Risk Parity & Volatility Skew

Here is the next installment from Michael Rulle’s white paper on Risk Parity.

In our series on Risk Parity, we have discussed the Invisible Gorilla Experiment, Benchmarks and the Efficient Frontier and the Tangency Portfolio.

Here we are going to discuss Risk Parity and the impact of volatility skew.

As noted in out last installment, the average notional or nominal weightings of the Risk Parity portfolio was 30/70 compared to the Tangency portfolio’s weighting of 25/75. Given that one is a “fixed nominal weighting” scheme and the other a “floating nominal weighting” scheme, it might seem surprising that the nominal weightings are so close.

There are good reasons for this. The study looked at the period from 1958 to 2011 to demonstrate, in part, why this is the case. In the short run, the Tangency portfolio will almost always be different than the Risk Parity portfolio. But in the long run Risk Parity weighting approaches the Tangency portfolio as the relative volatility declines or rises between the two asset classes. The relative weightings of a given asset will increase or decrease based on underlying assets. The study makes the point that declining volatility is generally associated with rising returns and vice versa. This implies that the risk weightings tend to move toward the higher long-term risk adjusted portfolio. We hypothesize a rationale for why this occurs.

The volatility skew in the equity market strongly influences the notional weightings in both two-asset class Risk Parity and Tangency portfolios. In the Tangency portfolio, the simple increase in equity values will cause it’s relative weighting to rise. A simple decrease in equity values (often when volatility rises) will cause its relative weighting to fall. The reasons relative weightings change in Risk Parity are a little more complex.

The changes in weightings within a Risk Parity portfolio are purely a function of changes in realized volatility. This benefits Risk Parity. The reason is two-fold. First, volatility tends to cluster, or exhibit positive serial correlation (large changes tend to be followed by large changes) as was first observed by Benoit Mandelbrot in the 1960s. This means that sizing of equities within a Risk Parity portfolio, relative to changes in volatility, also clusters and is not random.

Secondly, it has been shown, empirically, that there is a negative correlation between realized volatility in equities and equity returns. The higher the volatility observed, the lower is the expected return. When observing volatility on an annual basis, the upper quartile volatility years have an expected loss of 5%, while the lowest quartile years have an expected gain of 13.4%. These are not predictive but contemporaneous. This benefits Risk Parity as it adjusts weightings according to contemporaneous measures of volatility. It weights equity less when returns are expected to be lower, and weights equity more when returns are expected to be higher.

Papageorgiou, Reeves and Sherris in “Equity Investing with Targeted Constant Volatility Exposure,” demonstrated that from 1929 to 2013 a constant volatility Equity portfolio (such as used in Risk Parity) had an information ratio of 0.65 versus 0.51 for a normal dollar weighted portfolio of the S&P 500. Perchet, Corvalho, Heckel and Moulin in “Predicting the Success of Volatility Targeting Strategies,” explain how volatility clustering and the negative correlation between volatility and returns creates higher risk adjusted returns for the equity portfolio.

The relative weightings in a Risk Parity Portfolio are driven by the changes in volatility in both the equity and fixed income markets. However, it is the realized volatility in the equity markets which has the greater impact. Its volatility is inversely related to returns (as well as position sizing). Fixed income, on the other hand, while having a long term zero correlation with equities and demonstrating some conditional negative correlation (for example, during “flights to quality”) does not exhibit persistent volatility changes that are correlated to returns. On average, its change in weighting, due to changes in volatility, has neither a positive nor a negative impact on Risk Parity in the long run.

In the long run, therefore, the notional weightings in the Risk Parity portfolio mimic the notional weightings of the Market Portfolio (and, therefore, in the long run the Tangency Portfolio). Equity weightings rise relative to fixed income when equity prices rise in the Market Portfolio simply because of the higher prices, and the same occurs in the Risk Parity portfolio because volatility is typically declining at the same time. The opposite also occurs when equity prices fall and volatility increases.

In our next installment we will discuss Pension Funds, 60/40 and the Paradox of Alternatives.

Michael S. Rulle, Jr. is the founder and CEO of MSR Indices, LLC, a commodity trading advisor that offers an expansive range of index-tracking investment programs. This piece is an excerpt from a white paper titled: “The Gorilla in the Room: The obvious method of asset allocation most of us have never considered.”

Rulle inspired a family of indexes launched by S&P Dow Jones called S&P Risk Parity Indices, Rulle discussed Risk Parity at the 2019 TradersEXPO New York. Prior to founding MSR in 2015, he was president of Graham Capital Management, where he was directly responsible for the firm's discretionary portfolio managers.