Since then, the distribution of implied volatility has been specifically studied (see Carr and Wu (2003), Zhang and Xiang (2008), and Foresi and Wu (2005), among others). Other evidence also reveals relatively high correlations between implied volatilities of the US market and other markets (Tissaoui, 2019; Dutta, 2018). Third, assets listed in the US market will not face the problem of information asymmetry due to the difference in trading time.
If the moneyness levels in the grid are lower (higher) than those in the acquired options, we set the implied volatility to the same level as options with the lowest (highest) collectible moneyness levels. Then the foreign exchange rate of return is the daily change of the foreign currency in the US dollar.
Out-of-sample test
As for the control variables, we consider the interest rate and dividend yield, which have been proven to have the predictability of future returns (Rapach, Strauss, and Zhou, 2013). In addition, we include GDP growth rates in the model, which reflect the change in the macroeconomic situation. To remain consistent with excess returns, the control variables are all converted to continuous rates and annualized.
We report the t statistic that is based on the Newey and West (1986) standard error for all prediction measures. The t statistic of the zero coefficient was estimated from the standard errors of Newey and West (1986) and compared with the critical values for the one-tailed test.
Summary statistics
Option volume, turnover and seasonal GDP are used as control variables in the panel regression as control variables for liquidity and the size of the underlying economy. Further, the correlations between option volume and turnover, option volume and GDP are 0.58 and 0.54, respectively, implying that options trading liquidity is related to underlying asset liquidity and macroeconomic scales in the underlying countries or regions. . We also took into account the market value and trading volume of the underlying assets, but the correlation between these two variables and between each of them and the volume of options reaches more than 0.7.
Additionally, using the Augmented Dickey-Fuller test (Fuller, 2009), we tested for unit root for each of the option-implied measures and one-month lagged returns, and all p-values are below 5%. . Insert image 1 and image 2 here) (insert image 3 here). However, the implied volatilities of almost all non-model ETFs jumped sharply between the 2008 global financial crisis and the 2020 COVID-19 pandemic.
3 Empirical results
- Causality analysis
- Predictive power of the model-free implied moments
- Predictability of future returns via the model-free implied moments
- Panel prediction
- Global risk-neutral moments
- Global uncertainty indices
- Predictatability of future returns by global uncertainty indices
- Analysis of sorted portfolio
We then compare the predictive power of the model-free implied volatility against one-month forward returns with risk-neutral distribution measures. In addition, only the slope coefficients of SKEW of the South Korea and Taiwan ETFs show significant results in the out-of-sample test, whereas their in-sample results are only at a marginal significance level. Regarding the control variables, the future return is sensitive to the change in the US interest rate, where a 1% increase in the US interest rate will cause a decrease of approx. 7% in future returns of ETFs.
Among the V OLsorted portfolios, they are highly exposed to GDP-weighted global implied volatility and asymmetry, and the different exposure levels are also statistically significant. Our results in the previous work are generally more related to time series analysis, which is methodologically different from mimic portfolio analysis.
4 Robustness check
- Predictability of returns on local indices
- Exluding the impact of COVID-19
- Other option measures
- Predictability of non-overlapping returns
In this case, we hold cohort portfolios for each tercile portfolio and no more than 1/21 of the portfolios are rebalanced each day. The difference between the alpha of the third portfolio and that of the first is negative and statistically significant, which is also consistent with the results of the previous linear prediction in this paper. Nevertheless, the results differ from the results of cross-sectional analysis by Stilger, Kostakis, and Poon (2017), where our samples are proxies for market indices and the mean reversion effect may be much stronger than that of individual stocks.
For KU RT, most of the results are insignificant except for the difference between KU RT for portfolio 3 and 1, confirming that theSKEW is highly related to both V OLand KU RT. In panel regression, the cofficient between V OL and the future excess return is still statistically significant in the local indices, although the levels of the cofficient and t-statistics are all smaller than in the prediction of future returns of ETFs, but may also due to the limited placements in the tests. Regarding the control variables, the interest rate in the US, GDP growth and GDP in general can also predict future returns and volatility of the local indices.
As shown in Figure 1 and Figure 3, the non-model volatilities of all ETFs jumped sharply in 2020 due to the COVID-19 pandemic. Excluding the impact of the pandemic, the model-free implied volatilities of ETFs of Chile, India, Mexico, the Netherlands, Saudi Arabia, South Africa, South Korea, Spain, Sweden, and the United Kingdom can still significantly predict future returns, although their t-statistics generally become weaker than results over the entire period. This is also partly in line with the findings of Giota (2005), where high implied volatilities can increase the predictive power of positive future returns.
Evidence shows that, in terms of the predictability of the future return, the coecients of V OL and KU RT are still statistically significant, although their t-statistics all decrease in different levels. However, with respect to control variables, coefficients of GDP growth are not statistically significant before the COVID-19 pandemic and the significance levels for the coefficient of GDP are also slightly weaker, which may imply that the expectation of the future return of investors during the pandemic depends a lot on the macroeconomic environment in different countries or regions. For individual local yield forecasting, some of the coefficients of V OL agree with our main results, while the coefficients of the SKEW and KU RT are much weaker.
5 Conclusion
The figures show the trends in the risk-neutral implied volatilities of 28 MSCI country and region share ETFs from their option inception date to December 31, 2020. The risk-neutral implied volatilities are calculated from the option data received from surface files to OptionMetrics. The figures show the risk-neutral implied skew trends of 28 MSCI ishare country- and region-specific ETFs from their option inception date to December 31, 2020.
Risk neutral implied bias is calculated from the option data retrieved from the surface files in OptionMetrics. This figure shows risk-neutral implied volatility trends for SPY and the CBOE VIX index from January 10, 2005 to December 31, 2020. The risk-neutral implied volatility of SPY is calculated from the options data retrieved from the surface files in OptionMetrics.
The correlation between our SPY risk-neutral implied volatility and the CBOE VIX exceeds 0.99. For robustness, the correlation between our risk-neutral implied volatility of SPX calculated from price files and the CBOE VIX exceeds 0.99 in the sample period. This figure shows the trends in the risk-neutral implied skewness of the SPY and the CBOE SKEW index from January 10, 2005 to December 31, 2020.
The risk-neutral implied skewness of SPY is calculated from the option data obtained from the surface files in OptionMetrics. The correlation between our risk-neutral implied skewness of SPY and the CBOE SKEW index reaches 0.72. For robustness, the correlation between our risk-neutral implied volatility of SPX calculated from price files and the CBOE SKEW index reaches 0.84 in the sample period.
The second, fifth, and eighth columns represent the coefficients between the V OL, SKEW, and KU RT of a given ETF and the excess return over the next 21 trading days from the in-sample test. The second, fifth, and eighth columns represent the coefficients between the V OL, SKEW, and KU RT of a given ETF and the excess return over the next 21 trading days from the in-sample test.
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Appendix A Univariate prediction of future returns
