For example, the in-sample and out-of-sample R2 values of crude oil slope IV for predicting S&P 500 returns are 3.25% and 8.75%, respectively. Finally, we also analyze the predictability of the S&P 500 excess return using commodity market predictor variables. We extend the research to four commodity markets (crude oil, natural gas, gold and silver respectively) and offer a more comprehensive study of term structures and IV shape dynamics.
For example, the in-sample and out-of-sample R2 values of the crude oil slope IV to predict S&P 500 returns are 3.25% and 8.75%, respectively.
Quantifying IV curve
The three factors are called the level, slope and curvature of the IV smile, respectively. The reason we adopt VWLS is to focus our attention on more liquid options with a large trading volume that would contain more important information. However, if a small number of options contracts have relatively large trading volume for a particular day and.
In general, R2OLS is larger than R2V W LS, but OLS cannot emphasize the more active, high volume options that we target.
Measuring predictability
Therefore, we take ordinary least squares (OLS) as a complementary method to solve this problem.2 First, we calculate R squared based on VWLS and OLS. That is, only if R2V W LS is still less than R2OLS after adding a value greater than zero, do we use OLS to fit the function instead of VWLS. We use non-overlapping excess returns to estimate equation (8) and report an estimate of the slope coefficient ˆβ, the adjusted R2 statistic, and the Newey and West (1987) t-statistic using the optimal lag length. 2016), we also investigate the performance of the predictor variables in terms of out-of-sample prediction.
A set of out-of-sample excess return forecasts can then be obtained using a sequence of expanding windows.
Quantified IV curves
The standard deviation of the level decreases as the maturity increases, indicating that the estimated ATM IV would yield a mean-reverse in the long run. The term structure of the slope is downward sloping, meaning that the slopes become steeper with increasing maturity. In the SLV options market, the IV curves overall show the same trend as those of the three other markets, which is negatively skewed with a positive curvature.
In terms of a significance test, the level (curvature) coefficients are significant for some of the fitted IV curves in general and the slope coefficient is only significant for 86.48% of the IV curves.
Constant maturity IV curve dynamics
Finally, the IV curves of the GLD options have the largest proportion of significant coefficients of the three factors, while those of the UNG options have the smallest. The high average adjusted R2 of the above 93.62% indicates that our quantified IV curve fits the market IV very well. With respect to the natural gas market, the 30- and 180-day level factors seem to fluctuate more violently than those of the crude oil market shown in Figure 6a.
In other words, volatility spikes tend to coincide with the rapid rise in gas prices caused by the high demand for natural gas in the winter. For example, we can find that there are two obvious spikes in gas volatility around January 2014 and January 2015, both of which were very cold winters in the US. From Figure 6b, we can see that the difference between the 30-day and 180-day levels exhibits several spikes during the period when the gas volatility level increases.
In general, the dynamics of the level factor in the gold market tend to have a downward term structure in the sample period of Figure 7 with extremely low volatility in 2017. In addition, the skewness is always positive, and the slope and skewness of the 180-day maturity tend to fluctuate more frequently than 30-day term. Regarding another important precious metal product, the dynamics of the silver volatility level shows the same trend as the gold volatility on average.
The difference between the 30-day and 180-day levels is extremely negative when volatility rises, while it is usually positive at other times, consistent with the result for gold. Specifically, there are several sharp increases in the natural gas market because natural gas is the most volatile of the four markets with seasonal winter volatility peaks.
Predictive variables
The average slopes for all markets are negative (ie, -0.0133, respectively), suggesting that the excess return distributions for all four commodity markets have negative skewness in the risk-neutral probability measure. In addition, we report the statistics for the first differences of the three factors in Table 5. Turning to the risk-neutral cumulant predictors, we can see that the mean T C for USO, GLD, and SLV are negative, while the mean T C for UNG is positive.
In particular, UNG has the highest average F C value, while GLD has the lowest value. Looking at the first differences of T C and F C, UNG generally has the highest DT C and the lowest DF C. In general, for the crude oil and gold markets, the level and slope have a slightly positive correlation, while the level and curve have a negative correlation.
T C is strongly negatively correlated to level with a value of -0.8358 in the crude oil market, but highly positively correlated to Slopein other markets. For UNG, F C has a high correlation with LevellandCurv, while F C for USO, GLD and SLV only has a high correlation with Level. Regarding the correlation between T C and F C, it is not very large in absolute value in UNG, GLD and SLV, indicating that T C and F C could provide different information about the excess return.
The correlation between DT C (DF C) and T C (FC) is not very large, in absolute value, except for SLV.
Predictability of four commodity ETF returns
For GLD, due to the high correlation between DT C and DF C shown in Panel C of Table 6, both DF C and DT C have high adjusted R2 statistics for excess returns in the gold market. For SLV, FC and DT C are also good predictors of excessive returns in the silver market. To further investigate the prediction results, we use out-of-sample predictions to investigate whether the predictions from our predictive regression model outperform the historical average predictions.
We find that some predictors from the energy market have good out-of-sample results. For the crude oil market, DLevel has good out-of-sample predictive power, with an R2os statistic of 4.06% and statistical significance at the 10% level. This is consistent with Ruan and Zhang (2018), who present evidence that the first difference of volatility is also a good predictor with high R2os statistics.
For the natural gas market, Level and F C can significantly predict UNG excess returns with R2os statistics of 3.91% and 3.75%, respectively. In addition, we note that all predictors from the gold market have no out-of-sample predictive power and that F C from the silver market has some out-of-sample performance. In summary, we can see that the information embedded in IV smirks can significantly predict monthly excess returns in the four commodity markets.
In addition, some predictors from the energy market and the silver market have good out-of-sample predictive power. In particular, the R2os for the natural gas IV level for predicting excess returns is 3.91%.
Predictability of S&P 500 returns
In terms of the out-of-sample measure, all predictor variables from the gold market have no significant predictions of future S&P 500 returns. However, in terms of the out-of-sample test, all predictors show poor predictive performance for excess returns on the S&P 500 and fail to outperform the historical average. Consistent with Ruan and Zhang (2018), we investigate the excess return predictability of information embedded in IV smiles on a monthly basis based on in-sample and out-of-sample tests in four commodity markets.
Bedendo, Mascia and Stewart D Hodges, 2009, The dynamics of the volatility skew: A Kalman filter approach, Journal of Banking and Finance. Chatrath, Arjun, Hong Miao, Sanjay Ramchander, and Tianyang Wang, 2016, An Investigation of the Flow Properties of Crude Oil: Evidence from Risk-Neutral Moments, Energy Econ. The monthly excess is the return on ETFs that exceeds the risk-free rate.
This table shows the number of observations, average daily number of strikes, trading volume and open interest for the four commodity ETF options combined and for each maturity category after cleaning the option data. The table shows the fitted results for the IV function: IV(ξ)=α0+α1ξ+α2ξ2, where IV is the implied volatility and ξ is the default value of the option. The percentage of significant coefficients is the percentage of parameter estimates that are significant at the 5% significance level.
Level, Slope and Basket are IV factors at the end of each month which are interpolated for days between the end of the current month and the end of the forecast month. Level, slope and Curvare IV factors at the end of each month, which are interpolated for days between the end of the current month and the end of the forecast month. This figure shows the dynamics of the 30- and 180-day constant maturity ATM IV estimate, slope and curvature and the difference between the 180-day and 30-day in the crude oil market. a) IV level in two terms.
This figure shows the dynamics of the 30- and 180-day constant maturity estimate ATM IV, slope and curvature, and the difference between the 180-day and 30-day in the natural gas market. a) IV level in two terms. This figure shows the dynamics of the 30- and 180-day constant maturity estimate ATM IV, slope and curvature and the difference of the 180-day and 30-day gold market. a) IV level in two terms. This figure shows the dynamics of the 30- and 180-day constant maturity estimate ATM IV, slope and curvature and the difference between the 180-day and 30-day in the silver market. a) IV level in two terms.
