Journal of Adam Chen Longhui : Natural Gas Consumption Forecasting Based on Weather and Machine Learning, Tail risk hedging using cheap options , Isolation Forest Algo

Tail risk hedging using cheap options

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=8325&context=lkcsb_research

On average, there are 90 options in our hedge portfolio, of which only approximately 40 belongs to the SPX index constituent stocks

We discover that a simple heuristic which sort liquid equity put options by their dollar value to construct a portfolio of cheap options leads to a surprisingly robust hedging performance for tail risk.

Our analyses reveal that the superior performance stems from the empirical behavior of market level correlation – correlation is generally lower during good market conditions when stock returns are more diversified, but spikes up during bad market conditions when stock movements are concentrated. Instead of utilizing expensive SPX index options, the portfolio of cheap options constructed by our price-based heuristic provides matching hedging return during tail risk events due to the spike in market level correlation. During normal market conditions, the SPX index options exert significant portfolio drag due to their significant volatility risk premium. On the other hand, the portfolio of cheap options, in addition to their price economy, also benefited from the effect of diversification due to lower market level correlation, leading some of these options to move ITM during normal market conditions, further mitigating the detrimental effect portfolio drag.

Carr and Wu (2009) have demonstrated the existence of large volatility risk premium for both the SPX and Dow Jones indexes, inflating the option prices due to the implied volatilities being higher than the future realized volatility. This can be attributed to the implications of risk aversion, exposure to tail events, and fatter left tails of the physical index distribution in markets where volatility is traded (see Bakshi and Madan (2006))

Even if the underlying stocks of our option portfolio is not an exact replica of the SPX index constituents, the spike in market level correlation during crashes will enhance its hedging return to match the protection offered by SPX index options.

During up markets, the average correlation of the underlying stocks of our cheap option portfolio and the SPX index is 40.95% which resulted in an average of 18.93% of the options to move into-the-money (ITM). During down markets, the average correlation of the stocks and index increases to 48.58%, which resulted in an average of 50.24% of the cheap options to move ITM. During tail risk events, the average correlation spikes to 64.95%, with 65.36% of the cheap options moving ITM

Following our price based heuristic, we sort the OTM put options in our universe according to their dollar price. On each month end, we allocate a risk budget of 2% to acquire the cheapest 20% of the put options in our universe with equal dollar-weighting – this corresponds to 90 options each period on average, of which approximately 40 options’ underlying are SPX index constituent stocks.

We construct option portfolios from our option universe by sorting them according to (1) IV, (2) HV, and (3) IV − HV, and then allocate the same 2% risk budget to acquire the lowest 20% of the options in each case.

For volatility, we use the raw SPX index as the base case, and compute F-statistics of all hedge portfolios for comparison. We observe a volatility reduction from approximately 15% to 12% across all hedge portfolios. The improvement in volatility performance is statistically significant at the 0.01% level