Implied Correlation

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21 Aug, 2024

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Implied Correlation is a quantifiable measure of the estimated interrelationship between the price movement of various financial assets. Hence, it determines the degree to which various stocks within an index move in correlation to each other and aids in devising delta one and dispersion trading strategies.

It is determined from the pricing of options or other derivatives pertaining to those assets and analyzes the relative cost of the index options when compared with the individual stock options of the index. Moreover, it helps traders to gauge the diversification benefits of a portfolio by understanding the implied relationship between assets.

What Is Implied Correlation?

Implied correlation is the term used to describe the expected relationship between the price movements of several securities. It is determined from options pricing.
Traders and investors frequently use it to anticipate future market expectations and determine whether the portfolio offers diversification benefits.
It enables the traders to use efficient dispersion and delta-one trading strategies. On the other hand, realized correlation helps in portfolio diversification and risk management based on historical asset price movements.

Implied Correlation Explained

The implied correlation assesses the relationship between the implicit volatility of the options belonging to an index and those tracking the performance of the securities comprised within an index. Market participants widely use such indices for risk management purposes, enabling them to adjust systematic risk exposure levels and optimize diversification benefits.

The implied correlation fx determines the relationship between the implied volatilities of the two foreign exchange rates. Hence, it is a broader perspective on market expectations for the future price fluctuations of the underlying securities beyond the implied volatilities of options.

In 2008, The CBOE implied correlation index was published to assess the relative cost of options on the S&P 500 in comparison to individual stocks within the index, considering the top 50 SPX components based on their market capitalization. Indeed, the CBOE releases such index values every 15 seconds, i.e., four times a minute on every trading day. Hence, it assists in the evaluation of implied volatility and the potential impact of macroeconomic events on market expectations.

As per the PR Newswire report published in July 2022, CBOE Global Markets broadened its suite of CBOE implied correlation index by introducing eight new indices. These additions offer valuable insights into the average correlation among the securities falling under the S&P 500 Index. They empower market participants to understand the drivers behind volatility in equity markets and make suitable investment choices.

Examples

In the stock market, predictive accuracy is crucial. The implied correlation plays a critical role in gauging the expected relationships between the changes in the prices of different financial assets. Let us now understand its relevance through the following examples:

Example #1

Suppose the implied correlation between an index option and the weighted options portfolio tracking its components is considerably high. In this case, the index option remains unchanged when the options based on individual stocks comprised in the index don't fluctuate much. While the same shows high volatility when the latter fluctuates significantly.

Thus, it resembles low risk even if the trader invests in individual stock options in such a scenario. Now, say there is a low implied correlation between the index option's implied volatility and the implied volatility of the options tracking individual stocks within the index. Then, the traders should be careful while investing in single stock options to ensure diversification benefits are achieved.

Example #2

In mid-2023, the correlation among U.S. stocks has dropped significantly, nearing record lows, indicating divergent movements among many stocks. By the end of June 2023, the S&P 500 correlation had dropped to 0.22, with the CBBOE 3-Month Implied Correlation Index reaching a historic low of 17.59. While low correlation typically suggests lower risk and more opportunities for stock pickers, this trend may be misleading due to market gains being driven by a few mega-cap names.

Historically, low stock correlations have often resulted in high equity volatility. Contributing factors to the low correlation include the Federal Reserve nearing the end of its rate hiking cycle and the uneven performance between mega-caps and the rest of the market. Investors are advised to consider alternative strategies, such as equal-weight strategies or U.S. mid-caps, considering the market's narrowness.

The long dispersion trade and general selling of volatility have further lowered volatility and correlations. Consequently, this opens up the possibility of rapid surges in a bullish market. Despite the low correlation environment, index hedges have become more attractively priced for investors.

Implied Correlation vs Realized Correlation

The implied and realized correlations are two different statistical measures used in stock predictions and market analysis. Let us now discuss some of their prominent dissimilarities:

Basis	Implied Correlation	Realized Correlation
Definition	It is a measurement of the predicted correlation between the price movements of different financial instruments, derived from options pricing.	It refers to the interrelationship between the asset prices that takes place at the time of the swap. This involves considering the weighted average of the correlation coefficients in pairs based on the historical data for past performance analysis.
Approach	It is a forward-looking approach that predicts market sentiments.	It is a backward-looking approach to determining past asset performance.
Determines	Future market trend	Historical asset price movement
Volatility	The values change over the period with market volatility and expectations.	The values don't change as they depict the actual market volatility in the past.
Use	Making strategies for delta one and dispersion trading	Portfolio diversification, risk management strategies, and pricing model validation

Frequently Asked Questions (FAQs)

How to calculate implied correlation?

The CBOE S&P 500 implied correlation index calculation goes as follows:

1. Select the relevant index components.
2. Compute the weights of basket portfolio components by employing the

3. Use the suitable implied volatilities for every stock.
4. Calculate the index value using the implied correlation
implied correlation Formula

Is implied correlation worth calculating?

This index doesn't prove to be efficient for determining the performance of USD/DEM/CHF currency trios due to its lack of complete historical information. It is indeed worth using this index for analyzing the observed correlations in financial markets.

What is the difference between implied correlation and implied volatility?

Implied volatility is the degree of fluctuation in the prices of options, whereas the implied correlation is the interrelationship that exists between the implied volatilities of these options.