Cboe Implied Correlation Index (COR3M)
Cboe Implied Correlation Index (COR3M)White Paper 2021 Cboe Exchange, Inc. All rights reserved.
PurposeThis document describes the methodology underlying the Cboe S&P 500 Implied Correlation Index. The index is structuredto reflect changes in the relative premium between SPX index options and single-stock constituent options. Accounting forthe implied volatility relationship between the SPX index option and a weighted basket portfolio of single-stock options,Cboe S&P 500 Implied Correlation Index measures the market’s expectations of index component correlation. For a morerigorous overview of the index methodology, refer to the Cboe Implied Correlation Factsheet and Website.Contents Index Factsheet. 3 The Implied Correlation Index Calculation: Step-by-Step. 4 Step 1: Select the Relevant Index Components. 5 Step 2: Calculate Basket Portfolio Weights. 6 Step 3: Select Relevant Implied Volatilities. 7 Step 4: Calculate Implied Correlation Index. 8 Appendix: Theory and Implementation. 9Cboe Proprietary Information. Copyright 2021 Cboe. All rights reserved.Page 2
IntroductionIndex volatility is driven by a combination of two factors: the individual volatilities of index components and the correlationof index component price returns. Intuitively, one would expect that the implied volatility of an index option would rise with acorresponding change in the implied volatilities of index component options. Yet, there are instances when the index optionimplied volatility moves without a corresponding shift in the implied volatilities of index component options.The index measure isolates the impact of correlation changes on the index option implied volatility and provides a tradingsignal for volatility dispersion (correlation). Implied correlation provides a measure of the relative cheapness/richness ofindex options in relation to the index components. A long dispersion trade, which involves selling at-the-money index optionstraddles and purchasing at-the-money straddles in options on index components, would perform profitably under a highcorrelation regime.Since the introduction of the Cboe Volatility Index (the VIX index), Cboe has established a suite of tradable volatility productsand indices that quantify forward-looking volatility expectations through theoretically robust metrics. Through the Cboe S&P500 Implied Correlation Index, Cboe provides market participants with further granularity into the factors driving volatility,creates robust trading strategies and promotes greater transparency and integration of various products and strategies.Summary Product SpecificationsNameCboe Implied Correlation IndexIndex TypeEquity CorrelationVolatility UnitDelta Relative Calendar Day Price VolatilityTenors3MIndex OverviewThe Cboe S&P 500 Implied Correlation Indices are the first widely disseminated, market-based estimateof the average correlation of the stocks that comprise the S&P 500 Index (SPX). The Cboe S&P 500Implied Correlation Indexes offers insight into the relative cost of SPX options compared to the price ofoptions on individual stocks that comprise the S&P 500.Index PublisherCboe Global MarketsThe SPX option implied variance can be defined using the Harry Markowitz’s portfolio model1, assuming thenormality of returns, as follows:MethodologyOutlineThe implied correlation is a measure of the average correlation between SPX index components, denoted as .The pairwise correlation, , is replaced by the average correlation in the expression above.The implied index value can be solved by isolating the average correlation term:The correlation index is calculated by first finding the difference between the SPX option implied varianceand the implied variance of an uncorrelated portfolio of the top 50 SPX components by market capitalization.This value is then divided by the sum of pairwise weighted implied volatility products to calculate theimplied correlation value.Input DataFeed of trading day ATM Implied Volatility of SPX index options and SPX Index components options for thematurities above from Hanweck.Calculation Hours 8:30 a.m. to 3:00 p.m. Central Time (CT)1Harry Markowitz, Portfolio Selection, The Journal of Finance, Vol. 7, No. 1. (Mar., 1952), pp. 77-91.Cboe Proprietary Information. Copyright 2021 Cboe. All rights reserved.Page 3
The Implied Correlation Index Calculation: Step-by-StepThe Implied Correlation Index is a financial benchmark that provide instantaneous market estimates of expected correlationusing implied volatilities of SPX index and SPX component options. This index forms an essential tool to identify the drivers ofIndex Implied Volatility and evaluate the implications of major macroeconomic shocks on market expectations.This whitepaper shows a sample calculation of the Cboe 3M Implied Correlation Index. The implied correlation maturitiescan be calculated using the same methodology and differ only in the implied volatility tenors used. The generalizedformula used is:WhereIn the following sections, this paper goes over a sample implied correlation index calculation usingsample data from February 10, 2021.Cboe Proprietary Information. Copyright 2021 Cboe. All rights reserved.Page 4
Step 1: Select the Relevant Index ComponentsFor our backtested calculation at the end of each business day, SPX component weights are calculated using their float-adjusted market capitalizations. The top 50 components with the highest weights are included in the next business day’s SPXtracking portfolio. Additionally, the 51st to 55th highest weighted components are included in the next business day’s replacement pool. This pool is created to account for the event that one or more tracking portfolio components are excluded from the SPX index. In the event this occurs, non-zero weighted components of the replacement pool would replaceexcluded stocks in the tracking basket portfolio, forming a 50-stock SPX basket portfolio.For the intraday calculation, we would similarly use the top 50 stocks as determined using the previous business day’sclosing adjusted market capitalizations. The SPX basket portfolio components and weights do not change intraday.SPX Tracking Portfolio NP0.42%HD0.90%KO0.58%SPX Replacement Pool Cboe Proprietary Information. Copyright 2021 Cboe. All rights reserved.Page 5
All 50 tracking portfolio stocks will form the basket portfolio below, as none of the tracking portfolio stocks were excludedfrom the SPX index on February 10, 2021:Basket Portfolio SPX Weights (February 10, 2%HD0.91%KO0.58%Sum Total54.43%Step 2: Calculate Basket Portfolio WeightsMarket capitalization weights of basket portfolio components are calculated using the following:Cboe Proprietary Information. Copyright 2021 Cboe. All rights reserved.Page 6
On February 10th, AAPL’s weight in the basket portfolio is 12.05% (6.56%/54.43%). The weights of all stocks in the basketportfolio are shown below:SPX Basket Portfolio Weights (February 10, .76%HD1.67%KO1.07%Sum Total100.00%Step 3: Select Relevant Implied VolatilitiesFor each stock in the basket portfolio, we use Cboe Hanweck PhD 3M implied volatilities of 0.5 delta options. Impliedvolatilities quantify market expectations of 3M forward volatility. Implied volatilities are based on calendar days.For more information on how the implied volatilities are calculated please refer to the Cboe Hanweck Methodologyfactsheet at ew.SPX Basket Portfolio Implied Volatilities (February 10, HD26.50%KO23.07%Cboe Proprietary Information. Copyright 2021 Cboe. All rights reserved.SPX20.23%Page 7
Step 4: Calculate Implied Correlation IndexUsing the weight and implied volatility values for February 10, 2021, the implied correlation index can be calculated as follows:Step A: Find Implied Variance of Index OptionStep B: Find Implied Variance of the Uncorrelated Basket PortfolioStep C: Find the Sum of Pairwise Weighted Implied Volatility ProductsStep D: Calculate Implied Correlation:Cboe Proprietary Information. Copyright 2021 Cboe. All rights reserved.Page 8
Appendix: Theory and ImplementationBacktested Implied CorrelationCboe 3-Month Implied Correlation Index:Source: Cboe Hanweck and S&P SPICE (March 17, 2021)References Driessen, J., Maenhout, P. J., & Vilkov, G. (2009). “The Price of Correlation Risk: Evidence from Equity Options.” SSRNElectronic Journal, 64(3), 1377-1406. Driessen, J., Maenhout, P. J., & Vilkov, G. (2012). “Option-Implied Correlations and the Price of Correlation Risk.” SSRNElectronic Journal. Härdle, W. K., & Silyakova, E. (2016). “Implied basket correlation dynamics.” Statistics & Risk Modeling, 33(1-2), 1-20. Linders, D., & Schoutens, W. (2014). “A framework for robust measurement of implied correlation”. Journal ofComputational and Applied Mathematics, 271, 39-52. Markowitz, H. (1952). “Portfolio Selection.” The Journal of Finance, 7(1), 77-91.Historical Prices for the Cboe Implied Correlation Index may be found on the Cboewebsite at https://www.cboe.com/us/indices/dashboard/cor3m/. Contact us at:John HiattDerivatives Strategy 1.312.786.7779jhiatt@cboe.comParth ShahDerivatives Strategy 1.312.786.7157pshah@cboe.comOptions involve risk and are not suitable for all investors. Prior to buying or selling an option, a person must receive a copy of Characteristics and Risks of StandardizedOptions. Copies are available from your broker or from The Options Clearing Corporation at www.theocc.com. Futures trading is not suitable for all investors and involves therisk of loss. That risk of loss can be substantial and can exceed the amount of money deposited for a futures position. You should, therefore, carefully consider whether futurestrading is suitable for you in light of your circumstances and financial resources. For additional information regarding futures trading risks, see the Risk Disclosure Statementset forth in Appendix A to CFTC Regulation §1.55(c) and the Risk Disclosure Statement for Security Futures Contracts. The information in this document is provided for generaleducation and information purposes only. No statement(s) within this document should be construed as a recommendation to buy or sell a security or futures contract or toprovide investment advice. Supporting documentation for any claims, comparisons, statistics or other technical data in this document is available by contacting Cboe GlobalMarkets at www.cboe.com/Contact. Past performance is not indicative of future results. Parameters relating to past performance of strategies discussed are not capable ofbeing duplicated. These materials contain index performance data based on back-testing, i.e., calculations of how the index might have performed prior to launch. Backtested performance information is purely hypothetical and is provided in these materials solely for informational purposes. Back-tested performance does not representactual performance and should not be interpreted as an indication of actual performance. Index performance returns do not reflect management fees, transactions costs orexpenses. No representation is being made that any investment will or is likely to achieve a performance record similar to that shown. Cboe , Cboe Global Markets , CboeVolatility Index , and VIX are registered trademarks and Cboe US Treasury VolatilitySM, Fixed Income VIXSM, and Treasury VIXSM are service marks of Cboe Exchange, Inc. or itsaffiliates. All other trademarks and service marks are the property of their respective owners. 2021 Cboe Exchange, Inc. All Rights Reserved.Cboe Proprietary Information. Copyright 2021 Cboe. All rights reserved.Page 9
Index Implied Volatility and evaluate the implications of major macroeconomic shocks on market expectations. This whitepaper shows a sample calculation of the Cboe 3M Implied Correlation Index. The implied correlation maturities can be calculated using the same methodology and differ only in the implied volatility tenors used. The generalized
option's implied bond as a portfolio long Treasuries and short the put option. The option's implied bond is thus a defaultable zero-coupon bond and the implied spread is the credit spread of the implied bond. The second quantity is the normalized implied spread, which normalizes the implied spread by its option-implied expected default .
Cboe Russell 2000 30-Delta BuyWrite Index Page 2 of 7 the last disseminated value of the Russell 2000 Index before 12:00 pm ET is used. If the VWAP of the Russell 2000 Index and the last value before 12:00 pm
(PUTSM Index) and Cboe S&P 500 One-Week PutWrite Index (WPUTSM Index), and compared it to the performance of traditional benchmarks (S&P 500 , Russell 2000 , MSCI World, 30-year Treasury Bond (FTSE)) as well as the option buying strategy (Cboe S&P 500 5% Put Protection Index (PPUTSM)). We updated the results from the earlier study "A .
Regular trading will resume when the NBBO for a given symbol is determined to be healthy by the Cboe trading system. Cboe US Equities . 2.1 Message Format . FIX messages are ASCII formatted. The member will be provided with a . SenderCompId. and . SenderSubId. that must be sent on every m
Interactive Brokers Webcast September 2016 . CBOE OPTIONS INSTITUTE 2 . CBOE , Chicago Board Options Exchange and VIX are registered trademarks and CBOE Options Institute and Weeklys are service marks of Chicago Board Options . 7 Calendar Days to Expiration . Price . 7 Day Theta : I
Pursuant to Section 5c(c) of the Commodity Exchange Act (the "CEA") and 40.6(d)(2)(x) of the regulations of the Commodity Futures Trading Commission (the "Commission"), Cboe SEF, LLC ("Cboe SEF") hereby provides the Commission with a summary notice of a Cboe SEF rule amendment during the week of March 26, 2021 ("Rule Amendment").
Cboe Market Close (CMC) auction, a closing match process for non-Cboe securities, was approved by SEC on January 17, 2018 Subsequent appeals by competitors will delay the benefits of CMC for investors in U.S. equity markets Plan to continue to work proactively with the SEC on a favorable resolution
A CENSUS LIST OF WOOL ALIENS FOUND IN BRITAIN, 1946-1960 221 A CENSUS LIST OF WOOL ALIENS FOUND IN BRITAIN, 1946-1960 Compiled by J. E. LOUSLEY Plants introduced into Britain by the woollen industry have attracted increasing interest from field botanists in recent years and this follows a long period of neglect. Early in the present century Ida M. Hayward, assisted by G. C. Druce, made a .
