Since, as everyone says, “past performance is no guarantee of future results,” a history of close correlation between two assets, or between a single asset and a benchmark, is no guarantee of future correlation. The threat that a correlation upon which a particular investor has relied will cease to apply at some future date is, unsurprisingly, called the correlation risk. And the “bribe” an investor receives for taking on that risk is the correlation risk premium (CRP).
Can we break this down any further, or is the CRP a Democritean atom of a factor? That is the question behind a new study out of Muenster University, in which three scholars led by Nicole Branger, professor of financial engineering, break the correlation risk with regard to equities into two components: one related to the continuous movement of stock prices and the other to the risk of co-jumps. They propose a new way to identify both. Using their novel method, they reason that the sale of insurance against co-jumps in particular generates a sizeable annualized Sharpe ratio.
Co-jumps are what the term suggests, rare and discontinuous movements by two distinct assets in the same direction. Jumps have an important role in creating tail risk for investors. Empirical research on that subject goes back to a 2011 paper by Bollerslev and Todorov.
Volatility Risk and Jump Risk
The method employed by Branger, et al., to identify the two components of CRP involves the creation of delta-gamma-neutral and delta-vega-neutral option portfolios, only exposed to either volatility or jump risks, for both an index and its constituents. They create portfolios, in other words, to go long the index portfolio and short the basket of options on the constituents.
As the authors say, “resulting excess returns allow us to quantify the premiums associated with both types of correlation risk.” They identify two critical advantages to their options-based method. First, they are not required to estimate physical or risk-neutral expectations. Second, it does not involve calculations on high-frequency data. These authors worked only with daily data on four options for each underlying.
The continuous component they call the “volatility risk premium,” is distinct from the jump risk premium. The VRP for the S&P 100 index is negative, but the VRP for its constituents is on average positive. The JRP for the S&P 100, on the other hand, is not only positive, it is very large. The constituents have much smaller JRPs.
Thoughts on Method
The global financial crisis did not result in a change of the relative contributions of the S&P to the jump component, even though it did as one would expect increase covariations.
Interestingly, the data indicates that the JRP predicts future market returns up to three months. It has no such predictive power for longer horizons. The VRP on the other hand, has no short-term predictive power, but it does predict returns for horizons of between one and two years. This confirms the intuition that the two premia capture distinct market risks.
As long ago as 2001, Coval and Shumway suggested the use of zero-beta, at-the-money straddles to provide evidence as to whether volatility risk is priced into the returns of index options. This paper contributes to the same line of research.
Branger, et al. use data beginning in January 1996 and continuing through 2017. They account for dividends on the constituent stocks using data from OptionMetrics and CRSP. They eliminated options whose recorded prices differed by more than 1% from those implied by the binomial trees. They also excluded options whose European prices were zero. They clearly aimed at eliminating outliers and noise from their data.
One of their conclusions is that differing crisis have different effects on the two components of the CRP under study. The bursting of the Chinese stock bubble in 2007, for example, and the downgrade of the credit rating for European countries in 2010, both resulted in a large positive return for a straddle designed to capture the volatility premium. On the other hand, the Chinese stock market crash of 2015 and the fears associated with the sovereign debt crises in Spain and Italy in 2011, led to negative returns for the same strategy.
In Big Picture terms, the authors find that “the risk associated with co-jumps is of much greater importance for investors than the risk of correlated diffusive stock price movements,” which is why ensuring against co-jumps is such a prime alpha-making opportunity.