PutWrite versus BuyWrite: Yes, Put-Call Parity Holds Here Too

Source

PutWrite versus BuyWrite: Yes, Put-Call Parity Holds Here Too
https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=2894610

Author

Roni Israelov: AQR Capital Management, LLC

Abstract

The CBOE PutWrite Index has outperformed the BuyWrite Index by approximately 1.1 percent per year between 1986 and 2015. That is pretty impressive. But troubling. Yes – troubling – because the theory of put-call parity tells us that such outperformance should be almost impossible via a compelling no-arbitrage restriction. This paper explains the mystery of this outperformance, which has implications for portfolio construction.

Summary

Historically PutWrite index outperformed BuyWrite index even though the put-call parity suggests that such a discrepancy should not exist.
The author lay outs three constructional differences that could have caused the outperformance.

1. Naked beta position: By construction, BuyWrite index is a portfolio of short call option and long S&P500. Once the option expires, BuyWrite index still has a naked beta position which PutWrite does not. The author shows that this transitory equity exposure which lasts 4 hours explains most of the mismatches.
2. Delta: BuyWrite sells the most closest strike higher than the spot while PutWrite sells the lower strike. The author estimates the two nearest strikes have delta difference of 0.03.
3. Cash position: Collateral of BuyWrite is invested in 1 month T-bill while PutWrite invests in both 1 month and 3 month T-bill.