The high difference between the implied volatility of index options and subsequent realized volatility is a known fact. Trades routinely exploit this difference by selling options with consecutive delta hedging. There is, however, a more elegant way to exploit this risk premium – the dispersion trading.

The dispersion trading uses the known fact that the difference between implied and realized volatility is greater between index options than between individual stock options. The investor, therefore, could sell options on index and buy individual stocks options. Dispersion trading is a sort of correlation trading as trades are usually profitable in a time when the individual stocks are not strongly correlated and loses money during stress periods when correlation rises. Basic trade could be enhanced by buying options of firms with high belief disagreement (high analysts’ disagreement about firms’ earnings).

Fundamental reason

The academic paper shows that dispersion in analysts’ forecasts is strongly related to the implied volatility of index and single-name options. Research shows that option excess returns reflect the different exposure to disagreement risk. Investors who buy options of firms that are more prone to heterogeneity in beliefs are compensated in equilibrium for holding this risk. Volatility risk premia of individual and index options represent compensation for the priced disagreement risk. Hence, in the cross-section of options, the volatility risk premium depends on the size of the belief heterogeneity of this particular firm and the business cycle indicator. As the risk-neutral skewness, the volatility risk premium for index options can be larger or smaller depending on the size of disagreement and of the firm’s share.

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Markets Traded

Financial instruments

Confidence in anomaly's validity

Backtest period from source paper

Notes to Confidence in Anomaly's Validity

Indicative Performance

Period of Rebalancing

Notes to Indicative Performance

per annum after transaction costs, annualized (geometrically) monthly return of 1,2% from table 6

Notes to Period of Rebalancing

Estimated Volatility

Number of Traded Instruments

Notes to Estimated Volatility

annualized monthly standard deviation 4%, data from table 6

Notes to Number of Traded Instruments

20 options on individual stocks + 1 position in index option

Maximum Drawdown

Complexity Evaluation
Very complex strategy

Notes to Maximum drawdown

not stated

Notes to Complexity Evaluation

Sharpe Ratio

Simple trading strategy

The investment universe consists of stocks from the S&P 100 index. Trading vehicles are options on stocks from this index and also options on the index itself. The investor uses analyst forecasts of earnings per share from the Institutional Brokers Estimate System (I/B/E/S) database and computes for each firm the mean absolute difference scaled by an indicator of earnings uncertainty (see page 26 in the source academic paper for detailed methodology). Each month, investor sorts stocks into quintiles based on the size of belief disagreement. He buys stocks with the highest belief disagreement and sells the index put is an equally-weighted portfolio of 1-month index put options with Black-Scholes deltas ranging from -0.8 to – 0.2.

Hedge for stocks during bear markets

No - Absolutely not a hedge, dispersion trading strategy is a fat-tail strategy that loses a lot of money during crisis periods…

Source paper
- Abstract

Writers of index options earn high returns due to a significant and high volatility risk premium, but writers of options in single-stock markets earn lower returns. Using an incomplete information economy, we develop a structural model with multiple assets where agents have heterogeneous beliefs about the growth of firms’ fundamentals and a business-cycle indicator and explain the different volatility risk premia of index and single-stock options. The wedge between the index and individual volatility risk premium is mainly driven by a correlation risk premium which emerges endogenously due to the following model features: In a full information economy with independent fundamentals, returns correlate solely due to the correlation of the individual stock with the aggregate endowment (“diversification effect”). In our economy, stock return correlation is endogenously driven by idiosyncratic and systemic (business-cycle) disagreement (“risk-sharing effect”). We show that this effect dominates the diversification effect, moreover it is independent of the number of firms and a firm’s share in the aggregate market. In equilibrium, the skewness of the individual stocks and the index differ due to a correlation risk premium. Depending on the share of the firm in the aggregate market, and the size of the disagreement about the business cycle, the skewness of the index can be larger (in absolute values) or smaller than the one of individual stocks. As a consequence, the volatility risk premium of the index is larger or smaller than the individual. In equilibrium, this different exposure to disagreement risk is compensated in the cross-section of options and model-implied trading strategies exploiting differences in disagreement earn substantial excess returns. We test the model predictions in a set of panel regressions, by merging three datasets of firm-specific information on analysts’ earning forecasts, options data on S&P 100 index options, options on all constituents, and stock returns. Sorting stocks based on differences in beliefs, we find that volatility trading strategies exploiting different exposures to disagreement risk in the cross-section of options earn high Sharpe ratios. The results are robust to different standard control variables and transaction costs and are not subsumed by other theories explaining the volatility risk premia.

Other papers
Driessen, Meanhout, Vilkov: Option-Implied Correlations and the Price of Correlation Risk
- Abstract

Motivated by extensive evidence that stock-return correlations are stochastic, we analyze whether the risk of correlation changes (affecting diversification benefits) may be priced. We propose a direct and intuitive test by comparing option-implied correlations between stock returns (obtained by combining index option prices with prices of options on all index components) with realized correlations. Our parsimonious model shows that the substantial gap between average implied (39.5% for S&P500 and 46.0% for DJ30) and realized correlations (32.5% and 35.5%, respectively) is direct evidence of a large negative correlation risk premium. Empirical implementation of our model also indicates that the index variance risk premium can be attributed to the high price of correlation risk. Finally, we provide evidence that option-implied correlations have remarkable predictive power for future stock market returns, which also stays significant after controlling for a number of fundamental market return predictors.

Lisauskas: Dispersion Trading in German Option Market
- Abstract

There has been an increasing variety of volatility related trading strategies developed since the publication of Black-Scholes-Merton study. In this paper we study one of dispersion trading strategies, which attempts to profit from mispricing of the implied volatility of the index compared to implied volatilities of its individual constituents. Although the primary goal of this study is to find whether there were any profitable trading opportunities from November 3, 2008 through May 10, 2010 in the German option market, it is also interesting to check whether broadly documented stylized fact that implied volatility of the index on average tends to be larger than theoretical volatility of the index calculated using implied volatilities of its components (Driessen, Maenhout and Vilkov (2006) and others) still holds in times of extreme volatility and correlation that we could observe in the study period. Also we touch the issue of what is (or was) causing this discrepancy.

Carrasco: Studying the properties of the correlation trades
- Abstract

This thesis tries to explore the profitability of the dispersion trading strategies. We begin examining the different methods proposed to price variance swaps. We have developed a model that explains why the dispersion trading arises and what the main drivers are. After a description of our model, we implement a dispersion trading in the EuroStoxx 50. We analyze the profile of a systematic short strategy of a variance swap on this index while being long the constituents. We show that there is sense in selling correlation on short-term. We also discuss the timing of the strategy and future developments and improvements.

Choi: Analysis and Development Of Correlation Arbitrage Strategies on Equities
- Abstract

After the two years of studies in the area of mathematical finance at Univ ersity of Paris 1, I had a chance to work with an asset management team as a quantitative analyst at Lyxor Asset Management, Société Générale in Paris, France. My first task was to develop an analysis of the performances of the funds on hidden assets where the team’s main focus was on, such as Volatility Swap, Variance Swap, Correlation Swap, Covariance Swap, Absolute Dispersion, Call on Absolute Dispersion (Palladium). The purpose was to anticipate the profit and to know when and how to reallocate assets according to the market conditions. In particular, I have automated the analysis through VBA in Excel. Secondly, I had a research project on Correlation trades especially involving Correlation Swaps and Dispersion Trades. This report is to summarize the research I have conducted in this subject. Lyxor has been benefiting from taking short positions on Dispersion Trades through variance swaps, thanks to the fact that empirically the index variance trades rich with respect to the variance of the components. However, a short position on a dispersion trade being equivalent to taking a long position in correlation, in case of a market crash (or a volatility spike), we can have a loss in the position. Thus, the goal of the research was to find an effective hedging strategy that can protect the fund under unfavorable market conditions. The main idea was to apply the fact that dispersion trades and correlation swaps are both ways to have exposure on correlation, but with different risk factors. While correlation swap has a pure exposure to correlation, dispersion trade has exposure to the realised volatilities as well as the correlation of the components. Thus, having risk to another factor, the implied correlation of a dispersion trade is above (empirically, 10 points) the strike of the equivalent correlation swap. Thus, taking these two products and taking opposite positions in the two, we try to achieve a hedging effect. Furthermore, I look for the optimal weight of the two products in the strategy which gives us the return of the P&L, volatility of the P&L, and risk-return ratio of our preference. Moreover, I tested how this strategy would have performed in past market conditions (back-test) and under extremely bearish market conditions (stress-test).

Faria, Kosowski: The Correlation Risk Premium: Term Structure and Hedging
- Abstract

As the recent financial crisis has shown, diversification benefits can suddenly evaporate when correlations unexpectedly increase. We analyse alternative measures of correlation risk and their term structure, based on S&P500 correlation swap quotes, synthetic correlation swap rates estimated from option prices and the CBOE Implied Correlation Indices. An analysis of unconditional and conditional correlation hedging strategies shows that only some conditional correlation hedging strategies add value. Among the conditional hedge strategy’s conditioning variables we find that the level of the correlation risk factor and dispersion trade returns deliver the best results, while the CBOE Implied Correlation Indices perform poorly.

Maze: Dispersion Trading in South Africa: An Analysis of Profitability and a Strategy Comparison
- Abstract

A dispersion trade is entered into when a trader believes that the constituents of an index will be more volatile than the index itself. The South African derivatives market is fairly advanced, however it still experiences inefficiencies and dispersion trades have been known to perform well in inefficient markets. This paper tests the South African market for dispersion opportunities and explores various methods of executing these trades. The South African market shows positive results for dispersion trading; namely short-term reverse dispersion trading. Call options and Cross-Sectional Volatility (CSV) swaps are also tested. CSV swaps performed poorly whereas call options experienced annual returns well above the market.

Deng: Volatility Dispersion Trading
- Abstract

This papers studies an options trading strategy known as dispersion strategy to investigate the apparent risk premium for bearing correlation risk in the options market. Previous studies have attributed the profits to dispersion trading to the correlation risk premium embedded in index options. The natural alternative hypothesis argues that the profitability results from option market inefficiency. Institutional changes in the options market in late 1999 and 2000 provide a natural experiment to distinguish between these hypotheses. This provides evidence supporting the market inefficiency hypothesis and against the risk-based hypothesis since a fundamental market risk premium should not change as the market structure changes.

Faria, Kosowski, Wang: The Correlation Risk Premium: International Evidence
- Abstract

In this paper we carry out the first cross-country analysis of the correlation risk premium. We examine the statistical properties of the implied and realized correlation in European equity markets and relate the resulting premium to the US equity market correlation risk and a global correlation risk premium. We find evidence of strong co-movement of correlation risk premiums in European and US equity markets. Our results support the existence of a global correlation risk premium that is priced in international equity option markets. We document the dependence of the correlation risk premium on macroeconomic policy uncertainty and related variables.

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