance, was a period of wild fluctuations between inflation and deflation. The last three decades of extraordinary anti-correlation has been an era of falling rates, globalization, accommodative monetary policy, and very low volatility of CPI. The global economy is now at the zero bound whereby the effectiveness of competitive devaluations is coming into question.

It is not hard to imagine a regime whereby central banks lose credibility or are not capable of moderating swings in inflation in a way consistent with the past three decades. Any period of sustained correlation failure will result in rising  volatility and selling pressure across bonds and stocks in a self-reflexive cycle.


Modern portfolio theory relying on diversification and volatility targeting for alpha generation provides an illusion of safety but is simply exposing investors to alternative risks.  In exchange for price risk, investors are exposed to short correlation risk.  In exchange for lower portfolio volatility, investors are exposed negatively to portfolio gamma. Pure long convexity exposure is your only solution to this problem.

There can be significant risk in risk parity… many providers are established and smart investors and hopefully are aware of these risks. There is nothing wrong with owning a risk parity portfolio, which has performed admirably over the past two decades, but based on any longer view of financial history you are an irresponsible fiduciary if you are not hedging it with some form of long convexity exposure.