PutWrite versus BuyWrite: Yes, Put-Call Parity Holds Here Too
Roni Israelov: AQR Capital Management, LLC
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.
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.
- 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.
- 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.
- Cash position: Collateral of BuyWrite is invested in 1 month T-bill while PutWrite invests in both 1 month and 3 month T-bill.