Portfolio Construction

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

Topics - Portfolio Construction Derivatives

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

The CBOE S&P 500 PutWrite Index has outperformed the CBOE S&P 500 BuyWrite Index by approximately 1.1 percent per year between 1986 and 2015. That’s 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.

What’s Inside

This article explains why the CBOE S&P 500 PutWrite Index has historically outperformed the CBOE S&P 500 BuyWrite Index. I find that:

  • The PutWrite and BuyWrite Indices performed similarly on non-option expiration dates, just as put-call parity demands.
  • The difference in the strategies’ performance occurs on option expiration dates.
  • Options expire at the open, settling at the Special Open Quotation. The PutWrite and BuyWrite Indices do not replace their short option positions for approximately four hours. During this four hour window, the BuyWrite Index has a beta of 1.0 and the PutWrite Index has a beta of 0.0.
  • Negative equity returns during the time from the Special Open Quotation until the time the two indices replace their option exposure, approximately four hours later, explain the difference in historical performance of the two indices.


Portfolio construction matters. So does performance attribution. A quirk in the portfolio construction of the CBOE S&P 500 PutWrite and BuyWrite Indexes has led to the PutWrite Index outperforming the BuyWrite Index by about 1.1 percent per year. Performance attribution tells us that PutWriting is not superior to BuyWriting – that the difference in performance is due to average negative market returns during the morning on option expiration dates. If we do not expect equity returns to be negative on average during the morning of option expiration, there is no reason to expect the PutWrite Index to continue to outperform the BuyWrite Index. On the other hand, those who do expect equity returns to continue to be negative on these mornings, do not need to trade the PutWrite Index to capture this predictable source of return – they can short sell equities instead. Investors should first understand what drives returns and then explicitly construct their portfolios accordingly.

This document is not intended to, and does not relate specifically to any investment strategy or product that AQR offers. It is being provided merely to provide a framework to assist in the implementation of an investor’s own analysis and an investor’s own view on the topic discussed herein.

This document has been provided to you solely for information purposes and does not constitute an offer or solicitation of an offer or any advice or recommendation to purchase any securities or other financial instruments and may not be construed as such. The factual information set forth herein has been obtained or derived from sources believed by the author and AQR Capital Management, LLC (“AQR”) to be reliable but it is not necessarily all-inclusive and is not guaranteed as to its accuracy and is not to be regarded as a representation or warranty, express or implied, as to the information’s accuracy or completeness, nor should the attached information serve as the basis of any investment decision. This document is not to be reproduced or redistributed to any other person. The information set forth herein has been provided to you as secondary information and should not be the primary source for any investment or allocation decision. Past performance is not a guarantee of future performance. Diversification does not eliminate the risk of experiencing investment losses. 

This material is not research and should not be treated as research. This paper does not represent valuation judgments with respect to any financial instrument, issuer, security or sector that may be described or referenced herein and does not represent a formal or official view of AQR. The views expressed reflect the current views as of the date hereof and neither the author nor AQR undertakes to advise you of any changes in the views expressed herein. 

The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons. Charts and graphs provided herein are for illustrative purposes only. The information in this presentation has been developed internally and/or obtained from sources believed to be reliable; however, neither AQR nor the author guarantees the accuracy, adequacy or completeness of such information. Nothing contained herein constitutes investment, legal, tax or other advice nor is it to be relied on in making an investment or other decision. There can be no assurance that an investment strategy will be successful. Historic market trends are not reliable indicators of actual future market behavior or future performance of any particular investment which may differ materially, and should not be relied upon as such. Diversification does not eliminate the risk of experiencing investment losses.

The information in this paper may contain projections or other forward-looking statements regarding future events, targets, forecasts or expectations regarding the strategies described herein, and is only current as of the date indicated. There is no assurance that such events or targets will be achieved, and may be significantly different from that shown here. The information in this document, including statements concerning financial market trends, is based on current market conditions, which will fluctuate and may be superseded by subsequent market events or for other reasons.