Volatility risk premia – differences between options-implied and actual volatility – are valid predictors for risky asset returns. High premia typically indicate high surcharges for the risk of changes in volatility, which are paid by investors with strong preference for more stable returns. For commodities volatility risk premia should have become a greater factor as consequence of their “financialization”. New evidence suggests that indeed volatility risk premia on commodity currencies have predictive power for subsequent commodity returns, while crude and gold premia have predictive power for other asset classes in accordance with the nature of these commodities. Since estimation of these premia takes some skill and judgment this points to opportunities for macro trading with econometric support.

Haas Ornelas, José Renato and Roberto Baltieri Mauad (2017), “Volatility risk premia and future commodities returns”, BIS Working Papers No 619.

with brief quotes from Lombardi, Marco Jacopo and Andreas Schrimpf (2014), “Volatility concepts and the risk premium” and Ge, Wei (2016), “Understanding The Sources Of The Volatility Risk Premium”.

*The post ties in with this site’s lecture on implicit subsidies.*

*The below are excerpts from the paper. Emphasis and cursive text have been added. Some acronyms have been replaced by full names. Also, the terms variance risk premium, risk-neutral volatility and physical volatility have been replaced by their synonyms (volatility risk premium, implied volatility and realized volatility) to facilitate reading.*

### Understanding volatility risk premia

“Comparing measures of implied and statistical [*realized*] volatility, researchers…can infer the volatility risk premium. This premium can be thought of as __the compensation demanded by investors for bearing risk related to sharp changes in market volatility__. To isolate this premium, researchers often compare implied volatility [*derived from options prices*] with a projection of realized volatility over the same horizon…__When volatility spikes in stress episodes, investors’ attitude towards risk usually follows__, as investors are less willing to hold positions in risky assets or to provide insurance against sharp asset price changes.” [*Lombardi and Schrimpf*]

“The behavioral basis is risk aversion;__ most investors are even willing to sacrifice a certain amount of return in exchange for potentially more stable return streams__. Monetizing the volatility risk premium in portfolios is generally appropriate for investors with long investment horizons and who are less liquidity-constrained during times of market stress.” [*Ge*]

“[*Academic research suggests that*] the volatility risk premium for developed equity markets can predict future equity indexes returns…The intuition…is that, __when risk aversion sentiment increases, equity prices are quickly discounted, resulting in high futures returns__…Similar patterns can also be found on exchange rates…the volatility risk premium of exchange rate options can predict currency returns…We argue that commodities can be viewed as a risky asset.”

### The challenge of estimating volatility risk premia

“This paper empirically investigates whether several types of volatility risk premium (VRP) can predict future commodities movements…The most straightforward idea is to analyze the use of VRP of individual commodities to predict commodities returns. However, good quality and readily available data needed to calculate commodities VRP are available starting only after 2007. For this reason, we also analyze the use of the VRP from commodities currencies where we can build longer time-series.”

“The VRP calculation requires a measure of implied volatility of returns and a measure of realized volatility of returns. The __realized volatility…calculated with intraday data can provide better estimates__ of the true unobserved volatility than traditional measures based on daily data. This paper uses volatility based on 5-minute returns for the currencies VRPs and daily returns for the other VRP variables…[*We*] __calculate the implied volatility from options with several strikes__, and then take the square root. This is called a model-free implied volatility when no parametric model assumption is done. The VIX index, the most known volatility index, is calculated…using several options on the S&P500 index, with different strikes.”

“__Ideally, the volatility risk premium should be the difference of a implied measure and an expected realized measure, both for the same period__:…[*However,]* the expected future volatility is not available.

- The traditional way in the literature to address this issue is to
__use the current implied volatility and the past realized volatility with a period ending in the current date__…This method implicitly assumes that…volatility has a unit autocorrelation. However, realized volatility does not have a unit correlation, but rather behave in clusters. In this setting, there is a mismatch between the period for which volatility was forecasted and the period of the realized volatility. - Another approach is to
__use some volatility forecasting model for the expected realized volatility__instead of simple assuming unit autocorrelation…[*such as*] the “heterogeneous Autoregressive” method… While this is an improvement over the traditional approach…it considers only information coming from prices, and disregards information coming from other sources. When market participants interpret some non-price information to induce future volatility, this measure underestimates the true VRP, - An alternative approach is to…
__compare the risk-neutral volatility with realized volatility for the same period of the forecast__…This VRP “forward” approach… has the drawback of__using the risk-neutral volatility information that is some periods lagged__…[*and*] means a perfect forecast by agents.”

“All these three alternative approaches have systematic biases over the ideal way to calculate the VRP… In this paper, when intraday data is available, we use the [*volatility forecasting*] approach and the forward approach as a crosscheck. When we were not able to get intraday data, we use the traditional approach.”

### Empirical findings for commodities

“Our main variables consist of VRP data from currency and commodities. For currencies, we have data from options and intraday returns since 2003. For commodities, we use…shorter time-series…starting only after 2007.”

“Our regression results find __a positive and statistically significant relationship between volatility risk premia of commodity currencies and future commodities indexes returns__, but only for the period after the 2008 Global Financial Crisis. This result holds not only for the main broad spot commodity index, but also for sub-indexes like energy, metals and agriculture, and also for other asset classes like equities, currencies and corporate bonds. Furthermore, results hold for forecast periods of up to four months.”

“Oil VRP and future returns have also a positive relationship, but empirical evidence is weaker when compared to commodity currencies VRP…However, it shows predictive ability for precious and industrial metals, and for currencies against the US Dollar.”

“Perhaps the most interesting result of this paper is related to the gold VRP…Financial media and previous academic literature suggest that __gold serves as a safe haven in financial markets__. Our results corroborate this view…We find that gold VRP is negative most of the time, i.e., implied volatility is lower than realized volatility. Furthermore, __there is a negative relationship between gold VRP and future commodities and currency returns__. The more negative gold VRP goes, the higher are future returns. The idea behind is that gold options are relatively cheap during turbulent markets.”

“Overall, this paper contributes to the literature by showing evidence that __commodities-linked VRP can predict not only future commodities prices, but also other asset classes__. Nevertheless, this evidence is limited to the aftermath of the 2008 Global Financial Crisis. The mechanism of this prediction ability seems to be linked to risk aversion sentiment of financial markets.”