The Long View: Three Fallacies of Risk Parity

In a space where innovation is kept at bay, and orthodoxy and simplicity are appreciated by investors and encouraged by the regulators, risk parity as a concept has made remarkable inroads. Neither modern portfolio theory, nor asset-liability management or even liability-driven investing has had a comparable pace of adoption, and understandably so.
To begin with, funds following risk parity in their asset allocation have done reasonably well in the past, and although market regulators stipulate a disclaimer that past performance is no indication of the future, it only applies to private investors, while the sophisticated institutional investors may choose to believe that past track record deserves the benefit of doubt.
Of course, there is also the strong fundamental underpinning of risk parity: we cannot comfortably predict asset returns (plenty of evidence of that), and since different asset classes have different degrees of volatility, why not allocate funds in a way that they contribute the same amount of risk. Although, in principle, the resulting allocation is not optimal in the modern portfolio theory (MPT) sense, this is not an impediment, since none of the dominant pension fund asset allocation methodologies is optimal in the MPT sense.
The fact that risk parity manages to avoid return assumptions is indeed a very strong argument in favor of the methodology. Pension funds are all too familiar with more or less arbitrary return assumptions used in the conventional ALM processes. So the combination of sound fundamental basis and a good track record ought to convince and silence any skeptic, were it not for the three theoretical fallacies at the core of risk parity, which lead to one practical and very serious hurdle.
Fallacy 1: Volatility is not identical to risk. It is sensible to allocate funds in a way that they contribute the same amount to risk. In practice, volatility is used as the single measure of asset class risk, with an unintended but significant consequence: it makes asset allocation pro-cyclical. In such a setting, a core asset class, such as equities, will have a higher allocation when volatility is low and lower allocation when volatility is high. Of course, high volatility is observed in conjunction with sharply lower equity markets, while low volatility corresponds to higher equity markets. This means that a fund following risk parity approach is forced to buy equities expensive and sell cheap.
A counterargument here is that risk parity funds rebalance asset exposures very quickly, thus being “ahead of the volatility spikes”. But this begs the question whether the process is significantly different from momentum trading.
Fallacy 2: Leverage changes the distribution of asset returns. We may be, albeit reluctantly, persuaded to accept volatility as a single measure of risk. However, the next step in the process is to apply leverage to the fixed income portfolio in order to be able to achieve equity-like contribution to volatility. But the very fact of applying leverage changes the shape of distribution and introduces fat tails, which renders the already shaky use of volatility even more questionable. To put it simply, when we introduce leverage to the fixed income portfolio and achieve risk parity, in reality we have achieved volatility parity, not risk (of loss) parity. In fact, the more we try to achieve volatility parity, the farther removed we are from risk parity.
Fallacy 3: The relationship between asset returns and inflation is complex and unstable. Certain interpretations of risk parity imply asset allocation that achieves equal contribution of macroeconomic risks, i.e. growth and inflation. Asset classes are bundled together into groups that have similar behavior in various growth and inflation environments. The unit of risk measurement is still the volatility.  However, the main added assumption is that various asset classes have clear and unambiguous return patterns in various macroeconomic environments.
There is very little evidence of such clear patterns in practice. Although, theoretically, asset returns (of any asset) should hedge against inflation, in many countries the relationship between inflation and equity prices is negative[1], while in the UK, for instance, this relationship was positive. To complicate things even further, Hoesli, Lizieri & MacGregor[2], armed with more complex econometric models, have shown that in principle, asset returns are negatively correlated with short-term unexpected inflation, but positively correlated with long-term expected inflation. Overlaying this insight over the short-term trading portfolio of a typical risk parity fund one may conclude that the portfolio may be appropriate for the long-term but suffer in the short-term or the other way round. Clearly, there is very little conclusive relationship to build a robust process on.
In the end, a lot of theory above is just that – a competition between various incomplete abstract and autistic models that are inevitably too far from reality. Investors should not really care about these inconsistencies so long as the resulting portfolio appears to be sensible. Unfortunately, this latter hurdle proves to be the most severe for risk parity advocates: armed with decades of experience in financial markets, investors are reluctant to commit significant funds to fixed income assets. This is perhaps the simplest, yet the strongest argument against risk parity: building leveraged positions in assets that have done so well for so long and are backed by near insolvent entities seems just not sensible enough. Never mind the theory.